Widely tunable optical delay generatorK. Jamshidi,1,* A. Wiatrek,1 C. Bersch,2,3 G. Onishchukov,2 G. Leuchs,2,3 and T. Schneider1

1Institut für Hochfrequenztechnik, Hochschule für Telekommunikation, Gustav-Freytag Strasse 43–45, D-04277 Leipzig, Germany2Max Planck Institute for the Science of Light, Guenther-Scharowsky-Strasse 1/B 24, D-91058 Erlangen, Germany

3Institut für Optik, Information und Photonik, Universität Erlangen-Nürnberg, Staudtstrasse 7/B2, D-91058 Erlangen, Germany*Corresponding author: jamshidi@hft‑leipzig.de

Received July 8, 2010; revised September 9, 2010; accepted September 18, 2010;posted October 4, 2010 (Doc. ID 131292); published October 21, 2010

We propose and demonstrate a method for quasi storage of light based on periodic spectral filtering realized in thetime domain by amplitude modulation using frequency-to-time conversion. The delay can be tuned in a wide rangeby changing the frequency of an electrical modulation signal. In our experiments, the delay of single 2:5 ps pulsesvaried by 66 pulse widths. The technique works equally well for more complex optical data packets. Contrary toknown approaches, the method has a very large spectral bandwidth and can be implemented by either fiber orintegrated solutions using existing technologies. Because of the large bandwidth, fractional delays up to severaltens of thousands of pulse widths can be achieved potentially for subpicosecond pulses, which is a tremendousvalue regarding the implementation simplicity. © 2010 Optical Society of AmericaOCIS codes: 200.4490, 130.6750, 060.0060.

Various methods have been proposed up to now to pro-duce tunable delay or advancement of optical pulses[1,2]. The performance and usability of each methodcan be evaluated using several figures of merit, such asachievable delay, bandwidth and fractional delay, delaytuning, signal distortions, implementation simplicity, size,and ability to be integrated [1,3]. Therefore, each schememay find its niche applications depending on its strengthsand shortcomings [4]. One example is electromagneticallyinduced transparency (EIT). With EIT in atom ensemblesand Bose–Einstein condensates, it is possible to achievevery high delay times of more than 1 s [5]. However, EIT isexperimentally complicated and the exploited disper-sions are extremely narrowband. Furthermore, their cen-tral wavelengths are not in the range of most applications.With stimulated Brillouin [6] and Raman scattering (SBSandSRS), the dispersion in anoptical fiber canbe changedsimply by tuning the parameters of an optical pumpwave.But delays of only a fraction of a pulse width have beendemonstrated using broadband SRS [7]. In SBS systems,only an advancement of around one pulse duration anddelays up to four pulse durations have been realized [8,9].Moreover, strong signal distortions take place. Wave-length conversion methods are good candidates to pro-duce large delay values, but they require tunable lasersfor delay adjustment and they are the most complexand power-consuming solutions [4].Recently, a new method based on time-frequency

coherence and SBS was proposed [10]. A set of signalreplicas is generated in the time domain, and a properone can be selected by a time gate, extracting one replicafrom the set. However, a rather long optical fiber has tobe used to get an efficient SBS. Although such a quasi-light storage (QLS) system has the potential to store op-tical packets of up to several thousands of pulse widths,the signal bandwidth is limited to values less than theSBS shift (11GHz), unless a rather complex setup is used[11]. Also, the maximum storage time of this method islimited to ∼100 ns by the SBS gain bandwidth.In this Letter, a new QLS method realization without

these limitations is proposed. Because of a very largespectral bandwidth, the incoming signal bit rate is not

limited and very long fractional storage times are possi-ble. The scheme can be implemented using existing tech-nologies by either fiber or integrated solutions. Contraryto slow-light or wavelength-conversion methods, the pro-posed scheme is able to delay only pulses, packets, orbursts of data limited in time. However, recently therehas been much attention on packet-switched networksand processing of the packets/bursts because Internettraffic is packet based.

