Lorentz group in classical ray optics

Abstract

It has been almost 100 years since Einstein formulated his special theory of relativity in 1905. He showed that the basic space-time symmetry is dictated by the Lorentz group. It is shown that this group of Lorentz transformations is not only applicable to special relativity, but also constitutes the scientific language for optical sciences. It is noted that coherent and squeezed states of light are representations of the Lorentz group. The Lorentz group is also the basic underlying language for classical ray optics, including polarization optics, interferometers, the Poincaré sphere, one-lens optics, multi-lens optics, laser cavities, as well multilayer optics.

The Language of Einstein Spoken by Optical Instruments

“…Here also, the Lorentz group can play a fundamental role [10,11]. These latest developments in ray optics have been summarized in a recent review paper [12].…”

Vectorial Pauli algebraic approach in polarization optics. II. Interaction of light with the canonical polarization devices

“…(29), is kept (squared: e 2r ) in the expression of the output state of the Hermitian device, Eq. (32). It affects only the gain given by the device.…”

“…Its roots stand in the isomorphism between the group of transformations SL(2, C), used all along this paper (in a pure operatorial representation) and the Lorentz group O(3, 1) which describe the transformations in the special relativity. Well-known, this isomorphism was largely exploited in the last decade in the quasirelativistic formulation of the theory of polarization and, more generally, of the ''two-state'' (''two-beam'') systems [27,[32][33][34][35][36].…”

Time-varying polarization devices: vectorial Pauli algebraic approach

“…It has no component on the 1-axis of the sphere, i. e. it is situated all the time in the meridional plane (2,3). It oscillates on the sphere with amplitude 2Γ and an angular frequency Ω (Fig.…”

“…The polarization devices (and, more generally, anisotropic and dichroic media) 1 pertain to the very large class of "two-state" or "two-beam" physical systems, [2][3][4][5] the algebra of all these systems being the same. This algebra is that of the linear operators defined on a unitary space of dimension two over the field of complex numbers C 1 .…”