True Bound States in the Continuum in Compact All-Dielectric Structures

Bound states in the continuum (BICs), known for their theoretically infinite quality (Q) factors and strong field localization, hold great promise for high-performance photonic devices. However, conventional true BICs typically rely on infinitely periodic structures, and their realization in finite-sized compact structures faces fundamental challenges, which severely limits device miniaturization and integration. In this work, a compact BIC design method based on optical conformal mapping is proposed, where a conventionally infinite periodic structure extended along one direction is mapped into a finite-sized annular structure. This symmetry transition, i.e., from translational to rotational, enables structural miniaturization while fully preserving the eigenvalues and BIC type of the original system. These transformations require only the adjustment of background permittivity and source distribution, without introducing extreme material parameters. As a concrete example, we show through theoretical and numerical analysis that a transformed compact all-dielectric structure, consisting of a double annular dielectric grating embedded in a gradient-index dielectric background, can support true BICs in a finite region. This work provides a simple and general strategy for achieving true BICs in compact all-dielectric structures, paving the way toward miniaturized high-Q photonic devices.