Fast Inverse Nonlinear Fourier Transform For Generating Multi-Solitons In Optical Fiber

TL;DR

This paper introduces a fast inverse nonlinear Fourier transform algorithm for multi-solitons in optical fibers, significantly reducing computational complexity and enabling efficient generation of multi-solitonic signals for fiber-optic communications.

Contribution

It presents the first inverse NFT algorithm with \log^{2}D complexity for multi-solitons, improving computational efficiency in nonlinear Fourier analysis.

Findings

Achieves \log^{2}D complexity for inverse NFT of multi-solitons

Provides analysis of nonlinear Fourier spectra for multiple samples

Enables faster generation of multi-solitonic signals in optical fibers

Abstract

The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier transform in WDM systems with an appropriately defined nonlinear Fourier transform (NFT). The computational complexity of NFTs is a topic of current research. In this paper, a fast inverse NFT algorithm for the important special case of multi-solitonic signals is presented. The algorithm requires only $\mathcal{O}(D\log^{2}D)$ floating point operations to compute $D$ samples of a multi-soliton. To the best of our knowledge, this is the first algorithm for this problem with $\log^{2}$-linear complexity. The paper also includes a many samples analysis of the generated nonlinear Fourier spectra.