Hybrid Bound States in the Continuum beyond Diffraction Limit

Abstract

Bound states in the continuum (BICs) have greatly impacted our ability to manipulate light-matter interaction at the nanoscale. However, in periodic structures, BICs are typically realized below the diffraction limit, thus leaving a broad spectral domains largely unexplored. Here, we introduce a new type of at-$Γ$ BICs of photonic crystal (PhC) slabs supporting higher diffraction orders, which we call hybrid BICs (h-BICs), whereby symmetry protection and parameter tuning are utilized to suppress light emission in the zeroth- and higher-diffraction orders, respectively. By tuning certain structural parameters of the PhC slab, we fully characterize the dynamics of the topological structure of these h-BICs, including the generation, merging, splitting, and annihilation of circularly polarized states. We further show that the relative amount of light radiated in the first-order diffraction channels can be effectively controlled by simply breaking the $C_{4v}$ symmetry of the PhC slab. Our findings reveal a versatile approach to realize new types of BICs above the diffraction limit, and could potentially inspire new efforts towards development of novel photonic nanodevices, such as multi vortex-beam generators, frequency converters, and lasers.

Figures (5)

• Figure 1: Concept of h-BICs. (a) Left: schematics of a PhC slab supporting zeroth- and first-diffraction orders and formation mechanism of h-BICs. $C_L$ ($C_R$) are left- (right-) handed $C$ points with the same topological charge. SP means symmetry protection. Right: reciprocal lattice space whereby the solid (dashed) circle has radius of $\omega_{I}/c$ ($\omega_{II}/c$). h-BICs can exist for $\omega>\omega_{I}$. (b) Evolution of dispersion map of $Q$ and polarization singularities upon increase of $r$ or $d$.
• Figure 2: Characterization of h-BICs. (a) Band structure of TE-like modes. The gray region, below the light line (red dashed line), contains guided modes. Zeroth-, first-, and second-diffraction orders exist in the regions $\mathrm{I+II+III}$, $\mathrm{II+III}$, and III, respectively. Blue and green curves indicate TE-like bands and the h-BIC, respectively. (b) Dispersion map of $Q$-factor of at-$\Gamma$ h-BIC. (c) Evolution of $Q$-factor (left panel) and location of polarization singularities in the (1,0) order (right panel) vs. $r$, calculated for $\tilde{d}=0.5309$. The curves in the right panel correspond to the shaded region in the left one. (d) The same as in (c), but vs. $d$ at $\tilde{r}=0.2368$.
• Figure 3: Fourier modal analysis and far-field polarization. (a) Energy distribution among diffraction channels, determined for different $\tilde{r}$ at fixed $\tilde{d}=0.5309$. (b), (c) Polarization maps computed for (1,0) and (0,0) diffraction channels, respectively. Arrows denote the movement direction of $C$ points as $\tilde{r}$ increases. Red (blue) indicates left (right) handedness.
• Figure 4: $\mathbf{k}_{\parallel}$-space trajectories of half-charge $C$ points for (1,0) channel, as $\tilde{r}$ is varied at $\tilde{d}=0.5309$. Red (blue) dots denote $C$ points with $-1/2$ charge and left (right) handedness. Orange (turquoise) dots denote $C$ points with $+1/2$ charge and left (right) handedness. Right panels show, from bottom to top, maps of far-field polarization angle determined for $\tilde{r}$ = [list-final-separator=, and ]0.2327;0.2368;0.2407.
• Figure 5: Engineering the radiation pattern. (a) $C_{4v}$ symmetry breaking by tuning hole radius. (b), (c), (d) Dependence of $I_{0,1}$, $I_{1,0}/I_{0,1}$, and $Q$-factor, respectively, on $\Delta r_x$ and $\Delta r_y$. The orange dot corresponds to $\Delta r_x=4\nm$ and $\Delta r_y=-6nm$. (e), (f) $\mathbf{k}_{\parallel}$-space maps of polarization angle and intensity $I$ for (0,1) (left) and (1,0) (right) channels, respectively. The orange lines mark $\bar{k}_y=0$.