Fully relativisticlike formulation of multilayer optics

Monzón, J. J.; Sánchez-Soto, L. L.

doi:10.1364/josaa.16.002013

Cited by 42 publications

(28 citation statements)

References 10 publications

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“…Indeed, the group Sp(2) plays the central role in both quantum and classical optics, including multilayer optics [2]. It consists of two-by-two real matrices whose determinant is one.…”

Section: Introductionmentioning

confidence: 99%

Slide-rule-like property of Wigner’s little groups and cyclicSmatrices for multilayer optics

Georgieva

Kim

2003

Phys. Rev. E

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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. 42.25.Gy, 42.15.Dp, 02.20.Rt, 11.30.Cp

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“…Indeed, the group Sp(2) plays the central role in both quantum and classical optics, including multilayer optics [2]. It consists of two-by-two real matrices whose determinant is one.…”

Section: Introductionmentioning

confidence: 99%

Slide-rule-like property of Wigner’s little groups and cyclicSmatrices for multilayer optics

Georgieva

Kim

2003

Phys. Rev. E

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“…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].…”

Section: Action Of a Hermitian Operator On The Density Operator Of A mentioning

confidence: 99%

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

Tudor

2010

Optik

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“…Note that we have det M as = +1, which is equivalent to |R as | 2 + |T as | 2 = 1, and then the set of lossless multilayer matrices reduces to the group SU(1,1), whose elements depend on three independent real parameters [14,15]. The identity matrix corresponds to T as = 1 and R as = 0, so it represents an antireflection system without transmission phase shift.…”

Section: The Origin Of the Bandgap In Infinite Periodic Structuresmentioning

confidence: 99%

Characterizing the reflectance of periodic layered media

Monzón

Yonte

Sánchez-Soto

2003

Optics Communications

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It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor in an infinite periodic structure. We argue that such a procedure may become meaningless when dealing with structures with not very many periods. We propose an alternative approach based on a factorization of the multilayer transfer matrix in terms of three fundamental matrices of simple interpretation. We show that the trace of the transfer matrix sorts the periodic structures into three types with properties closely related to one (and only one) of the three fundamental matrices. We present the reflectance associated to each one of these types, which can be considered as universal features of the reflection in these media.Comment: 4 pages. 1 eps figure. To be published in Optics Communication

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Fully relativisticlike formulation of multilayer optics

Cited by 42 publications

References 10 publications

Slide-rule-like property of Wigner’s little groups and cyclicSmatrices for multilayer optics

Slide-rule-like property of Wigner’s little groups and cyclicSmatrices for multilayer optics

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

Characterizing the reflectance of periodic layered media

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