Robust ultrahigh Q guided mode resonances in rectangular lattices

Mode-coupling is an important method for enhancing the quality (Q) factors of guided mode resonances (GMRs) in photonic crystal slabs. In square lattices, GMRs inherently exhibit orthogonality and degeneracy due to C₄ symmetry, with different orders of GMRs typically displaying distinct frequencies at the Γ point. Here, we propose a versatile and highly effective approach to achieve ultrahigh Q GMRs in rectangular lattices by exploiting spatial degrees of freedom. Specifically, two distinct types of GMRs, supported by orthogonally oriented propagation directions, can robustly couple to form a hybridized GMR with an exceptionally ultrahigh Q value. Our theoretical analysis indicates that the formation of such hybridized GMRs requires merely the design of an appropriate period, based on the dispersion relations of the guided modes, obviating the need for complex structural modifications. This research offers a practical and innovative method for realizing ultrahigh Q GMRs in photonic crystal slabs, thereby providing more possibilities for light-matter interactions, nonlinear optics, and optoelectronic device applications.