Nonlinear Spectrum of Conventional OFDM and WDM Return-to-Zero Signals in Nonlinear Channel

The nonlinear Schrödinger equation (NLSE) is often used as a master path-average model for fiber-optic links to analyze fundamental properties of such nonlinear communication channels. Transmission of a signal in nonlinear channels is conceptually different from linear communications. We use here the NLSE channel model to explain and illustrate some new unusual features introduced by nonlinearity. In general, NLSE describes the co-existence of dispersive (continuous) waves and localized (here in time) waves: soliton pulses. The nonlinear Fourier transform method allows one to compute for any given temporal signal the so-called nonlinear spectrum that defines both continuous spectrum (analog to conventional Fourier spectral presentation) and solitonic components. Nonlinear spectrum remains invariant during signal evolution in the NLSE channel. We examine conventional orthogonal frequency-division multiplexing (OFDM) and wavelength-division multiplexing (WDM) return-to-zero signals and demonstrate that both signals at certain power levels have soliton component. We would like to stress that this effect is completely different from the soliton communications studied in the past. Applying Zakharov-Shabat spectral problem to a single WDM or OFDM symbol with multiple sub-carriers, we quantify the effect of statistical occurrence of discrete eigenvalues in such an information-bearing optical signal. Moreover, we observe that at signal powers optimal for transmission, an OFDM symbol with high probability has a soliton component.