IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 18, NO. 2, JANUARY 15, 2006 403 Electronic Precompensation of Optical Nonlinearity Kim Roberts, Member, IEEE, Chuandong Li, Leo Strawczynski, Maurice O’Sullivan, and Ian Hardcastle Abstract—We introduce digital precompensation for optical nonlinearities. A 10-Gb/s transmitter subsystem is described. Experimental results, across 320 and 1280 km of standard single-mode fiber (G.652) without any optical compensators, show substantial elimination of self-phase modulation. Some of the limits of this method are explored. Index Terms—Optical modulation, optical nonlinearities, optical transmission, self-phase modulation (SPM), signal processing. I. INTRODUCTION I T IS very desirable to operate high-capacity transmission systems on any fiber connection without the use of optical dispersion compensation [1]. Methods of digital electronic precompensation for arbitrary amounts of chromatic dispersion (CD) have been recently presented [2]–[4]. A 10-Gb/s optical signal has been transmitted across 5120 km of G.652 fiber with 82 433 ps/nm of uncompensated chromatic dispersion [5]. However, linear filtering used to compensate CD does not mit- igate nonlinear phenomena like self-phase modulation (SPM). Optical nonlinearities interact with the optical dispersion to degrade the performance of high-speed transmission systems. Optical phase conjugation is a well-known technique and has been proposed as a method to compensate for CD and SPM [6]. Various other techniques have also been investigated for compensating such channel distortion and improving transmis- sion performance in optical communication systems by using: 1) a dispersive medium with a negative nonlinear refractive index coefficient [7]; 2) postdetection electrical filtering [8]; 3) an adaptive optical equalizer [9]; or 4) phase modulators [10]. This letter demonstrates that digital electronic nonlinear compensation can eliminate nonlinear degradations due to SPM. II. ELECTRONIC NONLINEAR COMPENSATION Dual 20 GSamples per second 6-bit digital-to-analog con- verters (DACs) have been integrated in silicon [11]. When used to drive a dual-parallel Mach–Zehnder modulator (MZM) in a transmitter, any desired sequence of complex optical elec- trical-field (E-field) values can be generated, within the limits of the sampling rate and resolution. Previously, a linear digital Manuscript received August 22, 2005; revised November 1, 2005. K. Roberts, C. Li, and M. O’Sullivan are with Nortel, Ottawa, ON K2H 8E9, Canada (e-mail: krob@nortel.com; chuangli@nortel.com; osullms@nortel.com). L. Strawczynski was with Nortel, Ottawa, ON K2H 8E9, Canada. He is now retired at 479 Highland Avenue, Ottawa, ON K2A 2J5, Canada (e-mail: strawczynski@sympatico.ca). I. Hardcastle was with Nortel, Ottawa, ON K2H 8E9, Canada. He is now with Filtronic Compound Semiconductors, Ltd., Newton Aycliffe DL5 6JW, U.K. (e-mail: Ian.Hardcastle@filcs.com). Digital Object Identifier 10.1109/LPT.2005.862360 Fig. 1. Block diagram of nonlinear precompensation transmitter. This also forms arbitrary optical waveform generator. filter was used to generate signals that precompensate for more than 82 000 ps/nm of optical chromatic dispersion [5]. If, in addition, one uses nonlinear digital filters, the nonlinear optical propagation effects can also be precompensated. This is what is investigated in this letter. Fig. 1 shows such a precom- pensating transmitter. The detail of the memory block (dotted line) shows conceptually how nonlinear precompensation can be done. Here, the memory block includes all digital signal processing (DSP) functions. The calculation method can be described as follows. Con- sider the well-known technique of optical phase conjugation that uses the first half of the optical transmission path to build a signal that, after conjugation, is precompensated for the disper- sion and the SPM of the second half of the path [6]. Instead of conjugating at the midpoint of an optical path, one can consider an entire optical path to be the “second half” of a conjugation system, where the “first half” and the conjugating function are implemented digitally within the transmitter. In other words, we start with the desired waveform at the receiver. Then, the signal is back-propagated to the transmitter, which includes CD and SPM. The back-propagated signal is finally used to determine the nonlinear filter coefficients in the transmitter. Numerical op- timization and algebraic methods can also be used, taking into account the depth and number of nonlinear stages. III. EXPERIMENTAL RESULTS AND DISCUSSION The precompensation of SPM has been demonstrated using a recirculating loop consisting of four 80-km spans of G.652 fiber with erbium-doped fiber amplifiers (EDFAs) and polarization scrambling (Fig. 2). The desired optical waveform that will resolve into a 2 differential phase-shift keying (DPSK) signal at the receiver was calculated using the well-known split-step Fourier method [12] and loaded into the memory of an arbitrary optical waveform generator (Fig. 1). In this 1041-1135/$20.00 © 2005 IEEE