Bound States in the Continuum in double layer structures

We have theoretically investigated the reflectivity spectrums of single- and double-layer photonic crystal slabs and the dielectric multilayer stack. It is shown that light can be perfectly confined in a single-layer photonic crystal slab at a given incident angle by changing the thickness, permittivity or hole radius of the structure. With a tunable double-layer photonic crystal slab, we demonstrate that the occurrence of tunable bound states in the continuum is dependent on the spacing between two slabs. Moreover, by analytically investigating the Drude lossless multilayer stack model, the spacing dependence of bound states in the continuum is characterized as the phase matching condition that illuminates these states can occur at any nonzero incident angles by adjusting the spacing.