The core idea of the QLS method [10] is to sample thespectrum of the incoming signal with a periodic function.One can easily show, using properties of Fourier transfor-mation, that in the time domain this corresponds to theconvolution of the original signal with a pulse train thatresults in a set of signal replicas. In the new scheme pro-posed here, the sampling is realized by an amplitudemod-ulation in the time domain after a frequency-to-timeconversion (FTTC) of the signal using a dispersive com-ponent.Note that there is no violation of causality becausethe advancement is only relative to the central spectralcomponent and is never faster than the speed of light.FTTC has already been successfully used for pulse shap-ing, packet header recognition, and packet compression[12–15].

We use the FTTC idea to produce tunable delay or ad-vancement to the incoming optical signal by control of theelectricalmodulation signal. Theblockdiagramof thepro-posed scheme is sketched inFig. 1. AFTTCmodule is usedto map the frequency response (a) of the incoming signal,which can also be an optical pulse burst or a data packet[10], to the time domain (b) [12]. This module can be anycomponent with large group-velocity dispersion (GVD),e.g., arrayedwaveguide gratings, chirped fiber Bragg grat-ings, photonic crystal structures, or even a spool of opticalfiber. Having pure second-order dispersion is very impor-tant to realize a linear mapping from frequency to timedomain [12]. Therefore, chirped fiber gratings are goodcandidates, as they canhave high second-order dispersionand low value of higher order dispersion. Next, the signalis multiplied by a pulse train in the time domain, whichcorresponds now to the spectrum of the original signal.An electrical pulse generator with a proper selection of

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the pulse repetition rate and duty cycle can be used to pro-duce the samplingwaveform (c). Anoptical intensitymod-ulator, e.g., a zero-chirpMach–Zehndermodulator, is usedtomultiply the dispersed signal by the samplingwaveformin the time domain in order to get a periodically spaced setof signal spectral components (d). After that a time-to-frequency conversion (TTFC) module with the sameabsolute GVD as the FTTC module but of opposite signis used to reshape the pulses. The frequency representa-tion of the incoming signal is converted back to the timedomain, and a set of periodically spaced input signal co-pies is generated (e). Finally, an optical gate canbeused toextract a desired, delayed or advanced, signal copy fromthe generated pattern (g) by a proper signaling (f). Thedelay Td between the signal copies depends on the sam-pling rate R as

Td ¼ k2R ¼ Dλ2cR; ð1Þ

where D is the dispersion parameter (proportional to theGVD k2 ¼ Dλ2=c) of the dispersive elements, c is the speedof light, and λ is the signal center wavelength.The obvious limitation is that the packet length Tp

should be less than the distance between the copiesTd. Thus, the sampling rate R should satisfy the conditionR > Tp=k2, which means that the spectral samplingshould obviously be more frequent than the lowest signalmodulation frequency component. It is straightforwardto see that delays smaller than the characteristic signalduration would make proper gating for extraction of asignal copy unfeasible. A possible way to overcome thelimitation is to accept a delay of a few signal durations asan intrinsic one and operate the system at longer delaysonly because the tuning range, and not the absolute delayvalue, is of real importance. Then ordinary electro-opticmodulators driven by a pulse generator with a propertriggering by the signal can be used to extract the desiredsignal copy [10]. The switching speed of the modulatorcould additionally limit the minimum initial delay espe-cially for short signal durations, e.g., if a 40GHz modula-tor is being used, initial delays of less than∼25 ps cannotbe achieved because of gating limitations. An all-opticalultrafast time gate can be used to extract the loweramounts of delay at the cost of a more complexsetup [16].The main optical components of the proposed scheme

are two intensity modulators and two dispersivemodules.

So the method can be integrated using available technol-ogies. The implementation dimensions depend primarilyon the integrated optic techniques being used to producethe dispersive modules. As an example, a chirped fiberBragg grating with a length of about 150mm is requiredto produce the dispersion of 1500 ps=nm used in our ex-periments for FTTC and TTFC [17]. Also all-optical imple-mentation of intensity modulation using common opticalgating techniques is straightforward.

