A comprehensive study has been conducted on ultra-broadband optically pumped quantum dot (QD) ref... more A comprehensive study has been conducted on ultra-broadband optically pumped quantum dot (QD) reflective semiconductor optical amplifiers (QD-RSOAs). Furthermore, little work has been done on broadband QD-RSOAs with an optical pump. About 1 μm optical bandwidth, spanning 800 nm up to 1800 nm, is supported for the suggested device by superimposing nine groups of QDs. It has been shown that the device can be engineered to amplify a selected window or a group of desired windows. Moreover, the operation of the device has been thoroughly investigated by solving the coupled differential rate and signal propagation equations. A numerical algorithm has been suggested to solve these equations. As far as we are concerned, a broadband optically pumped QD-RSOA that can operate as a filter has been introduced.
The outbreak of the COVID-19 virus has faced the world with a new and dangerous challenge due to ... more The outbreak of the COVID-19 virus has faced the world with a new and dangerous challenge due to its contagious nature. Hence, developing sensory technologies to detect the coronavirus rapidly can provide a favorable condition for pandemic control of dangerous diseases. In between, because of the nanoscale size of this virus, there is a need for a good understanding of its optical behavior, which can give an extraordinary insight into the more efficient design of sensory devices. For the first time, this paper presents an optical modeling framework for a COVID-19 particle in the blood and extracts its optical characteristics based on numerical computations. To this end, a theoretical foundation of a COVID-19 particle is proposed based on the most recent experimental results available in the literature to simulate the optical behavior of the coronavirus under varying physical conditions. In order to obtain the optical properties of the COVID-19 model, the light reflectance by the str...
Physica A: Statistical Mechanics and its Applications, 2005
Volatility features of the Nordic day ahead power spot market for a 12-year period up till May 20... more Volatility features of the Nordic day ahead power spot market for a 12-year period up till May 2004 are studied. The daily logarithmic volatility was measured for this period to be about 16%. This level is well above what is observed for most other well-studied financial markets. Volatility clustering, log-normal distribution, and long-range correlations are found to be striking features of the volatility of power markets. In addition, a cyclic behavior of the time-dependent volatility can be observed for the Nordic power market. Furthermore, the volatility shows a dependence on the price level, and this is pronounced mostly when the spot price is low. The correlation in volatility is consistent with an inverse power-law decay, t Àn , superposed on an oscillating term. The numerical value of the exponent n is similar to what has been reported previously for stock markets.
The scattering of light from a weakly rough random silver surface characterized by a double recta... more The scattering of light from a weakly rough random silver surface characterized by a double rectangular power spectrum is studied by numerical simulations. This power spectrum can support both the enhanced back and forward scattering phenomena, which for weakly rough surfaces, are both related to the excitation of surface plasmon polaritons. Here we review these phenomena and present new results from a numerical study of the dependence of the diffuse scattering on the amplitudes (γi, i = 1, 2) of the two rectangular portions of the power spectrum. It is found that there exist an optimal range of ratios, γ2/γ1, over which forward scattering peaks can be observed. By just changing the correlations along the interface, while keeping all other parameters like roughness, polarization, and angle of incidence unchanged, the fraction of the incident light that is scattered diffusely can be as large as 16%, while for other parameters as small as 1%. Moreover, a change in the correlation function only, can result in a 3.5 times increase in the amount of light that is absorbed at the weakly rough metal interface (σ = 10 nm).
No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depen... more No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field of rough surface scattering of electromagnetic waves is addressed. This topic has implications and practical applications in fields as diverse as observational astronomy and the electronics industry. This article reviews the theoretical and computational foundation and methods used in the study of rough surface scattering. Furthermore, it presents and explains the physical origin of a series of multiple scattering surface phenomena. In particular what is discussed are: the enhanced backscattering and satellite peak phenomena, coherent effects in angular intensity correlation functions and second harmonic generated light (a non-linear effect).
Mask-based pattern generation is a crucial step in microchip production. The next-generation extr... more Mask-based pattern generation is a crucial step in microchip production. The next-generation extreme-ultraviolet-(EUV) lithography instruments with a wavelength of 13.5 nm is currently under development. In principle, this should allow patterning down to a resolution of a few nanometers in a single exposure. However, there are many technical challenges, including those due to the very high energy of the photons. Lithography with metastable atoms has been suggested as a cost-effective, less-complex alternative to EUV lithography. The great advantage of atom lithography is that the kinetic energy of an atom is much smaller than that of a photon for a given wavelength. However, up till now no method has been available for making masks for atom lithography that can produce arbitrary, high resolution patterns. Here we present a solution to this problem. First, traditional binary holography is extended to near-field binary holography, based on Fresnel diffraction. By this technique, we demonstrate that it is possible to make masks that can generate arbitrary patterns in a plane in the near field (from the mask) with a resolution down to the nanometer range using a state of the art metastable helium source. We compare the flux of this source to that of an established EUV source (ASML, NXE:3100) and show that patterns can potentially be produced at comparable speeds. Finally, we present an extension of the grid-based holography method for a grid of hexagonally shaped subcells. Our method can be used with any beam that can be modeled as a scalar wave, including other matter-wave beams such as helium ions, electrons or acoustic waves.
