Complex coupled-mode theory for optical waveguides

Abstract

A coupled-mode formulation is described in which the radiation fields are represented in terms of discrete complex modes. The complex modes are obtained from a waveguide model facilitated by the combination of perfectly matched boundary (PML) and perfectly reflecting boundary (PRB) condition. By proper choice of the PML parameters, the guided modes of the structure remain unchanged, whereas the continuous radiation modes are discretized into orthogonal and normalizable complex quasi-leaky and PML modes. The complex coupled-mode formulation is identical to that for waveguides with loss and/or gain and can be solved by similar analytical and numerical techniques. By identifying the phase-matching conditions between the complex modes, the coupled mode formulation may be further simplified to yield analytical solutions. The complex coupled-mode theory is applied to Bragg grating in slab waveguides and validated by rigorous mode-matching method. It is for the first time that we can treat guided and radiation field in a unified and straightforward fashion without having to resort to cumbersome radiation modes. Highly accurate and insightful results are obtained with consideration of only the nearly phase-matched modes.

Asymptotic solutions of eigenmodes in slab waveguides terminated by perfectly matched layers

“…We study the analytic properties of the PML modes because they have important applications as described in [5][6][7][8][9][10]17]. Our results should also be useful for numerical implementation of the mode matching method.…”

“…It also found an important application in the mode matching (or eigenmode expansion) method [5][6][7][8]. More recently, it has been applied in a new version of the coupled mode theory [9] and a scattering matrix formalism for modeling photonic integrated circuits [10].…”

Photonic coupling between quadrature states of light in a homogeneous and optically linear dielectric medium

“…The current electromagnetic coupled-mode theory [9][10][11][12] links the optical power coupling between two single-mode waveguides to the perturbation of the permittivity of the optical waveguide cladding and the unperturbed evanescent modal fields that existed in the absence of the second waveguide. But the tail end of these fields no longer exists physically, having been disturbed by the introduction of the other waveguide.…”

High-performance localized surface plasmon resonance fiber sensor based on nano-metal-gear array

“…The primary purpose was to discretize the continuum of non-guided radiation modes on the radiation spectrum. Subsequently, discrete guided modes, discrete LSPR modes, and discrete radiation modes were integrated to form a complete, orthogonal, and normalizable eigenmode expansion base [40][41][42][43][44][45].…”