Real transmission and reflection zeros of periodic structures with a bound state in the continuum

For lossless periodic structures with a proper symmetry, the transmission and reflection spectra often have peaks dips that are truly $100\%$ $0\%$, respectively. The full zero typically appear near resonant frequencies, they robust respect to structural perturbations preserve required symmetry. However, current theories on existence of incomplete difficult use. bound state in continuum (BIC), we present new theory real zeros correspond spectra. Our is relatively simple, complete, easy Numerical examples presented validate theory.