Direct measurement of the instantaneous linewidthof rapidly wavelength-swept lasers

Benjamin R. Biedermann, Wolfgang Wieser, Christoph M. Eigenwillig, Thomas Klein, and Robert Huber*Lehrstuhl für BioMolekulare Optik, Fakultät für Physik, Ludwig-Maximilians-Universität München,

Oettingenstrasse 67, 80538 Munich, Germany*Corresponding author: Robert.Huber@lmu.de

Received August 2, 2010; revised September 24, 2010; accepted September 24, 2010;posted October 7, 2010 (Doc. ID 132798); published November 2, 2010

The instantaneous linewidth of rapidly wavelength-swept laser sources as used for optical coherence tomography(OCT) is of crucial interest for a deeper understanding of physical effects involved in their operation. Swept lasersfor OCT, typically sweeping over ~15 THz in ~10 μs, have linewidths of several gigahertz. The high optical-frequency sweep speed makes it impossible to measure the instantaneous spectrum with standard methods. Hence,up to now, experimental access to the instantaneous linewidth was rather indirect by the inverse Fourier transformof the coherence decay. In this Letter, we present a method by fast synchronous time gating and extraction of a“snapshot” of the instantaneous spectrum with an electro-optic modulator, which can subsequently be measuredwith an optical spectrum analyzer. This newmethod is analyzed in detail, and systematic artifacts, such as sidebandgeneration due to the modulation and residual wavelength uncertainty due to the sweeping operation, arequantified. The method is checked for consistency with results from the common, more indirect measurementvia coherence properties. © 2010 Optical Society of AmericaOCIS codes: 110.4500, 140.3600.

Optical coherence tomography (OCT) [1] is a high-resolution optical imaging technique and is the main ap-plication for very rapidly wavelength-swept lasers withtuning rates of ∼1:5 THz=μs and tuning ranges of∼15 THz or more, such as Fourier domain mode-locked(FDML) lasers [2] or standard rapidly wavelength-sweptlasers [3].While recently the depth-scan rates in swept-source

OCT (SS-OCT) have been substantially increased by fas-ter wavelength-swept lasers [4], the maximum rangingdepths have not advanced comparably. Nevertheless,longer OCT ranging depths, achievable by a narrowerinstantaneous linewidth, or equivalently longer instanta-neous coherence length of the laser, would be preferredfor applications such as ophthalmology [5] and upper air-way imaging [6] and for ranging and sensing [7,8].To understand and optimize the linewidth of cw lasers

in general, several methods have been established. How-ever, they are not directly applicable to measure the in-stantaneous linewidth of very rapidly wavelength-sweptlasers, as are used for SS-OCT.The problem is that most of these known measurement

techniques probe the time-integrated linewidth or coher-ence length of a light source. For swept lasers, the totalspectral width is given by the wavelength sweep range oftypically ∼100 nm and the coherence length is ∼20 μm.These values correspond to the standard mathematicaldefinition of spectral width/linewidth and coherencelength. In SS-OCT they determine the achievable axial re-solution. However, in SS-OCT, another value, the socalled instantaneous linewidth or instantaneous coher-ence length, plays a crucial role, because it determinesthe maximum achievable ranging depth. The instanta-neous linewidth depends essentially on cavity dispersion,the width of the spectral filter [9], and the sweep speed[4] and is usually much larger than the linewidth of theunswept laser, which is of less practical relevance.The instantaneous linewidth represents the hypotheti-

cal linewidth of the source for a measurement with an

infinitely short acquisition time if time-bandwidth limita-tions would be negligible. Because a short measurementtime broadens the frequency/spectral resolution, the line-width cannot be directly measured. Further, because forany finite acquisition time, the laser changes its wave-length, no really instantaneous value for linewidth canbe measured.

For these reasons, in most cases only the “approximateaverage linewidth” over one wavelength sweep is de-duced by Fourier transform of the interference fringe vis-ibility [9–11]. Hence, an alternative access to this laserparameter allowing for additional spectral or temporalresolution is desirable.

In this Letter we present a method using an electro-optical modulator (EOM) as a fast shutter, driven syn-chronously to the sweep operation, transmitting only asmall fraction of each sweep, which is then spectrallyanalyzed. This method is checked for its inevitable sys-tematic artifacts, such as (i) spectral broadening by side-band generation due to modulation and (ii) spectralbroadening by the laser sweep operation during time gat-ing. Also, the method is compared to the more common,but indirect, measurement of linewidth using the coher-ence properties [9–11]. Here, we demonstrate the advan-tages of the new method by using it to analyze theoperation and coherence dynamics of an FDML laser,but the method could be applied to any other rapidlyswept laser source.

