Systematic Design of Antireflection Coating for Semi-infinite One-dimensional Photonic Crystals Using Bloch Wave Expansion

We present a systematic method for designing a perfect antireflection coating (ARC) for a semi-infinite one-dimensional (1D) photonic crystal (PC) with an arbitrary unit cell. We use Bloch wave expansion and time reversal symmetry, which leads exactly to analytic formulas of structural parameters for the ARC and renormalized Fresnel coefficients of the PC. Surface immittance (admittance and impedance) matching plays an essential role in designing the ARC of 1D PC's, which is shown together with a practical example.