Light-cone-proximal quasi-BICs for chiral lasing at grazing angles

TL;DR

This paper introduces a novel mechanism for creating chiral quasi-bound states in the continuum at large oblique angles using dielectric metasurfaces, enabling directional chiral lasing and efficient off-normal photonic devices.

Contribution

It proposes a new method to realize light-cone-proximal chiral q-BICs at large angles by tuning lattice geometry, expanding applications in directional chiral lasing.

Findings

Achieved near-unity circular dichroism at angles >50°

Demonstrated robust control of chiral resonances via lattice tuning

Enabled fully circularly polarized emission at grazing angles

Abstract

Chiral quasi-bound states in the continuum (q-BICs) have recently emerged in metaphotonics as resonances that combine ultrahigh quality factors with near-unity circular polarization. However, these states are typically confined to the Gamma-point (normal incidence) due to their symmetry-protected origins. We propose a new mechanism for realizing light-cone-proximal chiral q-BICs at large oblique angles, enabled by the divergence of the radiative local density of states near the light cone. Using dielectric metasurfaces with a monoclinic lattice and broken in-plane mirror symmetry, we demonstrate that tuning the lattice angle allows for robust control of these resonances. The resulting chiral q-BICs exhibit near-unity circular dichroism in transmission and fully circularly polarized emission at angles exceeding 50 degrees from normal. This approach paves the way for directional chiral lasing at grazing angles and for photonic devices operating efficiently in off-normal geometries.

Equations

$$Q\propto \frac{1}{|A(k_y,k_z){|}^2\rho (k_y,k_z)},$$

$$Q(k_y)\propto \frac{k_z(k_y)}{|A(k_y){|}^2}.$$

Full text

Introduction.— Dielectric metaphotonics has emerged as a powerful platform for efficient nanoscale light manipulation kuznetsov2016optically ; tseng2020dielectric . Over the past decade, metastructures supporting optical resonances have enabled enhanced light-matter interactions koshelev2020dielectric ; feng2023dual ; ma2025quantum , driven by resonances with exceptionally high quality factors ($Q$-factors) huang2023ultrahigh . A key focus has been on photonic bound states in the continuum (BICs) hsu2016bound ; kang2023applications , which suppress radiative losses either through symmetry protection (symmetry-protected BICs) or destructive interference (accidental BICs) koshelev2023bound . These states are characterized by polarization vortices in the far field zhen2014topological . Their symmetry-broken counterparts, quasi-BICs (q-BICs), feature finite but high $Q$-factors koshelev2018asymmetric ; liu2022thermal , and arise naturally from fabrication imperfections kuhne2021fabrication . These modes have been widely employed in biosensing tittl2018imaging , nonlinear optics liu2019high ; zograf2022high ; gromyko2025enabling , and lasing  kodigala2017lasing ; huang2020ultrafast ; wu2020room ; wang2020generating ; hwang2021ultralow ; do2025room ; cui2025ultracompact .

Introducing chirality into metaphotonic structures offers an additional degree of freedom to control light-matter interactions hentschel2017chiral ; schaferling2017chiral ; koshelev2023nonlinear . In particular, generating circularly polarized and collimated emission is highly desirable, as most conventional light sources emit linearly polarized or unpolarized light with poor directionality curto2010unidirectional ; liu2025single . The recently proposed concept of chiral q-BICs addresses this challenge by combining high $Q$ resonances with strong circular polarization in the far field gorkunov2020metasurfaces ; overvig2021chiral ; chen2023observation ; kuhner2023unlocking ; toftul2024chiral ; sinev2025chirality . However, most demonstrations of chiral q-BIC lasing remain limited to normal-incidence emission, as the underlying q-BICs typically originate from symmetry-protected BICs at the $\Gamma$-point of the Brillouin zone zhang2022chiral ; maksimov2022circularly ; gromyko2024unidirectional ; deng2025chiral ; chen2025ultraviolet .

