Nonlinear Fourier transform assisted high-order soliton characterization

Abstract

Nonlinear Fourier transform (NFT), based on the nonlinear Schrödinger equation (NLSE), is implemented for the description of soliton propagation, and in particular focused on propagation of high-order solitons. In nonlinear frequency domain, a high-order soliton has multiple eigenvalues depending on the soliton amplitude and pulse-width. During the propagation along the standard single mode fiber (SSMF), their eigenvalues remain constant, while the corresponding discrete spectrum rotates along with the SSMF transmission. Consequently, we can distinguish the soliton order based on its eigenvalues. Meanwhile, the discrete spectrum rotation period is consistent with the temporal evolution period of the high-order solitons. The discrete spectrum contains nearly 99.99% energy of a soliton pulse. After inverse-NFT (INFT) on discrete spectrum, soliton pulse can be reconstructed, illustrating that the eigenvalues can be used to characterize soliton pulse with good accuracy. This work shows that soliton characteristics can be well described in the nonlinear frequency domain. Moreover, as a significant supplement to the existing means of characterizing soliton pulses, NFT is expected to be another fundamental optical processing method besides an oscilloscope (measuring pulse time domain information) and a spectrometer (measuring pulse frequency domain information).

Unveiling Laser Radiation of Multiple Optical Solitons by Nonlinear Fourier Transform

“…The study of fiber laser radiation as a paradigm of dissipative systems is a thriving and intriguing area. Although some research in understanding their behavior has been made through theory and numerical modeling by NFT, [21,[23][24][25] comparing the theoretical and numerical results carefully with the experiment is essential. To this end, the study in this work makes a significant contribution.…”

“…[ 20,23] Also known as the inverse scattering transform, NFT can decompose the optical signal into a continuous spectrum and a discrete spectrum to obtain the corresponding nonlinear spectrum, and describe laser radiation with a mixture of soliton and embedded dispersive waves. [23][24][25] With the help of such a powerful signal processing tool, NFT can be used to effectively address the nonlinear transmission impairments arising in single-mode fiber transmission or provide a viewpoint on the new physics of soliton dynamics. [26][27][28][29][30] Further, using the NFT for signal processing of localized waveforms allows the pulses to be approximated by a limited number of discrete eigenvalues, simplifying the description compared to using a large number of linear spectral harmonics.…”

“…However, most previous research on utilizing NFT to characterize dissipative soliton dynamics is focused on theory and numerical simulation. [21,[23][24][25] Comparing the theoretical and numerical results carefully with the experiment is essential. Experimentally, using the NFT to characterize the laser radiation of a single steady or breathing soliton was demonstrated.…”