Passivelymode-lockedholmium-doped solitonﬁberringoscillator · Passivelymode-lockedholmium-doped solitonﬁberringoscillator Masterabschlussarbeit von ThomasBraatz imStudiengangOpticalEngineering/Photonics

Passively mode-locked holmium-dopedsoliton fiber ring oscillator

Masterabschlussarbeit

vonThomas Braatz

im Studiengang Optical Engineering/Photonics

an der HAWK Hochschule für angewandte Wissenschaft und Kunst

Hildesheim/Holzminden/Göttingen

Fakultät Naturwissenschaften und Technik in Göttingen

in Kooperation mit dem Deutschen Elektronen-Synchrotron

Erstprüfer: Frau Prof. Dr. Andrea KochZweitprüfer: Herr Prof. Dr. Franz X. Kärtner

May 2017

Acknowledgements

For the support and supervision while completing this thesis I would like tothank Prof. Dr. Andrea Koch, Professor at the University of Applied Sciencesand Arts in Göttingen, as well as Prof. Dr. Franz X. Kärtner, group leader ofthe Ultrafast Optics and X-Rays Division of the Center for Free-Electron LaserScience. I also would like to express appreciation to Dr. Ingmar Hartl, head ofthe FS-LA group at DESY, as well as the FS-LA group in general for providingme with a warm and welcoming work environment. Special thanks go to Dr.Axel Rühl for helping me shape the ideas for this thesis and for his continuoussupport with theoretical input. Further appreciation goes to Chenchen Wanand Vinicius Silva de Oliveira for their guidance with the practical work in thelaser laboratory as well as to Uwe Grosse-Wortmann for his instructions onthe assembly of the mode-lock detector.

v

Abstract

Ultrashort laser pulses are used in physical analysis techniques as well as inmaterials processing and are generated in passively mode-locked oscillators.However, those oscillators produce low pulse energies, but can be used asseeding sources for regenerative amplifiers. Operating with 2 µm wavelengthradiation, the amplified output is applicable for pumping optical paramet-ric amplifiers. This allows for generating and amplifying intense light in themid-infrared wavelength range. With usage of the high water absorption inthis wavelength range, this technology can be used for remote sensing and inspectroscopy.This thesis describes the reconditioning of a preexisting, not working mode-

locked holmium-doped fiber ring oscillator. The stability of this seed sourcehas been optimized by shielding off external influences and setting up a mode-lock detector. Furthermore, the output power has been adjusted to matchthe working range of the regenerative amplifier at hand by changing the seedsource to soliton operation.By extending the setup via additional fiber connectors a continuous monitor-

ing and characterization of different laser parameters, i.e. the optical spectrum,the pulse duration, pulse energy and longterm stability are ensured.In future, this improvement will offer an efficient use of power while ensuring

a reliable operation of the regenerative amplifier.

vii

Kurzfassung

Ultrakurze Laserpulse werden sowohl für physikalische Analyseverfahren alsauch für die Materialbearbeitung verwendet und in passiv modengekoppel-ten Oszillatoren erzeugt. Diese Oszillatoren erzeugen Pulse mit geringen En-ergien, dennoch können sie als Seeding-Quellen für regenerative Verstärkerverwendet werden. Bei der Verwendung von Strahlung mit einer Wellen-länge von 2 µm ist das verstärkte Ausgangssignal zum Pumpen von optischparametrischen Verstärkern geeignet. Dabei wird intensives Licht im mittlerenInfrarot-Wellenlängenbereich erzeugt und verstärkt. Die hohe Absorption vonWasser in diesem Wellenlängenbereich erlaubt es, diese Technologie für dieFernerkundung und in der Spektroskopie einzusetzen.Diese Arbeit beschreibt die Instandsetzung eines bereits vorhandenen, nicht

funktionsfähigen, modengekoppelten Holmium-dotierten Faserringoszillators.Darüber hinaus wurde die Stabilität dieser Seeding-Quelle durch eine Ab-schirmung von externen Einflüssen verbessert und durch die Einrichtung einesModenkopplungsdetektors optimiert. Weiterhin wurde die Leistung auf denArbeitsbereich des vorhandenen regenerativen Verstärkers durch einen Wech-sel in den Soliton-Betrieb angepasst.Durch die Erweiterung des Aufbaus mit zusätzlichen Faseranschlüssen wird

eine kontinuierliche Überwachung und Charakterisierung verschiedener Laser-parameter gewährleistet, d.h. das optische Spektrum, die Pulsdauer, die Pulsen-ergie und die Langzeitstabilität.Diese Verbesserung bietet künftig eine effizientere Nutzung der Leistung und

garantiert gleichzeitig einen zuverlässigen Betrieb des regenerativen Verstär-kers.

ix

List of Abbreviations

ADC analog-to-digital conversion

AOM acousto-optic modulator

CW continuous-wave

DAQ data acquisition

DIAL differential absorption light detection and ranging

EOM electro-optical modulator

FC/APC Fiber-optic Connector with Angled Physical Contact

FFT fast Fourier transformation

FIR far-infrared

FWHM full width at half-maximum

GVD group-velocity dispersion

HDF holmium-doped fiber

HHG high-harmonic generation

Ho Holmium

HWP half-wave plate

KLM Kerr-lens mode-locking

LED light-emitting diode

LIDAR light detection and ranging

MFD mode-field diameter

MIR mid-infrared

NA numerical aperture

xi

NB narrow bandwidth

ND neutral density

NPE nonlinear polarization evolution

OPA optical parametric amplifier

P-APM polarization-additive pulse mode-locking

PBS polarizing beam splitter

PCB printed circuit board

PSD power spectral density

QWP quarter-wave plate

RBW resolution bandwidth

RF radio frequency

RIN relative intensity noise

RMS root-mean-square

SMF single-mode fiber

SPM self-phase modulation

SSB single sideband

TEM transverse electromagnetic

TFP thin-film polarizer

Tm Thulium

UV ultraviolet

WDM wavelength division multiplexer

xii

List of Figures

2.1 Schematic of an optical fiber and its beam propagation insidethe core due to total internal reflection on the left. On the right,the quadratic refractive-index n2 as a function of the fiber radiusr in case of step-index fibers is shown. . . . . . . . . . . . . . . 4

2.2 Losses in dB/km in silica glass fiber depending on the wave-length, figure adapted from [6]. . . . . . . . . . . . . . . . . . . 6

2.3 Absorption spectrum of water, figure adapted from [1]. . . . . . 62.4 Absorption emission cross section spectra of Th and Ho-doped

silica. Figure taken from [7]. . . . . . . . . . . . . . . . . . . . . 72.5 Energy level of Ho-doped silica with two different pumping pro-

cesses, both resulting in an emission of 2 µm radiation. Figuretaken from [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.6 Schematic drawing of an evanescent field coupler. Figure adaptedfrom [8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.7 Gain bandwidth and cavity loss on the top and separated longi-tudinal modes supported by the cavity length (dashed) as wellas the number of allowed modes (solid). Figure adapted from[10]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.8 Schematic of Q-switching. Figure taken from [10]. . . . . . . . . 122.9 Modes with no fixed phase relation (a) and phase-matched modes

at one particular moment (b). The figure is adapted from [11]. . 132.10 Schematic of active mode-locking. Figure taken from [12]. . . . . 142.11 Schematic of (a) slow and (b) fast saturable absorber. Figures

taken from [12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.12 Schematic of KLM. Figure taken from [12]. . . . . . . . . . . . . 152.13 Schematic of P-APM. Figure taken from [14]. . . . . . . . . . . 162.14 Refractive index n and the group refractive index ng as a func-

tion of the wavelength. Figure taken from [13]. . . . . . . . . . . 192.15 Dispersion parameter D as a function of the wavelength λ. Fig-

ure taken from [13]. . . . . . . . . . . . . . . . . . . . . . . . . . 192.16 Pulse broadening of a hyperbolic-secant pulse along the z-direction

of a fiber. The figure is taken from [13]. . . . . . . . . . . . . . . 20

xiii

List of Figures

2.17 Time dependent intensity of a pulse on the top and its redis-tributed frequency components as a function of time. The figureis taken from [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.18 Optical spectrum of an erbium-doped fiber laser. The figure istaken from [18]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.19 Pulse train detected by a photodiode in (a) and the spectrumanalyzer’s signal in (b). The figure is adapted from [22]. . . . . . 28

3.1 Photograph of the setup including pump, oscillator and charac-terization sections. PD: Photodiode; AC: Autocorrelator. . . . . 31

3.2 Schematic drawing of the pump section. HWP: half-wave plate;TFP: thin-film polarizer; QWP: quarter-wave plate; SMF: single-mode fiber; ND attenuator: neutral-density attenuator; PD:photodiode; MLDET: mode-lock detector. . . . . . . . . . . . . 32

3.3 Photograph of the pump section. . . . . . . . . . . . . . . . . . 33

3.4 (a) Shows the beam profile after the telescope, (b) gives a topview of two fiber tips, i.e. one flat side for splicing and oneangle-cleaved side used for coupling and (c) depicts the fibercharacteristics of the angle-cleaved fiber tip measured by thesplicer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.5 Photograph of the fiber coupling. . . . . . . . . . . . . . . . . . 35

3.6 Schematic drawing of the oscillator. . . . . . . . . . . . . . . . . 36

3.7 Photograph before (a) and after (b) the splicing process of theSMF from the WDM output (left fiber) to the HDF (right fiber). 37

3.8 Photograph of the oscillator. . . . . . . . . . . . . . . . . . . . . 38

3.9 Schematic drawing of the characterization section. . . . . . . . . 39

3.10 Photograph of the characterization section. . . . . . . . . . . . . 40

3.11 Determination of the calibration factor by moving the cornermirror of the autocorrelator. . . . . . . . . . . . . . . . . . . . . 42

3.12 Photograph of the mode-lock detector while the oscillator isworking in the mode-locking operation indicated by the largecarrier power and low noise power. . . . . . . . . . . . . . . . . 43

3.13 Photograph of the stack of PCB with the photodiode board onthe top. The photodiode (PD) is not yet soldered and the out-put not yet connected to the micro controller board. Bandpassfiltered voltage signals corresponding to the carrier power canbe measured using the test point. . . . . . . . . . . . . . . . . . 44

xiv

List of Figures

4.1 Optical spectrum tuned to different center wavelengths by chang-ing the wave plate combination. . . . . . . . . . . . . . . . . . . 46

4.2 Optical spectrum with different bandpass filters. . . . . . . . . . 464.3 Autocorrelation without bandpass filters. . . . . . . . . . . . . . 484.4 Autocorrelation with 2050-12 bandpass filter. . . . . . . . . . . . 484.5 Autocorrelation with 2050-12 and 2085-10 bandpass filter. . . . 494.6 RF spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.7 Slope efficiency and output beam diameter. . . . . . . . . . . . . 504.8 Relative intensity noise of the oscillator output with different

narrow bandpass filters. . . . . . . . . . . . . . . . . . . . . . . 534.9 Relative intensity noise of the pump at 35 % and the oscillator

output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.10 Relative intensity noise of the pump at 60 % and the oscillator

output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.11 Phase noise and RF spectrum. . . . . . . . . . . . . . . . . . . . 564.12 Integrated timing jitter. . . . . . . . . . . . . . . . . . . . . . . 564.13 Long-term stability measured over 2 days using the mode-lock

detector. The inset shows the transition from mode-locking toCW state followed by a disabling of the pump. . . . . . . . . . . 57

xv

List of Tables

3.1 List of the oscillator’s main components and their specification. 343.2 List of the diagnostic tools used for characterizing the mode-

locked laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

xvii

Table of Contents

Acknowledgements v

Abstract vi

Kurzfassung viii

List of Figures xiii

List of Tables xv

1 Introduction 1

2 Theoretical Background 3

2.1 Fiber Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.1 Optical Fibers and Fiber Components . . . . . . . . . . 32.1.2 Operation Modes of Fiber Lasers . . . . . . . . . . . . . 10

