Quasi-Light-Storage based on time-frequency coherence

Quasi-Light-Storage based on time-frequency coherence Stefan Preußler 1 *, Kambiz Jamshidi 1,2 *, Andrzej Wiatrek 1, Ronny Henker 1, Christian-Alexander Bunge 1 and Thomas Schneider 1 1 Deutsche Telekom Hochschule für Telekommunikation Leipzig, Gustav-Freytag Str. 43 45, D-04277 Leipzig, Germany 2 jamshidi@hft-leipzig.de stefan.preuszler@hft-leipzig.de Abstract: We show a method for distortion-free quasi storage of light which is based on the coherence between the spectrum and the time representation of pulse sequences. The whole system can be considered as a black box that stores the light until it will be extracted. In the experiment we delayed several 5 bit patterns with bit durations of 500ps up to 38ns. The delay can be tuned in fine and coarse range. The method works in the entire transparency range of optical fibers and only uses standard components of optical telecommunications. Hence, it can easily be integrated into existing systems. 2009 Optical Society of America OCIS codes: (999.9999) Slow light; (290.5900) Scattering, stimulated Brillouin; (060.4370) Nonlinear optics, fibers References and links 1. R. W. Boyd, and D. J. Gauthier, Slow and Fast Light, in Progress in Optics 43, E Wolf, ed. (Elsevier, Amsterdam, 2002) 497 530. 2. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Light speed reduction to 17 meters per second in an ultracold atomic gas, Nature 397(6720), 594 598 (1999). 3. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Superluminal and slow light propagation in a roomtemperature solid, Science 301(5630), 200 202 (2003). 4. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Optical coherence tomography, Science 254(5035), 1178 1181 (1991). 5. S. E. Harris, and L. V. Hau, Nonlinear Optics at Low Light Levels, Phys. Rev. Lett. 82(23), 4611 4614 (1999). 6. J. L. Corral, J. Marti, J. M. Fuster, and R. I. Laming, True time-delay scheme for feeding optically controlled phased-array antennas using chirped-fiber gratings, IEEE Photon. Technol. Lett. 9(11), 1529 1531 (1997). 7. E. F. Burmeister, D. J. Blumenthal, and J. E. Bowers, A comparison of optical buffering technologies, Opt. Switching Networking 5(1), 10 18 (2008). 8. J. B. Khurgin, Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis, J. Opt. Soc. Am. B 22(5), 1062 1074 (2005). 9. R. S. Tucker, P. C. Ku, and C. J. C. Hasnain, Slow-Light Optical Buffers: Capabilities and Fundamental Limitations, J. Lightwave Technol. 23(12), 4046 4066 (2005). 10. E. Choi, J. Na, S. Y. Ryu, G. Mudhana, and B. H. Lee, All-fiber variable optical delay line for applications in optical coherence tomography: feasibility study for a novel delay line, Opt. Express 13(4), 1334 1345 (2005). 11. F. Xia, L. Sekaric, and Y. Vlasov, Ultracompact optical buffers on a silicon chip, Nat. Photonics 1(1), 65 71 (2007). 12. K. Y. Song, M. G. Herráez, and L. Thévenaz, Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering, Opt. Express 13(1), 82 88 (2005). 13. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, Tunable all-optical delays via Brillouin slow light in an optical fiber, Phys. Rev. Lett. 94(15), 153902 (2005). 14. Z. Dutton, and L. V. Hau, Storing and processing optical information with ultra-slow light in Bose-Einstein condensates, Phys. Rev. A 70(5), 053831 (2004). 15. Z. Zhu, D. J. Gauthier, and R. W. Boyd, Stored light in an optical fiber via stimulated Brillouin scattering, Science 318(5857), 1748 1750 (2007). 16. T. Sakamoto, T. Kawanishi, and M. Izutsu, 19x10 GHz Electro-Optic Ultra-Flat Frequency Comb Generation Only Using Single Conventional Mach-Zehnder Modulator, in Conference on Lasers and Electro-Optics and 2006 Quantum Electronics and Laser Science (Long Beach, CA, 2006), pp. 1 2 (C) 2009 OSA 31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15790