The spectral intensity SðωÞ of a light source can be re-corded by measuring the autocorrelation ΓðτÞ of light atdifferent times t in an (e.g., Michelson) interferometerwith arm length mismatch/delay τ ¼ Δz=c and apply-ing the Wiener–Khinchin theorem, which states thatspectrum and autocorrelation are linked by Fouriertransform:

ΓðτÞ ¼Z

∞

−∞

Eðt0ÞE�ðt0 þ τÞ þ E�ðt0ÞEðt0 þ τÞdt0;

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0146-9592/10/223733-03$15.00/0 © 2010 Optical Society of America

SðωÞ ¼Z

∞

−∞

ΓðτÞeiωτdτ:

This theorem is widely used in Fourier transform IR spec-trometers, and it can also be applied to measure the time-integrated spectrum of a swept laser, i.e., the sweepspectrum. However, when applied to swept lasers tomeasure the instantaneous spectrum, there is an ambi-guity problem, as the phase of the autocorrelation termchanges when either the delay τ or the wavelength of thelaser changes. Therefore, the time over which the auto-correlation term is integrated must be restricted. Attypical OCT fringe frequencies below 100 MHz, this cor-responds to measuring times on the order of 1 ns. Unfor-tunately, because of the narrow instantaneous linewidthand the high oscillation frequency of the autocorrelationsignal, this approach requires subwavelength samplingintervals in the interferometer over centimeter rangesat all different wavelengths of the sweep, resulting in alarge number of measurement points. A more practicalway is to measure the decrease in fringe visibility ofthe laser [11], which is the mean magnitude of the auto-correlation versus interferometer arm mismatch and of-ten called “roll-off” performance in the context of sweptlasers for OCT [9,10]. The roll-off is recorded for thewhole sweep; therefore, it is averaged over all wave-lengths. A method to record a wavelength dependentroll-off is to apply a window function to the recorded in-terferometric signal such that only fringes from the de-sired wavelength interval account for the roll-off.In the described roll-off measurements, the phase in-

formation is lost and, therefore, the Fourier transformof the magnitude of the autocorrelation will be singlesided and shifted to zero. If the instantaneous spec-trum is Gaussian shaped, it can be correctly recoveredfrom the roll-off measurement without knowledge ofthe phase. For other spectral shapes, usually the calcu-lated instantaneous spectrum is merely an estimate,and the value of the linewidth represents a lower limit.This limitation makes an alternative linewidth measure-ment technique desirable.We present an alternative approach to measure the in-

stantaneous spectrum of rapidly wavelength-sweptlasers. For the measurement, we use a polarization-maintaining (PM) FDML laser (Fig. 1) [12]. The gain med-ium is a semiconductor optical amplifier (SOA, CovegaCorp., “BOA 1132”), and the optical bandpass filter is aPM Fabry–Perot filter (FFP-TF, Lambda Quest, Inc.). Thelaser has a sweeping range of 95 nm [see Figs. 2(a) and 2(b)] at 20 mW output power. We use a fast amplitudemodulator in combination with a spectrometer, providingdirect access to the actual spectral shape. The methoduses a function generator to drive the FDML laser andto trigger a 1:6 ns [see Fig. 2(c)] electronic pulse (Pico-second Pulse Labs, model 2600). This pulse is used todrive an EOM (Photline “MX13”) such that it always cutsout a τgate ¼ 1:6-ns-long optical waveform at the samespectral position of the sweeps. The transmitted laserlight is then recorded with an optical spectrum analyzerwith 20 pm resolution, thus giving an average of the in-stantaneous linewidth.There are three effects leading to a broadening of the

