Periodic nonlinear Fourier transform for fiber-optic communications, Part I: theory and numerical methods

Morteza Kamalian, Jaroslaw E. Prilepsky, Son Thai Le, Sergei K. Turitsyn

Research output: Contribution to journalArticlepeer-review


In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Original languageEnglish
Pages (from-to)18353-18369
Number of pages17
JournalOptics Express
Issue number16
Early online date2 Aug 2016
Publication statusPublished - 8 Aug 2016

Bibliographical note

© 2016 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited.

Funding: EPSRC (UNLOC EP/J017582/1).

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