Circularly Polarized States Spawning from Bound States in the Continuum

Bound states in the continuum in periodic photonic systems like photonic crystal slabs are proved to be accompanied by vortex polarization singularities on the photonic bands in the momentum space. The winding structures of polarization states not only widen the field of topological physics but also show great potential that such systems could be applied in polarization manipulating. In this Letter, we report the phenomenon that by in-plane inversion ($C_2$) symmetry breaking, pairs of circularly polarized states could spawn from the eliminated bound states in the continuum. Along with the appearance of the circularly polarized states as the two poles of the Poincaré sphere together with linearly polarized states covering the equator, full coverage on the Poincaré sphere could be realized. As an application, ellipticity modulation of linear polarization is demonstrated in the visible frequency range. This phenomenon provides a new degree of freedom in modulating polarization. The $C$ points could also find applications in light-matter interactions. Further studying and manipulating the reported polarization singularities may lead to novel phenomena and physics in radiation modulating and topological photonics.

Figure 1

Schematic view of how circularly polarized states ($C$ points) spawn from a bound state in the continuum when in-plane inversion ($C_2$) symmetry is broken. $C$ points and lines of linearly polarized states ($L$ lines) could be found near $\mathrm{\Gamma }$ point. The asymmetric field of the mode induces extra in-plane multipole moments. $L(R)CP$: left(right)-handed circular polarization; L(R)H: left(right)-handed.

Figure 2

(a)–(c) The TE-like band structures and polarization maps in the vicinity of the $\mathrm{\Gamma }$ point of structures with different values of $\alpha$. We focus on band ${\mathrm{TE}}_2$, which is marked with bold dark line on the band structure diagram. On the polarization maps, the polarization states are represented by ellipses of which the red (blue) color corresponds to left-handed (right-handed) states. The enlarged map of the enclosed area in (b) will be shown in (e). (d) A schematic view of the structure and the definition of the asymmetry parameter $\alpha$. (e) The circular loops of polarization states mapped from the Brillouin zone (BZ) to the Poincaré sphere. The radius of the loops are 0.0025, 0.005, 0.01, 0.02, and 0.04 from orange to green. The data points are sampled per 10 degrees on every loop in the BZ.

Figure 3

(a) The band structures along $\mathrm{\Gamma }\text{−}X$ and $\mathrm{\Gamma }\text{−}{X}^{\prime }$ near the $\mathrm{\Gamma }$ point. (b) Different configurations of polarization main axis near the $\mathrm{\Gamma }$ point on bands ${\mathrm{TE}}_2$ (bottom, “lemon”), ${\mathrm{TM}}_2$ (middle, “star”), ${\mathrm{TM}}_5$ (top, “monstar”) of the structure with $\alpha =1$. The different colors correspond to the colored bands in (a).

Figure 4

The measured angle-resolved transmittance spectra in the visible range under circularly polarized incidence. (a) The spectra of the $\alpha =1$ sample, $LCP$ incidence. Vanished regions are pointed out by arrows, implying the existence of $C$ points after breaking the $C_2$ symmetry. The colors correspond to the colored bands in Fig. 3. (b) The spectra of the $\alpha =1$ sample, $RCP$ incidence. (c) The spectra of the $\alpha =0$ sample, $LCP$ incidence. The vanished regions marked by white arrows are the BICs. (d) Enlarged plots of the vanished regions in (c). Note that the $C$ points on band ${\mathrm{TE}}_2$ are in the direction $\varphi \sim \pm 3°$ to $\mathrm{\Gamma }\text{−}X$; thus the spectra along this direction are plotted.

Figure 5

(a) Experimental observation of the coverage on Poincaré sphere presented in the form of transmittance maps along the band ${\mathrm{TE}}_2$ in the visible frequency range. (b) Simulated and measured ellipticity maps of transmitted polarization states under $p$ incidence on the same band as in (a).