Understanding multilayers from a geometrical viewpoint.

  title={Understanding multilayers from a geometrical viewpoint.},
  author={Teresa Yonte and Juan J. Monz{\'o}n and Luis L. S{\'a}nchez-Soto and Jos{\'e} F. Cari{\~n}ena and Carlos L{\'o}pez-Lacasta},
  journal={Journal of the Optical Society of America. A, Optics, image science, and vision},
  volume={19 3},
We reelaborate on the basic properties of lossless multilayers. We show that the transfer matrices for these multilayers have essentially the same algebraic properties as the Lorentz group SO(2, 1) in a (2 + 1)-dimensional space-time as well as the group SL(2, R) underlying the structure of the ABCD law in geometrical optics. By resorting to the Iwasawa decomposition, we represent the action of any multilayer as the product of three matrices of simple interpretation. This group-theoretical… 

Spin transport and exchange coupling in ballistic magnetic multilayers

In this work we study a set of related problems in the theory of ballistic spin transport. We draw special attention to the phenomenon of exchange coupling, which is interesting both from the

Non-Euclidean symmetries of first-order optical systems.

The physical meaning of these geometrical operations for basic elements of first-order optical systems, such as free propagation and thin lenses, are elucidated and link them with physical parameters of the system.

Lempel-Ziv Complexity of Photonic Quasicrystals

The properties of one-dimensional photonic quasicrystals ultimately rely on their nontrivial long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be

Lempel-Ziv Complexity of Photonic Quasicrystals

The properties of one-dimensional photonic quasicrystals ultimately rely on their nontrivial long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be

A modeling approach to feature extraction for stacks of dielectric slabs with random permittivity

Stacks of dielectric slabs serve as models of a large variety of engineering structures such as Bragg gratings and Vertical-Cavity Surface-Emitting lasers (VCSELs). Depending on the application,

Invisibility and PT Symmetry: A Simple Geometrical Viewpoint

We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In

A Top-Down Account of Linear Canonical Transforms ?

We contend that what are called Linear Canonical Transforms (LCTs) should be seen as a part of the theory of unitary irreducible representations of the '2+1' Lorentz group. The integral kernel

Geometrical interpretation of optical absorption

We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 +

su(1,1) intelligent states

We construct all the intelligent states of the non-compact generators of su(1, 1) for every positive discrete representation of this Lie algebra, and discuss some of the properties of these states.



Iwasawa decomposition in first-order optics: universal treatment of shape-invariant propagation for coherent and partially coherent beams.

We present the Iwasawa decomposition theorem for the group ${\rm Sp}(2, R)$ in a form particularly suited to first-order optics, and we exploit it to develop a uniform description of the

Theory of reflection

This book deals with the reflection of electromagnetic and particle waves by interfaces. The interfaces can be sharp or diffuse. The topics of the book contain absorption, inverse problems,

Factorization of the transfer matrix for symmetrical optical systems

In the paraxial approximation a symmetrical optical system may be represented by a 2 × 2 matrix. It has been the custom to describe each optical element by a transfer matrix representing propagation

Time-domain ABCD matrix formalism for laser mode-locking and optical pulse transmission

ABCD matrix formalism in the time domain has been newly developed on the basis of laser beam and resonator analyses which were developed under a Gaussian paraxial approximation. We derive matrix

Origin of the Thomas rotation that arises in lossless multilayers

From the basic fact that the matrix that describes a lossless multilayer belongs to the group SU(1, 1), which is locally isomorphic to the (2+1)-dimensional Lorentz group SO(2, 1), we present a

A simple optical demonstration of geometric phases from multilayer stacks: The Wigner angle as an anholonomy

Abstract We re-elaborate on the theme of the Wigner rotation as an anholonomy or geometric phase, and show that this geometric phase can be easily observed in multilayers. We compute the value of the

Fully relativisticlike formulation of multilayer optics

It is shown that the matrix describing a general (transparent or absorbing) multilayer is an element of the group SL(2, C), which is locally isomorphic to the (3+1)-dimensional restricted Lorentz