2.2 Propagation of Ultrashort Pulses in Fibers . . . . . . . . . . . . 182.2.1 Group Velocity Dispersion . . . . . . . . . . . . . . . . . 182.2.2 Self-phase Modulation . . . . . . . . . . . . . . . . . . . 212.2.3 Solitons . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Characterization of Mode-locked Lasers with Ultrashort Pulses . 252.3.1 Pulse Characterization . . . . . . . . . . . . . . . . . . . 252.3.2 Output Power and Pulse Energy . . . . . . . . . . . . . . 272.3.3 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3.4 Mode-locking Stability . . . . . . . . . . . . . . . . . . . 30

3 Experimental Setup 31

3.1 Available Components . . . . . . . . . . . . . . . . . . . . . . . 323.2 Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.3 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . 393.4 Mode-lock Detector . . . . . . . . . . . . . . . . . . . . . . . . . 43

xix

4 Results and Discussion 454.1 Pulse Characterization . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.1 Optical Spectrum . . . . . . . . . . . . . . . . . . . . . . 454.1.2 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . 474.1.3 Pulse Energy . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.2.1 Relative Intensity Noise . . . . . . . . . . . . . . . . . . 524.2.2 Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.3 Mode-locking Stability . . . . . . . . . . . . . . . . . . . . . . . 57

5 Conclusion and Outlook 59

Bibliography 61

1 Introduction

Infrared laser systems are widely used for remote sensing, medical applicationand in spectroscopy. In particular, infrared lasers emitting at a wavelength of2 µm are used due to the strong water absorption at this wavelength. Suchradiation can be produced in active gain fibers doped with rare earth ionssuch as thulium or holmium. Examples for remote sensing techniques arelight detection and ranging (LIDAR) used for aerosol density measurementsand differential absorption LIDAR (DIAL), which allows for determination ofthe density of atmospheric components. Another advantage of laser systemsemitting radiation at 2 µm wavelength is that they suit well as pump sourcesfor optical parametric amplifiers (OPA). Those are used for generating andamplifying radiation with larger wavelengths, i.e. in the mid-infrared (MIR)wavelength range, which in turn can be used for remote sensing of other atmo-spheric compounds as well as chemical and biological hazards. [1] Additionally,the technique of high-harmonic generation (HHG) can be applied on the MIRlight for producing radiation at wavelengths in the visible or ultraviolet (UV)region. MIR laser play also an important role in surgeries, where they functionas an efficient tool for cutting by means of energy absorption. The resultingbreaking of chemical bonds is especially used for cutting biological tissue, be-cause it mainly consists of water. A major advantage of the usage of fiber isthat it serves a compact delivery of the radiation to the target location duringthe surgery and thus allows an easy handling of the tool.In general, all those applications require high power, which is achieved in ul-

trashort pulses since they exhibit high peak power due to the specifically shortpulse duration. Ultrashort pulses can be generated in passively mode-lockedoscillators. Unfortunately, they provide low pulse energies. Nevertheless, suchpulses can be amplified in regenerative amplifiers in which a pump source en-sures an active laser medium to maintain a population inversion. The incom-ing seed pulse from the mode-locked oscillator is amplified due to stimulatedemission. Placing the active laser medium inside a resonator allows for highamplification factors due to a multiple pass operation. [2]The holmium-doped yttrium lithium fluoride regenerative amplifier reported

in [3] is recommended to be seeded with a laser source operating at a wave-

1

1 Introduction

length of 2050 nm with pulse energies of 1-10 nJ at about 100 MHz repetitionrate.

In previous experiments the seed source exhibited a broad optical spectrum,which resulted in a reduction of the pulse energy from 1 nJ down to 60 pJ

due to the limiting spectral width of chirped volume bragg gratings used forpulse stretching. Pulse stretching is necessary before seeding the regenerativeamplifier to avoid damages of optical components inside the amplifier, whichmight be induced by a high peak power of the amplified pulses. [4]

The aim of this thesis is to repair and modify the previous laser sourceused for seeding the regenerative amplifier at hand in order to guarantee anefficient usage of power by narrowing the emitted optical spectrum and a stableoperation since additional amplification stages require a reliable operation ofthe seeding source. In this thesis the construction and characterization of aseeding source based on the concept of a passively mode-locked unidirectionalholmium-doped fiber ring oscillator operating in the soliton regime as reportedin [5] will be described.

The thesis is organized as follows. Chapter 2 describes the fundamentaltheory concerning optical fibers, their specification and doping materials usedfor generating radiation at 2 µm wavelength. Furthermore, some fiber compo-nents acting as the equivalents to common free-space optics will be introducedas well as different configurations of pulsed lasers. The theory chapter willalso discuss the effects of dispersion and self-phase modulation, two dominat-ing mechanisms which are responsible for the formation and propagation ofsolitons. The last section of this chapter will show different techniques tocharacterize lasers with ultrashort pulse durations.

In chapter 3 the available components will be presented, including the fibercoupling of the pump laser, the setup of the oscillator as well as the procedurefor initiating mode-locking. Furthermore, the installation of several measure-ment devices will be discussed, which allow a simultaneous characterization ofdifferent parameters, e.g. the output power, the repetition rate, the opticalspectrum and the pulse duration. Finally, the assembly and configuration ofa mode-lock detector, a device developed by the FS-LA DESY group, will beexplained.

All the results will be shown and discussed in chapter 4. Chapter 5 willsummarize the work and will give an outlook.

2

2 Theoretical Background

This chapter will provide an overview of optical fibers and pulse generationin lasers. Furthermore, the effects of group velocity dispersion and self-phasemodulation will be introduced, which are the dominating effects for the for-mation of soliton pulses in optical fibers. Finally, techniques for characterizingultrashort pulses from mode-locked lasers will be presented.

2.1 Fiber Lasers

This section will discuss the propagation of light in optical fibers, doping mate-rials for generating light at 2 µm wavelength and fiber equivalents to free-spaceoptics. Furthermore, the continuous-wave, q-switching and mode-locking op-eration states of lasers will be discussed.

2.1.1 Optical Fibers and Fiber Components

Based on the concept of total internal reflection optical fibers are widely usedfor guiding light over long distances with low transmission losses. Commonfields of application are, e.g. remote sensing, telecommunication engineeringand laser development. In general, an optical fiber consists of an inner coreand an outer cladding, where the core exhibits a slightly larger refractive index(n1) than the cladding (n2) for allowing the propagation based on total internalreflection. The critical angle, i.e. the incident angle inside the fiber where totalinternal reflection still occurs, can be derived from Snell’s Law

n1 sin(θi) = n2 sin(θt), (2.1)

where θi is the angle of the incident beam inside the core and θt is the angle ofthe transmitted beam in the cladding. For total internal reflection θt becomes90 so that the angle of the reflected beam θr is equal to θi, which is accordingto (2.1)

θi = θr = arcsin

(n2

n1

). (2.2)

3


Figure 2.1: Schematic of an optical fiber and its beam propagation inside thecore due to total internal reflection on the left. On the right, thequadratic refractive-index n2 as a function of the fiber radius r incase of step-index fibers is shown.

Hence, any beam with an angle larger than this critical angle θi will be guidedthrough the fiber as shown in figure 2.1. Using Snell’s Law again, one cantransfer the acceptance angle for coupling into the fiber and thus the numericalaperture

NA = n0 sin(αc) = n1 sin (90 − θi) = n1 cos (θi), (2.3)

where n0 represents the refractive index of the medium surrounding the fiberbefore coupling and αc is the maximal half-angle of the cone. With (2.2) andthe relation cos(arcsin(x)) =

√1− x2 the NA can be calculated to

NA =√n2

1 − n22, (2.4)

so that it is just dependent of the refractive indices of the core and the cladding.

The number of transverse modes propagating in a fiber depends on the Vparameter

V = k0a√n2

1 − n22, (2.5)

where k0 is the wave number and a is the core radius. For V < 2.405 thefiber supports only the fundamental transversal mode LP01. These fibers arecalled single-mode fibers (SMF). Such fibers exhibit a small core diameter (8to 12 µm) and a cladding diameter of about 125 µm. The NA and thus thedifference in the refractive indices n1 and n2 is also small. Commonly, thecore’s profile is a step-index, i.e. the refractive index of the core is constant,as shown in figure 2.1 on the right. In this work only single-mode fibers witha core and cladding composed of silica glass are used.

In general, losses in fiber can be summarized as coupling/splicing, absorp-tion/scattering and bending losses. For coupling the fundamental transverse

4

2.1 Fiber Lasers

electromagnetic modes of a free-space gaussian beam (TEM00) into a single-mode fiber it is straight forward to focus the beam in such a way that thebeam diameter at the 1/e2 intensity matches the fiber’s mode-field diameter(MFD). The resulting mode overlap of a gaussian TEM00 free-space beam andthe fundamental mode LP01 coupled in a SMF in general is about 90 %. Inorder to reduce Fresnel reflections on both surfaces for coupling into and out ofthe fiber it is recommended to cleave, i.e. a precisely controlled breaking of thefiber, the surfaces with an angle of about 8. For splicing two different typesof fibers, i.e. thermally fusing them together, both cleaved surfaces should beperpendicular and their MFDs should match, so that the light doesn’t leavethe fiber through the cladding.

The transmitted optical power PT as a function of the fiber length L andcan be calculated by

PT (z) = PI exp(−αL), (2.6)

where PI is the instantaneous power in W and α is the attenuation coefficientin units of km−1. Since it is more common to express the optical power indecibel units (dB) the attenuation coefficient can be transferred to

αdB = −10

Llog

PT

PI

(2.7)

with the units dB/km. The optical power P in W or mW can be converted toPdB in the units of dB or dBm by

PdB = 10 logP

Pref

, (2.8)

where Pref represents the reference power, e.g. 1 W or 1 mW. Besides thealready discussed coupling and splicing losses, the attenuation of optical powerin an optical fiber is caused by two wavelength dependent mechanisms, i.e.scattering and absorption.

Scattering in a fiber occurs due to impurities or particles in the core. Rayleighscattering is the main scattering effect in fiber optics which results from inho-mogeneities with a size much smaller than the wavelength of the light. If thescattered light propagates in an angle which is not supported for guiding thelight in the fiber it leaves the core and reduces the power. This type of scat-tering is λ−4 dependent so that with larger wavelength less Rayleigh scatteringoccurs. Other types of scattering that may arise are Mie scattering, Brillouinand Raman scattering. Mie scattering is less significant in optical fibers, be-cause it results from particles with a size around the wavelength, variations of

5


Figure 2.2: Losses in dB/km in silica glass fiber depending on the wave-length, figure adapted from [6].

the refractive index of core and cladding or changes in the diameter, which hadbeen reduced by modern optical fiber fabrication. Brillouin and Raman scat-tering are both intensity dependent effects that slightly change the wavelengthand also the direction, i.e. even back scattering is possible, of the photons dueto thermal influences and vibrations of the glass material, respectively.

Material absorption is the power loss due to the energy conversion of thepropagating lightwave into e.g. vibrations while interacting with certain fibermaterial components. In the ultraviolet region silica glass fibers have electronicresonances and vibrational resonances in the far-infrared (FIR) region. Wa-

Figure 2.3: Absorption spectrum of water, figure adapted from [1].

6

2.1 Fiber Lasers

ter vapor deposits OH-ions in the material during the manufacturing process,which cause fundamental loss peaks at 1.24 and 1.38 µm as can be seen fromfigure 2.2.The combination of Rayleigh scattering and material absorption of silica

glass shows a loss minimum around 1.55 µm. Light with this wavelength isproduced in an erbium-doped active laser medium and is used in telecommu-nication, because it allows overcoming large distances with low transmissionlosses.Although the attenuation for 2 µm wavelength radiation becomes large due

to IR vibrations it is still attractive for many applications such as remotesensing and medical methods. These applications mainly take advantage ofthe large water absorption peak at 2 µm (see figure 2.3), which also gives thiswavelength range the name eye-safe region.For producing 2 µm wavelength radiation, silica glass fibers can be doped

with optically active holmium (Ho) ions in order to create an active medium.The electronic states of the Ho ions in the holmium-doped fiber (HDF) canbe excited by absorption of optical pump light. From figure 2.4 it can be seenthat thulium (Tm) is an appropriate pump due to the intersection of the Tmemission cross section with the peak of the Ho absorption cross section around1.95 µm. This allows a build-up of a population inversion between the lowerlaser level 5I8 and the excited state 5I7. Pumping and emission occurs aroundsimilar wavelengths (see figure 2.5), which has on one hand the advantage thatno parasitic energy transitions, e.g. rapid non-radiative decays, occur. On one

Figure 2.4: Absorption emission cross section spectra of Th and Ho-dopedsilica. Figure taken from [7].

