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Luis Mochan

Universidad Nacional Autónoma de México, Instituto de Ciencias Físicas, Faculty Member

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Address: Instituto de Ciencias Físicas, Apartado postal 48-3, Cuernavaca, Mor. México

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Papers by Luis Mochan

$Research paper thumbnail of <title>Optical properties and scaling in fractal aggregates</title>$

<title>Optical properties and scaling in fractal aggregates</title>

by Guillermo Ortiz and Luis Mochan

4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications, 2001

Optical properties and scaling in fractal aggregates. [Proceedings of SPIE 4419, 752 (2001)]. Gui... more

$Research paper thumbnail of Scaling condition for multiple scattering in fractal aggregates$

Scaling condition for multiple scattering in fractal aggregates

by Guillermo Ortiz and Luis Mochan

Physica B: Condensed Matter, 2003

It is well known that under the first Born approximation, the differential cross-section ds=dO fo... more It is well known that under the first Born approximation, the differential cross-section ds=dO for light scattered by a fractal of dimension d f scales with wave vector Q as Q Àd f : The use of this formula to interpret experiments performed at frequencies close to the resonances of the system for which multiple scattering is not negligible is questionable. We study the scaling properties of the light scattered by colloidal aggregates employing a novel multi-resolution hierarchical algorithm which allows the study of large systems taking fully into account the long range of the interactions in multiple scattering calculations. We obtain the conditions under which scaling may be present and find that even under resonant conditions, the scattering cross-section may scale with the fractal dimension d f ; but only if the aggregate is larger than a dissipation and frequency-dependent length-scale L h ; confirming within a full vectorial calculation a result previously found for scalar interactions. For smaller aggregates, ds=dO might scale with a different exponent or it might not scale at all, depending on the frequency of light employed. This could explain the discrepancies between experiments performed on similar systems within the strong scattering regime. r

Bulk response of composites from finite samples

by Guillermo Ortiz, Catalina Lopez-Bastidas, and Luis Mochan

Physica B: Condensed Matter, 2003

The bulk macroscopic dielectric response of a disordered composite is calculated employing a larg... more The bulk macroscopic dielectric response of a disordered composite is calculated employing a large finite sample instead of an infinite one obtained by replicating a unit cell, as has usually been done. We explicitly account for boundary effects through the macroscopic depolarization field, and finite size corrections are minimized by the large size of the system. The generation of the composite and the calculation of the interactions between the great number of particles become feasible using a newly developed hierarchical multi-resolution scheme. The dielectric response of a composite made up of Ag spheres embedded in glass and the composition independent spectral density agree with those from previous simulations and we discuss their differences with analytical theories based on a renormalized polarizability. Confinement effects due to inhomogeneities close to the boundary of the system are also investigated. r

Efficient homogenization procedure for the calculation of optical properties of 3D nanostructured composites

by Guillermo Ortiz and Luis Mochan

Optics Express, 2010

We present a very efficient recursive method to calculate the effective optical response of metam... more We present a very efficient recursive method to calculate the effective optical response of metamaterials made up of arbitrarily shaped inclusions arranged in periodic 3D arrays. We apply it to dielectric particles embedded in a metal matrix with a lattice constant much smaller than the wavelength of the incident field, so that we may neglect retardation and factor the geometrical properties from the properties of the materials. If the conducting phase is continuous the low frequency behavior is metallic, and if the conducting paths are thin, the high frequency behavior is dielectric. Thus, extraordinary-transparency bands may develop at intermediate frequencies, whose properties may be tuned by geometrical manipulation.

