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Bound states in the continuum (BICs) theoretically have the ability toconfine electromagnetic waves in limited regions with infinite radiativequality ($Q$) factors. However, in practical experiments, resonances can onlyexhibit finite $Q$ factors due to unwanted scattering losses caused byfabrication imperfections. Recently, it has been shown that ultrahigh-$Q$guided-mode resonances (GMRs), which are robust to fabrication imperfections,can be realized by merging multiple BICs in momentum space. In this study, weanalytically and numerically investigate the merging and band transition ofaccidental BICs in planar photonic lattices. Accidental BICs can merge at theedges of the second stop band, either with or without a symmetry-protected BIC.We show that as the thickness of the photonic lattice gradually increases, themerged state of BICs transitions from the upper to the lower band edge. Usingcoupled-mode analysis, we present the analytical merging thickness at whichmultiple accidental BICs merge at the second-order $\Gamma$ point. Ourcoupled-mode analysis could be beneficial for achieving ultrahigh-$Q$ GMRs invarious photonic lattices composed of materials with different dielectricconstants.

Merging and band transition of bound states in the continuum in leaky-mode photonic lattices