Asymptotically circularly polarized bound states in the continuum

TL;DR

The paper introduces asymptotically circularly polarized bound states in the continuum (acp-BICs) in all-dielectric periodic structures and shows they occur as single-angle or all-angle types, with all-angle acp-BICs providing momentum-space CPSs of a single handedness and behaving as super-BICs. A physical criterion based on total reflection of circularly polarized waves is developed, and a perturbation theory is constructed to describe the emergence of true CPSs from acp-BICs under $C_2$ symmetric perturbations, complemented by a bifurcation framework. Numerical demonstrations in a PhC slab with elliptic holes and in TiO$_2$ rod gratings verify all-angle acp-BICs and the associated high-Q, chiral responses, including CPS loops and off-Gamma phenomena. The results offer a principled platform for singular and chiral optical responses in dielectric photonics and provide design rules for chiral lasing, emission and polarization-engineered devices.

Abstract

We study a class of bound states in the continuum (BICs) in all-dielectric periodic structures, near which resonant states approach ideal circularly polarized states (CPSs). We term these BICs {\em asymptotically circularly polarized BICs} ({\em acp}-BICs) and identify two types: single-angle and all-angle. Single-angle {\em acp}-BICs permit convergence to left- or right-handed CPSs only along a single momentum-space direction, whereas all-angle {\em acp}-BICs exhibit convergence to CPSs of a single handedness throughout the entire momentum space, rendering them exceptionally promising for chiral optical applications. We reveal that the existence of {\em acp}-BICs is underpinned by total reflection of circularly polarized waves. Moreover, all-angle {\em acp}-BICs qualify as super-BICs, with uniform nearby polarization being an intrinsic property. In addition, a bifurcation theory is developed to analyze the emergence of genuine CPSs from {\em acp}-BICs under $C_{2}$-symmetric structural perturbations. Our results suggest {\em acp}-BICs as a platform for singular and chiral optical responses in all-dielectric systems.

Figures (7)

• Figure 1: (a) Schematic of the PhC slab with a square lattice of elliptic air holes. (b) Top view of a unit cell. (c) and (d) Frequency and phase difference $\arg(\lambda_1/\lambda_2)$ of at-$\Gamma$ BICs as a function of slab height $h$. The green asterisk marks a single-angle acp-BIC. (e) Polarization pattern of resonant states near the acp-BIC marked by the green dot. Red and blue ellipses denote elliptic polarization with left- and right-handedness, while red and blue dashed lines indicate the angles $\theta_l$ and $\theta_r$, respectively. (f) Error $e(\delta) = ||\chi| - 1|$ quantifying deviation from circular polarization along $\theta=\theta_l,\,\theta_r$. (g) Degree of circular polarization $\chi$ as a function of $\theta$ for $\delta/2\pi = 0.01$. Red and blue forks mark the $\theta_l$ and $\theta_r$, respectively.
• Figure 2: All-angle acp-BICs with nearly CPSs along all directions. (a) and (b) Polarization patterns of resonant states near the all-angle acp-BICs marked by the green dots at $\varphi = 0.1$ and $0.2$, respectively. Blue ellipses denote elliptic polarization with right-handedness. (c) and (d) Degree of circular polarization $\chi$ as a function of $\theta$ at $\delta/2\pi = 0.01$. (e) and (f) High-order asymptotic scaling of $Q$ factor, $Q = \mathcal{O}(1/\delta^{6})$, at $\theta = \theta_s$.
• Figure 3: Bifurcation phenomena: CPSs emerging from the single-angle acp-BIC with $\varphi=0$ and the all-angle acp-BIC with $\varphi=0.2$. Note that all units are scaled by $10^{-2}$. (a) and (d) Trajectories of CPSs in $({\widetilde{\bm \kappa}},\eta)$ space with $\eta=(h-h_*)/L$. The two BICs are marked by green dots. A pair of off-$\Gamma$ BICs also emerge from the all-angle acp-BIC. (b) and (e) Projections of CPSs and BICs in momentum space, with arrows indicating the direction of increasing $h$. (c) and (f) Bifurcation diagrams for the pair of R-CPSs from the single-angle acp-BIC (c), and for one pair of R-CPSs together with the off-$\Gamma$ BICs from the all-angle acp-BIC (f).
• Figure A4: (a) Asymptotic behavior of $Q$ factor along $\theta_s$. (b) Polarization pattern of resonant states near the super-BIC.
• Figure A5: (a)--(c) Values of $a$, $b$, and $h$ versus $\varphi$ for all-angle acp-BICs. Blue forks mark the two all-angle acp-BICs discussed in the paper. (d) Polarization pattern of resonant states near the BIC at $\varphi=0$. (e) Higher-order asymptotic behavior of $Q$ factor along $\theta=0,\pi/4,\pi/2$.