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1470 OPTICS LETTERS / Vol. 29, No. 13 / July 1, 2004 Multiwavelength pulse generator using time-lens compression James van Howe, Jonas Hansryd, and Chris Xu School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853 Received January 15, 2004 We demonstrate a novel method of generating a multiwavelength pulse train by use of time-lens compression. In addition to pulse compression, this time lens simultaneously displaces the pulses according to their center wavelengths, resulting in a temporally evenly spaced multiwavelength pulse train. We further demonstrate a new aberration-correction technique based on the temporal analog of a spatial correction lens to improve the quality of the compressed pulses. Through the use of cw distributed-feedback lasers and electro-optic phase modulators, the all-fiber system allows complete tunability of temporal spacing, spectral profile, and repetition rate. © 2004 Optical Society of America OCIS codes: 200.4960, 070.1170, 060.4230, 320.7080. Optical wavelength-division multiplexing (WDM) parallel processing has shown great promise for ultrafast real-time sampling1 – 4; however, the complexity of the sampling source, which requires linear time – wavelength mapping, hampers practical implementation.3,5 Previous approaches to obtaining such a linearly chirped multiwavelength source, i.e., a source that generates a periodically repeating multiwavelength pulse train with precise interpulse spacing, relied on femtosecond mode-locked lasers to provide the necessary spectral bandwidth and required spectral slicing, spectral f lattening, and adjustable time delay.1,2 We demonstrate a novel method for generating a linearly chirped multiwavelength pulse train through use of a time lens.6 – 9 In addition to pulse compression, this time lens simultaneously displaces the pulses according to their center wavelengths, resulting in a temporally evenly spaced multiwavelength pulse train. Furthermore, we demonstrate a new aberration-correction technique to improve the quality of the compressed pulses. A time lens, in analogy to a spatial lens, works by imposing a quadratic phase on an incoming electric f ield in time instead of space.6 – 8 Our method utilizes sinusoidally driven LiNbO3 phase modulators to generate this phase prof ile. We f irst generate four temporally overlaid 33% duty cycle 10-GHz pulse trains, using four cw distributed-feedback (DFB) lasers (Fig. 1). For a single period and wavelength, we assume a Gaussian electric f ield: E 苷 E0 exp共2t2 兾2T0 2 兲 , electric field is simply µ ∂ 1 1 iC t2 . E 苷 E0 exp 2 2 T0 2 (3) Equation (3) describes a standard linearly chirped Gaussian pulse. With a fiber of length Z and dispersion parameter b2 to provide the linear dispersion needed for compression, the minimum pulse width is obtained when the output pulse is chirp free10: Z 苷 Zcf 苷 C LD , 1 1 C2 (4) where LD 苷 jT0 2 兾b2 j is the dispersion length of the fiber. Fulfilling this condition results in an output pulse width T苷 p T0 . 1 1 C2 (5) The analysis above for a single wavelength applies to a multiwavelength system as well, except that a carrierfrequency-dependent time delay is introduced because of dispersion. Although Vp of a phase modulator depends on the carrier wavelength (Vp ~ l), variation of Vp is negligible (,1%) in our experiment because of the narrow wavelength span needed. For an N-wavelength system of evenly spaced frequency Dn, (1) where T0 is the 1兾e pulse half-width, and impose a phase, ∂ µ 2Ct2 , 2pt V 艐 cos Dw 苷 p 2Vp Tm 2T0 2 (2) where V is the peak-to-peak drive voltage, Vp is the drive required for a p phase shift, Tm is the modulation period, and C 苷 共2p 3 V兾Vp 兲 共T0 2 兾Tm 2 兲. We have expanded the cosine to second order and neglected the constant phase term. After phase modulation, the 0146-9592/04/131470-03$15.00/0 Fig. 1. Experimental setup for generating a multiwavelength pulse train. Pulse trains were generated with and without a correction lens. The final compressed pulse train is also illustrated schematically. PC, pulse carver; MZ, Mach– Zehnder modulator; PMs, phase modulators. © 2004 Optical Society of America July 1, 2004 / Vol. 29, No. 13 / OPTICS LETTERS the time delay between adjacent frequency pulses as a result of dispersion is Dt 苷 2pb2 Zcf Dn . (6) The condition for evenly spaced pulses after chirp-free pulse compression can be met if Dt 苷 Tm µ ∂ 1 1 n 苷 2pb2 Zcf Dn , N (7) where n is an integer number n 苷 0, 1, 2 . . . . For successful WDM parallel processing, adjacent frequency pulses must not overlap spectrally, a condition that can always be satisf ied by choosing the