17. G. A. Sefler, and K.-I. Kitayama, Frequency Comb Generation by Four-Wave Mixing and the Role of Fiber Dispersion, J. Lightwave Technol. 16(9), 1596 1605 (1998). 18. T. Schneider, M. Junker, and K. U. Lauterbach, Theoretical and experimental investigation of Brillouin scattering for the generation of millimeter waves, J. Opt. Soc. Am. B 23(6), 1012 1019 (2006). 19. T. Schneider, Nonlinear Optics in Telecommunications (Springer-Verlag, Berlin, 2004). 20. T. Schneider, M. Junker, and K. U. Lauterbach, Potential ultrawide slow-light bandwidth enhancement, Opt. Express 14(23), 11082 (2006). 21. R. Henker, A. Wiatrek, K.-U. Lauterbach, M. J. Ammann, A. T. Schwarzbacher, and T. Schneider, Group velocity dispersion reduction in fibre-based slow light systems via stimulated Brillouin scattering, Electron. Lett. 44(20), 1185 1186 (2008). 22. P. Shen, N. J. Gomes, P. A. Davies, and W. P. Shillue, Generation of 2 THz Span Optical Comb in a Tunable Fiber Ring Based Optical Frequency Comb Generator in Proceedings of IEEE International Topical Meeting on Microwave Photonics (Fairmont Empress Hotel, Victoria, BC, 2007), 46 49. 23. A. Yeniay, J. M. Delavaux, and J. Toulouse, Spontaneous and Stimulated Brillouin Scattering Gain Spectra in Optical Fibers, J. Lightwave Technol. 20(8), 1425 1432 (2002). 1. Introduction The artificial delay of light pulses has attracted much recent interest since it has a number of very interesting possible applications [1 3]. Some of them are time resolved spectroscopy, nonlinear optics, optical coherence tomography and phased array antennas [4 6], for instance. One of the highly interested applications would be optical buffering which have been offered in the context of optical packet switching or optical burst switching [7 9]. Several different mechanisms like the reflection on gratings [10], the delay in resonator structures [11] and slow light propagation in material systems and optical fibers [12,13] can be used for this purpose. In material systems like atom gases or Bose-Einstein condensates stored or even stopped light was possible [14], for instance. Recently 2ns data pulses were stored up to 12ns by writing them into long lived acoustic excitations in optical fibers via the effect of stimulated Brillouin scattering (SBS) [15]. However, this method requires a lot of optical power for the write and read pulses. Furthermore, the storage time is restricted by the lifetime of the acoustic excitation. Each of these approaches show advantages and drawbacks in terms of the accuracy of control, pulse distortions, the amount of delay, the speed of operation and structural complexity. These delaying mechanisms can be divided into two categories [7]. In the first one, a large delay can be implemented with the capability of tuning the delay in coarse steps. In the second category, fine tuning of the delay is possible using slow light methods. In this case, usually the total amount of the delay is limited to several bits. Here, we propose a new method for delaying bursts of pulses with potential application in storage of the bursts, which is based on a simple fact of the coherence between time and spectral representation of a signal. This method can be implemented by standard components of optical telecommunications with tolerable optical powers. In an initial setup without up to date equipments, we were able to delay 5 bit bursts with the bit duration of 500ps up to 38ns. We believe that the capacity of the method to produce such large delays as well as its potential to tune the amount of delay both in fine and coarse levels is a great progress in the field of optical signal processing especially for optical storage of light and optical burst and packet switching. We explore the limitations of the proposed method and achieved the maximum time delay of 100ns for our implementation. This is an impressive value especially by considering that ordinary optical telecommunication system is used. This achievement is a notable breakthrough noticing the ease of tunability of this delay. 2. Theory Assume a complex-valued pulse f Pulse (t) in the time-domain (see Fig. 1 (a)), with a duration t, which has the complex spectral distribution F Pulse (ν) in the frequency-domain with a bandwidth of f (see Fig. 1 (b)). The multiplication of the pulse spectrum F Pulse (ν) with a spectral distribution F(ν) in the frequency-domain leads to convolution of their time-domain representations f Pulse (t) and f(t) (C) 2009 OSA 31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15791

