Photon-conserving Raman soliton attractors in focusing and defocusing Kerr media
Abstract
The sign of the Kerr nonlinear coefficient has long been regarded as irrelevant to the direction of the Raman-induced soliton self-frequency shift. Yet the standard generalized nonlinear Schrödinger equation (GNLSE) predicts a frequency shift that depends on the sign of the nonlinearity, which leads to an unphysical blue shift in the defocusing case. We resolve this inconsistency by deriving the time-domain form of the photon-conserving GNLSE (pcGNLSE) from its established frequency-domain counterpart. The derivation reveals that photon-number conservation imposes two sign modifications relative to the standard GNLSE: the Raman-shift coefficient acquires the absolute value of the Kerr nonlinear coefficient in place of its signed counterpart, and the self-steepening-Raman dissipation term likewise carries an absolute-value prefactor rather than a signed one. These two modifications jointly guarantee a universal spectral redshift and monotonically decreasing pulse energy during propagation, irrespective of the signs of the Kerr nonlinear coefficient and its frequency derivative. Applying the method of moments to the time-domain pcGNLSE with appropriate chirped ansätze, we derive closed-form evolution equations for five pulse parameters and establish explicit attractor conditions under which bright or dark Raman solitons propagate with constant peak power. Direct numerical integration of the pcGNLSE confirms all analytical predictions and demonstrates that the standard GNLSE fails qualitatively, predicting unphysical energy growth and spectral blueshift in the negative-nonlinearity regime. The results provide a rigorous analytical framework for Raman soliton dynamics in materials with negative third-order susceptibility, with direct implications for soliton-based devices in emerging semiconductor waveguide and microresonator platforms.
Related
- Large-space and Large-time Asymptotics for the Focusing Nonlinear Schrödinger Soliton Gas
- Photon-Return and Polar-Focusing Crossovers near Extremal Kerr
- Superregular solitonic solutions of the defocusing nonlocal nonlinear Schrodinger equation and their novel perspectives
- Power-conserving coupled-mode theory for high-index-contrast multiwaveguide systems from the field continuous at the interfaces
- Global convergence of an efficient splitting method for the defocusing Gross--Pitaevskii ground state problem
BibTeX
@misc{huang2026photonconserving,
title = {{Photon-conserving Raman soliton attractors in focusing and defocusing Kerr media}},
author = {Weiye Huang and Junhong Yang and Tao Sun and Qian Gao and Peilong Yang and Jintao Fan and Günter Steinmeyer and Jinhui Yuan and Chao Mei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.05244},
eprint = {2607.05244},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.05244},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Photon-conserving Raman soliton attractors in focusing and defocusing Kerr media
AU - Weiye Huang
AU - Junhong Yang
AU - Tao Sun
AU - Qian Gao
AU - Peilong Yang
AU - Jintao Fan
AU - Günter Steinmeyer
AU - Jinhui Yuan
AU - Chao Mei
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2607.05244
UR - https://arxiv.org/abs/2607.05244
AB - The sign of the Kerr nonlinear coefficient has long been regarded as irrelevant to the direction of the Raman-induced soliton self-frequency shift. Yet the standard generalized nonlinear Schrödinger equation (GNLSE) predicts a frequency shift that depends on the sign of the nonlinearity, which leads to an unphysical blue shift in the defocusing case. We resolve this inconsistency by deriving the time-domain form of the photon-conserving GNLSE (pcGNLSE) from its established frequency-domain counterpart. The derivation reveals that photon-number conservation imposes two sign modifications relative to the standard GNLSE: the Raman-shift coefficient acquires the absolute value of the Kerr nonlinear coefficient in place of its signed counterpart, and the self-steepening-Raman dissipation term likewise carries an absolute-value prefactor rather than a signed one. These two modifications jointly guarantee a universal spectral redshift and monotonically decreasing pulse energy during propagation, irrespective of the signs of the Kerr nonlinear coefficient and its frequency derivative. Applying the method of moments to the time-domain pcGNLSE with appropriate chirped ansätze, we derive closed-form evolution equations for five pulse parameters and establish explicit attractor conditions under which bright or dark Raman solitons propagate with constant peak power. Direct numerical integration of the pcGNLSE confirms all analytical predictions and demonstrates that the standard GNLSE fails qualitatively, predicting unphysical energy growth and spectral blueshift in the negative-nonlinearity regime. The results provide a rigorous analytical framework for Raman soliton dynamics in materials with negative third-order susceptibility, with direct implications for soliton-based devices in emerging semiconductor waveguide and microresonator platforms.
ER -