appropriate value of n. Equation (7) denotes the simplicity and f lexibility of such a system. Driving the phase modulator(s) at the desired modulation period and voltage determines Zcf . This in turn determines the necessary frequency spacing Dn for even pulse spacing, easily obtained with independently controlled cw DFB lasers. The experimental setup is shown in Fig. 1. Although more wavelength channels can be incorporated, we use four wavelengths for the purpose of demonstration. The four cw DFB lasers (ILX 79800D) are spaced 835 GHz (艐6.7 nm) apart so that no spectral overlap occurs after compression [n 苷 1 Eq. (7)]. After the WDM, we use a Mach – Zehnder modulator (JDS Uniphase OC-192) as a standard pulse carver; i.e., it is biased at maximum transmission and driven with a 5-GHz sinusoid. This generates four temporally overlaid 10-GHz 33% duty cycle pulse trains. The overlaid pulse trains are temporally compressed and displaced by the time-lens system, which consists of two low-Vp phase modulators (Sumitomo T.PMH1.5-11) driven synchronously at 4.5Vp each by a 10-GHz sinusoidal drive, and a 1.1-km spool of standard single-mode fiber with dispersion of 18.7 ps兾nm. The optical spectra before and after the time lens are shown in Fig. 2. The close match between measurement and theory demonstrates the reliability and predictability of our system. We measure the temporal spacing of the multiwavelength pulses two different ways: (1) by use of an oscilloscope (Agilent 86109A) (Fig. 3) and (2) by taking the second-order cross-correlation trace with an interferometric autocorrelator (Fig. 4). Because the impulse response function of the oscilloscope is limited to 18 ps, as shown in Fig. 3(a), we expected and observed a 40-GHz sinusoid when all channels were measured simultaneously [Fig. 3(b)]. The cross-correlation trace, which has femtosecond resolution, gives the more accurate measurement of the pulse spacing. Figure 4 shows a spacing of 25 ps with a small variation of 60.3 ps. This variation agrees with what is expected as a result of a nonzero dispersion slope of the SSMF, which can be eliminated by proper dispersion slope compensation. The experimental cross-correlation trace shows a remarkable match to theory (Fig. 4, inset). The difference in height of the large peaks can be explained by a slight walk-off over the large 100-ps delay of the autocorrelator. The 1471 lower height of the lower peaks in the experimental trace can be explained by the incoherence between the DFB lasers, which the theoretical trace does not take into account. Figure 5(a) shows the autocorrelation trace of a single-frequency pulse train. By use of a deconvolution factor obtained through numerical modeling, a deconvolved pulse width of 2.6 ps and hence a compression ratio of 13 is achieved. We note that this compression is approximately a factor of 2 smaller than that predicted by Eq. (5) (艐22). The discrepancy is due to the approximation of the sinusoidal phase modulation as quadratic. Simply, the quadratic approximation of a cosine wave is totally invalid beyond the inf lection point, where the curvature of the phase modulation changes sign. Any departure from an ideal quadratic phase in a time-lens system introduces aberrations. Proper Fig. 2. Optical spectra before and after the time lens in the absence of the correction lens, resolution bandwidth of 0.01 nm. The dashed spikes represent the initial spectra of the cw DFB lasers: (a) calculated, (b) measured. Fig. 3. Oscilloscope time traces of (a) each wavelength channel measured separately then overlaid, and (b) all channels measured simultaneously. There is no averaging on (a) or (b). The impulse response of the oscilloscope is 18.0 ps. Fig. 4. Cross-correlation trace demonstrating even pulse spacing. Inset, theoretical trace. 1472 OPTICS LETTERS / Vol. 29, No. 13 / July 1, 2004 Fig. 5. Autocorrelation trace of a single-wavelength channel (a) without a correction lens, autocorrelation FWHM 3.5 ps, and (b) with a correction lens, autocorrelation FWHM 4.2 ps. Taking into account the deconvolution factors gives pulse widths of 2.6 and 3.0 ps, respectively. imaging relies on the quadratic phase f iltering supplied by dispersion, as well as the quadratic phase modulation imposed on the incoming electric f ield.8 Higher-order dispersive or modulation terms will only distort the image. Aberrations from higher-order dispersion can be neglected in our system. Third-order dispersion, for example, is estimated to introduce only a 0.3% delay of the half-maximum spectral component of a compressed pulse from its ideal location.8 The leading aberration in our setup comes from