An artificial structure was discovered under a natural skylight inside Grutas de Tzinacamóztoc, i... more An artificial structure was discovered under a natural skylight inside Grutas de Tzinacamóztoc, in the vicinity of the archaeological site of Cantona. The structure is made up of piled rocks, defining a pentagonal enclosure with a central mound. Detailed measurements and computer modeling allowed tracing of the sunbeam path projected on the structure and on the cave floor, particularly for dates of astronomical and/or Mesoamerican calendrical importance. This corroborates the possible prehispanic use of this site as a complex and sophisticated gnomon.
En el Laboratorio de Óptica Cuántica (LOC) del departamento de Física de la Universidad Autónoma ... more En el Laboratorio de Óptica Cuántica (LOC) del departamento de Física de la Universidad Autónoma Metropolitana, unidad Iztapalapa (UAM-I) existe un tradicional interés por el tema de la interacción “radiación intensa - materia” y la óptica no lineal. En 1993, después de haber colaborado por varios meses en Cuba con colegas del Instituto de Materiales y Reactivos en la Electrónica (IMRE), expertos en PLD, Manuel Fernández Guasti propone montar una cámara de ablación láser en el LOC para experimentar con PLD. La intención es posibilitar la investigación en ese campo. Los objetivos, en términos generales serían: • Fabricar películas delgadas de materiales que se estudian en el LOC por sus respuestas ópticas no lineales [9]. • Experimentar con materiales que ofrezcan cierto interés en diversos campos de la física aplicada. • Relacionar parámetros experimentales con propiedades de las películas para optimizar su calidad. • Estudiar la dinámica y composición del plasma producido durante l...
The enhanced localized reflectivity at a plane where the refractive index derivatives are discont... more The enhanced localized reflectivity at a plane where the refractive index derivatives are discontinuous is increased using a periodic triangular stack. This optical system is studied using three different methods: a slowly varying refractive index approximate solution, numerical solutions to the nonlinear amplitude equation and the exact analytical solution using a matrix formalism. The field intensity within a photonic crystal with a periodic triangular profile is evaluated as a function of penetration depth and wavelength. These results are compared with the standard binary layered structures. (M. Fernández-Guasti). URL: http://luz.izt.uam.mx (M. Fernández-Guasti). Optics Communications 346 (2015) 133-140 m n n J J J J 2 , m i n n J J J J 2 , m i n n J J J J
Discontinuities in the derivatives of a continuous refractive index profile n(z) enhance reflecti... more Discontinuities in the derivatives of a continuous refractive index profile n(z) enhance reflection, such reflection planes may be used to devise dielectric mirrors or filters. A triangular stack profile is proposed as an example.
The electric field nonlinear amplitude equation is solved numerically, making no approximation re... more The electric field nonlinear amplitude equation is solved numerically, making no approximation regarding a smoothly or abruptly varying refractive index. This approach provides an alternative to compute the reflectivity of more realistic mirrors.
22nd Congress of the International Commission for Optics: Light for the Development of the World, 2011
Propagation of light in stratied media is described with Maxwell's partial dierential equations (... more Propagation of light in stratied media is described with Maxwell's partial dierential equations (PDE). Separation of variables allow to decouple the linear PDE's to obtain second order non autonomous linear ODEs for the electric and magnetic elds. In the last decades, the problem has been tackled with matrices whose elements are linearly independent solutions of the elds.
22nd Congress of the International Commission for Optics: Light for the Development of the World, 2011
The amplitude and phase representation of classic electromagnetic waves is used to model light pr... more 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.
22nd Congress of the International Commission for Optics: Light for the Development of the World, 2011
According to Fresnel formulae, at normal incidence on an abrupt interface, the reflected wave has... more According to Fresnel formulae, at normal incidence on an abrupt interface, the reflected wave has a phase difference of zero or π, if the second medium has a lower or larger refractive index than the first. However, what happens if the refractive indices of two media are the same at the interface but the derivative of the refractive index varies abruptly? Since the two media are not homogeneous because the refractive index derivative is finite, the problem cannot be tackled with the Fresnel formalism. In order to deal with this problem the amplitude and phase representation of plane electromagnetic waves is used. An invariant is obtained that permits the decoupling of the amplitude and phase equations, both of which, are nonlinear. The amplitude equation is then solved numerically. No approximations are made regarding how slow or fast refractive index varies compared to the wavelength. Interpretation of the amplitude equation solutions reveal that surfaces where any of the derivatives of the refractive index profile is discontinuous, do enhance reflection. At normal incidence, the reflected wave thus generated will have a phase difference that may be a multiple of π 2 , apparently contradicting the Fresnel equations.
