Nonlinear Fourier Transform of Truncated Multi-Soliton Pulses

TL;DR

This paper derives closed-form expressions for the nonlinear Fourier spectrum of truncated multi-soliton pulses and presents a method to determine eigenvalues from the continuous spectrum, aiding optical fiber communication.

Contribution

It provides the first simple closed-form formulas for the spectrum of truncated multi-solitons and introduces a novel method to extract eigenvalues from the continuous spectrum.

Findings

Closed-form expressions accurately approximate the nonlinear spectrum of truncated pulses.

The method effectively finds eigenvalues from the continuous spectrum.

Results support potential improvements in optical fiber data transmission.

Abstract

Multi-soliton pulses, as special solutions of the Nonlinear Schroedinger Equation (NLSE), are potential candidates for optical fiber transmission where the information is modulated and recovered in the so-called nonlinear Fourier domain. For data communication, the exponentially decaying tails of a multi-soliton must be truncated. Such a windowing changes the nonlinear Fourier spectrum of the pulse. The results of this paper are twofold: (i) we derive the simple closed-form expressions for the nonlinear spectrum, discrete and continuous spectrum, of a symmetrically truncated multi-soliton pulse from tight approximation of the truncated tails. We numerically show the accuracy of the closed-form expressions. (ii) We show how to find, in general, the eigenvalues of the discrete spectrum from the continuous spectrum. We present this method for the application in hand.