Sliderule-like property of Wigner's little groups and cyclic S-matrices for multilayer optics

Abstract

It is noted that two-by-two S-matrices in multilayer optics can be represented by the Sp(2) group whose algebraic property is the same as the group of Lorentz transformations applicable to two space-like and one time-like dimensions. It is noted also that Wigner's little groups have a sliderule-like property which allows us to perform multiplications by additions. It is shown that these two mathematical properties lead to a cyclic representation of the S-matrix for multilayer optics, as in the case of ABCD matrices for laser cavities. It is therefore possible to write the N-layer S-matrix as a multiplication of the N single-layer S-matrices resulting in the same mathematical expression with one of the parameters multiplied by N. In addition, it is noted, as in the case of lens optics, multilayer optics can serve as an analogue computer for the contraction of Wigner's little groups for internal space-time symmetries of relativistic particles.

arXiv commentRevTex 13 pages, Secs. IV and V revised and expanded

References in corpus (3)

• A geometrical setting for the classification of multilayers
• Iwasawa Effects in Multi-layer Optics
• Lens optics as an optical computer for group contractions

Cited by in corpus (10)

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• Rotations associated with Lorentz boosts
• The language of Einstein spoken by optical instruments
• ABCD Matrices as Similarity Transformations of Wigner Matrices and Periodic Systems in Optics
• Lens optics and the continuity problems of the ABCD matrix
• Lorentz group theory and polarization of the light
• The stabilizer group of honeycomb lattices and its application to deformed monolayers
• Optical Activities as Computing Resources for Space-time Symmetries
• Factorizations for 3-rotations and polarization of the light in Mueller-Stokes an Jones formalisms
• Transitivity in the theory of the Lorentz group and the Stokes -- Mueller formalism in optics