The amplitude and phase representation of classic plane electromagnetic waves is used to model li... more 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.
Reflectivity of a random monolayer, consisting of transparent spherical particles, is estimated u... more Reflectivity of a random monolayer, consisting of transparent spherical particles, is estimated using a graded refractive index model, an effective medium approach, and two scattering models. Two cases, a self-standing film and one with a substrate, are considered. Neither the surrounding medium nor the substrate are absorbing materials. Results at normal incidence, with different particle sizes, covering ratios and refractive indexes, are compared. The purpose of this work is to find under which circumstances, for reflectivity at normal incidence, a particle monolayer behaves as a graded refractive index film.
An artificial structure was discovered under a natural skylight inside Grutas de Tzinacamóztoc, i... more An artificial structure was discovered under a natural skylight inside Grutas de Tzinacamóztoc, in the vicinity of the archaeological site of Cantona. The structure is made up of piled rocks, defining a pentagonal enclosure with a central mound. Detailed measurements and computer modeling allowed tracing of the sunbeam path projected on the structure and on the cave floor, particularly for dates of astronomical and/or Mesoamerican calendrical importance. This corroborates the possible prehispanic use of this site as a complex and sophisticated gnomon.
Surfaces within a dielectric material, where the derivatives of a continuous and real refractive ... more 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 C m−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 (2 − m) π 2 for an increasing lowest order discontinuous derivative and −m π 2 for the decreasing case', is proved here.
Journal of Optics A: Pure and Applied Optics, 2009
The propagation of light in one-dimensional inhomogeneous deterministic media where the refractiv... more The propagation of light in one-dimensional inhomogeneous deterministic media where the refractive index varies on a wavelength scale is numerically evaluated without approximations. To this end, the field is written in amplitude and phase variables leading to a nonlinear amplitude differential equation. The numerical solutions to this Ermakov-type equation for five different refractive index profiles are presented. The amplitude oscillations are construed in terms of opposite phase or counter-propagating waves. The reflectivity is then evaluated for different interface thicknesses. The discontinuities in the first-and second-order derivatives are shown to produce an enhanced reflectivity even if the functions are continuous and monotonic.
A great number of investigations have been performed on the optical properties of alkali halide c... more A great number of investigations have been performed on the optical properties of alkali halide crystals doped with T1 + ions since the pioneering work of Hilsch . The first attempt to explain the mechanisms of absorption and luminescence due to T1 + ions was given by Seitz , who postulated that these ions substitute the cations in the host lattice and that the A, B and C absorption bands arise from electronic transitions from the 1Alg(S2) ground state to excited states of the sp configuration. In highly Tl+-doped alkali halide crystals new absorption and luminescence bands which do not appear in lightly doped crystals have been observed . These new bands, whose intensities vary with the square of the T1 + concentration, were attributed to T1 + dimer centres as suggested initially by Seitz, and later confirmed by Yuster and Delbeeq . At present, it has been possible to generate Tl+-doped phosphors used as luminophors in fluorescent lamps, like Ca3(PO4)2:TI +, and as scintillators, like NaI:T1 +, because of the high luminescence intensity of T1 + ion in the ultraviolet and visible ranges. In this way, it is important to continue the basic research on the spectroscopy of T1 + ions in ionic crystals. On the other hand, it is well known that Mn 2+ ions can be employed in important phosphors, but with the disadvantage that their d ~ d absorption transitions are difficult to pump sinee they are forbidden by spin and parity for electric dipole radiation in octahedral complexes. However, it has been recently found that efficient pumping of these ions in single crystals of NaC1 [5] and KBr [6] can be achieved using Sn 2+ ions as sensitizers, which have the same s2-configuration as the T1 +. In these crystals doped with very low concentrations of both types of ions the Sn2+---+ Mn 2+ energy transfer was found to occur in small clusters of Sn-Mn formed even in crystals severely quenched into acetona.
