Fabry-Perot bound states in the continuum in an anisotropic photonic crystal

An anisotropic photonic crystal containing two anisotropic defect layers is considered. It is demonstrated that the system can support a Fabry-Perot bound state in the continuum (FP-BIC). A fully analytic solution of the scattering problem as well as a condition for FP-BIC have been derived in the framework of the temporal coupled-mode theory.

Figure 1

(a) Model of an anisotropic PhC with two defects. (b) Reflectance of the PhC for $y$-waves (blue) and $x$-waves (red) calculated by the Berreman method. The parameters are $n_o=1$, $d_o=0.25\mu \text{m}$, $n_e=2$, $d_e=0.125\mu \text{m}$, $N=8$, $m=20$, ${\varphi }_1={\varphi }_2=0$ (dashed line), and ${\varphi }_1=2.4\pi /180$, ${\varphi }_2=2.5\pi /180$ (solid line). (c) Distributions of the local field intensity $|{\mathit{E}}_{\mathit{x},\mathit{y}}{|}^2/{\left|{\mathit{E}}_0\right|}^2$ at a frequency of $\omega /2\pi =1.00045\mu {\text{m}}^{-1}$ corresponding to the resonance in (b). (d) TCMT model of an anisotropic PhC with two defects.

Figure 2

Reflectance spectra obtained using (a)–(c) the Berreman transfer-matrix method and (d)–(f) the TCMT model at $N=3$ (a),(d); $N=4$ (b),(e); and $N=7$ (c),(f). The other parameters are the same as in the caption to Fig. 1.

Figure 3

Reflectance spectra obtained using (a)–(c) the Berreman transfer-matrix method and (d)–(f) the TCMT model at $N=8$ (a),(d); $N=10$ (b),(e); and $N=12$ (c),(f). The other parameters are the same as in the caption to Fig. 1. The blue dashed line in (a) at an angle of ${\varphi }_1=2.4\pi /180$ corresponds to the spectrum in Fig. 1. The red lines in (a)–(c) correspond to eigenfrequencies ${\omega }_1$ (dashed line) and ${\omega }_2$ (solid line) obtained from Eq. (36). The red cross corresponds to the FP-BIC frequency position obtained from Eqs. (43) and (44).

Figure 4

Reflectance spectra obtained within the TCMT model at $N$ = 24 (a), 25 (b), 26 (c), 27 (d), 28 (e), and 32 (f). The remaining parameters are the same as those in the caption to Fig. 1. Red crosses correspond to FP-BIC frequency positions obtained from Eqs. (43) and Eq. (44).