Complex-cubic Ginzburg–Landau equation-based model for erbium-doped fiber-amplifier-supported nonreturn-to-zero communications

Abstract

The propagation of nonreturn-to-zero pulses, composed by a superposition of two exact shock-wave solutions of a complex-cubic Ginzburg-Landau equation linearly coupled to a linear nondispersive equation, is studied in detail. The model describes the distributed (average) propagation in a dual-core erbium-doped fiberamplifier-supported optical-fiber system where stabilization is achieved by means of short segments of an extra lossy core that is parallel and coupled to the main one. The linear-stability analysis of the two asymptotic states of the shock wave in combination with direct numerical simulations provide necessary conditions for optimal propagation of the nonreturn-to-zero pulse. The enhancement of the propagation distance by at least an order of magnitude, under a suitable choice of the parameters, establishes the beneficial role of the passive channel.

Localized Modes in a Circular Array of Coupled Nonlinear Optical Waveguides

“…It is envisioned that this collective coupling will render the whole system far more controllable than a planar one and easier to stabilize. There are numerous indications in the literature (concerning cCGL, however) which are in support of this conjecture [Efremidis & Hizanidis, 2002;Malomed & Winful, 1984].…”

“…As far as the applied optics is concerned the discrete Nonlinear Schrödinger equation (dNLS) was first introduced as a working model in semiconductor laser arrays in optics [Wang & Winful, 1988;Christodoulides & Joseph, 1988;Otsuka, 1999;Schmidt-Hattenberger et al, 1991;Eisenberg et al, 1998]. More recently, the dCGL takes the lead in several works [Efremidis & Hizanidis, 2002;Efremidis & Christodoulides, 2003;Maruno et al, 2003]: It is worth mentioning that while in cCGL equation-based systems, selflocalized (solitary) solutions as well as dissipative solitons have been found [Pereira & Stenflo, 1977;Nozaki & Bekki, 1984;Hocking & Stewartson, 1992] (among an extraordinary universe of pattern formation and chaotic behavior), no coherent structures have been found in dCGL equation-based systems until very recently [Efremidis & Christodoulides, 2003;Maruno et al, 2003].…”

Centrally Coupled Circular Array of Optical Waveguides: The Existence of Stable Steady-State Continuous Waves and Breathing Modes

“…It is envisioned that this collective coupling will render the whole system far more controllable than a planar one and easier to stabilize. There are numerous indications in the literature (concerning cCGL, however) which are in support of this conjecture [19][20]. The paper is organized as follows: In the next Section the model equations and the stability of zero solution are discussed.…”