7


Figure 2.5: Energy level of Ho-doped silica with two different pumping pro-cesses, both resulting in an emission of 2 µm radiation. Figuretaken from [7].

hand an increase of the upper laser lifetime of the Ho ions is supported, allpump energy is stored in the excited state and can be extracted in a single,short pulse. On the other hand less heat arises from such energy transfersdue to motion. In any case, the gain fiber as an active medium in comparisonto doped crystals offer a large surface, so that no thermal management isnecessary in case of fiber lasers.

The amplification process is initiated by forming a laser cavity, thus stim-ulated emitted radiation propagates through the active medium for multipletimes. This laser cavity can either be a conventional resonator, where thebeam is reflected at the ends of the cavity and thus exhibits a bidirectionalbeam path. Otherwise the laser cavity can consist of a ring oscillator, wherethe end of the cavity is fed back to its beginning closing the ring, so that anunidirectional propagation can be accomplished.

In fiber optics, the equivalents to free-space optics, such as partially re-flecting mirrors or beam splitters as well as dichroic mirrors are fiber cou-plers/splitters and wavelength division multiplexer (WDM) couplers, respec-tively.

The most common fiber coupler/splitter consists of two single-mode fibersclosely placed in parallel to each other. In total, it provides four ports, where

8

2.1 Fiber Lasers

light with a certain power and wavelength is coupled into one of the two inputports and transfers its power in the interaction zone into the other fiber, re-sulting in a power splitting ratio between the two output ports. The conceptof power distribution from one fiber to the other is dependent on the fabri-cation process. In evanescent field couplers two fibers are twisted in order tocreate a tight contact. The fibers cladding is then almost etched to the sizeof the fiber cores and becomes the common cladding. This allows the evanes-cent field, i.e. the part of the electromagnetic wave which enters the claddingduring the total internal reflection, to transfer from the common cladding intothe other fiber core. The length of the interaction zone in this type of couplercan be controlled by the number of fiber twists and defines the power splittingratio of the coupler. [8] In fused couplers the cores of the two fibers are fusedtogether and create a taper, i.e. a common core, where the light splits intothe individual output fibers. During the fusion both fibers are pulled in orderto reduce the fused core sizes precisely, which determines the splitting powerratio. [9]WDM couplers are similar passive fiber components, where different wave-

lengths can enter a common input port and the power gets split in the dif-ferent wavelength portions. The insertion loss, i.e. the port-to-port loss, iswavelength dependent due to fabrication process. Especially, WDM couplersfind application in fiber ring oscillators, where one WDM input port serves forcoupling pump light into the laser cavity using the output port, which has a

Figure 2.6: Schematic drawing of an evanescent field coupler. Figure adaptedfrom [8].

9


low insertion loss for the pump wavelength. Light with the laser wavelengthis generated in a gain fiber, which is spliced to the second input port of theWDM coupler. This port of the WDM coupler has a high insertion loss for thepump wavelength with respect to the port spliced to the gain fiber and a lowinsertion loss for the laser wavelength. Hence, the WDM coupler transmitsthe laser wavelength and dumps most of the power of the residual pump lightto the second output port.

2.1.2 Operation Modes of Fiber Lasers

Fiber lasers are realized in three different operation states, i.e. continuous-wave(CW), Q-switched and mode-locked.

In CW laser light is generated without being interrupted and radiation ispermanently emitted through the output coupler. This is achieved by con-tinuously pumping the active medium in the laser cavity. Hence, the gain ofstimulated radiation emission γ0(ν) is always larger than the losses αr that oc-cur inside the cavity, so that the laser operates consistently above its thresholdand maintains an almost constantly stable output power. The wavelength ofthe emitted radiation depends on the kind of optically active medium, i.e. incase of fibers the dopants of the gain fiber segment. On one hand, it is possiblethat lasers emit a specific wavelength only, i.e. a narrow linewidth in the op-tical spectrum. These are called single-frequency or single-longitudinal-mode

Figure 2.7: Gain bandwidth and cavity loss on the top and separated longi-tudinal modes supported by the cavity length (dashed) as well asthe number of allowed modes (solid). Figure adapted from [10].

10

2.1 Fiber Lasers

lasers and provide almost monochromatic radiation. On the other hand thewavelength can spread over a defined range, thus it contains multiple longi-tudinal modes. Rather than the wavelength λ the frequency ν is used in thiscontext which can be obtained from the condition

ν =c0

λ, (2.9)

where c0 is the speed of light in vacuum. In general, multiple longitudinalmodes are supported by the cavity. If each experience a phase shift of amultiple of 2π during one roundtrip it allows them to oscillate as independent,free-running modes. In the frequency domain these modes are separated by

∆ν =c

2d=c

L, (2.10)

where d is the distance of a resonator with two mirrors, L is the length of afiber ring oscillator, and c is the speed of light in the medium. The number ofmodes gaining amplification in the laser cavity can be calculated from [10]

M =B

∆ν, (2.11)

where B is the width of the spectral band for which the gain exceeds the losses.In conclusion, the amount of longitudinal modes depends on the atomic gainbandwidth of the active laser medium, the cavity losses and its length. Single-frequency lasers can be obtained by selecting only one longitudinal mode. Forexample this can be done by increasing the losses αr until only the fundamentalmode ν0 oscillates. Of course, the mode itself suffers from the loss resultingin a weak output power. Another way would be to decrease the cavity lengthin order to increase the mode spacing ∆ν. However, a drawback is that thisalso reduces the active gain in length, i.e. pumping and thus amplificationis less efficient. A more practical way is the use of an intracavity selectivefilter. In free-space optics this can be e.g. an etalon, which changes the opticalpath length of the cavity and thus the mode spacing. For fibers a fiber bragggrating could be used, where a special arrangement of alternating refractiveindices reflects a specific wavelength and transmits the residual ones, similar asa dichroic mirror. CW lasers can be modified into pulsed lasers by placing anexternal optical switch, also called modulator, outside the cavity transmittingthe radiation during a short time. This method is rather unsatisfactorily sincepower is lost, whenever the modulator absorbs the radiation and the pulseintensity never exceeds the CW power.

11


Figure 2.8: Schematic of Q-switching. Figure taken from [10].

Q-switching is a method for creating pulses with nanosecond pulse dura-tions and much higher peak powers by means of a modulator inside the cavity.Figure 2.8 depicts a time dependent schematic of the process. In principle,permanent pumping ensures a build-up of the population inversion while theabsorbing modulator prevents oscillation and thus the amplification. When-ever the population inversion is at its maximum the modulator reduces thecavity losses, the population inversion disintegrates due to stimulated emissionand amplification takes place. Finally a short, intense laser pulse builds up andsustains during a couple of roundtrips. Active Q-switching is realized using,e.g. acousto-optic modulators (AOM) or electro-optical modulators (EOM)and passive Q-switching utilizing saturable absorbers. AOM and EOM makeuse of an electric field for producing the necessary losses. In an AOM theelectric field generates a sound wave, which scatters the photons, whereas inan EOM the electric field changes the refraction index due to the electro-opticor Pockels effect, and thus deflects the photons on a voltage dependent path.The saturable absorber obtains an intensity dependent transmission, where thetransmission increases with increasing intensity. In general, the Q-switchingtechnique finds application in time-resolved experiments or ablation processesin materials processing. The duration of the pulse depends on a few parame-ters, for example the cavity length, the repetition rate and the pump power,as well as the type of gain medium determining the amount of storable energy.

In contrast to the free-running modes that oscillate independently in a CWor Q-switched laser, these modes can be externally adjusted in their relativephase (see figure 2.9) and cause a coherent interference. An intracavity mod-ulator, which is synchronized to the cavity roundtrip time, produces such aninterference of these modes, thus a single pulse propagates inside the laser

12

2.1 Fiber Lasers

Figure 2.9: Modes with no fixed phase relation (a) and phase-matched modesat one particular moment (b). The figure is adapted from [11].

cavity. The technique is called mode-locking and opens the sub-nanosecondpulse width regime. The output of a mode-locked laser is a train of pulses,where the period between two pulses depends on the cavity roundtrip time,calculated by the inverse of equation (2.10)

TR =1

∆ν. (2.12)

The pulse width is inversely proportional to the number of modes supportedby the cavity [10]

T0 =TRM

=1

M∆ν. (2.13)

Since the number of modes is quite large for media with a broad lasing band-width, they permit on one hand the evolution of short and intense laser pulsesand on the other hand the tuning of the center wavelength over a large range.In principle, initiating mode-locking requires an event that causes the phasesof the modes to match and allows a pulse to build up. Once this conditionis fulfilled the modulator ensures the transmission of the overlapping modesfor the short moment of passing it. Any other randomly arranged modes getblocked due to the high losses generated by the modulator. As in the case ofQ-switching, mode-locked lasers are distinguished in active and passive mod-ulators.

In active mode-locking an amplitude modulator, e.g. an AOM oder EOM,creates a cosinusoidal loss modulation. Each roundtrip the single pulse arrivesat the modulator, which ensures that gain exceeds losses for this particular

13


Figure 2.10: Schematic of active mode-locking. Figure taken from [12].

short moment.

As shown in figure 2.10 the peak passes the gain window and experiencesamplification. However, the wings get attenuated, because losses already ex-ceed the gain causing the pulse to shorten. This also means that the shorterthe pulse gets the less losses appear and less changes of the pulse durationis achieved. Furthermore, electric signals can not be arbitrarily raised, thusactive mode-locking can only be used to achieve sub-nanosecond pulses.

For entering sub-picosecond pulse durations and thus the ultrashort pulseregime the method of passive mode-locking becomes necessary. In this casethe modulator is a saturable absorber, which becomes more transparent forhigher intensities or energies. In contrast to active mode-locking, no externalsource is required to manipulate the cavities transparence. Instead, the pulseitself causes the losses necessary for pulse shortening and thus determines theduration of the gain window. However, restriction is given by the recovery timeof the saturable absorber, i.e. the time necessary for the saturable absorberto turn back from transparent to the absorbing, high loss state. Hence, onedistinguishes fast and slow saturable absorber, where the latter provides arecovery time much larger than the pulse duration. However, under certainconditions slow saturable absorber still achieve significant pulse shortening.The schematic principle is shown in figure 2.11 (a). First, any parasitic light,e.g. background light or other long pulses potentially evolved in the cavity, getsuppressed by high losses. Second, the leading edge of the pulse is shaped dueto the losses, whereas the peak of the pulse causes the absorber to saturateand amplification occurs. Fast gain depletion, i.e. reduction of the populationinversion of the active laser medium, allows again a quick predominance of thelosses, thus the trailing wing is also shortened and parasitic light in the cavityis suppressed again. This becomes possible if the lifetime of the excited stateis comparable to the cavity roundtrip time. [11]

14

2.1 Fiber Lasers

Figure 2.11: Schematic of (a) slow and (b) fast saturable absorber. Figurestaken from [12].

Fast saturable absorbers don’t have such a dynamic gain behavior, but ratherwork in a regime where the active laser medium provides a constant gain duringthe process, as shown in figure 2.11 (b). In this case both sides of the pulsewings are formed by the loss modulation of the saturable absorber providing aresponse time similar to the pulse duration. However, pulses can’t be shorteneddown to pulse widths smaller than the response time of the saturable absorbersused, thus limitation is present due to the delay during the energy depletion.Such kind of saturable absorbers as discussed so far are called real saturableabsorbers. Even shorter pulses can be achieved by using artificial saturableabsorbers, where nonlinear effects cause the loss modulation rather than theabsorption of the peak intensity. Examples for passive mode-locking techniquesachieved with artificial fast saturable absorbers are Kerr-lens mode-locking(KLM) for free-space lasers and nonlinear-polarization evolution (NPE) forfiber lasers.

KLM relies on the optical Kerr effect which gives an intensity dependentrefractive index according to the equation [13]

n(λ, I) = nL(λ) + nNLI, (2.14)

where nL is the linear part of the refractive index dominating at low intensities

Figure 2.12: Schematic of KLM. Figure taken from [12].