Second harmonic generation from small particle aggregates

by Guillermo Ortiz and Luis Mochan

Novel nanofabrication techniques are capable of producing nanoparticles with controled structures... more Novel nanofabrication techniques are capable of producing nanoparticles with controled structures which include small clusters, self-assembled particles, quantum dots, vesicles, etc. The non-linear optical scattering of these structures are important for applications, and can be used for their physical characterization. The second harmonic (SH) field radiated by a single small spherical particle has surface and bulk, dipolar and quadrupolar contributions

Nonadditivity of Poynting vector within opaque media

by Guillermo Ortiz and Luis Mochan

Journal of the Optical Society of America A, 2005

The energy flux within an opaque medium near an interface is not the sum of an incident plus a re... more The energy flux within an opaque medium near an interface is not the sum of an incident plus a reflected term, as there is a synergistic contribution to the time averaged Poynting vector which involves simultaneously both the incident and reflected fields. Therefore, the well known formula R + T = 1, where R is the reflectance and T the transmittance, does not hold, and furthermore, R and T loose their accepted meaning. We illustrate the perils of assuming energy flux additivity by calculating the transmission and reflection spectrum of a film over a substrate normally illuminated by incoherent light at frequencies in the neighborhood of an optical resonance. We also show that the usual relation between the scattering, absorption, and extinction cross sections for particles immersed within a dissipative host have to be modified to account for the non additivity.

Macroscopic optical response and photonic bands

by Guillermo Ortiz, Jose Perez, and Luis Mochan

New Journal of Physics, 2013

We develop a formalism for the calculation of the macroscopic dielectric response of composite sy... more We develop a formalism for the calculation of the macroscopic dielectric response of composite systems made of particles of one material embedded periodically within a matrix of another material, each of which is characterized by a well-defined dielectric function. The nature of these dielectric functions is arbitrary, and could correspond to dielectric or conducting, transparent or opaque, absorptive and dispersive materials. The geometry of the particles and the Bravais lattice of the composite are also arbitrary. Our formalism goes beyond the long-wavelength approximation as it fully incorporates retardation effects. We test our formalism through the study of the propagation of electromagnetic waves in two-dimensional photonic crystals made of periodic arrays of cylindrical holes in a dispersionless dielectric host. Our macroscopic theory yields a spatially dispersive macroscopic response which allows the calculation of the full photonic band structure of the system, as well as the characterization of its normal modes, upon substitution into the macroscopic field equations. We can also account approximately for the spatial dispersion through a local magnetic permeability and analyze the resulting dispersion relation, obtaining a region of left handedness.

$Research paper thumbnail of Scaling of light scattered from fractal aggregates at resonance$

Scaling of light scattered from fractal aggregates at resonance

by Guillermo Ortiz and Luis Mochan

Physical Review B, 2003

Due to the scale invariance of fractal aggregates, light scattered from them often decays as a po... more Due to the scale invariance of fractal aggregates, light scattered from them often decays as a power of the scattering wave vector. The exponent in this power law has been usually interpreted as the geometrical fractal dimension. However, the validity of this interpretation is questionable for frequencies close to the resonances of the system, for which multiple scattering becomes important.

Effective optical response of metamaterials

by Guillermo Ortiz and Luis Mochan

Physical Review B, 2009

We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit t... more We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit the frequency dependent macroscopic dielectric response tensor ǫ M ij (ω) of metamaterials made of a matrix with inclusions of any geometrical shape repeated periodically with any lattice structure. We illustrate the formalism calculating ǫ M ij (ω) for several structures. For dielectric rectangular inclusions within a conducting material we obtain an anisotropic response which may change from conductor-like at low ω to dielectric-like with resonances at large ω, attaining a very small reflectance at intermediate frequencies which can be tuned through geometrical tailoring. A simple explanation allowed us to predict and confirm similar behavior for other shapes, even isotropic, close to the percolation threshold.

Nonadditivity of poynting vector within opaque media

by Guillermo Ortiz and Luis Mochan

Journal of the Optical Society of America. A, Optics, image science, and vision, 2005

The energy flux within an opaque medium near an interface is not the sum of an incident plus a re... more The energy flux within an opaque medium near an interface is not the sum of an incident plus a reflected term, as there is a synergistic contribution to the time averaged Poynting vector which involves simultaneously both the incident and reflected fields. Therefore, the well known formula R + T = 1, where R is the reflectance and T the transmittance, does not hold, and furthermore, R and T loose their accepted meaning. We illustrate the perils of assuming energy flux additivity by calculating the transmission and reflection spectrum of a film over a substrate normally illuminated by incoherent light at frequencies in the neighborhood of an optical resonance. We also show that the usual relation between the scattering, absorption, and extinction cross sections for particles immersed within a dissipative host have to be modified to account for the non additivity.