Chiral lasing at oblique angles with high directionality has received comparatively little attention, though it holds significant potential ha2018directional ; ha2022room . Existing approaches remain complex: synthetic valley engineering enables large-angle emission chen2023compact ; xing2025chiral , but cannot suppress undesired output at normal incidence. Brillouin zone folding can generate chirality points ($C$-points) jeong2025obtuse , yet hampers selective amplification due to uniformly high $Q$-factors across momentum space. A simpler, more robust route to directional chiral lasing remains largely unexplored.

In this Letter, we introduce a double symmetry-breaking strategy for realizing chiral q-BICs in resonant dielectric metasurfaces at large oblique angles approaching grazing incidence, as illustrated in Fig. 1(a). Unlike conventional approaches [Figs. 1(b,c)], we employ accidental BICs, which, upon breaking the lattice symmetry, split into q-BICs and $C$-points. Near the light cone, lattice deformation shifts the q-BICs and $C$-points differently in momentum space due to the rapid increase in the radiative density of states. This enables robust alignment of the $Q$-factor peak with a $C$-point at oblique incidence, forming what we term a “light-cone-proximal chiral q-BIC”. Full-wave simulations confirm that such resonances can generate highly directional, circularly polarized (CP) emission at angles exceeding $50^{\circ}$ from normal. This opens a practical route toward compact, efficient sources of circularly polarized light with engineered emission directionality.

Concept.— To demonstrate the concept of light-cone-proximal BICs, we consider a resonant metasurface comprising a high-index dielectric membrane with a monoclinic unit cell containing a larger circular and a smaller rectangular hole [Fig. 1(a)]. The fundamental optical mode exhibits two sharp $Q$-factor peaks in momentum space near the light cone, which coincide with $C$-points—locations where the far-field degree of circular polarization (DCP), defined as the third Stokes parameter $S_{3}=(I^{R}-I^{L})/(I^{R}+I^{L})$, reaches $\pm 1$, with $I^{R,L}$ denoting right- and left-circularly polarized radiation intensities. This alignment of $Q$-factor maxima and $C$-points results in highly directional, circularly polarized emission in two beams at angles exceeding $50^{\circ}$. Enhancement of emission along other directions is much less and can be neglected.

In contrast, conventional $C$-point designs liu2019circularly ; wang2020routing ; seo2021circularly ; tian2022optical do not align $Q$-factor maxima with $C$-points [Fig. 1(b)]; the $Q$-factor peak at the $\Gamma$-point corresponds to linearly polarized emission, while $C$-points occur at lower $Q$-factors within narrow angular ranges ($<10^{\circ}$). A more recent alternative, chiral q-BICs based on symmetry-protected BICs, produce circularly polarized emission confined to normal incidence, as the $Q$-factor rapidly drops away from the $\Gamma$-point [Fig. 1(c)].

Metasurface design & theoretical framework.— We consider a resonant metasurface composed of a high-index dielectric membrane (thickness $h=200$ nm, permittivity $\varepsilon=12.25$) suspended in air and patterned with a monoclinic unit cell [Fig. 2(a)]. The lattice is defined by vectors $\mathbf{a}=2p\sin(\theta/2)\hat{x}$ and $\mathbf{b}=p\sin(\theta/2)\hat{x}+p\cos(\theta/2)\hat{y}$, where $\theta$ is the lattice angle and $p=520$ nm. Each unit cell contains a circular hole of radius $R=140$ nm and a smaller square hole of width $w=40$ nm placed 200 nm away from the circular hole center. The impact of a substrate is discussed in SI supp .

We simulate the optical response using eigenmode and scattering calculations via the open-source RCWA package Inkstone alexysong_inkstone , which is well-suited for periodic structures near light cones and Rayleigh anomalies tikhodeev2002quasiguided ; gromyko2022resonant . Details of the numerical methods and comparisons with COMSOL finite-element simulations are provided in SI supp . The dispersion of the mode of interest is marked by an arrow in Fig. 2(b), and its electric field profile is shown in Fig. 2(c).

