On computing high-dimensional Riemann theta functions

Riemann theta functions play a crucial role in the field of nonlinear Fourier analysis, where they are used to realize inverse nonlinear Fourier transforms for periodic signals. The practical applicability of this approach has however been limited since Riemann theta functions are multi-dimensional Fourier series whose computation suffers...

Fiber-Optic Communications Using Nonlinear Fourier Transforms: Algorithms and a Bound

Due to the ever increasing global connectivity, the demand on the fiber-optic communication infrastructure is projected to keep increasing rapidly. A major factor currently limiting transmission capacity is the fiber nonlinearity. Some researchers have suggested the application of nonlinear Fourier transforms to exploit the fiber nonlinearity...

Bounds on the Transmit Power of b-Modulated NFDM Systems in Anomalous Dispersion Fiber

The performance of various nonlinear frequency division multiplexed (NFDM) fiber-optic transmission systems has been observed to decrease with increasing signal duration. For a class of NFDM systems known as b-modulators, we show that the nonlinear bandwidth, signal duration, and power are coupled when singularities in the nonlinear spectrum are...

Exact NFDM transmission in the presence of fiber-loss

Nonlinear frequency division multiplexing (NFDM) techniques encode information in the so-called nonlinear spectrum which is obtained from the nonlinear Fourier transform (NFT) of a signal. NFDM techniques so far have been applied to the nonlinear Schrödinger equation (NLSE) that models signal propagation in a lossless fiber. Conventionally, the...

Fast nonlinear Fourier transform algorithms using higher order exponential integrators

The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of highly accurate low-complexity algorithms remains a challenge. In this paper, we present new fast forward NFT...

Improved Fast Inverse Nonlinear Fourier Transform for Multi-solitons: A Discrete Darboux Based Approach

The relation between the input of an ideal optical single-mode fiber and the corresponding fiber output constitutes a nonlinear system that can be described using the nonlinear Schrödinger equation. This nonlinear system has the interesting property that it can be solved analytically using nonlinear Fourier transforms. To utilize this property,...

Discrete Darboux based fast inverse nonlinear Fourier transform algorithm for multi-solitons

A fast algorithm for constructing multi-solitons with linear complexity in the number of samples and eigenvalues is introduced. The algorithm is shown to be significantly faster than the conventional Darboux transform in a numerical example, with acceptable error.