Energy transfer to an anharmonic diatomic system

by Luis Mochan and J. Recamier

Molecular Physics, 2009

We model an anharmonic diatomic molecule using deformed creation and annihilation operators such ... more We model an anharmonic diatomic molecule using deformed creation and annihilation operators such that the energy spectrum generated by a Hamiltonian of the harmonic oscillator's form written in terms of deformed operators is similar to that of a Morse potential. We construct an approximate time evolution operator and evaluate transition probabilities which are compared with those obtained by an expansion in a basis of Morse eigenfunctions. The algebraic results compare favorably with the numerical results.

Effect of plasma waves on the optical properties of conducting superlattices

Phys Rev B, 1987

We calculate the dispersion relation of the electromagnetic normal modes and the reflectance of s... more We calculate the dispersion relation of the electromagnetic normal modes and the reflectance of superlattices made of highly doped semiconductors and of metals, taking into account plasma waves, spatial dispersion, and retardation. We obtain a variety of modes made up of interacting surface and bulk plasmons, which yield a rich structure in the reflectance spectra.

Local Field Effect on the Second Order Susceptibility of Si

Aps March Meeting Abstracts, Mar 1, 1996

We develop a polarizable bond model for the calculation of the linear and non-linear response of ... more We develop a polarizable bond model for the calculation of the linear and non-linear response of tetrahedrally bonded centrosymmetric semiconductors, taking into account the local field effect. We characterize the linear response of each bond by a polarizability tensor with axial and radial independent components. In addition, each bond responds non-linearly to the non-uniform local field with a second order polarizability which is related to the linear one. The linear polarizabilities are fitted to the bulk dielectric response and to the surface induced reflectance anisotropy of the (110) face. Different neighbors contribute large gradients to the local field; these cancel among themselves within the bulk, but they are unbalanced at the surface, where they yield a sizable contribution to the non-linear macroscopic susceptibility. We show that this local field induces a large resonance in the SHG spectra, in agreement with recent experimental observations.(W. Daum et al, Phys.Rev.Lett. 71), 1234 (1993), and J. F. McGilp et al, Opt.Eng. 33, 3895 (1994). We also calculate the SHG symmetry of several faces and find that they reproduce qualitatively the experimental results.

On Casimir forces for media with arbitrary dielectric properties

Revista Mexicana De Fisica, Jul 18, 2002

We derive an expression for the Casimir force between slabs with arbitrary dielectric properties ... more We derive an expression for the Casimir force between slabs with arbitrary dielectric properties characterized by their reflection coefficients. The formalism presented here is applicable to media with a local or a non-local dielectric response, an infinite or a finite width, inhomogeneous dissipative, etc. Our results reduce to the Lifshitz formula for the force between semi-infinite dielectric slabs by replacing the reflection coefficients by the Fresnel amplitudes.

Second harmonic generation at crystal surfaces

J Phys Condens Matter, 1993

ABSTRACT

Diagrammatic approach to the effective dielectric response of composites

Phys Rev B, 1989

We formulate a diagrammatic approach for the calculation of the macroscopic dielectric response o... more We formulate a diagrammatic approach for the calculation of the macroscopic dielectric response of a collection of spheres at random positions and embedded in a homogeneous medium. Through infinite summations of specific classes of diagrams, we derive some known results and we also obtain extensions to a recent theory for the renormalization of the polarizability in the Maxwell Garnett scheme.

Exactly Solvable Model of Surface Sum Frequency Generation

We develop a model for surface sum frequency generation (SFG) consisting of a semiinfinite system... more We develop a model for surface sum frequency generation (SFG) consisting of a semiinfinite system made up of a continuous distribution of harmonic polarizable entities each of which responds non-linearly to the gradient of the field. The near discontinuity of some field components at the surface yields a finite surface susceptibility tensor characterized by the parameters a(omega_3=omega_1+omega_2) and b(omega_3), as

Effective Dielectric Response of Metamaterials

We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit t... more We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit the frequency dependent macroscopic dielectric response tensor ǫ M ij (ω) of metamaterials made of a matrix with inclusions of any geometrical shape repeated periodically with any lattice structure. We illustrate the formalism calculating ǫ M ij (ω) for several structures. For dielectric rectangular inclusions within a conducting material we obtain an anisotropic response which may change from conductor-like at low ω to dielectric-like with resonances at large ω, attaining a very small reflectance at intermediate frequencies which can be tuned through geometrical tailoring. A simple explanation allowed us to predict and confirm similar behavior for other shapes, even isotropic, close to the percolation threshold.