Over the last decade, an enormous interest and activity in complex networks have been witnessed w... more Over the last decade, an enormous interest and activity in complex networks have been witnessed within the physics community. On the other hand, diffusion and its theory, have equipped the toolbox of the physicist for decades. In this paper, we will demonstrate how to combine these two seemingly different topics in a fruitful manner. In particular, we will review and develop further, an auxiliary diffusive process on weighted networks that represents a powerful concept and tool for studying network (community) structures. The working principle of the method is the observation that the relaxation of the diffusive process towards the stationary state is non-local and fastest in the highly connected regions of the network. This can be used to acquire non-trivial information about the structure of clustered and non-clustered networks.
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichl... more The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of the diffracted Bragg beams. From the results of these calculations the diffraction efficiencies of several of the lowest order diffracted beams are calculated as functions of the polar and azimuthal angles of incidence. The angular dependencies of the diffraction efficiencies display features that can be identified as Rayleigh anomalies for both types of surfaces. In the case of a Neumann surface additional features are present that can be attributed to the existence of surface waves on such surfaces. Some of the results obtained through the use of the Rayleigh equation are validated by comparing them with results of a rigorous Green's function numerical calculation.
In recent publications, the authors have considered inverse statistics of the Dow Jones Industria... more In recent publications, the authors have considered inverse statistics of the Dow Jones Industrial Averaged (DJIA) [1, 2, 3]. Specifically, we argued that the natural candidate for such statistics is the investment horizons distribution. This is the distribution of waiting times needed to achieve a predefined level of return obtained from detrended historic asset prices. Such a distribution typically goes through a maximum at a time coined the optimal investment horizon, τ ρ , which defines the most likely waiting time for obtaining a given return ρ. By considering equal positive and negative levels of return, we reported in [2, 3] on a quantitative gain/loss asymmetry most pronounced for short horizons. In the present paper, this gain/loss asymmetry is re-visited for 2/3 of the individual stocks presently in the DJIA. We show that this gain/loss asymmetry established for the DJIA surprisingly is not present in the time series of the individual stocks. The most reasonable explanatio...
2017 International Applied Computational Electromagnetics Society Symposium - Italy (ACES), 2017
We show how to design a one-dimensional randomly rough interface between two dielectric media tha... more We show how to design a one-dimensional randomly rough interface between two dielectric media that, when illuminated at normal incidence by a Gaussian beam, produces a transmitted beam whose spectral density in the mean interface has a Gaussian form, while its spectral degree of coherence in this plane has a nearly arbitrary form.
An approach is presented for the inversion of experimental in-plane, co-polarized light scatterin... more An approach is presented for the inversion of experimental in-plane, co-polarized light scattering data in p and s polarization to obtain the normalized surface-height autocorrelation function and the rms-roughness of a two-dimensional randomly rough metal surface. The approach is based on an expression, obtained on the basis of second-order phase perturbation theory, for the contribution to the mean differential reflection coefficient from the light scattered diffusely by the rough surface. The inversion scheme is validated by using several sets of computer generated scattering data for rough silver surfaces defined by Gaussian surface height correlation functions. The reconstructions obtained by this approach are found to be rather accurate for weakly rough surfaces illuminated by pand s-polarized incident light; this is also true in cases where the contributions to the input data from multiple scattering of surface plasmon polaritons is not insignificant. Finally, the inversion s...
