The Quantum Split-Step Fourier Algorithm for Nonlinear Optical Waveguides

• URL: http://arxiv.org/abs/2606.24643v1
• Date: Tue, 23 Jun 2026 14:40:27 GMT
• Title: The Quantum Split-Step Fourier Algorithm for Nonlinear Optical Waveguides
• Abstract summary: We introduce the Quantum Split-Step Fourier (QSSF) algorithm for nonlinear optical waveguides.<n>QSSF is a numerical framework that combines split-step propagation of the nonlinear Schrdinger equation with a commutator-preserving Bogoliubov evolution of quantum fluctuations.<n>It provides a practical information-theoretic diagnostic for quantum correlations in nonlinear frequency conversion, supercontinuum generation, and multimode squeezed-light formation in ultrafast waveguide platforms.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the Quantum Split-Step Fourier (QSSF) algorithm for nonlinear optical waveguides, a numerical framework that combines split-step propagation of the nonlinear Schrödinger equation with a commutator-preserving Bogoliubov evolution of Gaussian quantum fluctuations. The method propagates the classical mean field together with the Bogoliubov matrices $U$ and $V$, from which reduced second moments, covariance matrices, symplectic eigenvalues, and entropic measures are constructed for arbitrary spectral windows. Applied to soliton-driven resonant radiation, QSSF shows that the selected radiation band acquires a steadily increasing von Neumann entropy and a corresponding loss of purity, quantifying its entanglement with the rest of the spectrum in the lossless Gaussian setting. The analysis also reveals a surprisingly pronounced low-dimensional structure: although the radiation occupies many Fourier bins, its reduced Gaussian state is dominated by only a few Williamson modes. QSSF therefore provides a practical information-theoretic diagnostic for quantum correlations in nonlinear frequency conversion, supercontinuum generation, and multimode squeezed-light formation in ultrafast waveguide platforms.

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