The Casimir Effect for Arbitrary Optically Anisotropic Materials

We extend a fictitious-cavity approach to calculate the Casimir effect for cavities bounded by fl... more We extend a fictitious-cavity approach to calculate the Casimir effect for cavities bounded by flat anisotropic materials. We calculate the energy, force and torque in terms only of the optical coefficients of the walls of the cavity. We calculate the Casimir effect at zero and finite temperature for some simple systems. As a non trivial application, we calculate the torque between a semi-infinite anisotropic plate and an anisotropic film. We study the effect of the film thickness in the torque and find an optimal width that maximizes the torque.

$Research paper thumbnail of <title>Optical properties and scaling in fractal aggregates</title>$

<title>Optical properties and scaling in fractal aggregates</title>

4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications, 2001

ABSTRACT Within the first born approximation, the calculated angular distribution of the light sc... more ABSTRACT Within the first born approximation, the calculated angular distribution of the light scattered by a fractal decays as a power of the scattering wavevector Q, with an exponent given by the fractal dimension df. This has been frequently used experimentally to characterize optically the geometry of fractal systems. The validity of the result above has been questioned for frequencies close to the resonances of the system, for which the first born approximation fails. In this paper we apply a recently developed hierarchical algorithm to calculate the self-consistent near field and the scattered electromagnetic field for 2D colloidal aggregates excited at their resonant frequencies. The local environment of the strongly polarized regions manifests itself in the angular dependence of these scattered intensity corresponding to large Q. For Q within the mass scaling region, the scattering does decay as Q-df for some frequencies, similar to the geometrical structure factor S(Q), but shows no scaling whatsoever for others.

$Research paper thumbnail of <title>Optical properties and scaling in fractal aggregates</title>$

<title>Optical properties and scaling in fractal aggregates</title>

by Guillermo Ortiz and Luis Mochan

4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications, 2001

Optical properties and scaling in fractal aggregates. [Proceedings of SPIE 4419, 752 (2001)]. Gui... more

$Research paper thumbnail of Scaling condition for multiple scattering in fractal aggregates$

Scaling condition for multiple scattering in fractal aggregates

by Guillermo Ortiz and Luis Mochan

Physica B: Condensed Matter, 2003

It is well known that under the first Born approximation, the differential cross-section ds=dO fo... more It is well known that under the first Born approximation, the differential cross-section ds=dO for light scattered by a fractal of dimension d f scales with wave vector Q as Q Àd f : The use of this formula to interpret experiments performed at frequencies close to the resonances of the system for which multiple scattering is not negligible is questionable. We study the scaling properties of the light scattered by colloidal aggregates employing a novel multi-resolution hierarchical algorithm which allows the study of large systems taking fully into account the long range of the interactions in multiple scattering calculations. We obtain the conditions under which scaling may be present and find that even under resonant conditions, the scattering cross-section may scale with the fractal dimension d f ; but only if the aggregate is larger than a dissipation and frequency-dependent length-scale L h ; confirming within a full vectorial calculation a result previously found for scalar interactions. For smaller aggregates, ds=dO might scale with a different exponent or it might not scale at all, depending on the frequency of light employed. This could explain the discrepancies between experiments performed on similar systems within the strong scattering regime. r

