Abstract
On a periodic dielectric slab (waveguide), there are a variety of modes such as resonant, guided, improper and leaky modes. A special class of guided modes that may exist inside a continuum of radiation modes is the so-called bound states in the continuum (BICs). In this paper, we show the existence of complex modes on open dielectric periodic structures. A complex mode is a solution with real frequency and complex Bloch wavenumber, confined around a lossless waveguide and it does not carry power along the propagation direction. For a number of examples, we calculate complex modes, and determine their starting points related to regular guided modes. In addition, using theoretical and numerical studies, we establish links between the complex modes and BICs.
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