IEEE PHOTONICS TECHNOLOGY LE’lTERS, VOL. zyxwvutsrqpo 8, NO. 1, JANUARY 1996 133 Coherent Crosstalk in Multichannel FSKDD Lightwave Systems Due to Four-Wave Mixing in Semiconductor Optical Amplifiers D. J. Blumenthal, zyxwvuts Member, ZEEE, and N. zyxwv C. Kothari Abstract-Coherent crosstalk in multichannel lightwave trans- mission systems due to four-wavemixing in semiconductor optical amplifiers is analyzed. For direct detection of evenly spaced frequency channels, coherent beating between signal and inter- modulation products occurs when the channel bit rate is greater than the laser linewidth. Crosstalk and maximum input power limitations for an FSK/DD system are calculated for up to 100 channels and channel spacing up to 100 GHZ. It is shown that the spectral hole burning and dynamic carrier heating gain mechanisms must be included in addition to carrier modulation and gain saturation to accurately predict both incoherent and coherent crosstalk for channel spacing greater than 5 GHz. Degradation of the eye pattern due to coherent crosstalk is shown to exceed the incoherent contributions by up to 33 dB even when laser phase statistics and bit pattern statistics are accounted for. The result of this crosstalk mechanism is a predicted decrease in the maximum input power per channel to -43 dBm for 100 channels at 100 GHz channel spacing and -52 dBm for 100 channels at 5-GHz channel spacing for an optical SNR of 23 dB, representing a decrease in input power per channel of 25 dBm over incoherent crosstalk limitations alone. I. INTRODUCTION EMICONDUCTOR optical amplifiers (SOA’s) show S promise as compact amplifiers in frequency division multiplexed (FDM) optical transmission systems. Crosstalk induced by amplifier nonlinearities must be understood and minimized to make these systems practical. Previous models of multichannel crosstalk in SOA’s assumed that primary and crosstalk fields are uncorrelated and accumulate incoherently zyxwvut [ 11-[3]. However, in multigigabit systems with MHz linewidth lasers, the phase noise is negligible during the detection process [4] requiring that coherent interaction between fields be considered if the frequency difference between interacting fields falls within the receiver bandwidth. This coherent interaction is data dependent and can lead to BER floors and channel drop-out. In this letter, we analyze the effect of coherent crosstalk, induced by FWM in SOA’s on multichannel FSK direct detection (FSWDD) systems. For multichannel amplification of FSK or PSK signals, FWM is the dominant crosstalk mechanism [3]. The two conditions required for coherent Manuscript received June 23, 1995; revised September 1, 1995. This work was supported by the National Science Foundation under a National Young Investigator (NYI) award and by support from Bell Northern Research. The authors are with the Microelectronics Research Center (MiRC), School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA. Publisher Item Identifier S 1041-1 135(96)00506-X. crosstalk are that the source linewidths are less than the bit rate and that the frequency difference of the interfering signals fall within the receiver bandwidth. For evenly spaced frequency systems, FWM fields coincide with primary channels. If the channel spacing is not exactly even, as may be the case with nonfrequency locked sources, the resulting beat frequencies that fall within the receiver bandwidth will have constant phase over the bit interval and coherent degradation will be detected. Prior work on multichannel crosstalk in SOA’s considered only incoherent contributions from FWM and assumed that carrier modulation was the only process contributing to FWM gain, leading to significant crosstalk for channel spacings less than 1 GHz zyxwvu [3]. It has recently been shown that, in addition to carrier modulation, carrier heating and hole burning contribute significantly to FWM gain for frequency differences of up to several THz zyxwv [5]. Therefore, these fast processes must be included in the crosstalk model to account for long range interaction in a multiple channel systeim. The model presented here differs from previous models in that it accounts for coherent interaction among signal and FWM fields, bit statistics and phase statistics of the data and sources, and inclusion of hole burning, carrier heating, carrier modulation, and gain saturation in the FWM gain. We assume an N channel FSWDD system with nominal channel frequency zyxwv f, and spacing Au. A space is transmitted on frequency f, - Af and a mark is transmitted on frequency zy f, + A f. After the SOA, the mark frequency of the center channel is passed through a narrowband optical filter and direct detected. Within the SOA, two-tone b;WM mixing between fields at frequencies w, and w3 generates fields at frequencies 2w, - wj and 2w, - wz, and three-tone mixing between fields at frequencies w,, wJ, and Wk generates fields at frequencies w,,k = w, + wj - wk over all possible combinations of i, j and IC where i # j # IC. FWM in traveling wave SOA’s involves scattering of an incident optical field off index and gain gratings created by beat frequency induced modulation of carriers and carrier occupation probabilities [6]. Fields A, and Ak interfere in the SOA to produce a grating at frequency R,I, that scatters the field A, into a new field A,,h, such that for small P,,t/P, and large unsaturated gain, A,3k zyxwv G -qj k e3g0 z/2~-3p0ut/zps A, (0) A, (0)A; (0) , (1) 1041-1135/96$05.00 0 1996 IEEE