908 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 4, APRIL 2005 Bit-Error-Ratio Improvement With 2R Optical Regenerators M. Rochette, J. N. Kutz, J. L. Blows, D. Moss, J. T. Mok, and B. J. Eggleton Abstract—We show that an all-optical optical regenerator can improve the bit-error ratio (BER) of a signal passing through it only if the regenerator has different power transfer functions for the logical ones and logical zeros. A regenerator that operates with a single transfer function—which constitute most of optical regen- erators reported in the literature—cannot improve the BER, but can only reduce the BER degradation when, for example, placed before optical amplifiers. Of all the optical regenerators reported to date, only the one proposed by Mamyshev, based on filtering a self-phase modulated signal, has different transfer functions for the logical ones and the logical zeros. This makes the Mamyshev scheme a superior candidate for ultrahigh-speed all-optical regen- eration. Index Terms—All-optical devices, nonlinear optics, optical signal processing, signal regeneration. I. INTRODUCTION O PTICAL regenerators are of significant interest as a means of preventing the accumulation of signal distortion in high bit-rate lightwave transmission systems. The majority of all-optical regenerators have a power transfer function that provides signal reamplification and reshaping (2R) and this has been realized through nonlinear phenomena such as self-phase modulation (SPM) [1]–[5], nonlinear interferometry within an optical loop mirror [6], [7], four-wave mixing [8], parametric amplification [9], saturable absorption [10], or gain dynamics in a semiconductor optical amplifier [11]. The transfer function is engineered so that the probability distribution functions (pdfs) of the logical ones and logical zeros entering the regenerator are compressed to produce noise-flattened bits, thereby increasing the signal-to-noise ratio. Numerous papers have experimentally and theoretically demonstrated a reduction in the bit-error ratio (BER) or an increase of the -factor in systems with cascaded erbium-doped fiber amplifiers (EDFAs) by the addition of optical regenerators between the EDFAs [2]–[7], [10]. In this letter, we show theoretically and numerically that an optical regenerator that operates on the principle of a single- Manuscript received November 18, 2004; revised December 14, 2004. This work was supported by the Australian Research Concil under ARC Centres of Excellence Program and by the Natural Science and Engineering Research Concil of Canada (NSERC) postdoctoral fellowships. M. Rochette, J. L. Blows, D. Moss, J. T. Mok, and B. J. Eggleton are with the Centre for Ultrahigh Bandwidth Devices for Optical Systems (CUDOS), University of Sydney, Sydney, NSW 2006, Australia (e-mail: rochette@physics.usyd.edu). J. N. Kutz is with the Department of Applied Mathematics, University of Washington, Seattle, WA 98195-2420 USA (e-mail: kutz@amath.wash- ington.edu). Digital Object Identifier 10.1109/LPT.2005.843950 Fig. 1. Schematic of the regeneration principle. (1) Initial signal; (2) signal distorded by ASE noise; (3) signal after regeneration with a single transfer-function-based regenerator (1TF) and a dual transfer-function-based regenerator (2TF). : Time axis. : Amplifier. power transfer function—which constitutes the majority of all- optical regenerators reported so far—is incapable of improving the BER of the signal passing through it. That is, such a regen- erator does not improve a system BER when placed just before the receiver. Nonetheless, a single transfer function regenerator compresses the noise on the logical ones and the logical zeros, which has the property of reducing the BER degradation from subsequent EDFAs stages. We also show that an optical regenerator that provides a dif- ferent transfer function for the logical ones and the logical zeros can reduce the BER of the signal passing through it—we define this as an intrinsic BER improvement. The SPM-based regen- erator of the form proposed by Mamyshev [1] provides distinct transfer functions for the logical ones and the logical zeros and has been shown to have an intrinsic BER and -factor improve- ment [2], [3]. In Mamyshev regenerators, not only is the noise compressed in the same manner as by single transfer-function- based regenerators, but additionally, noise is partly removed in the regeneration process. II. THEORY The schematic of a system comprising both types of optical regenerators is presented in Fig. 1. The optical pulse train emitted from a transmitter accumulates noise after propagation through a cascade of EDFAs and is being regenerated by a single or dual transfer function regenerator. In both cases, the noisy pulse train is reshaped in the regeneration process but only the dual transfer function intrinsically improves the BER. To demonstrate this, we evaluate the BER before and after single and dual transfer-function-based regenerators. Theoret- ical BER evaluation requires the pdf for the logical ones and for the logical zeros . Assuming an ideal two-level signal (i.e., with logical ones and logical zeros) superposed 1041-1135/$20.00 © 2005 IEEE