  Bound states in the continuum (BICs) in photonic crystals represent the
unique solutions of wave equations possessing an infinite quality-factor. We
design a type of bilayer photonic crystal and study the influence of symmetry
and coupling between TE and TM polarizations on BICs. The BIC modes possess
$C_{3v}$ symmetry in the x-y plane while the mirror-flip symmetry in the
z-direction is broken, and they provide selective coupling into different
layers by varying frequency. The enhanced TE-TM coupling due to broken
mirror-flip symmetry in the z-direction gives rise to high-Q factor BIC states
with unique spatial characteristics. We show the emergence of such BIC states
even in the presence of coupling between the TE- and TM-like modes, which is
different from the existing single polarization BIC models. We propose to study
BICs in multilayer systems, and the results may be helpful in designing
photonic settings to observe and manipulate BICs with various symmetries and
polarizations for practical applications.
