Relationship between total reflection and Fabry-Perot bound states in the continuum

TL;DR

This work analyzes the existence of FP-BICs near total reflection in Fabry-Perot cavities formed by two parallel periodic dielectric layers. It introduces a one-evanescent-wave approximation to derive a simple FP-BIC condition and validates it through numerical experiments on arrays of circular and triangular cylinders. The results show FP-BICs near total reflection are favored when the periodic layer has reflection symmetry in the periodic direction or when the Bloch wavenumber is zero, while asymmetric structures with nonzero $eta_0^*$ often do not host near-total-reflection BICs. Overall, total reflection does not universally guarantee FP-BICs, and the findings clarify the roles of symmetry, wavenumber, and parametric tuning for designing high-Q photonic devices.

Abstract

Bound states in the continuum (BICs) have interesting properties and important applications in photonics. A particular class of BICs are found in Fabry-Perot (FP) cavities formed by two parallel periodic dielectric layers separated by a distance $h$. A periodic dielectric layer can totally reflect a plane incident wave with a particular frequency and a particular wavenumber. Existing FP-BICs are found when $h$ is close to the values deduced from a phase-matching condition related to the reflection coefficient, but they are obtained in FP-cavities where the periodic layers have a reflection symmetry in the periodic direction. In this paper, we further clarify the connection between total reflections and FP-BICs. Our numerical results indicate that if the wavenumber is zero or the periodic layers have a reflection symmetry in the periodic direction, FP-BICs can indeed be found near the parameters of total reflections. However, if the wavenumber is nonzero and the periodic layer is asymmetric (in the periodic direction), we are unable to find a FP-BIC (with a frequency and a wavenumber near those of a total reflection) by tuning $h$ or other structural parameters. Consequently, a total reflection does not always lead to a FP-BIC even when the parameters of the FP-cavity are tuned.

Figures (9)

• Figure 1: A Fabry-Perot cavity consisting of two periodic layers seperated by a distance $h$. The periodic layers are invariant in $x$, periodic in $y$ with period $L$, perpendicular to the $z$ axis, and have a thickness of $2d$. They are mirror reflections (with respect to the $z=0$ plane) of each other.
• Figure 2: Three periodic arrays of cylinders with period $L$ in the $y$ direction. Cross sections of the cylinders: (a) circular disks with radius $a$, (b) equilateral triangles with side length $L_t$ and a reflection symmetry in $y$, (c) equilateral triangles with side length $L_t$ and a reflection symmetry in $z$.
• Figure 3: Field patterns (real part of $u$) of BIC1 and BIC5 as in Table \ref{['circular1']}.
• Figure 4: Field patterns (real part of $u$) of BIC2 and BIC4 as in Table \ref{['triang1']}.
• Figure 5: Field pattern (real part of $u$) of BIC1 in Table \ref{['triang2']}.