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J. J. Monzon

Publications and source records attributed to J. J. Monzon.

16 recordsLinked to original sources
arXiv2022

Anticaustics in a Fabry-Perot interferometer

We address the response of a Fabry-Perot interferometer to a monochromatic point source. We calculate the anticaustics (that is, the virtual wavefronts of null path difference) resulting from the successive internal reflections occurring in the system. They turn to be a family of ellipsoids (or hyperboloids) of revolution, which allows us to reinterpret the operation of the Fabry-Perot from a geometrical point of view that facilitates comparison with other apparently disparate arrangements, such as Young's double slit.

physics.optics↗
arXiv2012

The transfer matrix: a geometrical perspective

We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical resonators. In all these cases, the transfer matrix has the same algebraic properties as the Lorentz group in a (2+1)-dimensional spacetime, as well as the group of unimodular real matrices underlying the structure of the abcd law, which explains many subtle details. We elaborate on the geometrical interpretation of the transfer-matrix action as a mapping on the unit disk and apply a simple trace criterion to classify the systems into three types with very different geometrical and physical properties. This approach is applied to some practical examples and, in particular, an alternative framework to deal with periodic (and quasiperiodic) systems is proposed.

cond-mat.stat-mech↗
arXiv2008

Escherlike quasiperiodic heterostructures

We propose quasiperiodic heterostructures associated with the tessellations of the unit disk by regular hyperbolic triangles. We present explicit construction rules and explore some of the properties exhibited by these geometric-based systems.

cond-mat.stat-mech↗
arXiv2006

Integral estimator of broadband omnidirectionality

By using the notion of wavelength- and angle-averaged reflectance, we assess in a systematic way the performance of finite omnidirectional reflectors. We put forward how this concept can be employed to optimize omnidirectional capabilities. We also apply it to give an alternate meaningful characterization of the bandwidth of these systems.

physics.optics↗
arXiv2005

Perfect antireflection via negative refraction

We suggest a geometrical framework to discuss the action of slabs of negatively refracting materials. We show that these slabs generate the same orbits as normal materials, but traced out in opposite directions. This property allows us to confirm that the action of any lossless multilayer can be optically cancelled by putting it together with the multilayer constructed as the inverted mirror image, with $ε$ and $μ$ reversed in sign.

physics.optics↗
arXiv2005

Geometrical aspects of first-order optical systems

We reconsider the basic properties of ray-transfer matrices for first-order optical systems from a geometrical viewpoint. In the paraxial regime of scalar wave optics, there is a wide family of beams for which the action of a ray-transfer matrix can be fully represented as a bilinear transformation on the upper complex half-plane, which is the hyperbolic plane. Alternatively, this action can be also viewed in the unit disc. In both cases, we use a simple trace criterion that arranges all first-order systems in three classes with a clear geometrical meaning: they represent rotations, translations, or parallel displacements. We analyze in detail the relevant example of an optical resonator.

physics.optics↗
arXiv2004

Vectorlike representation of one-dimensional scattering

We present a self-contained discussion of the use of the transfer-matrix formalism to study one-dimensional scattering. We elaborate on the geometrical interpretation of this transfer matrix as a conformal mapping on the unit disk. By generalizing to the unit disk the idea of turns, introduced by Hamilton to represent rotations on the sphere, we develop a method to represent transfer matrices by hyperbolic turns, which can be composed by a simple parallelogramlike rule.

quant-ph↗
arXiv2004

A vectorlike representation of multilayers

We resort to the concept of turns to provide a geometrical representation of the action of any lossless multilayer, which can be considered as the analogous in the unit disk to the sliding vectors in Euclidean geometry. This construction clearly shows the peculiar effects arising in the composition of multilayers. A simple optical experiment revealing the appearance of the Wigner angle is analyzed in this framework.

physics.optics↗
arXiv2003

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.

physics.optics↗
arXiv2003

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.

physics.optics↗
arXiv2003

Characterizing the reflectance of periodic layered media

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.

physics.optics↗
arXiv2001

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.

physics.optics↗
arXiv2001

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.

quant-ph↗
arXiv2001

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.

physics.optics↗
arXiv2001

Understanding multilayers from a geometrical viewpoint

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 spacetime, 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 structure allows us to introduce bilinear transformations in the complex plane. The concept of multilayer transfer function naturally emerges and its corresponding properties in the unit disc are studied. We show that the Iwasawa decomposition reflects at this geometrical level in three simple actions that can be considered the basic pieces for a deeper undestanding of the multilayer behavior. We use the method to analyze in detail a simple practical example.

physics.optics↗