<p>This work presents a Python-based numerical simulation framework for integrated quantum photonic systems governed by the nonlinear Schrödinger equation (NLSE). The study models excitation, guided propagation, and detection of femtosecond optical pulses in chip-scale waveguides using the split-step Fourier method. To ensure both numerical clarity and physical relevance, two parameter regimes are employed: a normalized (dimensionless) formulation for algorithmic validation and envelope stability analysis, and a physically realistic SI-valued formulation for modeling soliton dynamics and broadband nonlinear effects. Input conditions include Gaussian and hyperbolic secant pulse envelopes with central wavelength <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda _0 = 1550\)</EquationSource> </InlineEquation> nm and peak power ranging from 0.5 to 5 W. Representative waveguide lengths of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L = 2\)</EquationSource> </InlineEquation> mm are considered with grid resolutions of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Delta z = 0.01\)</EquationSource> </InlineEquation> mm and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Delta t = 0.1\)</EquationSource> </InlineEquation> fs. In the physical regime, dispersion and nonlinearity are modeled using parameters consistent with experimentally reported platforms, including <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\beta _2 \approx -0.7\,\textrm{ps}^2/\textrm{m}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\gamma \sim 10^2\,\textrm{W}^{-1}\,\textrm{m}^{-1}\)</EquationSource> </InlineEquation>. Simulation results demonstrate that low-dispersion regimes preserve temporal and spectral pulse integrity, while anomalous dispersion conditions produce soliton formation and spectral broadening consistent with reported supercontinuum generation in AlGaAs and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\hbox {Si}_3{N}_4\)</EquationSource> </InlineEquation> waveguides. Transverse mode analysis confirms single-mode confinement, and phase evolution maps reveal coherent phase wrapping essential for quantum interference applications. A probabilistic photodetection model yields normalized detection rates consistent with experimentally reported efficiencies of InGaAs SPADs and superconducting nanowire single-photon detectors. The proposed framework provides an experimentally consistent and extensible NLSE-based simulation pipeline, supporting the co-design and optimization of nonlinear integrated photonic circuits for quantum information processing.</p>

Simulation of ultrafast photonic circuits via nonlinear Schrödinger dynamics and quantum detector modeling

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发表日期：

2026年2月11日

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Dennis Delali Kwesi Wayo

摘要

This work presents a Python-based numerical simulation framework for integrated quantum photonic systems governed by the nonlinear Schrödinger equation (NLSE). The study models excitation, guided propagation, and detection of femtosecond optical pulses in chip-scale waveguides using the split-step Fourier method. To ensure both numerical clarity and physical relevance, two parameter regimes are employed: a normalized (dimensionless) formulation for algorithmic validation and envelope stability analysis, and a physically realistic SI-valued formulation for modeling soliton dynamics and broadband nonlinear effects. Input conditions include Gaussian and hyperbolic secant pulse envelopes with central wavelength \(\lambda _0 = 1550\) nm and peak power ranging from 0.5 to 5 W. Representative waveguide lengths of \(L = 2\) mm are considered with grid resolutions of \(\Delta z = 0.01\) mm and \(\Delta t = 0.1\) fs. In the physical regime, dispersion and nonlinearity are modeled using parameters consistent with experimentally reported platforms, including \(\beta _2 \approx -0.7\,\textrm{ps}^2/\textrm{m}\) and \(\gamma \sim 10^2\,\textrm{W}^{-1}\,\textrm{m}^{-1}\) . Simulation results demonstrate that low-dispersion regimes preserve temporal and spectral pulse integrity, while anomalous dispersion conditions produce soliton formation and spectral broadening consistent with reported supercontinuum generation in AlGaAs and \(\hbox {Si}_3{N}_4\) waveguides. Transverse mode analysis confirms single-mode confinement, and phase evolution maps reveal coherent phase wrapping essential for quantum interference applications. A probabilistic photodetection model yields normalized detection rates consistent with experimentally reported efficiencies of InGaAs SPADs and superconducting nanowire single-photon detectors. The proposed framework provides an experimentally consistent and extensible NLSE-based simulation pipeline, supporting the co-design and optimization of nonlinear integrated photonic circuits for quantum information processing.