Bound States in the Continuum and Unidirectional Guided Resonances Enabled by Competing Fourier Harmonics near the Fourth Stop Band

Abstract

Bound states in the continuum (BICs) and unidirectional guided resonances (UGRs) are singular radiative eigenstates in planar photonic lattices characterized by complete or directional suppression of out-of-plane radiation, respectively. Here, we show that, near the fourth stop band, the formation of BICs and UGRs can be understood within a unified two-pathway radiation model, in which the Bloch eigenmode radiates through indirect and direct pathways mediated by the first and second Fourier harmonics of the dielectric modulation, respectively. In vertically symmetric photonic lattices, when the two radiation components cancel each other out in both the upward and downward directions, BICs emerge. The model yields an analytical BIC condition that can be satisfied by tuning a single lattice parameter, the duty cycle $\rho$, and is confirmed by finite-element simulations. By contrast, in vertically asymmetric photonic lattices, the upward and downward radiation-cancellation conditions no longer coincide, allowing UGRs to arise when the cancellation condition is satisfied in only one direction. We introduce a zero-contrast grating (ZCG), in which the upper protruding grating region produces pronounced up-down asymmetry, and show that two off-$\Gamma$ UGRs emerge and can be merged at the $\Gamma$ point by tuning the lattice parameters.