Design of All-Dielectric 2D Periodic Structure Supporting Bound State in Continuum at a Prescribed Frequency

Bound states in the continuum (BIC) have recently gained significant attention within the research community. In this work, we propose a design procedure to achieve a structure that supports a BIC at a specified frequency, eliminating the need for optimization-based or heuristic approaches. The procedure leverages closed-form formulas for the transfer matrix, which relates the Bloch-Floquet modes on both sides of an all-dielectric, two-dimensional periodic structure. The proposed methodology is demonstrated through an example that generates a BIC at 10GHz, with its performance validated by full-wave simulations, and whose geometry can be conveniently scaled to operate at other desired frequencies.