Bulk response of composites from finite samples

by Guillermo Ortiz, Catalina Lopez-Bastidas, and Luis Mochan

Physica B: Condensed Matter, 2003

The bulk macroscopic dielectric response of a disordered composite is calculated employing a larg... more The bulk macroscopic dielectric response of a disordered composite is calculated employing a large finite sample instead of an infinite one obtained by replicating a unit cell, as has usually been done. We explicitly account for boundary effects through the macroscopic depolarization field, and finite size corrections are minimized by the large size of the system. The generation of the composite and the calculation of the interactions between the great number of particles become feasible using a newly developed hierarchical multi-resolution scheme. The dielectric response of a composite made up of Ag spheres embedded in glass and the composition independent spectral density agree with those from previous simulations and we discuss their differences with analytical theories based on a renormalized polarizability. Confinement effects due to inhomogeneities close to the boundary of the system are also investigated. r

Efficient homogenization procedure for the calculation of optical properties of 3D nanostructured composites

by Guillermo Ortiz and Luis Mochan

Optics Express, 2010

We present a very efficient recursive method to calculate the effective optical response of metam... more We present a very efficient recursive method to calculate the effective optical response of metamaterials made up of arbitrarily shaped inclusions arranged in periodic 3D arrays. We apply it to dielectric particles embedded in a metal matrix with a lattice constant much smaller than the wavelength of the incident field, so that we may neglect retardation and factor the geometrical properties from the properties of the materials. If the conducting phase is continuous the low frequency behavior is metallic, and if the conducting paths are thin, the high frequency behavior is dielectric. Thus, extraordinary-transparency bands may develop at intermediate frequencies, whose properties may be tuned by geometrical manipulation.

Second harmonic generation from small particle aggregates

by Guillermo Ortiz and Luis Mochan

Novel nanofabrication techniques are capable of producing nanoparticles with controled structures... more Novel nanofabrication techniques are capable of producing nanoparticles with controled structures which include small clusters, self-assembled particles, quantum dots, vesicles, etc. The non-linear optical scattering of these structures are important for applications, and can be used for their physical characterization. The second harmonic (SH) field radiated by a single small spherical particle has surface and bulk, dipolar and quadrupolar contributions

Nonadditivity of Poynting vector within opaque media

by Guillermo Ortiz and Luis Mochan

Journal of the Optical Society of America A, 2005

The energy flux within an opaque medium near an interface is not the sum of an incident plus a re... more The energy flux within an opaque medium near an interface is not the sum of an incident plus a reflected term, as there is a synergistic contribution to the time averaged Poynting vector which involves simultaneously both the incident and reflected fields. Therefore, the well known formula R + T = 1, where R is the reflectance and T the transmittance, does not hold, and furthermore, R and T loose their accepted meaning. We illustrate the perils of assuming energy flux additivity by calculating the transmission and reflection spectrum of a film over a substrate normally illuminated by incoherent light at frequencies in the neighborhood of an optical resonance. We also show that the usual relation between the scattering, absorption, and extinction cross sections for particles immersed within a dissipative host have to be modified to account for the non additivity.

Macroscopic optical response and photonic bands

by Guillermo Ortiz, Jose Perez, and Luis Mochan

New Journal of Physics, 2013

We develop a formalism for the calculation of the macroscopic dielectric response of composite sy... more We develop a formalism for the calculation of the macroscopic dielectric response of composite systems made of particles of one material embedded periodically within a matrix of another material, each of which is characterized by a well-defined dielectric function. The nature of these dielectric functions is arbitrary, and could correspond to dielectric or conducting, transparent or opaque, absorptive and dispersive materials. The geometry of the particles and the Bravais lattice of the composite are also arbitrary. Our formalism goes beyond the long-wavelength approximation as it fully incorporates retardation effects. We test our formalism through the study of the propagation of electromagnetic waves in two-dimensional photonic crystals made of periodic arrays of cylindrical holes in a dispersionless dielectric host. Our macroscopic theory yields a spatially dispersive macroscopic response which allows the calculation of the full photonic band structure of the system, as well as the characterization of its normal modes, upon substitution into the macroscopic field equations. We can also account approximately for the spatial dispersion through a local magnetic permeability and analyze the resulting dispersion relation, obtaining a region of left handedness.