15


and nNL is the nonlinear part which starts to increase with high peak intensitiesand is expressed in the units m2/W. Since the response of nonlinearities is fastthis effect is well suited for short pulses with high pulse energies, which thusexhibit high peak intensities. Such pulses cause the refractive index to increasehaving the effect of self-focussing, i.e. the more the refractive index increasesthe smaller gets the beam in the medium. Finally, an aperture inside thelaser cavity, as shown in figure 2.12, produces high losses for non-focussedbackground light, whereas lower losses occur for focussed pulses, which passthe aperture and oscillate in the laser cavity.

Passive mode-locking of fiber lasers can be achieved using the NPE tech-nique, which is based on polarization-additive pulse mode-locking (P-APM).As shown in figure 2.13 an elliptically polarized pulse experiences an intensitydependent polarization rotation inside the fiber segment due to the Kerr effect.An analyzer transfers the elliptical to linear polarization, which is transmittedthrough a polarizer. Certain orientation of a waveplate turns the linear po-larized light in such a way that it compensates for the nonlinear polarizationevolved in the Kerr medium. Hence, this technique allows for high transmis-sion of pulse peaks with high intensities, whereas the wings experience higherlosses at the polarizer due to less rotation in the Kerr medium. NPE in fibersbenefits from the high peak intensities due to a small fiber core diameter andfrom the simplicity of the setup. However, it is very sensitive for perturba-tion induced by the environment, e.g. changes in temperature or mechanicalvibrations. [15]

In conclusion, active mode-locking allows an efficient shortening of longpulses, but is restricted by the limitation of the velocity of electrical signals.In contrast, slow saturable absorbers provide a constant pulse shaping behav-ior, since the modulation by itself controls the amount of shortening, but it is

Figure 2.13: Schematic of P-APM. Figure taken from [14].

16

2.1 Fiber Lasers

restricted to conditions of the gain medium. Finally, fast saturable absorbersincrease the efficiency of shortening the pulses due to the instantaneously act-ing nonlinear processes. However they require already existing short pulsessince the shortening of longer pulses using this method is less efficient. Thismay also cause problems for starting the mode-locking process without anyexternal influences, such as abrupt changes in the cavity length. In general,pulses of passively mode-locked lasers utilizing fast saturable absorbers are theshortest produceable events ever induced by humankind and find applicationin, e.g. materials processing or pump-probe experiments. Rather than thermalprocesses the ablation or excitation relies on other physical phenomena, suchas coulomb explosions or two-photon absorption.

17


2.2 Propagation of Ultrashort Pulses in Fibers

In this section group velocity dispersion and self-phase modulation will bepresented, which are two dominating effects that allow for a formation andpropagation of soliton pulses in oscillators.

2.2.1 Group Velocity Dispersion

The propagation of an electromagnetic wave in a medium, e.g. air or an opticalfiber, results in an interaction with its bound electrons. Absorption occurswhen the optical frequency ω and thus the wavelength λ (with ω = 2πc0/λ)reaches the mediums characteristic resonance. In general, this effect leads to adependency of the refractive index n on the optical frequency ω and is calledchromatic dispersion. The Sellmeier equation gives an approximation of thedependency on the refractive index by [13]

n2(ω) = 1 +m∑j=1

Bjω2j

ω2j − ω2

j

, (2.15)

where Bj is the strength of the jth resonance at the corresponding resonancefrequency ωj. Since a short pulse contains a broad optical spectrum dispersionhas a crucial effect on the pulse propagation in a fiber. Each wavelength ex-periences a different refractive index and thus a different velocity c = c0/n(λ),which causes the pulse width to increase, i.e. the pulse broadens. In fiberoptics the mode-propagation constant β can be expressed by [13]

β(ω) = n(ω)ω

c= β0 + β1(ω − ω0) +

1

2β2(ω − ω0)2 + ..., (2.16)

where β1 is the ratio of group refractive index ng and speed of light in vacuumc0 and thus determines the speed of the pulse envelope vg [13]

β1 =1

c0

(n+ ω

dn

dω

)=ng

c0

=1

vg. (2.17)

A dependency of the refractive index n and the group refractive index ng asa function of the wavelength λ is shown in figure 2.14. The parameter β2

contains information about the broadening of the pulse and is also called thegroup-velocity dispersion (GVD) parameter. It is calculated from [13]

β2 =1

c0

(2dn

dω+ ω

d2n

dω2

)' ω

c0

d2n

dω2' λ3

2πc20

d2n

dλ2(2.18)

18


Figure 2.14: Refractive index n and the group refractive index ng as a func-tion of the wavelength. Figure taken from [13].

in ps2/km. Rather than β2 the dispersion parameter is often expressed in [13]

D = −2πc0

λ2β2, (2.19)

with the units ps/(km · nm). A dependency of the GVD parameter D as afunction of the wavelength λ is shown in figure 2.15. It is noticeable, that withincreasing wavelength D changes from a negative to a positive value at around1.3 µm. In cases where D is negative (β2 positive then according to (2.19))the fiber acts in the normal dispersion regime, where larger wavelengths (lowerfrequencies) propagate faster than shorter wavelengths. Otherwise, for positive

Figure 2.15: Dispersion parameter D as a function of the wavelength λ. Fig-ure taken from [13].

19


D values the fiber obtains anomalous dispersion, i.e. shorter wavelengths travelfaster than longer wavelengths.

The effect of pulse broadening induced by GVD depends on the initial pulsewidth. For examination whether GVD has a relevant effect on the pulse prop-agation it is useful to know the actual propagation length, i.e. the physicalfiber length L, and to define the dispersion length LD [13]

LD =T 2

0

|β2|, (2.20)

where T0 is the initial pulse width. In cases where L << LD GVD has noremarkable influence and the pulse is not significantly broadened. However, ifL >> LD GVD has an influence and broadens the pulse. The increased pulsewidth T (z) as a function of the propagation distance z can be calculated for agaussian shaped pulse from [13]

T (z) = T0[1 + (z/LD)2)]1/2. (2.21)

On one hand from equation (2.20) and (2.21) it can be seen that the amount ofpulse broadening depends on the initial pulse width T0 and the GVD parameterbut does not rely on the sign of β2, thus normal and anomalous dispersion canlead to the same effective broadening. Furthermore, pulse broadening dependson the shape of the pulse, where pulses with steep leading and trailing edgesexperience increased pulse broadening. Nevertheless, gaussian and hyperbolic-secant pulses show similar broadening. An example of the position dependent

Figure 2.16: Pulse broadening of a hyperbolic-secant pulse along the z-direction of a fiber. The figure is taken from [13].

20


pulse broadening and the resulting decrease in peak intensity is shown in figure2.16.

2.2.2 Self-phase Modulation

As already discussed in section 2.1.2 and shown in equation (2.14) the refractiveindex of a medium is changeable through high intensities. In general, theseintensities are produced in single-mode fibers using short pulses with high pulseenergies. Especially in combination with the small core diameter and thus thesmall effective area Aeff high intensities are generated and are responsible forthe appearance of nonlinear effects. Similar to the condition for GVD, a fiberbehaves nonlinear if the physical fiber length L is larger than the nonlinearlength LNL, which is given by [13]

LNL = (γP0)−1, (2.22)

where P0 is the peak power and γ is the nonlinear parameter [13]

γ =nNLω0

c0Aeff

=2πnNL

λ0Aeff

(2.23)

with units of rad/(Wm). The time dependent intensity and thus the variationof the refractive index n as a function of time results on one hand in a changein the nonlinear phase of the electromagnetic wave φNL(z, T ), which is inducedby the pulse itself. This effect is called self-phase modulation (SPM) and thechange in phase is determined by [13, 16]

φNL(z, T ) = γP0z = nNLω0

c0

Iz =2π

λnNLIz, (2.24)

where z is the propagation in a medium, which is assumed to be lossless. Onthe other hand the changing nonlinear phase φNL(z, T ) results in a symmetricgeneration of new frequency components, which is called SPM-induced spec-tral broadening. In general, the pulse energy is redistributed from the centerfrequency ω0 to the new generated frequencies and results in a time depen-dent frequency ω(t) = ω0 + δω(T ), where the time dependent change of thefrequency is the time derivative of the nonlinear phase

δω(T ) =dφNL

dT=

2π

λnNLz

dI

dT. (2.25)

From figure 2.17 it can be seen that the optical spectrum with new frequen-cies obtains a time dependancy. Since the change of frequencies is negative for

21


Figure 2.17: Time dependent intensity of a pulse on the top and its redis-tributed frequency components as a function of time. The figureis taken from [17].

the leading edge of the pulse, the generated lower frequency components (largerwavelengths) travel in the front of the pulse, while the higher frequencies areshifted to the trailing part of the propagating pulse. As already discussed insection 2.2.1 this is a similar effect as in the case of normal dispersion. It shouldbe pointed out that SPM results in a broadening of the optical spectrum causedby an intensity dependent nonlinear phase shift and remains constant in thetemporal domain, whereas GVD broadens the pulse duration due to a wave-length dependent linear phase without any changes in the optical spectrum.Although normal dispersion and SPM rely on different phenomena their coex-istence can have a supporting effect and results in an increased broadening ofthe pulse duration due to the temporal separation of the spectral components.However, the pulse broadening induced by a medium with anomalous disper-sion (short wavelengths travel fast) can be compensated in combination withexactly the counteracting SPM resulting in a constant temporal pulse profileover long distances, which is especially desired in optical fiber communication.A pulse propagating in a fiber, where the anomalous dispersion is balancedwith the SPM is called an optical soliton.

22


2.2.3 Solitons

In section 2.2.1 it was concluded that in general dispersion causes a pulse tobroaden. In the case of anomalous dispersion pulse broadening occurs due tothe fact that short wavelengths travel faster than long wavelengths. The exactopposite is shown in section 2.2.2, where SPM is responsible for shifting lowfrequencies and thus long wavelength to the front of the pulse (see figure 2.17bottom), whereas the shorter wavelengths are moved to the trailing edge of thepulse. The superposition of these two effects results in a preservation of thepulse shape, i.e. the temporal intensity profile, as well as the optical spectrumof the pulse along the propagation distance. The condition for balancing GVDinduced pulse broadening by means of the frequency variation due to SPM isthat the dispersive length LD must be equal to the nonlinear length LNL. Thepropagating pulse is then called a fundamental soliton

N2 =LD

LNL

= 1, (2.26)

where the parameter N is referred to as the soliton order. Using equation(2.20) and (2.22) the peak power P0 is determined by

P0 =|β2|T 2

0 γ(2.27)

and thus a discrete pulse energy is given by a certain pulse width T0. Theshape of a fundamental soliton is described by a hyperbolic secant function,

Figure 2.18: Optical spectrum of an erbium-doped fiber laser. The figure istaken from [18].

23


which will be further discussed in section 2.3.1. Due to the stability of solitonsthe evolution and their propagation are not affected by small perturbation ordeviations in peak power and thus in the soliton order N . [16] However, forsmall pulse durations, i.e. sub-picosecond pulse widths, spectral sidebands aregenerated. These sidebands, also called Kelly sidebands, are located in defineddistances from the center wavelength. An example of the optical spectrum ofan erbium-doped soliton laser including the characteristic Kelly sidebands isshown in figure 2.18. Kelly sidebands arise due to the fact that the solitonis influenced during one roundtrip by periodical perturbations in the cavity.These disturbances are represented on one hand by the amplification in thegain fiber and on the other hand in terms of losses arising, e.g. from the outputcoupler, free-space coupling sections and splices. After such a perturbation thesoliton reshapes itself by depleting excessive energy into a dispersive wave co-propagating with the soliton. [19] In general, such a dispersive wave would notfurther affect the propagation of the soliton. But in cases where the relativephase per roundtrip between dispersive wave and soliton is an integer multipleof 2π both interfere constructively which results in a superposition visible inthe optical spectrum. [18]

24

2.3 Characterization of Mode-locked Lasers with Ultrashort Pulses

2.3 Characterization of Mode-locked Lasers

with Ultrashort Pulses

For characterizing mode-locked lasers and evaluating their operation state, itis necessary to measure various parameters with different measurement equip-ment.The optical spectrum can be measured using an optical spectrometer and

includes besides the wavelength also information about the pulse duration.The latter can be measured using an autocorrelator since the pulse durationsof ultrashort pulses are beyond the response time of conventional photodiodesdelivering electrically detectable power signals. Photodiodes in turn are usedin combination with a spectrum analyzer for measuring the repetition rate ofthe pulse train in a radio frequency (RF) spectrum. Furthermore, a power me-ter can be used for determining the average output power with respect to thelaunched input power, which gives in combination with the repetition rate thecorresponding pulse energies. Another important issue regarding the stabilityof the laser is its noise behavior, which in general is measured using a photo-diode and additional analyzing equipment. Finally, long-term measurementsregarding the mode-locking stability is also recommended, in order to ensure areliable performance of the laser, which should resist environmental influencesguaranteeing an operation without disturbances.The following four sections will explain these characterization methods in

more detail.

