Variations on the adiabatic invariance: the Lorentz pendulum

We analyze a very simple variant of the Lorentz pendulum, in which the length is varied exponentially, instead of uniformly, as it is assumed in the standard case. We establish quantitative criteria for the condition of adiabatic changes in both pendula and put in evidence their substantially different physical behavior with regard to adiabatic invariance.Comment: To appear in American Journal of Physic

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 appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via M\"{o}bius transformations, as parallel displacements, a geometric action that has no Euclidean analogy.Comment: 13 pages. No figure. Accepted for publication in Symmetr

The many facets of the Fabry-Perot

We address the response, both in amplitude and intensity, of a Fabry-Perot from a variety of viewpoints. These complementary pictures conspire to achieve a comprehensive and consistent theory of the operation of this system.Comment: 15 pages, 9 figure

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.Comment: 50 pages, 24 figure

Simple quantum model for light depolarization

Depolarization of quantum fields is handled through a master equation of the Lindblad type. The specific feature of the proposed model is that it couples dispersively the field modes to a randomly distributed atomic reservoir, much in the classical spirit of dealing with this problem. The depolarizing dynamics resulting from this model is analyzed for relevant states.Comment: Improved version. Accepted for publication in the Journal of the Optical Society of America

Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals

We determine the range of thicknesses and refractive indices for which omnidirectional reflection from quasiperiodic multilayers occurs. By resorting to the notion of area under the transmittance curve, we assess in a systematic way the performance of the different quasiperiodic Fibonacci multilayers.Comment: 5 pages, 4 color figures. Comments welcome