$Research paper thumbnail of Scaling of light scattered from fractal aggregates at resonance$

Scaling of light scattered from fractal aggregates at resonance

by Guillermo Ortiz and Luis Mochan

Physical Review B, 2003

Due to the scale invariance of fractal aggregates, light scattered from them often decays as a po... more Due to the scale invariance of fractal aggregates, light scattered from them often decays as a power of the scattering wave vector. The exponent in this power law has been usually interpreted as the geometrical fractal dimension. However, the validity of this interpretation is questionable for frequencies close to the resonances of the system, for which multiple scattering becomes important.

Effective optical response of metamaterials

by Guillermo Ortiz and Luis Mochan

Physical Review B, 2009

We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit t... more We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit the frequency dependent macroscopic dielectric response tensor ǫ M ij (ω) of metamaterials made of a matrix with inclusions of any geometrical shape repeated periodically with any lattice structure. We illustrate the formalism calculating ǫ M ij (ω) for several structures. For dielectric rectangular inclusions within a conducting material we obtain an anisotropic response which may change from conductor-like at low ω to dielectric-like with resonances at large ω, attaining a very small reflectance at intermediate frequencies which can be tuned through geometrical tailoring. A simple explanation allowed us to predict and confirm similar behavior for other shapes, even isotropic, close to the percolation threshold.

Nonadditivity of poynting vector within opaque media

by Guillermo Ortiz and Luis Mochan

Journal of the Optical Society of America. A, Optics, image science, and vision, 2005

The energy flux within an opaque medium near an interface is not the sum of an incident plus a re... more The energy flux within an opaque medium near an interface is not the sum of an incident plus a reflected term, as there is a synergistic contribution to the time averaged Poynting vector which involves simultaneously both the incident and reflected fields. Therefore, the well known formula R + T = 1, where R is the reflectance and T the transmittance, does not hold, and furthermore, R and T loose their accepted meaning. We illustrate the perils of assuming energy flux additivity by calculating the transmission and reflection spectrum of a film over a substrate normally illuminated by incoherent light at frequencies in the neighborhood of an optical resonance. We also show that the usual relation between the scattering, absorption, and extinction cross sections for particles immersed within a dissipative host have to be modified to account for the non additivity.

Energy transfer to an anharmonic diatomic system

by Luis Mochan and J. Recamier

Molecular Physics, 2009

We model an anharmonic diatomic molecule using deformed creation and annihilation operators such ... more We model an anharmonic diatomic molecule using deformed creation and annihilation operators such that the energy spectrum generated by a Hamiltonian of the harmonic oscillator's form written in terms of deformed operators is similar to that of a Morse potential. We construct an approximate time evolution operator and evaluate transition probabilities which are compared with those obtained by an expansion in a basis of Morse eigenfunctions. The algebraic results compare favorably with the numerical results.

Effect of plasma waves on the optical properties of conducting superlattices

Phys Rev B, 1987

We calculate the dispersion relation of the electromagnetic normal modes and the reflectance of s... more We calculate the dispersion relation of the electromagnetic normal modes and the reflectance of superlattices made of highly doped semiconductors and of metals, taking into account plasma waves, spatial dispersion, and retardation. We obtain a variety of modes made up of interacting surface and bulk plasmons, which yield a rich structure in the reflectance spectra.

Local Field Effect on the Second Order Susceptibility of Si

Aps March Meeting Abstracts, Mar 1, 1996

We develop a polarizable bond model for the calculation of the linear and non-linear response of ... more We develop a polarizable bond model for the calculation of the linear and non-linear response of tetrahedrally bonded centrosymmetric semiconductors, taking into account the local field effect. We characterize the linear response of each bond by a polarizability tensor with axial and radial independent components. In addition, each bond responds non-linearly to the non-uniform local field with a second order polarizability which is related to the linear one. The linear polarizabilities are fitted to the bulk dielectric response and to the surface induced reflectance anisotropy of the (110) face. Different neighbors contribute large gradients to the local field; these cancel among themselves within the bulk, but they are unbalanced at the surface, where they yield a sizable contribution to the non-linear macroscopic susceptibility. We show that this local field induces a large resonance in the SHG spectra, in agreement with recent experimental observations.(W. Daum et al, Phys.Rev.Lett. 71), 1234 (1993), and J. F. McGilp et al, Opt.Eng. 33, 3895 (1994). We also calculate the SHG symmetry of several faces and find that they reproduce qualitatively the experimental results.

