A very efficient solver for bound states in the continuum based on total internal reflection of Bloch waves

(a) Total internal reflection of two Bloch waves at the interface of the photonic crystal. (b) Guiding condition: as a Bloch wave is reflected twice, it duplicates itself. (c) Conventional and generalized conditions for the waveguide mode. Here, the generalized waveguide mode is precisely the BIC. Credit: Science China Press

Continuum bound states (BIC) are a special class of resonant states. Although they have the same momentum and energy as free space propagation modes, they are not coupled to them and therefore have infinite lifetimes. This unique property has generated great research interest. BICs have application prospects in many fields, including lasers, sensors, filters and many more. However, until now, there has been no efficient algorithm for BICs, and in previous studies, researchers have generally focused on region BICs with a single radiation channel. There are few studies of BICs in the high frequency region with multiple radiation channels.

Recently, the research group of Professor Dezhuan Han of Chongqing University and the research group of Professor Jian Zi of Fudan University, using the physical mechanism of total internal reflection of Bloch waves, developed an algorithm BIC for the photonic crystal slab.

When total internal reflection of multiple Bloch waves occurs at the interface of the photonic crystal slab, the phase shift of each Bloch wave is used to establish a database in wave vector-frequency space. By considering the guiding condition, BICs can be located quickly and accurately.

Compared to other algorithms, this algorithm has the following two distinct advantages: (1) It can search for BICs with very high accuracy in a large parameter space (for example, when the phase shift database is established, it takes only ~10ms second to find all BICs for a specific value of slab thickness), greatly reducing BIC search time. (2) It can identify BICs in the high-frequency region with multiple radiation channels, thus expanding the application range of BICs. When there are many (≥3) radiation channels in free space, this can also quickly optimize the quality factor of quasi-BICs.

A very efficient solver for bound states in the continuum based on total internal reflection of Bloch waves

(a) Schematic view of the radiation channels of a multichannel guided resonance. (bd) Evolution of quality factors and polarization maps for different thicknesses. Credit: Science China Press

The researchers obtained the analytical formula of the total internal reflection of Bloch waves under the weak contrast boundary condition, and thus obtained the boundary behavior of BICs. For multi-channel BICs, their unique topological properties are revealed – they arise from the accidental coincidence of topological charges in different radiation channels in momentum space. It should be mentioned that for conventional BICs below the diffraction limit, splitting an integer topological charge into two half-integer charges requires breaking the spatial symmetry of the structure; however, for multi-channel BICs beyond the diffraction limit, even without spatial symmetry breaking, this splitting can still occur.

The research has been published in National Science Review and the BIC algorithm developed in this work is published on Github for use in the design and application of photonic crystal tiles by other researchers.

Generation and Application of High-Q Resonance in All-Dielectric Metasurfaces

More information:
Peng Hu et al, Bound states in the continuum based on total internal reflection of Bloch waves, National Science Review (2022). DOI: 10.1093/nsr/nwac043

Github: github.com/PMRG-LE707/bicks

Provided by Science China Press

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