In the symmetric case ($w=0$), a hexagonal lattice ($\theta=60^{\circ}$) supports a symmetry-protected BIC with topological charge $-2$ at the $\Gamma$-point, which splits into two accidental BICs as $\theta$ increases yoda2020generation ; wang2022realizing . For a monoclinic lattice with $\theta=67^{\circ}$ and broken six-fold symmetry, the $Q$-factor map in momentum space [Fig. 2(d)] reveals two divergent peaks at $k_{x}=0$, $k_{y}p/2\pi\approx\pm 0.25$, each associated with a polarization vortex (topological charge $-1$) visible in the $S_{3}$ map.

To induce chirality and break the symmetry for the second time, we introduce the square hole ($w=40$ nm), which breaks both $zy$-mirror and two-fold rotational symmetry [Fig. 2(e)]. Each accidental BIC then splits into a pair of $C$-points zhen2014topological and a q-BIC, which is defined as the position of the $Q$-factor maximum. The q-BICs remain linearly polarized, while the $C$-points appear symmetrically around them, with their separation tunable via $w$. Further increasing $\theta$ shifts both features in momentum space [Fig. 2(f)]. At $\theta\approx 71.5^{\circ}$, each q-BIC merges with a $C$-point, forming a chiral q-BIC.

Fig. 2(g) illustrates the distinct behavior of q-BICs and $C$-points near the light cone. While $C$-points (blue/red) follow a trajectory similar to that of accidental BICs in the $w=0$ case (gray line), remaining unaffected by the light cone due to their topological origin lepeshov2023topological , q-BICs (black) are not topologically protected and deviate from linear trajectories as they approach the light cone.

This behavior is governed by the divergence of the radiative local density of states (LDOS). According to Fermi’s golden rule ochiai2001nearly , the radiative $Q$-factor for a mode at wavevector $k_{x}=0$, $k_{y}>0$ is given by:

[TABLE]

where $A$ is the mode coupling coefficient supp , and $\rho\propto\omega/(ck_{z})$ is the 1D vacuum LDOS that diverges near the light cone andreani2006photonic , where $k_{z}(k_{y})=\sqrt{\omega^{2}/c^{2}-k_{y}^{2}}$ and $\omega$ is the mode frequency. This gives:

[TABLE]

We validate Eq. (2) by calculating $A(k_{y})$ as the overlap integral between the incident plane wave and the normalized electric field. As shown in Fig. 2(h), $1/|A(k_{y})|^{2}$ (blue line) increases monotonically with $k_{y}$, while $k_{z}/|A(k_{y})|^{2}$ (red dashed line) exhibits a clear maximum at $k_{y}\approx 0.33\cdot 2\pi/p$ and decreases rapidly at larger $k_{y}$. This matches the $Q$-factor from the eigenmode simulations (black line) above the light cone, confirming the mechanism. After crossing the light cone, the mode becomes guided and exhibits an infinite $Q$-factor. We refer to the resulting chiral q-BICs, formed via merging of a q-BIC and a $C$-point near the light cone, as light-cone-proximal chiral q-BICs.

Emission control for chiral lasing.— We analyze the scattering and emission properties of the metasurface with $\theta=72^{\circ}$ and $w=40$ nm. The transmission spectra for right- and left-circularly polarized (RCP and LCP) light, $T^{R}$ and $T^{L}$, are shown in Fig. 3(a). As the resonance approaches the light cone, it becomes increasingly narrow and fully vanishes in $T^{R}$ at $k_{y}\approx 0.31\cdot 2\pi/p$, while remaining visible in $T^{L}$, indicating the presence of a $C$-point.

