IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 10, NO. 5, SEPTEMBER/OCTOBER 2004 885 Dynamics of Dual-Frequency Solitons Under the Influence of Frequency-Sliding Filters, Third-Order Dispersion, and Intrapulse Raman Scattering N.-C. Panoiu, D. Mihalache, D. Mazilu, I. V. Mel’nikov, J. S. Aitchison, Senior Member, IEEE, F. Lederer, and R. M. Osgood, Jr., Fellow, IEEE Abstract—We analyze the structure of the optical field emerging from a superposition of two soliton-like pulses with different fre- quencies and arbitrary phase-shift between them, and show that the optical output contains either symmetric or antisymmetric two- soliton states. Furthermore, we study numerically the dynamics of these emerging two-soliton states under the influence of pertur- bative effects that are important for optical communications sys- tems: frequency-sliding filters, third-order dispersion, and intra- pulse Raman scattering. Index Terms—Frequency-sliding filters, intrapulse Raman scat- tering, optical solitons, third-order dispersion, wavelength-division multiplexing (WDM). I. INTRODUCTION O VER THE last decade, it has been experimentally proven that soliton data transmission combined with wave- length-division multiplexing (WDM) can be a powerfool tool capable of substantial increasing of the bit-rate transmission ca- pacity of optical communication systems [1], [2]. However, the intrinsic Kerr nonlinearity that is exploited to balance the group velocity dispersion, inevitably causes the interaction among solitons transmitted through different channels. This interaction may hamper the transmission capacity of both classic [3]–[7] as well as dispersion-managed (DM) soliton systems [8]–[10] even in the ideal case of free propagation of the solitons. Moreover, optical amplifiers periodically distributed along the fiber system to compensate the loss, along with inelastic soliton collision, may also cause serious degradation of the signal [11]–[17]. The multifrequency soliton can be generated from a superpo- sition of optical pulses launched into a monomode optical fiber. Manuscript received January 12, 2004; revised August 9, 2004. This work was supported by the NIST Advanced Technology Program Cooperative Agree- ment under Grant 70NANB8H4018. The work of D. Mihalache and D. Mazilu was supported by Deutsche Forschungsgemeinschaft, Bonn. The work of I. V. Mel’nikov and J. S. Aitchison was supported by the Natural Sciences and En- gineering Research Council of Canada. N.-C. Panoiu and R. M. Osgood, Jr. are with the Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 USA. D. Mihalache and D. Mazilu are with the Department of Theoretical Physics, Institute of Atomic Physics, MG 76900 Bucharest, Romania. I. V. Mel’nikov and J. S. Aitchison are with the E. S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON M5S 3G4, Canada (e-mail: igor.melnikov@utoronto.ca). F. Lederer is with the Institute of Solid State Theory and Theoretical Optics, Friedrich Schiller University Jena, Jena D-07743, Germany. Digital Object Identifier 10.1109/JSTQE.2004.837211 Its dynamics can be modeled by a nonlinear Schrödinger equa- tion accordingly modified that allows to exploit such powerful tool as the inverse scattering transform (IST) and its perturbation formalism. Recently, we employed this formalism and studied the soliton structure of a superposition of soliton-like op- tical pulses launched into a monomode optical fiber [18], [19], as well as the influence of perturbations that preserve the sym- metry of the initial pulse, namely bandwidth-limited amplifica- tion, nonlinear amplification, and amplitude and phase modula- tion [20], [21] (for a review, see [22]). The soliton structure of the optical field has been determined by employing an IST nu- merical method [23], whereas the symmetry-preserving external perturbations allowed to make use of an IST adiabatic perturba- tion formalism [24], [25]. In this paper, we extend our analysis onto such perturbations as frequency-sliding filters, third-order dispersion, and intrapulse Raman scattering. They play an im- portant role in optical communications systems but break the symmetry of the propagating optical pulses (solitons). Thus, we present a comprehensive numerical treatment of their influence on the dynamics of dual-frequency solitons in the optical fiber. The paper is organized as follows. In Section II, we discuss the structure of the optical field emerging from the superposition of two soliton-like optical pulses that are launched in different channels, that is, have different frequencies. Then, Section III numerically describes the influence of frequency-sliding filters, third-order dispersion, and intrapulse Raman scattering on the propagation of the emerging pulses. Finally, in the last section, the results are summarized and discussed. II. SOLITON OUTPUT FROM A SUPERPOSITION OF TWO SOLITON–LIKE PULSES In this section we briefly discuss the structure of the optical field emerging from a superposition of two soliton-like optical pulses with different frequencies. A detailed derivation of the results presented in this section can be found in [18]. We begin by considering two particular cases, namely the two input pulses are in-phase or out-of-phase, and then we discuss the general case in which the phase shift between the two pulses is arbitrary. In the case of negative group velocity dispersion and self-fo- cusing Kerr nonlinearity of the fiber, the optical pulse evolution obeys the following nonlinear Schrödinger equation (NLSE): (1) 1077-260X/04$20.00 © 2004 IEEE