F ( ν ) F( ν ) f ( t) f ( t). (1) Pulse The arrow denotes the Inverse Fourier transform from the frequency into the time domain and the star represents the convolution fpulse ( τ ) f ( t τ ) dτ. If the pulse spectrum F Pulse (ν) is multiplied by n equally spaced narrow frequency components δ(ν n ν) with the spacing ν a Dirac comb Ш the result is a sampling version of the pulse spectrum; i.e. every frequency component of the comb is weighted with the corresponding amplitude of the pulse distribution (see Fig. 1(d)). Pulse 1 ν FS ( ν ) = FPulse ( n ν ) δ ( ν n ν ) = FPulse ( ν ) n= ν Ш ν (2) So, the time domain representation of the resulting pulse can be specified as 1 n fs ( t) = fpulse ( t) Ш ( ν t) = fpulse t. (3) ν n= ν A physical realizable system has to be causal so that no signal can be seen at the output before the pulse enters the input, hence 0 n<. If τ = 1/ ν is higher than the temporal width of the pulse, f S (t) describes an infinite number of copies of the original pulse with the temporal distance τ (see Fig. 1 (c)). This copying is the core idea of the proposed method to delay the desired pulse. So, the desired delayed copy of the original signal can be extracted by multiplying f S (t) with an appropriate rectangular windowing of the signal in the time-domain using a rectangular pulse, which is shown in Fig. 1(c). The simplified model devised above can describe the basic fundamentals of the proposed method. There are some facts which should be considered to explore the limitations of this method. We will consider two limitations as will be discussed more in the next sections. At first, we note that the frequency comb may not be uniform or its bandwidth can be finite, so that its bandwidth does not cover the original pulse. This limitation can be circumvented by convolving each pulse by the inverse Fourier transform of the envelope of the frequency comb. This leads to an increase in the width of the pulses after delaying. Next ideal assumption is that a zero bandwidth Dirac delta function can be used for sampling, which cannot be realized. So, we should assume a non-zero bandwidth for each branch of the comb, i.e. δ. This non-zero bandwidth leads to creation of an envelope for the delayed pulses in the time domain, Τ, which results to finite delays for the original pulse. As can be seen in Fig. 1(e), the duration of the envelope is responsible for the total duration of the input signal copies. This duration is proportional to the inverse of the bandwidth of each branch of the comb. In Fig. 1(f) the frequency representation of a signal sampled with a finite bandwidth is shown accordingly. (C) 2009 OSA 31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15792

3. Experiment Fig. 1. Time and frequency-domain representation of the pulses. Time (a) and frequency (b) representation of original pulse, time (c) and frequency (d) representation of the ideal spectrally sampled pulse, time (e) and frequency (f) representation of finite bandwidth spectrally sampled pulse. The principle of our experiment is shown in Fig. 2. A Gaussian input pulse (a) is multiplied with a frequency comb (b) in the frequency-domain. The result is a pulse train with equidistant copies of the input pulse in the time-domain (c). One of the pulses is extracted by a time-domain multiplication of the pulse train with a rectangular function (d) in a modulator (Switch). The result is a delayed, distortion-free copy of the input pulse (e). (C) 2009 OSA 31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15793

Fig. 2. Principle idea. The X denotes the multiplication in the frequency-domain and the Switch is a modulator. To prove the concept experimentally, we build a setup to produce a frequency comb by a modulation of an optical carrier with a sinusoidal signal [16]. The frequency of the sinusoid defines the spacing between the frequency lines. In principle every other method which produces a frequency comb, four wave mixing for example, can be used as well [17]. The multiplication of the frequency comb with the pulse spectrum in the frequency-domain is carried out via the nonlinear effect of stimulated Brillouin scattering (SBS) [18,19] in a standard single mode fiber (SSMF). SBS in a waveguide like a SSMF is an interaction between counter propagating waves mediated by an acoustic wave. Each of the narrow lines of the comb, propagating in one direction, can produce a gain or a loss for a part of the counter propagating pulse spectrum via the acoustic wave if their frequencies are up or down shifted with respect to the pulse. The acoustic wave in the waveguide defines the frequency shift f B and the line width γ of gain and loss. Hence, the frequency component f P of the comb amplifies the part of the pulse spectrum which fits in the bandwidth of SBS mechanism, γ, if shifted downwards by f P -f B, and it attenuates the part at f P + f B if shifted upwards. In a SSMF the Brillouin shift f B is around 11GHz and the bandwidth γ is around 30MHz for a carrier wavelength of 1550nm. Hence as long as the frequency of the modulating sinusoidal signal is higher than γ, the different SBS gain or loss lines do not overlap with each other. On the other hand, the gain and loss area can overlap and compensate at f P if the whole frequency comb extends over f B. Therefore, the maximum bandwidth of the delayable pulse sequence is restricted by f B. But, this can simply be enhanced by the incorporation of additional pumps [20]. In our setup we use the SBS as a frequency selective amplifier. Hence, the frequency comb is down shifted by f B. This has the advantage that the delayed pulses will be amplified additionally. The temporal distance between the different copies τ = 1/ ν is controlled by the frequency of the sinusoidal signal which results in a frequency comb with a spacing of ν. Therefore, fine and coarse tuning of the time delay is simply possible by a change of the modulation frequency which generates the frequency comb and by a time shift of the rectangular window function. If time delays of smaller than 1bit are required, ν can be made smaller than the natural Brillouin gain bandwidth. In this case the frequency comb works as a single broadened Brillouin gain and delays the pulse sequence by the group index change initiated by SBS [21]. 4. Results The experimental setup is shown in Fig. 3. Two 5 bit patterns, each with an overall temporal width of 2.5ns were generated by a digital data analyzer (Pattern) which corresponds to 500ps bit duration. Only the first pattern is changed and measured in our experiments. The distance between the first and second pattern is about 250ns and after 498.5ns the whole pattern starts (C) 2009 OSA 31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15794