2.3.1 Pulse Characterization

In section 2.1.2 it was already discussed and in equation (2.13) shown thatmode-locked lasers with a broad optical spectrum, i.e. a large number oflocked modes, produce very short pulses.An optical spectrometer is an instrument for measuring the intensity of in-

coming light with respect to the different wavelengths within the spectrum.Commonly, a movable grating diffracts the individual wavelengths on a detec-tor. The light can be either coupled into the spectrometer using a free-spacebeam or directly via a fiber connector. From the recorded optical spectrum thecenter wavelength λ0 and the full width at half-maximum (FWHM) λFWHM,i.e. the wavelength range at half of the intensity, can be determined. Transfer-ring the wavelengths into frequencies using equation (2.9) the correspondingfrequency value of the FWHM ∆νFWHM can be used in combination with thetime-bandwidth product of a given pulse shape for identifying the lower limit

25


of the pulse duration T0. As already discussed in section 2.2.3 the shape ofsoliton pulses are well described by a hyperbolic secant function, so that thetime-bandwidth product is given by [20]

∆νFWHM · T0 = 0.315. (2.28)

Hence, knowing the shape of the pulse and the FWHM of the optical spectrumresults in a value for a pulse duration representing the lower limit. Suchpulses are called transform limited pulses, i.e. they are unchirped. Unchirpedpulses show no time dependency of the frequency or wavelength within thepulse duration. Such a time dependency can, as already discussed in section2.2, be induced by SPM and dispersion. Due to the balancing of these twoeffects solitons show the ability of producing almost transform limited pulses.However, it is necessary to measure the exact pulse duration to proof whetherit is unchirped or how much chirp is present.

Photodiodes are not able to measure the duration of ultrashort pulses dueto a slow response time compared to such a short event. One can overcomethis restriction by using an autocorrelator in which the pulse itself works as aruler for measuring its own duration. Such an instrument consists of a con-ventional Michelson interferometer, a nonlinear crystal and a photodetector.The Michelson interferometer splits the pulse train into two optical paths andrecombines them again. The optical path in one arm is kept fixed, whereas theother arm is equipped with a moving mirror. This allows a precise variationof the time in which the recombined pulses overlap and thus allows a timedependent scanning of one pulse over the other. A non-collinear focussing ofthe superimposing pulses on a nonlinear crystal, where the second harmonicis generated whenever the pulses overlap in time, allows a background-freemeasurement. The distance of the mirror movement can be transferred to acertain time delay τ , so that the intensity with respect to the time delay can berecorded. Finally, the FWHM of the intensity autocorrelation curve τFWHM,AC

is directly correlated to the pulse duration T0. Again, the shape of the pulseplays an important role, so that a deconvolution factor is used for calculat-ing the corresponding pulse duration from a certain intensity autocorrelationcurve by [20]

τFWHM,AC = 1.542 · T0, (2.29)

where the factor 1.542 is the deconvolution factor for a hyperbolic secantshaped pulse. The autocorrelator reported in [21] uses two parallel rotatingmirrors rather than one moving mirror for inducing a continuous delay in order

26


to display the autocorrelation trace on an oscilloscope. A corner mirror in thefixed beam path of the Michelson interferometer is mounted on a translationstage. Tuning the position of this mirror results in a time variation of theautocorrelation trace. As in a conventional autocorrelator the displacement ofthe corner mirror can be transferred to a calibration factor which correlatesthe time delay of the pulse with the timescale on the oscilloscope. The detailedoperation of this kind of autocorrelator will be further explained in section 3.3.

2.3.2 Output Power and Pulse Energy

The output power can be measured by a power meter, e.g. a thermopile. Suchan instrument absorbs the incoming radiation and converts the resulting tem-perature difference to an electric signal. The internal wavelength dependingcalibration finally delivers the actual optical power Popt. The pulse energy Ep

can thus be calculated by

Ep =Popt

frep

, (2.30)

where frep is the repetition rate. The repetition rate of a mode-locked lasercan be measured by a photodiode, which detects each pulse of the pulse train,connected to an oscilloscope or a spectrum analyzer as shown in 2.19 (a). Theoscilloscope gives the corresponding periodic signal in the time domain. Incase of using a spectrum analyzer, which performs a fast Fourier transfor-mation (FFT), the resulting signal is converted to the frequency domain. Aperfect wave form in the time domain would correspond to a sharp peak in thefrequency domain. However, due to noise the signal obtains sidebands, whichcause a the frequency signal to broaden as shown in 2.19 (b).

2.3.3 Noise

Noise in mode-locked lasers is an undesired effect since it may influence theresults of the particular application. In fact it can be reduced by varioustechnical approaches but never vanishes completely. In general, noise arisesfrom different sources, e.g. from instabilities of the pump source, acousticvibrations, changes in ambient temperature and externally induced electricalinfluences as well as from amplification of spontaneous emission in the gainmedium. For mode-locked lasers one distinguishes the amplitude noise andthe phase noise. The amplitude noise represents random fluctuations of thepulse energy. Phase noise is represented by fluctuations of the phase of awave resulting in a broad peak rather than a discrete line of the frequency

27


Figure 2.19: Pulse train detected by a photodiode in (a) and the spectrumanalyzer’s signal in (b). The figure is adapted from [22].

spectrum as shown in figure 2.19. This section describes the measurement andcharacterization of these two types of noise.

Amplitude noise

Amplitude noise is measured in the frequency domain rather than an averagedpower value for a defined duration. This offers the advantage of providing indi-cations for possible noise sources correlated with different frequencies. Hence,determining the predominating origin of the noise allows a systematic reduc-tion by improving the setup. Examples for such frequency depending noisesources are relaxation oscillations, power supplies, vibrations or electromag-netic influences. Relaxation oscillations are correlated with the lifetime of theexcited state in the gain medium and appear as a broad peak. Noise frompower supplies is located at multiples of 60 Hz or several tens or hundreds ofkilohertz and is visible as discrete spectral lines. Finally, vibrations or elec-tromagnetic influences appear as spurious lines. [22] Furthermore, amplitudenoise is defined in a relative expression in order to be able to easily comparedifferent measurements, taken with different equipment and laser systems atdifferent power levels. Hence, the relative intensity noise (RIN) is defined as[22]

RIN(f) =

(Popt(f)

Popt, c

)2

, (2.31)

where Popt(f) is the optical power spectrum per 1 Hz bandwidth with the unitdB/Hz and Popt, c is the average output power. Thus, the signal is normalizedto the carrier power and is expressed by the unit dBc/Hz. Since the squared

28


optical power is proportional to the electrically detected power [22] equation(2.31) can be written as

RIN(f) =P (f)

Pc

, (2.32)

where P (f) is the power spectral density (PSD), i.e. the frequency dependingelectrical power in 1 Hz bandwidth with units dB/Hz and Pc is the electricalDC power of the carrier in unit dB. While P (f) can be measured by a vectorsignal analyzer in combination with an irradiated photodiode, the carrier powercan easily be determined by connecting the photodiode output to a voltmeter.The electrical carrier power is calculated from

Pc =V 2

Ri

, (2.33)

where V is the measured voltage and Ri represents the input resistance whichis typically 50 Ω. It should be pointed out that it is necessary to transfer PDC todB units using equation (2.8) before calculating the RIN with equation (2.32).Finally, the RIN in dBc/Hz as a function of the frequency can be plottedusing a logarithmic scale. Solving equation (2.8) to P in W the equation canbe used to transfer the RIN(f) from dBc/Hz to 1/Hz units, so that the RINcurve can be integrated over a defined frequency range. Applying the squareroot and multiplying the value with 100 result in a final root-mean-square(RMS) amplitude noise value in % RMS

RIN%RMS = 100 ·

√∫ fmax

fmin

RIN(f). (2.34)

Phase Noise

Random phase variations create sidebands in the frequency domain due tofluctuations in the time domain, i.e. instead of a single spectral line the band-width of the frequency signal is broadened. A varying pulse period TR inmode-locked lasers, e.g. due to temporally induced variations of the cavitylength, thus introduces a phase noise which is related to a timing jitter. Forphase noise measurements it is necessary to isolate the phase noise from therandom amplitude fluctuation of a periodic signal. In a phase noise analyzerthis separation is achieved by mixing the signal from the device under test, i.e.the periodic signal on an irradiated photodiode by a mode-locked laser, withthat of a tunable and highly stable reference oscillator. The latter is tunedin such a way that both oscillators provide identical frequencies. A balancedmixer performs a multiplication of the two wave signals and introduces a 90

29


phase shift. The resulting signal is directly correlated with a phase differ-ence, where a perfect match of the two oscillator signals would correspond to 0V. Hence, phase variation can be directly detected with a spectrum analyzer,which provides in practice a phase noise measured at different offset frequenciesof the carrier frequency. This measured phase noise is represented as the singlesideband (SSB) power spectrum in 1 Hz bandwidth relative to the carrier withunits dBc/Hz and is denoted as L(f). For proper phase noise measurementsthe signal of the photodiode needs to be amplified to a value within the de-tection range of the phase noise analyzer. Furthermore, the frequency of thesignal needs to be bandpass filtered to the fundamental repetition rate of thelaser or any of its harmonics. Finally, L(f) can be transferred to an integratedRMS timing jitter ∆tRMS in a defined range of frequencies by [22]

∆tRMS =1

N2πfrep

√2

∫ f2

f1

L(f)df, (2.35)

where N is the number of the harmonic of the fundamental repetition ratefrep. The frequency range for integrating the RMS timing jitter of mode-lockedlasers is commonly f1 = 10 kHz to f2 = 10 MHz.

2.3.4 Mode-locking Stability

During the operation of regenerative amplifiers it is crucial to ensure a sta-ble operation state of the seed oscillator. Especially during the transitionfrom CW to mode-locking operation spikes with high peak power may appear,which experience amplification and could damage sensitive components of theregenerative amplifier. The mode-lock detector is a device providing a monitorfor the mode-locking state, for various power values, e.g. the oscillator outputand the pump power, and offers a relay for switching off the pump if the seed’smode-locking operation is interrupted. In principle, the mode-lock detectorconsists of a photodiode detecting the periodic pulse train of the oscillator.This power signal is filtered in the frequency domain by two bandpass filtersseparating the signal into two parts, the noise and the carrier power. The noisesignal obtains the power in the lower frequencies around 10 Hz to 100 kHz,while the carrier power is measured at the repetition rate of the oscillator. Incases where the oscillator works in the mode-locking regime the carrier poweris high compared to the power of the noise signal. Whenever the mode-lockingstate is lost the carrier power drops and the noise power dominates.

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3 Experimental Setup

The experimental setup of the passively mode-locked holmium-doped solitonfiber ring oscillator and its characterization can be divided in three sections.It consists of two closed boxes, i.e. one for coupling the pump laser into fiberand the other for the oscillator itself. The third section represents a setup ofdifferent measuring devices. A photograph of the setup including the pump,oscillator and characterization section as well as the mode-locked detector isshown in figure 3.1. This chapter will present the construction of those threesections as well as the assembly of the mode-lock detector.

Figure 3.1: Photograph of the setup including pump, oscillator and charac-terization sections. PD: Photodiode; AC: Autocorrelator.

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3.1 Available Components

The main components used for the construction of the passively mode-lockedholmium-doped soliton fiber ring oscillator are listed in table 3.1.