An artificial structure was discovered under a natural skylight inside Grutas de Tzinacamóztoc, i... more An artificial structure was discovered under a natural skylight inside Grutas de Tzinacamóztoc, in the vicinity of the archaeological site of Cantona. The structure is made up of piled rocks, defining a pentagonal enclosure with a central mound. Detailed measurements and computer modeling allowed tracing of the sunbeam path projected on the structure and on the cave floor, particularly for dates of astronomical and/or Mesoamerican calendrical importance. This corroborates the possible prehispanic use of this site as a complex and sophisticated gnomon.
En el Laboratorio de Óptica Cuántica (LOC) del departamento de Física de la Universidad Autónoma ... more En el Laboratorio de Óptica Cuántica (LOC) del departamento de Física de la Universidad Autónoma Metropolitana, unidad Iztapalapa (UAM-I) existe un tradicional interés por el tema de la interacción “radiación intensa - materia” y la óptica no lineal. En 1993, después de haber colaborado por varios meses en Cuba con colegas del Instituto de Materiales y Reactivos en la Electrónica (IMRE), expertos en PLD, Manuel Fernández Guasti propone montar una cámara de ablación láser en el LOC para experimentar con PLD. La intención es posibilitar la investigación en ese campo. Los objetivos, en términos generales serían: • Fabricar películas delgadas de materiales que se estudian en el LOC por sus respuestas ópticas no lineales [9]. • Experimentar con materiales que ofrezcan cierto interés en diversos campos de la física aplicada. • Relacionar parámetros experimentales con propiedades de las películas para optimizar su calidad. • Estudiar la dinámica y composición del plasma producido durante l...
The enhanced localized reflectivity at a plane where the refractive index derivatives are discont... more The enhanced localized reflectivity at a plane where the refractive index derivatives are discontinuous is increased using a periodic triangular stack. This optical system is studied using three different methods: a slowly varying refractive index approximate solution, numerical solutions to the nonlinear amplitude equation and the exact analytical solution using a matrix formalism. The field intensity within a photonic crystal with a periodic triangular profile is evaluated as a function of penetration depth and wavelength. These results are compared with the standard binary layered structures. (M. Fernández-Guasti). URL: http://luz.izt.uam.mx (M. Fernández-Guasti). Optics Communications 346 (2015) 133-140 m n n J J J J 2 , m i n n J J J J 2 , m i n n J J J J
Discontinuities in the derivatives of a continuous refractive index profile n(z) enhance reflecti... more Discontinuities in the derivatives of a continuous refractive index profile n(z) enhance reflection, such reflection planes may be used to devise dielectric mirrors or filters. A triangular stack profile is proposed as an example.
The electric field nonlinear amplitude equation is solved numerically, making no approximation re... more The electric field nonlinear amplitude equation is solved numerically, making no approximation regarding a smoothly or abruptly varying refractive index. This approach provides an alternative to compute the reflectivity of more realistic mirrors.
22nd Congress of the International Commission for Optics: Light for the Development of the World, 2011
Propagation of light in stratied media is described with Maxwell's partial dierential equations (... more Propagation of light in stratied media is described with Maxwell's partial dierential equations (PDE). Separation of variables allow to decouple the linear PDE's to obtain second order non autonomous linear ODEs for the electric and magnetic elds. In the last decades, the problem has been tackled with matrices whose elements are linearly independent solutions of the elds.
22nd Congress of the International Commission for Optics: Light for the Development of the World, 2011
The amplitude and phase representation of classic electromagnetic waves is used to model light pr... more 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.
22nd Congress of the International Commission for Optics: Light for the Development of the World, 2011
According to Fresnel formulae, at normal incidence on an abrupt interface, the reflected wave has... more According to Fresnel formulae, at normal incidence on an abrupt interface, the reflected wave has a phase difference of zero or π, if the second medium has a lower or larger refractive index than the first. However, what happens if the refractive indices of two media are the same at the interface but the derivative of the refractive index varies abruptly? Since the two media are not homogeneous because the refractive index derivative is finite, the problem cannot be tackled with the Fresnel formalism. In order to deal with this problem the amplitude and phase representation of plane electromagnetic waves is used. An invariant is obtained that permits the decoupling of the amplitude and phase equations, both of which, are nonlinear. The amplitude equation is then solved numerically. No approximations are made regarding how slow or fast refractive index varies compared to the wavelength. Interpretation of the amplitude equation solutions reveal that surfaces where any of the derivatives of the refractive index profile is discontinuous, do enhance reflection. At normal incidence, the reflected wave thus generated will have a phase difference that may be a multiple of π 2 , apparently contradicting the Fresnel equations.
