Fig. 1. (a) Geometry of the considered integrated structure. I, R, and T denote the incident, reflected, and transmitted TE-polarized guided modes, respectively. (b) 2D effective index model and corresponding refractive indices.

Fig. 2. (a) Reflectance and (b) transmittance of the TE-polarized mode versus the angle of incidence θ and ridge width w. Horizontal dashed lines show the cutoff angles θsup, θsub, θTM, and θTM,r. Field distributions in the structure at the points marked with asterisks in (a) are shown in Fig. 3. Dashed red curves in (b) show the dispersion of quasi-TM modes calculated using the approximate Eq. (4). (c) Reflectance and (d) transmittance of a plane wave upon refraction by a thin film (effective index model) are also shown.

Fig. 3. Electric field distributions in the structure at resonance conditions: (a) w=326  nm, θ=52.66°; (b) w=470  nm, θ=47.58°.

Fig. 4. (a) Magnified fragment of the rigorously calculated reflectance spectrum shown in Fig. 2(a). Red dashed curves show mode dispersion obtained from the model in Section 4 using Eq. (12). (w,θ) points shown with white circles and black crosses were obtained from Eqs. (18) and (16). White circles predict the BIC locations, whereas black crosses correspond to the “low-Q” resonances. (b) Model reflectance spectrum |R|2 calculated using Eq. (8).

Fig. 5. Rigorously calculated (a) excitation angle θ and (b) quality factor Q of the mode versus ridge width w. (c) Angular reflectance spectra of the structure at different ridge widths. Red line shows the spectrum of the structure supporting a BIC. Black points in (b) and (c) depict the BIC location.

Fig. 6. Plane wave diffraction by a slab supporting two cross-polarized waves coupled at the interfaces.