University tropolitana Iztapalapa

Mexico City, Mexico

University tropolitana Iztapalapa

Mexico City, Mexico

Time filter

Source Type

Fernandez-Guasti M.,University tropolitana Iztapalapa
Journal of Modern Optics | Year: 2015

Reflection and refraction at an abrupt dielectric interface at normal incidence are evaluated using an amplitude and phase (amph) formalism. The optical properties of a stack with two quarter-wavelength layers are then calculated. The characteristics of a mirror constructed with quarter-wavelength layers are discussed using the amplitude and phase representation. Floquet nonlinear theorem is invoked to describe the multi-layered system. Results are consistent with Fresnel formulae and conventional matrix methods for stratified periodic media. However, the amph formalism offers several advantages: (i) it is capable of showing the field properties as it propagates though the stack, (ii) it gives a lucid physical insight because the variables involved have a clear physical meaning, and (iii) the mathematical description is simple. © 2014 Taylor & Francis.


Fernandez-Guasti M.,University tropolitana Iztapalapa
International Journal of Bifurcation and Chaos | Year: 2016

The quadratic iteration is mapped within a nondistributive imaginary scator algebra in 1 + 2 dimensions. The Mandelbrot set is identically reproduced at two perpendicular planes where only the scalar and one of the hypercomplex scator director components are present. However, the bound three-dimensional S set projections change dramatically even for very small departures from zero of the second hypercomplex plane. The S set exhibits a rich fractal-like boundary in three dimensions. Periodic points with period m, are shown to be necessarily surrounded by points that produce a divergent magnitude after m iterations. The scator set comprises square nilpotent elements that ineluctably belong to the bound set. Points that are square nilpotent on the mth iteration, have preperiod 1 and period m. Two-dimensional plots are presented to show some of the main features of the set. A three-dimensional rendering reveals the highly complex structure of its boundary. © 2016 World Scientific Publishing Company.


Fernandez-Guasti M.,University tropolitana Iztapalapa
Journal of Optics (United Kingdom) | Year: 2015

The solution to a non-autonomous second order ordinary differential equation is presented. The real function, dependent on the differentiation variable, is a squared hyperbolic tangent function plus a term that involves the quotient of hyperbolic functions. This function varies from one limiting value to another without having any singularities. The solution is remarkably simple and involves only trigonometric and hyperbolic trigonometric functions. The solution is analyzed in the context of wave propagation in an inhomogeneous one-dimensional medium. The profile is shown to act as a perfect anti-reflection interface, providing a possible alternative route to the fabrication of reflectionless surfaces. © 2015 IOP Publishing Ltd.


Diamant R.,University tropolitana Iztapalapa
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2011

The amplitude and phase representation of classic electromagnetic waves is used to model light propagating through a stratified medium, with a continuous refractive index profile. This medium is assumed to be isotropic, non magnetic, electrically neutral, transparent, dielectric, with a linear response, but letting the electric permittivity vary along the z direction. No approximations regarding a slowly or strongly varying refractive index, compared to the wavelength, are made. This is particularly convenient when the refractive index varies on a wavelength scale. The case of a thin film at normal incidence is studied for various thicknesses and interface ranges. The corresponding nonlinear amplitude differential equation is numerically solved. The amplitude oscillations are construed in terms of counter-propagating waves and the film's reflectivity is evaluated. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).


Fernandez-Guasti M.,University tropolitana Iztapalapa
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2011

The reciprocity principle requests that if an observer, say in the laboratory, sees an event with a given velocity, another observer at rest with the event must see the laboratory observer with minus the same velocity. The composition of velocities in the Lorentz-Einstein scheme does not fulfill the reciprocity principle because the composition rule is neither commutative nor associative. In other words, the composition of two non-collinear Lorentz boosts cannot be expressed as a single Lorentz boost but requires in addition a rotation. The Thomas precession is a consequence of this composition procedure. Different proposals such as gyro-groups have been made to fulfill the reciprocity principle. An alternative velocity addition scheme is proposed consistent with the invariance of the speed of light and the relativity of inertial frames. An important feature of the present proposal is that the addition of velocities is commutative and associative. The velocity reciprocity principle is then immediately fulfilled. This representation is based on a transformation of a hyperbolic scator algebra. The proposed rules become identical with the special relativity addition of velocities in one dimension. They also reduce to the Galilean transformations in the low velocity limit. The Thomas gyration needs to be revised in this nonlinear realization of the special relativity postulates. The deformed Minkowski metric presented here is compared with other deformed relativity representations. © 2011 SPIE.