The amplitude and phase representation of classic plane electromagnetic waves is used to model li... more 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.
Reflectivity of a random monolayer, consisting of transparent spherical particles, is estimated u... more Reflectivity of a random monolayer, consisting of transparent spherical particles, is estimated using a graded refractive index model, an effective medium approach, and two scattering models. Two cases, a self-standing film and one with a substrate, are considered. Neither the surrounding medium nor the substrate are absorbing materials. Results at normal incidence, with different particle sizes, covering ratios and refractive indexes, are compared. The purpose of this work is to find under which circumstances, for reflectivity at normal incidence, a particle monolayer behaves as a graded refractive index film.
An artificial structure was discovered under a natural skylight inside Grutas de Tzinacamóztoc, i... more An artificial structure was discovered under a natural skylight inside Grutas de Tzinacamóztoc, in the vicinity of the archaeological site of Cantona. The structure is made up of piled rocks, defining a pentagonal enclosure with a central mound. Detailed measurements and computer modeling allowed tracing of the sunbeam path projected on the structure and on the cave floor, particularly for dates of astronomical and/or Mesoamerican calendrical importance. This corroborates the possible prehispanic use of this site as a complex and sophisticated gnomon.
Surfaces within a dielectric material, where the derivatives of a continuous and real refractive ... more 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 C m−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 (2 − m) π 2 for an increasing lowest order discontinuous derivative and −m π 2 for the decreasing case', is proved here.
Journal of Optics A: Pure and Applied Optics, 2009
The propagation of light in one-dimensional inhomogeneous deterministic media where the refractiv... more The propagation of light in one-dimensional inhomogeneous deterministic media where the refractive index varies on a wavelength scale is numerically evaluated without approximations. To this end, the field is written in amplitude and phase variables leading to a nonlinear amplitude differential equation. The numerical solutions to this Ermakov-type equation for five different refractive index profiles are presented. The amplitude oscillations are construed in terms of opposite phase or counter-propagating waves. The reflectivity is then evaluated for different interface thicknesses. The discontinuities in the first-and second-order derivatives are shown to produce an enhanced reflectivity even if the functions are continuous and monotonic.
A great number of investigations have been performed on the optical properties of alkali halide c... more A great number of investigations have been performed on the optical properties of alkali halide crystals doped with T1 + ions since the pioneering work of Hilsch . The first attempt to explain the mechanisms of absorption and luminescence due to T1 + ions was given by Seitz , who postulated that these ions substitute the cations in the host lattice and that the A, B and C absorption bands arise from electronic transitions from the 1Alg(S2) ground state to excited states of the sp configuration. In highly Tl+-doped alkali halide crystals new absorption and luminescence bands which do not appear in lightly doped crystals have been observed . These new bands, whose intensities vary with the square of the T1 + concentration, were attributed to T1 + dimer centres as suggested initially by Seitz, and later confirmed by Yuster and Delbeeq . At present, it has been possible to generate Tl+-doped phosphors used as luminophors in fluorescent lamps, like Ca3(PO4)2:TI +, and as scintillators, like NaI:T1 +, because of the high luminescence intensity of T1 + ion in the ultraviolet and visible ranges. In this way, it is important to continue the basic research on the spectroscopy of T1 + ions in ionic crystals. On the other hand, it is well known that Mn 2+ ions can be employed in important phosphors, but with the disadvantage that their d ~ d absorption transitions are difficult to pump sinee they are forbidden by spin and parity for electric dipole radiation in octahedral complexes. However, it has been recently found that efficient pumping of these ions in single crystals of NaC1 [5] and KBr [6] can be achieved using Sn 2+ ions as sensitizers, which have the same s2-configuration as the T1 +. In these crystals doped with very low concentrations of both types of ions the Sn2+---+ Mn 2+ energy transfer was found to occur in small clusters of Sn-Mn formed even in crystals severely quenched into acetona.
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