1,116 research outputs found
Simple trace criterion for classification of multilayers
The action of any lossless multilayer is described by a transfer matrix that
can be factorized in terms of three basic matrices. We introduce a simple trace
criterion that classifies multilayers in three classes with properties closely
related with one (and only one) of these three basic matrices.Comment: To be published in Optics Letter
Hyperbolic reflections as fundamental building blocks for multilayer optics
We reelaborate on the basic properties of lossless multilayers by using
bilinear transformations. We study some interesting properties of the
multilayer transfer function in the unit disk, showing that hyperbolic geometry
turns out to be an essential tool for understanding multilayer action. We use a
simple trace criterion to classify multilayers into three classes that
represent rotations, translations, or parallel displacements. Moreover, we show
that these three actions can be decomposed as a product of two reflections in
hyperbolic lines. Therefore, we conclude that hyperbolic reflections can be
considered as the basic pieces for a deeper understanding of multilayer optics.Comment: 7 pages, 7 figures, accepted for publication in J. Opt. Soc. Am.
General unit-disk representation for periodic multilayers
We suggest a geometrical framework to discuss periodic layered structures in
the unit disk. The band gaps appear when the point representing the system
approaches the unit circle. We show that the trace of the matrix describing the
basic period allows for a classification in three families of orbits with quite
different properties. The laws of convergence of the iterates to the unit
circle can be then considered as universal features of the reflection.Comment: 3 pages, 2 eps-figures. To be published in Optics Letter
A geometrical setting for the classification of multilayers
We elaborate on the consequences of the factorization of the transfer matrix
of any lossless multilayer in terms of three basic matrices of simple
interpretation. By considering the bilinear transformation that this transfer
matrix induces in the complex plane, we introduce the concept of multilayer
transfer function and study its properties in the unit disk. In this
geometrical setting, our factorization translates into three actions that can
be viewed as the basic pieces for understanding the multilayer behavior.
Additionally, we introduce a simple trace criterion that allows us to classify
multilayers in three types with properties closely related to one (and only
one) of these three basic matrices. We apply this approach to analyze some
practical examples that are representative of these types of matrices.Comment: 8 pages, 5 figures. To be published in J. Opt. Soc. Am.
Fresnel coefficients as hyperbolic rotations
We describe the action of a plane interface between two semi-infinite media
in terms of a transfer matrix. We find a remarkably simple factorization of
this matrix, which enables us to express the Fresnel coefficients as a
hyperbolic rotation.Comment: 6 pages, 3 figure
Constructing Fresnel reflection coefficients by ruler and compass
A simple and intuitive geometical method to analyze Fresnel formulas is
presented. It applies to transparent media and is valid for perpendicular and
parallel polarizations. The approach gives a graphical characterization
particularly simple of the critical and Brewster angles. It also provides an
interpretation of the relation between the reflection coefficients for both
basic polarizations as a symmetry in the plane
Histología del telson del escorpión Buthus occitanus Amoreux (!789) del primer estadio (Scorpiones, Buthidae)
Iwasawa Effects in Multi-layer Optics
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 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.Comment: RevTex 10 pages including 1 psfi
Rotations associated with Lorentz boosts
It is possible to associate two angles with two successive non-collinear
Lorentz boosts. If one boost is applied after the initial boost, the result is
the final boost preceded by a rotation called the Wigner rotation. The other
rotation is associated with Wigner's O(3)-like little group. These two angles
are shown to be different. However, it is shown that the sum of these two
rotation angles is equal to the angle between the initial and final boosts.
This relation is studied for both low-speed and high-speed limits. Furthermore,
it is noted that the two-by-two matrices which are under the responsibility of
other branches of physics can be interpreted in terms of the transformations of
the Lorentz group, or vice versa. Classical ray optics is mentioned as a case
in point.Comment: LaTeX, 16 Pages, 4 epsfigure
Optimizing omnidirectional reflection by multilayer mirrors
Periodic layered media can reflect strongly for all incident angles and
polarizations in a given frequency range. Quarter-wave stacks at normal
incidence are commonplace in the design of such omnidirectional reflectors. We
discuss alternative design criteria to optimize these systems.Comment: 9 pages, 6 figures. To be published in J. Opt. A: Pure and Applied
Optic
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