Resonant-state expansion of light propagation in non-uniform waveguides

Abstract

A new rigorous approach for precise and efficient calculation of light propagation along non-uniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoing-wave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the wave equation for light propagation in a non-uniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients depending on the coordinate along the waveguide. We illustrate the method on several examples of non-uniform planar waveguides and evaluate its efficiency compared to the aperiodic Fourier modal method and the finite element method, showing improvements of one to four orders of magnitude. A similar improvement can be expected also for applications in other fields of physics showing wave phenomena, such as acoustics and quantum mechanics.

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• Brillouin-Wigner perturbation theory in open electromagnetic systems
• Resonant state expansion applied to three-dimensional open optical systems
• Resonant state expansion applied to two-dimensional open optical systems
• Resonant-state expansion of dispersive open optical systems
• Resonant state expansion applied to planar waveguides
• Resonant state expansion applied to planar open optical systems
• Exciton effective mass enhancement in coupled quantum wells in electric and magnetic fields

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