Non-generic bound states in the continuum in waveguides with lateral leakage channels.

For optical waveguides with a layered background which itself is a slab waveguide, a guided mode is a bound state in the continuum (BIC), if it coexists with slab modes propagating outwards in the lateral direction; i.e., there are lateral leakage channels. It is known that generic BICs in optical waveguides with lateral leakage channels are robust in the sense that they still exist if the waveguide is perturbed arbitrarily. However, the theory is not applicable to non-generic BICs which can be defined precisely. Near a BIC, the waveguide supports resonant and leaky modes with a complex frequency and a complex propagation constant, respectively. In this paper, we develop a perturbation theory to show that the resonant and leaky modes near a non-generic BIC have an ultra-high Q factor and ultra-low leakage loss, respectively. Recently, many authors studied merging-BICs in periodic structures through tuning structural parameters. It has been shown that resonant modes near a merging-BIC have an ultra-high Q factor. However, the existing studies on merging-BICs are concerned with specific examples and specific parameters. Moreover, we analyze an arbitrary structural perturbation given by δF(r) to waveguides supporting a non-generic BIC, where F(r) is the perturbation profile and δ is the amplitude, and show that the perturbed waveguide has two BICs for δ > 0 (or δ < 0) and no BIC for δ < 0 (or δ > 0). This implies that a non-generic BIC can be regarded as a merging-BIC (for almost any perturbation profile F) when δ is considered as a parameter. Our study indicates that non-generic BICs have interesting special properties that are useful in applications.

Spectral Galerkin mode-matching method for applications in photonics.

Many engineered photonic devices can be decomposed into parts where the material properties are independent of one or more spatial variables. Numerical mode-matching methods are widely used to simulate such photonic devices due to the efficiency gained by treating the separated variables analytically. Existing mode-matching methods based on piecewise polynomials are more accurate than those based on the global Fourier basis or low-order finite difference, finite-element schemes, but they may exhibit numerical instability when a large number of eigenmodes are used. To overcome this difficulty, we introduce the spectral Galerkin mode matching method (SGMM) based on a global piecewise-polynomial basis and a Galerkin method to solve the eigenmodes. It is shown that the numerical eigenmodes of SGMM preserve the pseudo-orthogonality of the analytical eigenmodes. This property leads to linear systems that are typically well-conditioned. Numerical examples indicate that SGMM is more stable than other mode matching methods, and gives reliable results even when a large number of eigenmodes are used.