Indirect link between resonant and guided modes on uniform and periodic slabs

Abstract

A uniform or periodic dielectric slab can serve as an optical waveguide for which guided modes are important, and it can also be used as a diffraction structure for which resonant modes with complex frequencies are relevant. Guided modes are normally studied below the lightline where they exist continuously and emerge from points on the lightline, but isolated guided modes may exist above the lightline and they are the so-called bound states in the continuum. Resonant modes are usually studied above the lightline (defined using the real part of the complex frequency), but they are not connected to the guided modes on the lightline. In this work, through analytic and numerical calculations for uniform and periodic slabs, we establish an indirect link between the resonant and guided modes. It is shown that as the (Bloch) wavenumber is increased, a resonant mode continues its existence below the lightline, until it reaches its end at an Exceptional Point (EP) where a pair of improper modes emerge, and one branch of improper modes eventually approaches the lightline at the starting point of a guided mode. Leaky modes with a real frequency and a complex (Bloch) wavenumber (propagation constant) are also related to the improper modes. They emerge at EPs in eigenvalue formulations where the frequency is regarded as a parameter. Our study is based on a non-Hermitian eigenvalue formulation that includes resonant, improper and leaky modes, and provides a complete picture for different kinds of eigenmodes on uniform and periodic slabs.

References in corpus (3)

• The physics of exceptional points
• Loss-induced suppression and revival of lasing
• Light stops at exceptional points

Cited by in corpus (8)

• Abundance of cavity-free polaritonic states in resonant materials and nanostructures
• Bound states with complex frequencies near the continuum on lossy periodic structures
• Approximating transmission and reflection spectra near isolated nondegenerate resonances
• Resonant field enhancement in lossy periodic structures supporting complex bound states in the continuum
• Real transmission and reflection zeros of periodic structures with a bound state in the continuum
• Complex modes in an open lossless periodic waveguide
• Computing diffraction anomalies as nonlinear eigenvalue problems
• Frequency perturbation theory of bound states in the continuum in a periodic waveguide