Since the pump laser is equipped with a fixed output collimator it is neces-sary to couple the free-space beam into the fiber, rather than splicing a barefiber tip directly to the input of the oscillator. Hence, all mechanical and opti-cal components used for coupling the pump light into the oscillator are locatedon a separated breadboard and are isolated by a box. In the following this isreferred to as the pump section. A schematic drawing is given in figure 3.2and a photograph of the opened housing is depicted in figure 3.3.

The linear polarized output of the pump laser passes a half-wave plate andmeets a thin-film polarizer (TFP) in a 65 angle. Rotating the half-waveplate (HWP) allows for precise power adjustments due to the polarizationdepending reflectivity or transmission of the polarizer. Vertically polarized(i.e. s-polarized) light is completely reflected, whereas horizontally polarized(i.e. p-polarized) light passes the TFP. The transmitted beam is absorbed bya beam block and the reflected beam travels through a telescope. It consistsof a combination of plano-convex lenses with focal lengths of 100 mm and50 mm for reducing the beam diameter to the half of its initial size from 5to about 2.6 mm. The alignment is carried out using a camera for observing

Figure 3.2: Schematic drawing of the pump section. HWP: half-wave plate;TFP: thin-film polarizer; QWP: quarter-wave plate; SMF: single-mode fiber; ND attenuator: neutral-density attenuator; PD: pho-todiode; MLDET: mode-lock detector.

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the beam diameter in various distances for collimating the beam. The beamdiameter after the telescope is shown in figure 3.4 (a). Two mirrors fixed inmountings with adjustable screws allow a precise manipulation of the beam forcoupling into the fiber. Before, the beam passes a quarter-wave plate (QWP)for changing the polarization state from linear to elliptical polarization. TheSMF is fixed using copper tape and a magnetic stripe in a V-groove, whichis screwed on an XYZ translation stage. The beam is coupled into the fiberusing a coated aspheric lens with a focal length of 11 mm. A more detailedexplanation of the procedure for efficient fiber coupling is given later. TheSMF is spliced to a series of fiber couplers with different splitting ratios. 80 %

of the coupled power is directly delivered to the oscillator. The resulting20 % power is divided again, where 90 % of the power is used for observingthe coupled power with a power meter and the output of the 10 % port isattenuated by a neutral density (ND) attenuator before it is focussed on aphotodiode. In the final setup the ND attenuator is replaced by bendingand glueing the fiber on a post to introduce a certain amount of bendingloss, which prevents the photodiode from saturation. Finally, the fiber tip isspliced to an FC/APC (Fiber-optic Connector with Angled Physical Contact)fiber connector, which is directly attached to the photodiode of the mode-lockdetector. For reducing Fresnel reflections on the surface of the fiber tip iscleaved with a 7.6 angle. A photograph of the fiber tip placed inside thesplicer and the resulting measurements of the angle are given in figure 3.4 (b)

Figure 3.3: Photograph of the pump section.

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Component Company Main parametersPump laser IPG λc=1938 nm, Pmax=10 W, øbeam=5 mm

TFP Layertec θi=65

SMF Thorlabs NA=0.11, øcore=11 µm, øclad=125 µm80/20 coupler AFR Pthreshold=10 WOther couplers AFR Pthreshold=400 mW

WDM Gooch & Housego α1940 nm=23 dB, α2050 nm=0.4 dBHDF Nufern NA=0.15, øcore=10 µm, øclad=130 µm

Faraday isolator EOT øaperture=4 mm, T=89%, αiso=30 dBIsolator Thorlabs øaperture=3.6 mm, T=88%, αiso=33 dBNB filters Spectrogon λc=2050 nm and λc=2080 nm

Table 3.1: List of the oscillator’s main components and their specification.

and (c), respectively.

In figure 3.5 the procedure of coupling the pump laser beam into the fiberis illustrated. As a first step the XYZ translation stage is roughly adjustedusing the three provided micrometer screws. This is done in such a way thatan FC/APC fiber holder can easily be moved through the profile. The fiberholder functions as an aperture and is moved several times from the front tothe back during the beam adjustments. While mirror 1 is used for guiding thebeam through the aperture when it’s located in the front position, mirror 2 isadjusted for the case the fiber holder is in the back position. The power meterbehind the translation stage is used for observing the power until it showssimilar maximum values for both positions of the aperture. Hence, the beam

Figure 3.4: (a) Shows the beam profile after the telescope, (b) gives a topview of two fiber tips, i.e. one flat side for splicing and one angle-cleaved side used for coupling and (c) depicts the fiber character-istics of the angle-cleaved fiber tip measured by the splicer.

34


is centered and horizontally aligned with respect to the XYZ translation stage.As a next step the fiber holder is removed and replaced by the V-groove as canbe seen from figure 3.3 including the fixed fiber. Furthermore, the focussinglens with 11 mm focal length is screwed on the fixed part of the translationstage. Since the power meter doesn’t provide a fast and sensitive response itis replaced by a photodiode connected to an oscilloscope and the X Y and Zposition is tuned for optimizing the signal. By measuring the power beforefocussing and at the end of a short fiber segment the coupling efficiency ismaximized to about 72 %. Finally, the remaining fiber components are splicedto the fiber.The breadboard is put on a foam with lead inside for reducing acoustical

and mechanical vibrations. Furthermore, a housing is constructed around thepump section. It consists of a framework of rails fixed on the breadboardwith foam tape in between. Acrylic glass with a layer of dense rubber tapefor blocking acoustical vibrations from outside and preventing scattering lightfrom inside to exit is fixed to the rails using wing nuts and washers screwed tothreaded bolts, which are inserted into the rails. The bare fiber terminationsleave the housing at two locations. On one hand the output fiber is fixed be-tween two washers and is guided in between the foam tape and the breadboard(see figure 3.3 on the left) towards the oscillator. On the other hand the twomonitoring ports, i.e. the 90 % and 10 % outputs from the coupler, share theslit in the front of the housing for leaving the box, which initially serves as theinput of the yellow pump fiber as shown in figure 3.1.

Figure 3.5: Photograph of the fiber coupling.

35


3.2 Oscillator

The oscillator consists of different fiber segments and fiber components as wellas optical free-space paths as illustrated in the schematic drawing in figure3.6. The fiber from the pump section is guided into the oscillator section andis directly spliced to the input port of the WDM which provides low lossesfor the pump wavelength, i.e. 1940 nm. Hence, the output port of the WDMis spliced to an 88 cm fiber segment, which is doped with holmium ions andthus represents the active gain in the oscillator. Although the SMF outputof the WDM and the HDF vary slightly in their cladding and core diameters(see table 3.1) the splicing results in a proper fusion of the fiber segments ascan be seen from figure 3.7. The end of the HDF is angle-cleaved and fixedin a V-groove on an XYZ translation stage. Furthermore, the output beam iscollimated by a coated aspheric lens with a focal length of 4 mm. The beamis coupled back into a 214 cm SMF segment provided with an FC/APC con-nector using another XYZ translation stage which is equipped with the sametype of lens and a fiber holder. In between this free-space path the artificialsaturable absorber, i.e. a combination of QWP, HWP, Faraday isolator and asecond QWP, is positioned, where the first polarizing beam splitter (PBS) ofthe Faraday isolator serves as the output coupler of the mode-locked laser. TheSMF is spliced to a fiber coupler with 99:1 splitting ratio, where the 99 % portis spliced to the remaining input port of the WDM providing low losses for thelasing wavelength, i.e. 0.4 dB for 2050 nm, and high losses for the pump light,

Figure 3.6: Schematic drawing of the oscillator.

36

3.2 Oscillator

Figure 3.7: Photograph before (a) and after (b) the splicing process of theSMF from the WDM output (left fiber) to the HDF (right fiber).

i.e. 23 dB for 1940 nm. Eventually, the ring of the oscillator is closed and theremaining pump light is removed from the cavity. The 1 % port is spliced to an-other fiber coupler with a 50:50 splitting ratio providing two monitoring portsfor observing the optical spectrum and power level inside the ring oscillator. Inorder to prevent back reflections into the oscillator a second isolator is placedbehind the output coupler followed by a combination of narrow bandpass (NB)filters used for removing the Kelly sidebands of the soliton spectrum. The NBfilters provide different central wavelengths and transmitting bandwidths, i.e.2050 nm and 2085 with 12 nm and 10 nm, respectively. Since the second band-pass filter is optimized for a larger center wavelength compared to the laser’soperation wavelength at 2050 nm it is arranged in an angled position, whichallows for the transmission of lower wavelengths. Finally, the output beam iscoupled into fiber using a mirror and a third translation stage equipped witha coated aspheric lens with 11 mm focal length and an FC/APC fiber holder.From figure 3.8 it can be seen that in order to characterize the parameters ofthe mode-locked oscillator the free-space beam is temporarily guided directlythrough a hole in the oscillator housing rather than coupled into fiber.

The conditions for initiating mode-locking are on the one hand that thepump power inside the cavity has to be high enough to overcome the lasingthreshold and provides enough power for starting the evolution of a domi-nating polarization direction inside the fiber caused by the Kerr effect. Onthe other hand the three waveplates of the artificial saturable absorber haveto be orientated in such a way that the preferred polarization is transmittedthrough the output coupler, i.e. the first polarizer of the Faraday isolator, andthus maintains inside the cavity, whereas other polarization states are reflectedand removed from the cavity. It should be pointed out that there is not onlyone perfect combination of waveplate orientations leading to the evolution ofultrashort lasers pulses thus there are multiple combination possibilities forinitiating mode-locking. For starting mode-locking a random fluctuation is

37


required which causes longitudinal modes to match in phase what allows themto interfere coherently. However, simple increasing of the pump power doesn’tresult in self-starting of the oscillator. In fact, mode-locking is achieved by fastchanges in the optical path length of the cavity due to induced birefringence inthe gain fiber. This is achieved by carefully touching or bending the gain fiberin a case where the waveplates are properly orientated and a certain pumppower is provided to allow a soliton pulse to evolve.

Just like the enclosing box of the pump section, the housing of the oscillatoris provided with foam tape between breadboard and rails. This allows fordecoupling possible mechanical vibrations induced on the wall and guided tothe breadboard thus also directly to the fiber since it is directly fixed on thebreadboard using kapton tape. Since the delivery fiber from the pump sectionis guided underneath a rail and is fixed between two washers (see figure 3.8 onthe right) the foam tape also provides a smooth and safe environment betweenbreadboard and rail. As can be seen in the top right corner of figure 3.8 thehousing is screwed to the breadboard with compact table clamps inserted in theprofile of the rails. For the output and the monitoring ports holes are drilledinto the wall of the box into which FC/APC fiber connectors are mounted.

Figure 3.8: Photograph of the oscillator.

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3.3 Measurement Setup


To characterize the constructed mode-locked laser different kinds of measuringequipment are set up that allow for simultaneous measurements of various laserparameters, e.g. the output power, the repetition rate, the optical spectrumand the pulse duration. A schematic drawing of the setup is illustrated in figure3.9 and an overview of the diagnostic tools used including their specificationsis given in table 3.2.The free-space beam leaving the oscillator passes a HWP and is split by a

PBS into two beams, where the power of each path is adjustable through theHWP.The power of the reflected beam is reduced by an ND attenuator and fo-

cussed by a lens with a 50 mm focal length on a photodiode. Two types ofphotodiodes, i.e. either a fast or a slow one, are used for the measurementsdepending on the device connected. On one hand for measuring the repetitionrate with a spectrum analyzer the fast photodiode is used offering a cutofffrequency of more than 12.5 GHz. On the other hand in case of amplitudenoise measurements the slow photodiode with a cutoff frequency of 140 MHz

in combination with a transimpedance amplifier delivers low noise and a highsensitivity in combination with a vector signal analyzer. Phase noise mea-surements are carried out using the fast photodiode connected to a series ofbandpass filters and an amplifier for filtering the fundamental harmonic andamplifying the power signal to the operation range of the phase noise analyzer,respectively.The beam that is transmitted through the PBS is adjusted to the height

Figure 3.9: Schematic drawing of the characterization section.

