Optical bound state in the continuum in the one-dimensional photonic structures: transition into a resonant state

Introduction. Optical bound states in the continuum (BIC) are localized states with energy lying above the light line and having infinite lifetime. Any losses taking place in real systems result in transformation of the... [ view full abstract ]

Introduction.

Optical bound states in the continuum (BIC) are localized states with energy lying above the light line and having infinite lifetime. Any losses taking place in real systems result in transformation of the bound states into resonant states with finite lifetime. 

In this work we analyze transformation of BIC into a resonant state due to surface roughness and leakage into substrate in a grating based on silicon-on-insulator wafer.

Results and discussion.

Since the array is periodic in the x-direction, the eigenstates of the structure are characterized by the frequency f, the wave vector along the bars k_y and by the Bloch quasi-wave vector k_x restricted to the 1rst Brillouin zone. For the proposed design, BIC occurs when the k_y component of wave vector is zero.

We consider two cases: (i) 'ideal ', because it describes a periodic array in silica medium; (ii) 'practical ' with a silicon substrate and surrounding air. For 'ideal' case, the calculated dispersion curves of the three lower TE modes are shown in Fig. 1(d). One can see from Fig. 2(b,e) that the Q-factor of the TE₁ mode tends to infinity at Γ-point of k-space (normal incidence) and field become perfectly confined in grating.

For the 'practical ' case, the substrate weakly affects the position of the eigenmode, but results in leaky losses. It might seem that substrate should not destroy the at-Γ BIC since it is protected by in-plane symmetry which is not broken by the substrate. However, it is true only for the subwavelength regime when higher diffraction channels are closed. In our case, evanescent fields of the at-Γ BIC transform in the silicon substrate to propagating waves and BIC becomes a resonant state.

Another inherent feature of experimental samples is surface roughness, which leads to parasitic loss via scattering. Figure 3 shows how two concurrent loss mechanisms – scattering due to surface roughness and leakage into substrate – contribute to the suppression of the resonance lifetime and specify the condition when one of the mechanisms becomes dominant.

To confirm results experimentally, we fabricated a grating from SOI and performed angle-resolved reflectivity measurements.