Iwasawa Effects in Multi-layer Optics

Abstract

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 space-like and one time-like dimensions, or the $Sp(2)$ 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 rays. It is shown that the Iwasawa effect can be observed in multi-layer optics, and a sample calculation of the S-matrix is given.

RevTex 10 pages including 1 psfig

References in corpus (3)

• Wigner Rotations and Iwasawa Decompositions in Polarization Optics
• Interferometers and Decoherence Matrices
• Binary Representations of ABCD Matrices

Cited by in corpus (9)

• Photon generation from vacuum in nondegenerate cavities with regular and random periodic displacements of boundaries
• Sliderule-like property of Wigner's little groups and cyclic S-matrices for multilayer optics
• Lens optics as an optical computer for group contractions
• Rotations associated with Lorentz boosts
• The language of Einstein spoken by optical instruments
• Biperiodic superlattices and the transparent state
• Wigner's Space-time Symmetries based on the Two-by-two Matrices of the Damped Harmonic Oscillators and the Poincaré Sphere
• Factorizations for 3-rotations and polarization of the light in Mueller-Stokes an Jones formalisms
• Internal Space-time Symmetries of Particles derivable from Periodic Systems in Optics