again. A Mach-Zehnder modulator (MZM) and a laser diode (LD) with a carrier wavelength of 1550nm were used to transform the pattern into the optical domain (Fig. 3(a)). The output power of the signal was 4dBm. All modulators were connected to polarization controllers (not shown in Fig. 3) to achieve the maximum intensity. The pattern was coupled into a 5km SSMF. A frequency comb (Fig. 3(b)) was coupled into the same fiber from the opposite side via an optical circulator (C). It was created with a dual-drive Mach-Zehnder modulator (DD- MZM), which was driven by a sinusoidal signal with a frequency of 290MHz, so that τ was 3.4ns, and an electrical power of 25dBm. The two arms of the modulator were driven by a DC voltage of 5.1V and 4.7V. By changing the bias voltage, the power and phase ratio at the two modulator drives the modulation characteristics can be changed so that the frequency comb is flattened [16]. The frequency comb was amplified by an Erbium doped fiber amplifier (EDFA) and coupled into the fiber via the circulator. The output power of the EDFA was fixed to 25dBm. Fig. 3. Principal experimental setup. LD: laser diode; MZM: Mach-Zehnder modulator; SSMF: standard single mode fiber; EDFA: Erbium doped fiber amplifier; Pattern: digital data analyzer; DD-MZM: dual-drive Mach-Zehnder modulator; Rect.: pulse generator to create a rectangular window; Tr.: Trigger. The insets show the measured values for (a) specific bit pattern, (b) frequency comb, (c) rectangular window and (d) extracted pattern. The choice of the delayed pattern in the time-domain is simply carried out by a Mach- Zehnder modulator (MZM2). This modulator was driven in the lower quadratic operating point with a rectangular function in order to operate as a switch. Simple optical switches could be used for this purpose as well. An On-off optical switch can behave as a temporal filter to extract the desired delayed pulse. This switch is useful if much higher bit rates (when electronic devices cannot support the speed of sampling) is used for the pulse bursts. The signal is extracted when the switch is turned on. The switch should have short cycle times so that only the selected pattern will be extracted. (C) 2009 OSA 31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15795

In our proof of concept setup, the rectangular function (Fig. 3(c)) is produced by a pulse generator (Rect.) which is triggered by the first bit of the pattern. The pulse generator offers several opportunities for fine tuning the delay. In a real system the trigger signal could be generated from the incoming optical pattern itself by a photodiode and it could be delayed electronically. It would also possible to generate the rectangular function with a waveform generator without any trigger signal. If the rectangular window is on a high level the signal passes the modulator and the selected pattern is extracted (Fig. 3(d)). After this, they are detected by the optical entrance of an oscilloscope (Osci). Fig. 4. Delayed and extracted 11101 pattern. The black line shows the reference. Because of the large delay the time axis is interrupted. In Fig. 4 several extracted patterns with different delays can be seen together with the reference signal (black line). The reference is the output signal which occurs if the SBS filter is not active and the signal goes through the switch. The patterns were extracted after 34.8ns (green line) and 38.2ns (blue line). For a better representation of the reference and the extracted patterns the time axis has been cut off. It was also possible to extract other copies of the pattern before and after this point by changing the position of the rectangular window. Concerning this, the system can be tuned completely in the range of the theoretical limitations. To demonstrate the fine tune ability of the system the frequency of the comb was changed. With a reduced frequency of 287MHz the spacing between the individual copies was increased. So the pattern was shifted up in time and delayed for 38.4ns (red line). To extract it correctly the rectangular window had to be adjusted in time. By varying the frequency of the comb in a small range it is possible to delay the pattern more or less. (C) 2009 OSA 31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15796