A similar asymmetry is observed in the emission enhancement spectra for RCP and LCP components in Fig. 3(b), calculated via the reciprocity principle sauvan2013theory ; lobanov2015controlling (see SI supp for details). The LCP emission dominates at resonance, confirming strong chiral selectivity. The corresponding circular dichroism (CD) in transmission, defined as $\textrm{CD}=(T^{R}-T^{L})/(T^{R}+T^{L})$, and the emission degree of circular polarization (DCP) are shown in Fig. 3(c). Notably, the emission DCP provides a clearer picture of the mode’s chirality, as it is less affected by non-resonant contributions.

To further quantify chirality, we evaluate the DCP at the emission enhancement peaks across $k_{y}$. As shown in Fig. 3(d), the peak at $\sim 60^{\circ}$ corresponds to near-unit chirality ($\textrm{DCP}\approx 1$), and all emission points with enhancement above 80% maintain $\textrm{DCP}>0.83$. The momentum-space DCP profile extracted from eigenmode simulations (solid black line) in the $s$–$p$ polarization basis closely matches the emission DCP [Fig. 3(e)]. While the $x$–$y$ basis (dashed line) is commonly used for mode characterization, it becomes inaccurate at large angles, necessitating the use of the $s$–$p$ basis. A slight angular shift is observed between the emission enhancement peak and the $Q$-factor maximum (blue line), attributed to variations in mode volume and near-field parameters.

Finally, we propose a chiral lasing concept based on light-cone-proximal chiral q-BICs. We explore the metasurface emission properties in 3D parameter space $(k_{x},k_{y},f=\omega/2\pi)$. Figs. 4(a,b) show the emission intensity enhancement and DCP at selected frequencies from 206 THz to 216 THz near the q-BIC resonance. Maximum emission occurs at $(k_{x},k_{y},f)=(0,0.31\cdot 2\pi/p,210~\text{THz})$ and rapidly decreases with variation in any parameter. This is confirmed by the plots of peak enhancement versus $k_{x}$ [Fig. 4(c)]. Assuming lasing occurs above an 80% enhancement threshold, these results highlight the metasurface as a promising platform for highly directional, circularly polarized emission at large angles.

Conclusion & Discussion.— We introduce a novel mechanism for realizing light-cone-proximal chiral q-BICs at large oblique angles, enabled by the divergence of the radiative local density of states near the light cone. By breaking in-plane mirror symmetries within a monoclinic lattice and tuning its lattice angle, we achieve robust chiral q-BICs in fully planar dielectric metasurfaces that are compatible with standard fabrication processes on low-index substrates.

A key advantage of this design is the tunability of the q-BICs’ position in momentum space via the lattice angle. This enables efficient control over the resonant emission direction across a broad range of polar angles ($0^{\circ}$ to $70^{\circ}$). At a specific lattice angle, the system exhibits near-unity circular dichroism and generates circularly polarized far-field emission, all while bypassing the normal-incidence constraint typically associated with conventional chiral q-BICs. These resonances combine high-$Q$ factors and excellent polarization control comparable with those observed at the $\Gamma$-point, yet are accessible at large emission angles. This makes light-cone-proximal chiral q-BICs highly promising for directional chiral lasing, potentially supporting dual beams propagating at approximately $\sim 60^{\circ}$ from the surface normal.

Moreover, the planar design avoids the need for out-of-plane symmetry elements, offering greater structural flexibility and ease of fabrication. Suitable platforms for experimental realization include silicon metasurfaces integrated with quantum emitters or multiple-quantum-well semiconductor metasurfaces.

Beyond dual-beam operation, our approach can be extended to support multiple light-cone-proximal q-BICs at distinct momentum points, enabling selective suppression or generation of multibeam emission with different polarizations. Overall, the concept of light-cone-proximal q-BICs opens new avenues for the development of compact, efficient devices that generate directional, circularly polarized light at large angles, with impactful applications in polarimetric sensing, integrated optical computing, nonlinear optics, and quantum photonics.