Iwasawa effects in multilayer optics

There are many two-by-two matrices in layer optics. It is shown that they can be formulated in terms of a three-parameter group whose algebraic property is the same as the group of Lorentz transformations in a space with two spacelike and one timelike dimensions, or the $\mathrm{Sp}\left(2\right)\mathrm{}$ group which is a standard theoretical tool in optics. Among the interesting mathematical properties of this group, the Iwasawa decomposition drastically simplifies the matrix algebra under certain conditions, and leads to a concise expression for the S matrix for transmitted and reflected waves. It is shown that the Iwasawa effect can be observed in multilayer optics, and a sample calculation of the S matrix is given.