preprint
Analytical research examines the propagation of exact dark-bright vector solitons in birefringent optical fibres subject to polarization-dependent dispersion, Kerr nonlinearity, and cross-phase modulation. By applying travelling-wave reduction and implicit function pairs, closed mathematical expressions are established for pulse amplitudes, widths, frequency shifts, and propagation constants. A real mixed state requires the dispersion ratio to exceed the inverse of the cross-phase modulation coefficient, with the bright component vanishing when they are equal. The individual fibre parameters govern distinct physical effects: dispersion contrast controls state onset and amplitude sharing, the Kerr coefficient sets the total power scale, and cross-phase coupling governs mutual trapping. Morphological analysis demonstrates that stronger dispersion contrast and cross-phase coupling fill the dark pulse notch, whereas the Kerr coefficient leaves the normalized profile unchanged. These relationships link theoretical solutions directly to observable waveform features.
Solitons are stable light pulses capable of travelling through optical fibres without spreading, making them important for advanced telecommunications and fibre lasers. Understanding how fibre properties such as birefringence and nonlinearity dictate pulse shapes allows engineers and researchers to predict and control optical signal behaviour more accurately in complex waveguide systems.
This theoretical work provides a coefficient-level framework relevant to designers of nonlinear optical waveguides, specialised fibre lasers, and advanced optical communication networks. Because the findings are purely analytical and focus on mathematical parameter relationships rather than physical device testing, the research remains at an early stage. Further experimental validation in physical fibres is required before practical hardware implementations or commercial waveguide designs can be developed.
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This study analytically examines how polarization-dependent group-velocity dispersion, Kerr nonlinearity, and incoherent cross-phase modulation govern exact dark-bright vector-soliton propagation in a birefringent optical fibre. A common travelling-wave reduction combined with the lowest-order implicit Bogning-function pair yields closed expressions for the dark-background amplitude, bright-pulse amplitude, common inverse width, carrier-frequency shifts, and propagation constants. For symmetric nonlinear coefficients, a real mixed state exists only when Rβ>1/σ; at equality, the bright component vanishes continuously, while the equal-dispersion model with the standard cross-phase coefficient does not support the selected tanh-sech pair. The analytical relations separate the roles of the waveguide properties: Rβ controls branch onset and amplitude partition, γ fixes the absolute power scale, and σ regulates mutual nonlinear trapping. A total-intensity morphology analysis introduces the notch-filling factor F=B2/A2 and normalized notch depth D=1-F, showing that stronger dispersion contrast and cross-phase coupling progressively fill the dark notch, whereas the Kerr coefficient does not alter the normalized profile. Polarization-resolved propagation plots, amplitude maps, total-intensity representations, and morphology maps connect the exact solution directly to measurable waveform features. The results provide a coefficient-level framework for determining how the properties of a strongly nonlinear and dispersive optical waveguide shape a locked dark-bright vector state.
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DOI: 10.1364/opticaopen.33265245.v1
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