On Casimir forces for media with arbitrary dielectric properties

Revista Mexicana De Fisica, Jul 18, 2002

We derive an expression for the Casimir force between slabs with arbitrary dielectric properties ... more We derive an expression for the Casimir force between slabs with arbitrary dielectric properties characterized by their reflection coefficients. The formalism presented here is applicable to media with a local or a non-local dielectric response, an infinite or a finite width, inhomogeneous dissipative, etc. Our results reduce to the Lifshitz formula for the force between semi-infinite dielectric slabs by replacing the reflection coefficients by the Fresnel amplitudes.

Second harmonic generation at crystal surfaces

J Phys Condens Matter, 1993

ABSTRACT

Diagrammatic approach to the effective dielectric response of composites

Phys Rev B, 1989

We formulate a diagrammatic approach for the calculation of the macroscopic dielectric response o... more We formulate a diagrammatic approach for the calculation of the macroscopic dielectric response of a collection of spheres at random positions and embedded in a homogeneous medium. Through infinite summations of specific classes of diagrams, we derive some known results and we also obtain extensions to a recent theory for the renormalization of the polarizability in the Maxwell Garnett scheme.

Exactly Solvable Model of Surface Sum Frequency Generation

We develop a model for surface sum frequency generation (SFG) consisting of a semiinfinite system... more We develop a model for surface sum frequency generation (SFG) consisting of a semiinfinite system made up of a continuous distribution of harmonic polarizable entities each of which responds non-linearly to the gradient of the field. The near discontinuity of some field components at the surface yields a finite surface susceptibility tensor characterized by the parameters a(omega_3=omega_1+omega_2) and b(omega_3), as

Effective Dielectric Response of Metamaterials

We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit t... more We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit the frequency dependent macroscopic dielectric response tensor ǫ M ij (ω) of metamaterials made of a matrix with inclusions of any geometrical shape repeated periodically with any lattice structure. We illustrate the formalism calculating ǫ M ij (ω) for several structures. For dielectric rectangular inclusions within a conducting material we obtain an anisotropic response which may change from conductor-like at low ω to dielectric-like with resonances at large ω, attaining a very small reflectance at intermediate frequencies which can be tuned through geometrical tailoring. A simple explanation allowed us to predict and confirm similar behavior for other shapes, even isotropic, close to the percolation threshold.

The Casimir Effect for Arbitrary Optically Anisotropic Materials

We extend a fictitious-cavity approach to calculate the Casimir effect for cavities bounded by fl... more We extend a fictitious-cavity approach to calculate the Casimir effect for cavities bounded by flat anisotropic materials. We calculate the energy, force and torque in terms only of the optical coefficients of the walls of the cavity. We calculate the Casimir effect at zero and finite temperature for some simple systems. As a non trivial application, we calculate the torque between a semi-infinite anisotropic plate and an anisotropic film. We study the effect of the film thickness in the torque and find an optimal width that maximizes the torque.

$Research paper thumbnail of <title>Optical properties and scaling in fractal aggregates</title>$

<title>Optical properties and scaling in fractal aggregates</title>

4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications, 2001

ABSTRACT Within the first born approximation, the calculated angular distribution of the light sc... more ABSTRACT Within the first born approximation, the calculated angular distribution of the light scattered by a fractal decays as a power of the scattering wavevector Q, with an exponent given by the fractal dimension df. This has been frequently used experimentally to characterize optically the geometry of fractal systems. The validity of the result above has been questioned for frequencies close to the resonances of the system, for which the first born approximation fails. In this paper we apply a recently developed hierarchical algorithm to calculate the self-consistent near field and the scattered electromagnetic field for 2D colloidal aggregates excited at their resonant frequencies. The local environment of the strongly polarized regions manifests itself in the angular dependence of these scattered intensity corresponding to large Q. For Q within the mass scaling region, the scattering does decay as Q-df for some frequencies, similar to the geometrical structure factor S(Q), but shows no scaling whatsoever for others.