Periodic double-layer structures

The method of exponential matrices is used to develop a unified approach to the investigation of double-layer periodic systems in the general case of an arbitrary optical thickness of the layers. This approach gives the exact results for homogeneous layers and the WKB approximation is used for inhomogeneous layer systems. The exact expressions are derived for the amplitude reflection and transmission coefficients of TE and TM waves incident obliquely on a periodic structure consisting of homogeneous layers. The expressions contain only elementary functions and no Chebyshev polynomials. Similar expressions for the reflection and transmission coefficients are derived for a periodic system of inhomogeneous layers. An analysis is made for various optical thicknesses of the layers. It is shown that there is a series of hitherto unknown conditions under which a multilayer system does not reflect TE and TM waves.