In the experimental setup, used for proof of principle,2:5 ps pulses at a 1:25GHz repetition rate were trans-mitted through 90 km of standard single-mode fiber(SSMF) for FTTC. The intensity of the signal after theSSMF was modulated by a rectangular waveform withvarious repetition rates in a common 10Gbit=s lithiumniobate intensity modulator. The electrical modulationsignal (sampling waveform) was provided by a 20GS=sarbitrary waveform generator (AWG) with one pointset to 1 and two points set to 0 (duty cycle of 33%). TheAWG output was additionally amplified by a broadbandelectrical amplifier. The large portion of the SSMF disper-sion was compensated by two dispersion-compensatingfibers with a GVD of −870 ps=nm and −660 ps=nm. A fine-tuning of the dispersion compensation was done with thehelp of an optical waveshaper, which added another−60 ps=nm. The output signal of the waveshaper was de-tected by a 100Gbit=s photodiode and analyzed with thehelp of a 70GHz sampling oscilloscope. In order to pre-serve a sufficient signal-to-noise ratio for later detection,the signal was amplified by erbium-doped fiber amplifiersafter 50 km, after 90 km of fiber, and before the wave-shaper. The signal power was kept low enough to avoidself-phase modulation. Because of the polarization-modedispersion (PMD) of the fibers used, the pulses at the out-put of the system were around 4:5ps, as measurementswith an autocorrelator have shown. Of course the signal-to-noise ratio of a single delayed or advanced signal pack-et will be less than that of the input signal because thesignal is distributed to all components of the comb. A de-tailed noise analysis and the quantum optical descriptionof the scheme will be the topics of future studies.

The experimental results are presented in Fig. 2. In thisfigure all pulse amplitudes are normalized to the maxi-mum value of the waveform. Also, the time scale isnormalized to the duration of the incoming pulse to reflectthe fractional delay or advancement. Because the resolu-tion of the oscilloscope used for measurements of the sig-nal time profile was not sufficient, 4:5 ps pulses have a

Fig. 1. (Color online) Basic schematic of the method: IM, intensity modulator.

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duration of 8:3 ps in the oscillogram. With a maximumsampling waveform repetition rate of 6:7GHz, it was pos-sible to advance the signal by more than −83 ps and delaythe signal bymore than 82 ps. This corresponds to a tuningrange of about �33 pulse widths. As expected, the delayand advancement are proportional to the sampling wave-form repetition rate (see Fig. 3). For the experimentalparameters (90 km of SSMF with a GVD of 17 ps=nm=km) and using Eq. (1), we can get positive and negativedelays in picoseconds, where R in GHz: Δt ≅ 12 × R,which is in a good agreement with the experimental data.In principle, the maximum values of the delay and ad-

vancement are restricted only by the repetition rate ofthe sampling waveform and the GVD used for FTTC/TTFC. The first one is limited by the bandwidth of theintensity modulator and the second one by the accompa-nied signal attenuation and distortions. It should be men-tioned that similar to chirped-pulse amplification [18],other impairments such as PMD and higher order disper-sion effects should be carefully avoided or compensatedfor to achieve ultimate limits of the proposed method.There are practically no limitations on the spectral band-width of the signal, contrary to the SBS-based QLSmethod—the bandwidth of which is limited by the SBSparameters. Because the delay is independent of thepulse width, the same delay values would correspond toa much larger fractional tuning range for shorter pulses.Thus, for 1 ps pulses, a GVD of 5000 ps=nm and a sam-pling waveform repetition rate up to 90GHz one wouldhave a tuning range of about �1000 pulse widths. A po-tential improvement of 1 order of magnitude can beachieved by using more sophisticated techniques suchas all-optical implementation of intensity modulation atthe expense of a more complex setup. In this case, amode-locked laser can be used to generate the samplingwaveform and nonlinear effects in a fiber, or a semicon-ductor optical amplifier can be used to multiply the in-coming waveform with the sampling one [16].

We gratefully acknowledge financial support from theGerman Research Foundation (DFG) under SCHN 716/

6-2. Additionally, the authors would like to thank C. A.Bunge, S. Preussler, R. Henker, and J. Klinger from theHochschule für Telekommunikation in Leipzig for fruitfuldiscussions and C. Stephan and T. Röthlingshöfer fromthe Max Planck Institute for assistance with the experi-mental setup.

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Fig. 3. (Color online) Fractional delay and advancement as afunction of the sampling waveform repetition rate. The blackline shows the advancement and the blue line shows the delayobtained for the experimental setup parameters using Eq. (1).The red squares show the measured delay, and the green circlesshow the measured advancement. The red and green lines showthe linear fit of the measured advancement and delay.

Fig. 2. (Color online) Experimental results for sampling wave-forms with various repetition rates.

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