Origin of the Thomas rotation that arises in lossless multilayers

From the basic fact that the matrix that describes a lossless multilayer be longs to the group SU(1, 1), which is focally isomorphic to the (2 + 1)-dim ensional Lorentz group SO(2, 1), we present a natural identification of the parameters of the multilayer with those of a Lorentz transformation. We sh ow that the phase that appears when one is studying the reflection and tran smission of light on a compound multilayer is simply the relativistic Thoma s rotation. We propose a simple optical experiment to determine the angle o f this rotation. (C) 1999 Optical Society of America [S0740-3232(99)02410-2 ].