Fernandez-Guasti M.,University tropolitana Iztapalapa
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2011

Wave phenomena involve perturbations whose behavior is equivalent in space and time. The perturbations may be of very different nature but they all have to conform with the notion of a field, that is, a scalar or vector quantity-defined for all points in space. Some wave phenomena are described in terms of only one field. For example water waves where the perturbation is the level above or below from the equilibrium position. Nonetheless, electromagnetic waves require the existence of two fields. I shall argue that in fact, all wave phenomena involve two fields although we sometimes perform the description in terms of only one field. To this end, the concept of cyclic or dynamical equilibrium will be put forward where the system continuously moves between two states where it exchanges two forms of energy. In a mechanical system it may be, for example, kinetic and potential energy. Differential equations that form an Ermakov pair require the existence of two linearly-independent fields. These equations possess an invariant. For the time dependent harmonic oscillator, such an invariant exists only for time dependent potentials that are physically attainable. According to this view, two fields must be present in any physical system that exhibits wave behavior. In the case of gravity, if it exhibits wave behavior, there must be a complementary field that also carries energy. It is also interesting that the complex cosmic tension field proposed by Chandrasekar involves a complex field because complex functions formally describe two complementary fields. © 2011 SPIE.


Diamant R.,University tropolitana Iztapalapa | Fernandez-Guasti M.,University tropolitana Iztapalapa
Optics Communications | Year: 2013

The amplitude and phase representation of classic plane electromagnetic waves is used to model light propagating through transparent stratified media, with a continuous refractive index profile. Numeric solutions for the nonlinear amplitude equation at normal incidence are obtained. Discontinuities of the refractive index derivatives exhibit reflection enhancement. Depending on the order of the discontinuity, the phase change upon reflection obtained from the numerical results can be ±π/2 in addition to the usual 0, or ±π. © 2012 Elsevier B.V.


Mejia-Centeno I.,University tropolitana Iztapalapa | Mejia-Centeno I.,Mexican Institute of Petroleum | Castillo S.,Mexican Institute of Petroleum | Fuentes G.A.,University tropolitana Iztapalapa
Applied Catalysis B: Environmental | Year: 2012

In this work we study the formation of NH3, N2O and H2 side products during operation of three-way catalytic converters (TWC) in a simulated engine exhaust. We used a commercial Pd-only TWC and supported Pd model catalysts in light-off and during constant temperature tests under rich conditions. N2O is observed primarily during light-off and its low temperature formation (110-320°C) proceeds via reduction of NO by CO when O2 is present, or by H2 in its absence. We detected also N2O formation at 500°C that has not been reported previously, proceeding via reduction with CO.NH3 is formed in the 200-600°C range via reduction of NO by H2. The H2 required to produce NH3 is generated via steam reforming and water gas-shift reactions over the catalysts. On a molar basis, the H2 emission is about five-fold higher than that of NH3 during cold start of TWC. We determined the effect of SO2 level during constant temperature experiments at 500°C, extending the work of Gandhi and Shelef [1]. In CeO2-containing catalysts the interaction with SO2 favors the production of N2O, but lowers that of NH3, apparently by suppressing selectively the reaction path leading to H2 needed for the reaction. Our study suggests that the use of low and ultra-low sulfur gasoline by cars equipped with TWC lowers the emission of N2O to the atmosphere during high temperature operation but enhances the production of NH3 and H2. This is a matter of concern because NH3 is involved in the formation of nano, fine and ultra fine inorganic particles in the atmosphere. © 2012 Elsevier B.V.


Diamant R.,University tropolitana Iztapalapa | Fernandez-Guasti M.,University tropolitana Iztapalapa
Journal of Optics (United Kingdom) | Year: 2014

Surfaces within a dielectric material, where the derivatives of a continuous and real refractive index profile are discontinuous, are shown to enhance reflection. To this end, the amplitude and phase representation of electromagnetic waves is used to model light propagating normally through a transparent medium with a continuous refractive index profile that varies only in one spatial direction. The amplitude equation is solved under the slowly varying refractive index approximation (SVRI). To isolate the effect of a single surface where the refractive index derivatives are discontinuous, an n(z) profile is proposed that is analytical, smooth and slowly varying except for a single piecewise junction. At this junction, n(z) is continuous but some of the mth order derivatives are not. Two different SVRI approximated solutions are joined at the discontinuity plane and, by demanding that boundary conditions are satisfied, a general complex reflection coefficient is obtained. By categorizing profiles according to the lowest order discontinuous derivative at the junction, a simple expression for the reflection coefficient can be written. Results are compared favorably with previous numerical solutions. Furthermore, a conjecture by the authors in a previous paper, 'for a Cm-1 refractive index profile type, where m stands as the order of the lowest order discontinuous derivative, phase change upon reflection at the discontinuity plane is for an increasing lowest order discontinuous derivative and for the decreasing case', is proved here. © 2014 IOP Publishing Ltd.


Fernandez-Guasti M.,University tropolitana Iztapalapa
European Physical Journal Plus | Year: 2014

The invariant transformations of a deformed Lorentz metric are explored. These transformations are described by the product operation with a unit magnitude element in hyperbolic scator algebra. The real scator set forms a group under the addition and product operations in a restricted space. However, the product is not distributive over addition. The restricted space condition is equivalent to the time-like subspace in special relativity. In 1+1 dimensions (time and one spatial variable), the deformation vanishes and the scator metric becomes identical to the Lorentz metric. In higher dimensions, time dilation and parallel space contraction are preserved albeit with slight quantitative modification. However, the deformed transformation also exhibits a transverse spatial elongation. © 2014, Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg.

Loading University tropolitana Iztapalapa collaborators
Loading University tropolitana Iztapalapa collaborators