measured linewidth. First, there is the sweep-to-sweep

jitter, i.e., the timing jitter of a certain wavelength rangewithin different sweeps. We measured this value to be0:8 ns using a monochromator and analyzing the timingjitter of the transmitted light intensity during FDML op-eration. It should be underlined that this value of jittermay be higher for non-FDML lasers, making this artifactmore dominant. The 0:8 ns jitter leads to a small broad-ening of<13 pm owing to averaging in the OSA. As a sec-ond effect, the 1:6 ns modulation of the light generatessidebands in the transmitted spectrum. By Fourier trans-form of the time gate, we calculated this effect to causean ∼4 pm broadening. The third effect causing artifactsresults from the fact that the laser changes its frequencyduring the transmission time gate of the modulator. Asthe sweep speed is proportional to the derivative of thesinusoidal drive waveform [see Fig. 2(a)], this effect de-pends on the temporal position of the timing gate, beingmaximal in the sweep center with a calculated broaden-ing of 27 pm. Further temporal narrowing of the 1:6 nstime gate would reduce this effect, and at an optimum∼0:5 ns time gate, modulation broadening and sweepbroadening both would be roughly 10 pm. Adding upall three effects to the spectral resolution of the OSA,we estimate roughly an ∼35 pm apparatus function ofour setup. To support these theoretical calculations,we made the linewidth measurement with different gatelengths and observed that the measured linewidth isdominated by the instantaneous linewidth for gate timesbelow 5 ns. For linewidth measurements of lasers withhigher sweep speeds, the gate window would have tobe further decreased. At sweep speeds of 1 MHz at a100 nm optical bandwidth, we calculated a minimumachievable broadening of 34 pm, so that this method isstill valuable for instantaneous linewidths larger that100 pm.

To compare the commonly used roll-off measurementswith our method, the linewidths of our FDML laser weremeasured at different frequencies for six different

Fig. 1. (Color online) Setup of (a) the PM FDML laser and (b)the two different linewidth measurement techniques.

Fig. 2. (Color online) (a) Time-wavelength characteristic ofthe FDML laser. (b) Time integrated spectrum of the laser.(c) Intensity of the 1:6 ns pulse used to drive the EOM.

3734 OPTICS LETTERS / Vol. 35, No. 22 / November 15, 2010

wavelengths. In Fig. 3(a), the instantaneous spectrummeasured with both methods is shown. The spectrumcalculated from the roll-off is symmetrical and doesnot reproduce the asymmetries in the lineshape thatcan be measured with the new method. We found thelineshape to be asymmetric with a pedestal on the shortwavelength side for detuning the laser to lower frequen-cies and a pedestal on the long wavelength side for higherfrequencies. At the resonance frequency of the laser, thelineshape was found to be symmetric.In Fig. 3(b), the FWHMmeasured by Fourier transform

is plotted versus frequency and versus time within thesweep. The corresponding wavelengths can be read inFig. 2(a). It can be seen that the linewidth is minimalat a certain frequency. Because of cavity dispersion, thisfrequency depends on the wavelength, and the curve ofminimum linewidth can be used as an estimate for thedispersion, which has its minimum at 1310 nm. At higherand lower frequencies, the linewidth increases, leading toa steeper roll-off in OCT. The qualitatively same behaviorcan be seen in Fig. 3(c), where the linewidths measuredwith the EOM are plotted. As expected, the mean valuesfor the linewidth are larger.To compare the linewidths with respect to wavelength

and FDML frequency, the ratio of the FHWM (EOM/roll-off) of both methods is plotted in Fig. 3(d). The line-width of the EOM method is expected to be larger,

leading to a ratio larger than 1. It can be seen fromthe graph that this is true (with an average value of1.24), except for a small region. The reason for this de-viation is unclear, while the varying ratios of measuredlinewidths are expected to originate from different(asymmetrical) shapes of the actual spectrum and vary-ing sweep to sweep jitter.

In conclusion, we have demonstrated a more directmethod to measure the instantaneous linewidth of a ra-pidly swept laser. It has been shown that the newmethodis capable of measuring the actual shape of the spectrumand that the linewidths match to within a factor of 1.7with those obtained by Fourier transform. These findingswill allow for further detailed measurements of the in-stantaneous linewidth, which is expected to build the ba-sis for a comprehensive understanding and to furtheroptimize rapidly wavelength swept and FDML lasers inthe future.

We would like to acknowledge support from W. Zinthat the Ludwig-Maximilians-Universität Munich. This re-search was sponsored by the Emmy Noether programof the German Research Foundation (DFG) (DFG—HU1006/2-1) and the European Union (EU) project FUNOCT (FP7 HEALTH, contract no. 201880).

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Fig. 3. (Color online) (a) Instantaneous spectra of the FDMLlaser measured with both techniques (57687 Hz, 1300 nm,low- to high-frequency sweep). (b) Linewidth in picometersmeasured by Fourier transform of the roll-off versuswavelength and laser frequency. (c) Linewidth measured byelectronic gating. (d) Ratio of the linewidths: electronicgating/FFT-roll-off.

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