39


Device Company Main parametersPower meter Gentec Thermopile, Pmax = 30 WPhotodiode Newport InGaAs, fcutoff > 12.5 GHzPhotodiode Hamamatsu InGaAs, fcutoff = 140 MHzSpectrometer Ocean Optics NIRQuest, λrange: 1890 - 2140 nmOscilloscope R&S fmax = 100 MHz

Spectrum analyzer Rigol frange: 9 kHz - 1.5 GHzVector signal anaylzer Agilent/HP frange: DC - 10 MHzPhase noise analyzer Holzworth 0 < Pinput < 20 dBm

Autocorrelator Femtochrome LiIO3 crystal, Si Photodiode

Table 3.2: List of the diagnostic tools used for characterizing the mode-locked laser.

of the autocorrelator’s input and is brought to a horizontal propagation withrespect to the optical table by means of two mirrors. Before entering the au-tocorrelator a small fraction of the beam power is reflected by a wedge andpropagates into the spectrometer. For observing the optical spectrum insidethe oscillator cavity rather than the bandpass filtered output spectrum a patchcable can be connected between one of the monitoring ports and the spectrom-eter. The second monitoring port is connected via fiber to the photodiode ofthe mode-lock detector. The remaining power transmitted by the wedge passes

Figure 3.10: Photograph of the characterization section.

40


a HWP, which rotates the linear polarization to s-polarization, and is guidedinto the autocorrelator. Since the beam is split, recombined and focussed intoa nonlinear crystal the alignment of the autocorrelator with respect to theincoming beam requires careful handling and patience.

As a first step the autocorrelator is aligned horizontally setting three footscrews while measuring the alignment with a bull’s eye spirit level. Further-more, the orientation of the autocorrelator is adjusted so that the beam passesthe center of the input aperture. Aligning the autocorrelator is carried outfirst regarding the reference path, which is transmitted by the beamsplitterand should hit the left side of the first mirror. This allows the returning beamfrom the corner mirror to come back on the right side of the first mirror asdepicted in figure 3.9. At this point the autocorrelator’s orientation is wellaligned and is clamped to the optical table. The returning reference path isreflected by the beamsplitter and is focussed downwards by a concave mirrorinto a nonlinear crystal thus the fundamental beam appears on the right sidenext to the aperture of the photodiode. The delayed beam, which is initiallyreflected by the beamsplitter, travels through the combination of rotating par-allel mirrors representing the continuous path length variation and hits a longhorizontally aligned mirror. Due to the rotation of the two parallel mirrors thebeam is horizontally scanned over this mirror. Its orientation is adjusted usingtwo set screws for manipulating the reflected beam in such a way that afterpassing the rotating mirrors again it transmits through the beamsplitter andis focussed by the concave mirror into the nonlinear crystal. In this case thefundamental harmonic of the delayed beam appears on the left side next tothe photodiode. This non-collinear superposition allows for background-freemeasurements since the generated second harmonic (shown as a green beam infigure 3.9) travels in the center of both fundamental beams directly pointingon the photodiode.

Measurements are carried out by detecting two types of signals from theautocorrelator with an oscilloscope. While one channel is fed with a triggersignal with a duration corresponding to the rotation frequency of the parallelmirrors, the second signal corresponds to the power of the second harmonicdetected by the photodiode. This signal will only appear if the two beams arewell aligned and the phase matching angle of the crystal is correct. The lattercan be tuned with a micrometer screw which causes a rotation of the nonlinearcrystal. In this application a maximum signal on the oscilloscope is achieved bysetting the screw to 2.81 mm. Finally, the symmetric autocorrelation curve onthe oscillator contains information about the pulse duration. For calculating

41


the pulse width a calibration factor needs to be determined used for convertingthe ms timescale on the oscilloscope, which shows multiple pulses scanned overthe reference pulses, into the actual timescale determining the pulse durationduring which a superposition of reference and delayed pulses generate thesecond harmonic. The calibration factor is determined by moving the cornermirror over a certain distance what causes a shift of the autocorrelation curveon the oscilloscope. As shown in figure 3.11 a mirror displacement of s =

6.6 mm results in a time shift of t = 1.464 ms on the oscilloscope. Since thebeam in the reference path moves twice the increased distance the induceddelay in the time domain corresponds to

τ =2s

c= 44.03 ps. (3.1)

Finally, the calibration factor is determined to be

τ

t=

44.03 ps

1.464 ms= 30.075 ps/ms, (3.2)

which can be used for transferring the timescale of the oscilloscope and thusallows for determining the FWHM of the autocorrelation curve τFWHM,AC con-taining the actual pulse duration according to equation (2.29).

In conclusion, the setup depicted in figure 3.10 allows for simultaneous mea-surements for characterizing the mode-locked laser pulses.

Figure 3.11: Determination of the calibration factor by moving the cornermirror of the autocorrelator.

42

3.4 Mode-lock Detector

3.4 Mode-lock Detector

In general, the mode-lock detector consists of four stacked printed circuitboards (PCB) and offers two input photodiodes for detecting the oscillatorand pump power.

Functioning as the fundamental PCB the photodiode board is located atthe bottom of the stack collecting the oscillator’s power on a photodiode. Thedetected signal is amplified and split, where one of the signals is bandpassfiltered by an LC circuit particularly working at the oscillator’s repetitionrate. This signal is referred to as the carrier power. The second portion ofthe split power signal is directed to the second PCB, i.e. the noise board. Itfilters the signals in the lower frequency range which represent the noise power.Furthermore, the noise board provides an additional photodiode for detectingthe pump light. Analog signals from the first and second PCB are transferredto the third, i.e. the micro controller board. It contains several analog-to-digital converters (ADC), which deliver the digital data to a micro controller.It transfers the raw ADC values into power values in dBm units according toa programmable calibration and visualizes both of them on the display of thetop PCB as shown in figure 3.12. Furthermore, the micro controller boarddetects the actual operation, e.g. high (low) carrier power for mode-locking(CW), and switches a relay in case of changing states.

Figure 3.12: Photograph of the mode-lock detector while the oscillator isworking in the mode-locking operation indicated by the largecarrier power and low noise power.

43


Soldering the surface-mount components, i.e. resistors, capacitors, induc-tors and light-emitting diodes (LED), on the PCB is carried out by dilutingtin-solder on the solder pads with an electrically driven syringe, placing thecomponents on the corresponding positions and carefully laying the preparedPCB into a soldering bath. After the soldering process additional componentsthat obtain a larger size, i.e. capacitors and inductors as well as photodiodes,test points, wire, the power supply connector, coaxial RF and other connectorsused for transferring signals to the different PCB, are soldered using a conven-tional soldering machine. Finally, the four PCB are connected and screwedtogether as shown in figure 3.13.

The transformation of raw ADC to dBm power values relies on calibrationfactors stored in the micro controller, which can be set via serial connectionto a computer and sending defined commands to the micro controller. Theadjustment is carried out by measuring the oscillators output power and theinput power before coupling into the fiber with a power meter and combinethe measured values with the corresponding raw ADC values so that finallythe values on the display correspond to the power measurements.

Figure 3.13: Photograph of the stack of PCB with the photodiode board onthe top. The photodiode (PD) is not yet soldered and the out-put not yet connected to the micro controller board. Bandpassfiltered voltage signals corresponding to the carrier power canbe measured using the test point.

44

4 Results and Discussion

This chapter will present and discuss the characterization of the pulse, the noisemeasurements and the long-term stability of the mode-locking state. For thepulse characterization the optical spectrum, the pulse duration, the repetitionrate and the output power are measured. Noise measurements are carried outin terms of relative intensity noise and phase noise.

4.1 Pulse Characterization

In this section the results for the measured optical spectrum, the pulse durationand the pulse energy will be presented and discussed.

4.1.1 Optical Spectrum

During the attempts of initiating mode-locking with random adjustments ofthe three waveplates of the artificial saturable absorber the CW peak in theoptical spectrum changes its center wavelength depending on the orientationof the waveplates. With the waveplates in an appropriate orientation withrespect to each other as well as to the incoming polarization the laser startsmode-locking at a pump power of about 2 W and by carefully penetrating thegain fiber. 2 W pump power corresponds to about 1.1 W in the cavity assuminga coupling efficiency of 72 % and 20 % power coupled to the monitoring ports.Mode-locking is indicated by a rapid broadening of the CW peak around itsinitial center frequency and an appearance of Kelly sidebands.As the position of the CW peak in the optical spectrum is tunable, so is the

center wavelength of the mode-locking operation. Figure 4.1 shows five solitonspectra at different center wavelengths (the blue spectrum for the shorter andred for the longer wavelengths) with a normalization with respect to the inten-sity at 2060 nm. The center wavelength of the mode-locked oscillator is tunedover a 20 nm range from 2045 up to 2065 nm. Each of the spectra is recordedby interrupting the mode-locking state, tuning the waveplates roughly thusthe CW peak changes followed by gentle tuning while touching the gain fiberuntil the oscillator starts mode-locking. Tuning the center wavelength without

45


Figure 4.1: Optical spectrum tuned to different center wavelengths by chang-ing the wave plate combination.

losing mode-locking is also achieved in a range of approximately 5 nm by gentlychanging the HWP and adjusting the other two QWP simultaneously.

Since the regenerative amplifier operates at a center wavelength of 2050 nm

further pulse characterization is carried out for soliton pulses tuned to thisparticular center wavelength. The final values for the angles read from themounting of the different waveplates are QWP1 = 54, HWP = 194 and

Figure 4.2: Optical spectrum with different bandpass filters.

46


QWP2 = 191 where the subscript numbering corresponds to the direction ofthe beam propagation. The evolved polarization inside the fiber depends onthe placing and fixation of the fibers on the breadboard. Any change of theorientation of the fiber will change the birefringence and thus those values maychange if the fiber was rearranged. Furthermore, the Kelly sidebands are re-moved using different bandpass filters as shown in figure 4.2. For each recordedspectrum the total output power and the FWHM of the optical spectrum aremeasured. The spectra are normalized to the intensity of the unfiltered spec-trum at 2050 nm. With a pump power of 2 W and without any bandpass filtersused the output power is 440 mW and the FWHM is 7.3 nm. Not shown infigure 4.2 is that this spectrum also contains pump light. Placing one bandpassfilter removes the pump light completely and causes a significant reduction ofthe Kelly sidebands with resulting 59 mW output power and 6.2 nm FWHM.Finally, the Kelly sidebands vanish by placing a second bandpass filter in anangled position with an output power of 37 mW and 5.2 nm FWHM.In the following measurements of the autocorrelation, the power and the

amplitude noise the color definition from figure 4.2 is preserved regarding thedifferent bandpass filtered pulses.

4.1.2 Autocorrelation

Pulse width measurements are carried out saving the autocorrelation curveon the oscilloscope with a time resolution of 100 µs/div. The time domain istransferred by multiplying the data with the calibration factor derived in equa-tion (3.2). Furthermore, the intensity of the peak of the autocorrelation curveis normalized and shifted to 0 s. Finally, the FWHM of the autocorrelationcurve is measured and used for calculating the duration of the soliton pulseaccording to equation (2.29). In addition, the transform limit is calculatedusing equation (2.28) based on the FWHM of the optical spectrum in figure4.2 and is plotted with dashed lines.The autocorrelation curve of the soliton with an unfiltered optical spectrum

is depicted in figure 4.3 with a pulse duration of 860 fs and a transform limit of605 fs. Clearly visible is a ringing background arising from the Kelly sidebandswith longer pulse durations. The autocorrelation curve is slightly asymmetricdue to imperfections in the alignment of the autocorrelator.Output pulses transmitted through one bandpass filter produce the auto-

correlation curve shown in figure 4.4. The decrease in FWHM of the opticalspectrum increases the pulse duration to 1020 fs with a transform limit of710 fs.

47


Figure 4.3: Autocorrelation without bandpass filters.

Finally, in figure 4.5 the autocorrelation curve of the soliton pulses withcompletely removed Kelly sidebands using two bandpass filters is illustrated.The pulse duration is increased to 1225 fs with a transform limit of 850 fs.

In general, the measured pulse durations are larger than the transform limitsthus the pulses are chirped. Comparing the pulse duration measurementsto the corresponding transform limits by dividing transform limit throughmeasured pulse duration give a percentage value of about 70 %.

Figure 4.4: Autocorrelation with 2050-12 bandpass filter.

48


Figure 4.5: Autocorrelation with 2050-12 and 2085-10 bandpass filter.