higher-order phase modulation terms. This distortion is responsible for the sidelobes that are visible in the autocorrelation trace of the compressed pulses [Fig. 5(a)]. The approximation of the cosine phase modulation drive as quadratic is valid only under a small portion of the cusp of the sinusoid. Restricting the temporal object to a time aperture of ta 艐 Tm 兾2p is suggested to keep the next higher-order term negligible (approximately 2% of the quadratic term).6 However, there are two penalties associated with such a restriction. First, it is necessary to begin with much shorter pulses. In our system, input pulses would need to be less than 16.0 ps. This corresponds to a duty cycle of 16% or less, which is difficult to achieve with the pulse carving technique. Second, and perhaps more importantly, restricting the time aperture leads to a much smaller compression ratio. Our calculations show that a compression ratio of only 4 can be achieved with a 16.0-ps input pulse. We demonstrate a new approach to eliminating aberration without significantly sacrif icing the compression ratio. Instead of restricting the time aperture, we add a correction lens, which is analogous to aberration correction in spatial imaging (Fig. 1). The correction lens consists of another phase modulator but this time driven at 1.0Vp by a 20-GHz sinusoidal drive (twice the frequency of the compression lens and 11% of the drive). Fourier analysis allows any periodic function to be decomposed into a sum of harmonics. Our correction lens essentially adds the next harmonic in the Fourier decomposition of a quadratic. The suppression of the sidelobes, shown in Fig. 5(b), demonstrates the effectiveness of the correction scheme. The slightly smaller compression ratio of 11 in the aberration-corrected system is explained by the fact that the additional lens acts as a weak negative lens. In helping the system assimilate a truer parabolic drive, the correction lens gives a chirp with a sign opposite to that of the compression lens, thereby decreasing compression strength slightly. A new dispersion of 23.0 ps is used to satisfy the chirp-free condition, requiring a new frequency spacing of 680 GHz for even pulse spacing. Further aberration correction can be added to the system by incorporating lenses of higher-order Fourier harmonics. The limit to the amount of correction desired is determined by the bandwidth limitations of the LiNBO3 phase modulators (currently #50 GHz for commercial devices). Although a separate correction stage is used in our setup, we note that it is possible to combine the compression and correction drive voltages into a single rf drive and therefore use a single broadband phase modulator to obtain the same results. In addition, the f iber spool can be replaced with other dispersive devices such as a fiber Bragg grating, making the system even more compact and eliminating the potential problem of slow timing jitter (wander) from temperature f luctuations. In conclusion, we have demonstrated a novel multiwavelength pulse generator based on time-lens compression with aberration correction. Our system is all-fiber and relies on linear optics, allowing easy use and near-exact reproducibility and predictability. Our source not only reduces the complexity of previous systems but also adds f lexibility and control. The power and wavelength of the cw DFB lasers can be independently and precisely tuned to achieve the desired spectral prof ile and temporal spacing, and the repetition rate of the pulses can be continuously varied electronically over a large range. We anticipate that the growing technological advances in phase modulators will extend this technique toward generating even shorter pulse widths at higher repetition rates. J. van Howe’s e-mail address is [email protected]. References 1. J. U. Kang and R. D. Esman, Electron. Lett. 35, 60 (1999). 2. A. S. Bhushan, P. V. Kelkar, B. Jalali, O. Boyraz, and M. Islam, IEEE Photon. Technol. Lett. 14, 684 (2002). 3. P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, IEEE Trans. Microwave Theory Technol. 49, 1840 (2001). 4. P. Rabiei and A. F. J. Levi, J. Lightwave Technol. 18, 1264 (2000). 5. C. Xu and X. Liu, Opt. Lett. 28, 986 (2003). 6. B. H. Kolner, IEEE J. Quantum Electron. 30, 1951 (1994). 7. A. A. Godil, B. A. Auld, and D. M. Bloom, IEEE J. Quantum Electron. 30, 827 (1994). 8. C. V. Bennett and B. H. Kolner, IEEE J. Quantum Electron. 37, 20 (2001). 9. L. F. Mollenauer and C. Xu, in Conference on Lasers and Electro-Optics (CLEO), Vol. 73 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper CPDB1. 10. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).