Fig. 5. Different extracted patterns. (a) a 10101 pattern and (b) shows it for a 11001 pattern. To approve that the concept is valid for other patterns, various bit patterns have been considered. In Fig. 5 the delay for a 10101 and a 11001 pattern can be seen. The delay times and values for the frequency comb are those used in Fig. 4. 5. Discussion As can be seen in Figs. 4 and 5, the delayed pulses have been impaired compared to the original pulse. This impairment is due to our insufficient setup, regarding the number of frequency branches in the comb or finite frequency response of the rectangular function used for extracting the delayed burst. At the moment, there are 7 frequency branches in the comb with 290MHz distance which results into 1.74GHz total bandwidth of the frequency comb (see Fig. 3 inset (b)). This comb can be used to sample the 2Gbps data stream. The problem is that the two side branches of the comb are not as strong as the other branches, which may cause the distortion of the original pulse. The insufficiency of the frequency comb bandwidth leads to a low pass filtering that flattens the edges of the original pulses. This limitation can be overcome by increasing the number of comb frequency branches using various well known methods [16,17,22]. Additionally, the ringing of the extracted pulses can be seen at the end of the extracted burst which can be suppressed by using a better rectangular switching function. As described in the theory section, the main limitation for delaying the pulses using this method is the finite bandwidth of the branches of the frequency comb. In our implementation, we have used the SBS mechanism to multiply the signal with the desired frequency comb. In this case, the bandwidth of the sampled spectrum is governed by the gain bandwidth of the SBS mechanism, which is around 30MHz. This leads to a maximum delay of 33ns. As stated in [23], the gain bandwidth of SBS mechanism is narrowed by increasing the pump power to higher values. 10MHz bandwidth of SBS mechanism can be achieved easily by increasing the level of pump power, which leads to 100ns maximum attainable delay. If higher order effects like dispersion and polarization mode dispersion being controlled, shorter pulses can be used, and hence more number of bits can be delayed accordingly. Let us assume an ordinary 10Gbps optical communication system which uses 100ps pulses. In this case the maximum delay of 1000 bits can be accomplished. The reconfiguration rate of the proposed scheme depends on the electrical response of the sine wave and rectangular pulse generators and the modulators. This can be improved upon by using high speed electrical components and modulators. So, we think that after the maximum delay imposed by our system, reconfiguration can be done with no delay. When a simple optical switch is used, the reconfiguration rate also depends on the reconfiguration rate of the optical switch. (C) 2009 OSA 31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15797

Another specification of the proposed method is that it is suitable for delaying packets or bursts of bits. It means that it is not possible to delay the stream of bits using this method in its current form. 6. Conclusion As shown for the first time, to the best of our knowledge, a delay of pulse sequences up to several bit counts is possible by the exploitation of time-frequency coherence. The system simply consists of an equidistant frequency-domain sampling of the signal spectrum and a following time-domain switch. If the whole system is taken into account, it can be seen as a kind of light storage. We achieved a storage time of up to 38ns for 500ps pulses and 2.5ns pulse bursts. A simple fine and coarse tuning of the storage time is possible by a change of the sinusoidal signal, which controls the frequency distance between the scan lines ν, and a shift of the rectangular window. As described in the text, pulse delay limitation imposed by the bandwidth of the frequency comb lines as well as the bandwidth of SBS gain, which can reach up to 100ns. Our proof of concept setup shows several insufficiencies. The number of the scan frequencies and the flatness of the frequency comb could be enhanced by other modulators or other techniques for frequency comb generation, for instance. So, we believe that very high storage times are possible with this method. Acknowledgements We gratefully acknowledge the financial support of the German Research Foundation (reference number: SCHN 716/6-1). A. Wiatrek and R. Henker gratefully acknowledge the financial support of the Deutsche Telekom AG. Additionally the authors would like to thank I. Rennert and J. Klinger from HfT Leipzig and J. Reif from BTU Cottbus for the fruitful discussions. (C) 2009 OSA 31 August 2009 / Vol. 17, No. 18 / OPTICS EXPRESS 15798