4.1.3 Pulse Energy

The pulse energy of the soliton without Kelly sidebands (black curve in figure4.2) is determined with respect to the input power using a power meter. Eachmeasured power value can be transferred to a pulse energy in combination withthe repetition rate of the oscillator according to equation (2.30).First of all the repetition rate is measured with the fast photodiode attached

to the spectrum analyzer. The repetition rate is measured to be f0 = 55 MHz

with a resolution bandwidth (RBW) set to 100 kHz. With an output powerof 37 mW the electrical power in the spectrum analyzer is −22 dBm. As canbe seen from figure 4.6 the harmonics appear over the full span width withoutpeaks in between and an almost constant electrical power indicating propermode-locking. Next the mode-locking threshold is determined by reducing theinput power using the HWP and TFP combination in the pump section, i.e.

Figure 4.6: RF spectrum.

49


rotating the HWP until mode-locking drops into CW mode. The correspond-ing threshold power represents the starting point of the slope efficiency curvein figure 4.7. It shows the measured output power on the left axis and thecalculated pulse energy on the right axis with respect to the input power. Theinput power is measured with a power meter before the fiber coupling lensin the pump section, the output power is measured behind the two bandpassfilters in the oscillator section. All these measured values have been verifiedwith those shown on the display of the mode-lock detector. Since the outputbeam is blocked by the power meter the optical spectrum is observed usingthe fiber coupled monitor port. With an increase of the pump power the pulsepropagating in the oscillator increases in terms of energy. Due to Kerr non-linearity this results in a change of the evolved polarization state thus thewaveplates of the artificial saturable absorber require an adjustment for reach-ing the maximum possible pulse energy. Furthermore, an increase of pumppower causes a shift of the center wavelength to larger values. Rotating theHWP of the artificial saturable absorber clockwise (with respect to the beampropagation direction) brings the center wavelength back to its initial valueof 2050 nm. Tuning the second QWP also clockwise reduces the Kelly side-bands of the soliton pulse oscillating in the cavity without changing the centerwavelength and results in a maximized output power. As shown in figure 4.7the output power increases linearly from about 1 to 2 W pump power witha slope of 2.38 % to almost 40 mW corresponding to approximately 700 pJ.Within this power regime the mode-locking is quite stable against externally

Figure 4.7: Slope efficiency and output beam diameter.

50


induced influences, such as bumping the optical table, clapping hands andslight knocking the oscillator’s housing. Further increase of the pump powerup to more than 3 W increases with a lower slope. However, in this pumpregime the mode-locking operation becomes much more sensitive to externalinfluences thus mode-locking easily drops to CW operation. Also reinitiatingmode-locking becomes more difficult thus it is more easy to tune the cen-ter wavelength to about 2060 nm in CW mode using the HWP and reducethe center wavelength again after mode-locking is initiated. Furthermore, theabsolute limit is reached for pump powers of 3.2 W and leads to a maximumoutput power of 50 mW corresponding to 900 pJ. Further increase of the pumppower either doesn’t even support mode-locking at 2050 nm or ends up in multipulsing, i.e. more than one pulse is oscillating in the cavity. This is clearly vis-ible in the RF spectrum as additional spikes in between the harmonics appearor in the optical spectrum as a superposition of two soliton spectra, where oneis slightly shifted in the center wavelength.

51


4.2 Noise

This section will show and discuss the results for amplitude noise measurementsregarding different bandpass filtering arrangements and different power regimesof the pump laser as well as phase noise measurements.

4.2.1 Relative Intensity Noise

The relative intensity noise measurements are carried out first by measuring theDC voltage with a voltmeter connected to the output of the slow photodiodeand transimpedance amplifier combination. Next the voltmeter is removedand the output is connected to the input of the vector signal analyzer, whichmeasures the PSD in dBm/Hz. Measurements are carried out in multiple stepsover defined frequency ranges with increasing RBW settings in order to plot theresults over a logarithmic frequency range. The resulting PSD measurementsare stitched together and transferred to RIN values according to equations(2.32) and (2.33) thus the results are plotted over the full frequency rangefrom 1 Hz to 10 MHz in a logarithmic scale. In general, all RIN plots includethe noise floor which results from measurements with a blocked photodiode.

The RIN of differently bandpass filtered output pulses, i.e. with and with-out Kelly sidebands as shown in figure 4.2 are measured. Furthermore, RINmeasurements are carried out to compare the completely filtered output soli-ton with the pump running in low and high power operation. In both casesthe input power of the oscillator is maintained equal thus in case of the highpower operation of the residual power is dumped to the beam block using theHWP and TFP combination in the pump section.

Influence of sideband filtering on the RIN

The top of figure 4.8 shows the three measured RIN curves measured at theoscillator output with different bandpass filter configurations for suppressingthe Kelly sidebands. In general, for all curves noise is dominated in the fre-quency range from 1 to 10 Hz due to mirror vibrations and acoustical noise.Discrete spectral lines appear in the range from 30 Hz to 20 kHz induced by thepower supply. Especially, the spike at 60 Hz is clearly visible. Furthermore,the broad peak between 100 an 200 kHz, i.e. the relaxation oscillation, is themain source of amplitude noise. At higher frequencies the noise drops to lessthan −130 dBc/Hz but doesn’t reach the noise floor at −145 dBc/Hz. Com-plete bandpass filtering results in a −10 dB offset with respect to the unfilteredcurve. Finally, the relaxation oscillation peak is reduced by 20 dB.

52

4.2 Noise

Figure 4.8: Relative intensity noise of the oscillator output with differentnarrow bandpass filters.

Using equation (2.34) the integrated RIN in %RMS is plotted from highto low frequencies with respect to the right axis in the bottom of figure 4.8.Filtering the Kelly sidebands results in a reduction from 0.95 %RMS down to0.13 %RMS, which is sufficiently low for seeding regenerative amplifiers.

Influence of the pump operation

For comparing the influence of the pump operation, measurements at the 10 %

monitoring output in the pump section as well as at the oscillator output arecarried out. In the measurements the pump runs at 35 % and 60 % of thepump current. The power inside the cavity is kept in both cases at the samevalue by dumping the residual power to the beam block behind the TFP inthe pump section. In the following RIN plots the pump is shown in black and

53


Figure 4.9: Relative intensity noise of the pump at 35 % and the oscillatoroutput.

the oscillator in blue.

Comparing figure 4.9 and 4.10 it is noticeable that increasing the pumpoperation state on one hand reduces the spurs in the region from 30 Hz to20 kHz for both, the pump and the oscillator RIN curve. On the other handthe relaxation oscillation of the pump is slightly reduced by about 4 dB. Still,this causes the relaxation oscillation coupled to the oscillator to significantlydecrease by about 10 dB. In contrast to the oscillator the RIN of the pump ap-proaches the noise floor at about 1 MHz. In case of low pump power operationthe integrated RIN is calculated to 1.08 %RMS for the pump and 0.13 %RMSfor the oscillator. For high pump power operation in turn the integrated RINis calculated to 0.84 %RMS for the pump and 0.07 %RMS for the oscillator.

Nevertheless, significant longterm fluctuations of the pump power appear

54

4.2 Noise

Figure 4.10: Relative intensity noise of the pump at 60 % and the oscillatoroutput.

at higher pump currents, which even cause the oscillator to lose mode-lockingif the waveplates of the artificial saturable absorber in the oscillator section(as explained in section 4.1.3) or the HWP in the pump section were notreadjusted. Hence, although the integrated RIN is lower it is not recommendedto operate at high pump power.

4.2.2 Phase Noise

As explained in section 2.3.3 phase noise measurements require bandpass fil-tering of one harmonic in the RF spectrum and amplifying the signal to thedetection range of the phase noise analyzer. As can be seen from the insetof figure 4.11 the RF spectrum is filtered to the fundamental harmonic. Thesecond harmonic is suppressed of more than 30 dB, whereas the third doesn’t

55


Figure 4.11: Phase noise and RF spectrum.

appear at all. Compared to figure 4.6 the signal is amplified from −22 dBm

to 10 dBm, which matches the phase noise analyzer’s detection range, as canbe seen from table 3.2. The resulting measurements for the SSB phase noiseis shown in figure 4.11. It can been seen that the SSB phase noise decreaseswith about 40 dB per decade and the relaxation oscillation arises again.

Figure 4.12: Integrated timing jitter.

Using equation (2.35) an integrated timing jitter from 1 kHz to 10 MHz iscalculated to 2.5 ps. As shown in figure 4.12 the relaxation oscillation at about150 kHz mainly generates the timing jitter, i.e. the timing jitter is limited dueto amplitude noise that couples to the phase noise. This might be reduced byreplacing the pump laser with another which has less amplitude noise.

56

4.3 Mode-locking Stability

4.3 Mode-locking Stability

To prove a satisfying long-term stability of the oscillator its mode-locking stateis monitored with the mode-lock detector and a data acquisition (DAQ) device.The carrier power and the noise power can be observed by measuring voltagesignals at test points located on the photodiode board (see figure 3.13) andnoise board, respectively. Since the carrier power is high and the noise poweris low in case of mode-locking and vice versa for CW operation the long-termstability can be observed by connecting both analog outputs, i.e. the testpoints on the PCB, to a DAQ device. In case of a mode-locked oscillatorwith 1.5 W input power and resulting 30 mW output power the carrier signalcorresponds to 2 V and the noise signal to 1 V. As shown in figure 4.13 thisoperation state is maintained for more than two days. The transition is shownin detail in the inset, where the noise signal increases to 1.5 V and the carriersignal decreases turning into fluctuations between 1 and 1.5 V. Finally, thepump power is switched off resulting in a carrier signal and noise signal of0.5 and 0.25 V, respectively. The denoted power values in dBm are read fromthe mode-lock detector’s display. The termination of mode-locking happenedwhen the observation period was ended intentionally.

Figure 4.13: Long-term stability measured over 2 days using the mode-lockdetector. The inset shows the transition from mode-locking toCW state followed by a disabling of the pump.

57

5 Conclusion and Outlook

A holmium-doped fiber ring oscillator used for seeding a holmium-doped yt-trium lithium fluoride regenerative amplifier has been repaired and modified.The change to soliton operation will allow full usage of the seeding power dueto a narrower optical spectrum.The preexisting setup has been completely disassembled to check the func-

tioning of all fiber components and to ensure that all splice connections producelow losses. Furthermore, a modular design of a box has been set up around thepump section, which on one hand allows for an easy removal of the walls if ad-justments become necessary and on the other hand reduces external influences.In order to monitor different parameters various fiber couplers have been addedto the pump and the oscillator section. The latter’s housing has been also im-proved by decoupling vibrations and providing fiber connectors that allow aneasy and versatile attachment of monitoring equipment. A mode-lock detectorhas been assembled and configured, which allows a permanent observation ofdifferent power values. Furthermore, the device ensures a reliable and safeoperation of the regenerative amplifier and prevents it from damages causedby possible interruptions of the mode-locking state of the seeding source.Finally, an extensive characterization has been performed, where the setup

of different measuring equipment allowed for simultaneous measurements ofimportant parameters. In the optical spectrum the center wavelength hasbeen shown to be tunable from 2045 to 2065 nm. The generated sidebandshave been completely removed using bandpass filters with a fixed center wave-length at 2050 nm. Differently filtered spectra have been analyzed in theirpulse duration, pulse energy and amplitude noise. Without bandpass filtersthe lowest pulse duration achieved was 860 fs. The bandpass filtered soliton hasa maximum pulse energy of 900 pJ, which is more than an order of magnitudelarger than the pulse energy provided for seeding the regenerative amplifier inthe previous setup. The amplitude noise of the oscillator has been minimizedto 0.07 %RMS and the integrated timing jitter of 2.5 ps has been measured.However, the pump laser has been found to be working unstable at high poweron the longterm time scale and seemed to be the main source of noise. Fur-thermore, the oscillator has been shown to be mode-locked for more than two

59

5 Conclusion and Outlook

days without interruption.In conclusion, the seed source has been repaired, modified and optimized

allowing for a reliable functionality as the front-end of an amplifier chain.The amplified 2050 nm wavelength radiation can finally be used for examplefor pumping optical parametric amplifiers for generating intense light in themid-infrared wavelength range, e.g. used for spectroscopic experiments.

60

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