Raul Donangelo, ∗ Mogens H. Jensen, † Ingve Simonsen, 4, ‡ and Kim Sneppen § Instituto de Fisica ... more Raul Donangelo, ∗ Mogens H. Jensen, † Ingve Simonsen, 4, ‡ and Kim Sneppen § Instituto de Fisica da UFRJ, Caixa Postal 68528, 21941-972 Rio de Janeiro, Brazil The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark Department of physics, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark (Dated: February 2, 2008)
An approach is introduced for the non-parametric reconstruction of the statistical properties of ... more An approach is introduced for the non-parametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data. Starting from expressions within the Kirchhoff approximation for the light scattered diffusely by a two-dimensional randomly rough surface, an analytic expression for the normalized surface height correlation function is obtained as an integral over the in-plane and co-polarized scattering data with the introduction of only a couple of additional approximations. The inversion approach consists of two main steps. In the first step the surface roughness is estimated. Next, this value is used to obtain the functional form of the surface height correlation function without initially assuming any particular form for this function (non-parametric inversion). The input data used in validating this inversion approach consist of in-plane and co-polarized scattering data obtained for different forms of the correlation function by either computer simulations or by experiments for two-dimensional randomly rough dielectric or metallic surfaces. Good agreement was obtained between the correlation function and surface roughness obtained during the reconstruction and the corresponding quantities assumed when generating the input scattering data; this was the case for both dielectric and metallic surfaces, for both p-and s-polarized light, and for different polar angles of incidence. The proposed inversion approach provides an accurate, efficient, robust and contact-less method based on in-plane and co-polarized scattering data for the non-parametric characterization of the statistical properties of isotropic two-dimensional randomly rough dielectric and metallic surface.
International Journal of Antennas and Propagation, 2018
By the use of phase perturbation theory we show that if a single realization of a one-dimensional... more By the use of phase perturbation theory we show that if a single realization of a one-dimensional randomly rough interface between two dielectric media is illuminated at normal incidence from either medium by a broadband Gaussian beam, it produces a scattered field whose differential reflection coefficient closely matches the result produced by averaging the differential reflection coefficient produced by a monochromatic incident beam over the ensemble of realizations of the interface profile function.
Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces is studied for th... more Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces is studied for the purpose of using the intensity scattered from them to obtain the Hurst exponent and topothesy that characterize the self-affine roughness. By the use of the Kirchhoff approximation a closed form mathematical expression for the angular dependence of the mean differential reflection coefficient is derived under the assumption that the surface is illuminated by a plane incident wave. It is shown that this quantity can be expressed in terms of the isotropic, bivariate (α-stable) Lévy distribution of a stability parameter that is two times the Hurst exponent of the underlying surface. Features of the expression for the mean differential reflection coefficient are discussed, and its predictions compare favorably over large regions of parameter space to results obtained from rigorous computer simulations based on equations of scattering theory. It is demonstrated how the Hurst exponent and the topothesy of the self-affine surface can be inferred from scattering data it produces. Finally several possible scattering configurations are discussed that allow for an efficient extraction of these self-affine parameters.
By the use of both perturbative and non-perturbative solutions of the reduced Rayleigh equation, ... more By the use of both perturbative and non-perturbative solutions of the reduced Rayleigh equation, we present a detailed study of the scattering of light from two-dimensional weakly rough dielectric films. It is shown that for several rough film configurations, Selényi interference rings exist in the diffusely scattered light. For film systems supported by dielectric substrates where only one of the two interfaces of the film is weakly rough and the other planar, Selényi interference rings are observed at angular positions that can be determined from simple phase arguments. For such single-rough-interface films, we find and explain by a single scattering model that the contrast in the interference patterns is better when the top interface of the film (the interface facing the incident light) is rough than when the bottom interface is rough. When both film interfaces are rough, Selényi interference rings exist but a potential cross-correlation of the two rough interfaces of the film can be used to selectively enhance some of the interference rings while others are attenuated and might even disappear. This feature may in principle be used in determining the correlation properties of interfaces of films that otherwise would be difficult to access.
By the use of the Rayleigh method we have calculated the angular dependence of the reflectivity a... more By the use of the Rayleigh method we have calculated the angular dependence of the reflectivity and the efficiencies of several other diffracted orders when the periodically corrugated surface of an isotropic elastic medium is illuminated by a volume acoustic wave of shear horizontal polarization. These dependencies display the signatures of Rayleigh and Wood anomalies, usually associated with the diffraction of light from a metallic grating. The Rayleigh anomalies occur at angles of incidence at which a diffracted order appears or disappears; the Wood anomalies here are caused by the excitation of the shear horizontal surface acoustic waves supported by the periodically corrugated surface of an isotropic elastic medium. The dispersion curves of these waves in both the nonradiative and radiative regions of the frequency-wavenumber plane are calculated, and used in predicting the angles of incidence at which the Wood anomalies are expected to occur.
A comprehensive study has been conducted on ultra-broadband optically pumped quantum dot (QD) ref... more A comprehensive study has been conducted on ultra-broadband optically pumped quantum dot (QD) reflective semiconductor optical amplifiers (QD-RSOAs). Furthermore, little work has been done on broadband QD-RSOAs with an optical pump. About 1 μm optical bandwidth, spanning 800 nm up to 1800 nm, is supported for the suggested device by superimposing nine groups of QDs. It has been shown that the device can be engineered to amplify a selected window or a group of desired windows. Moreover, the operation of the device has been thoroughly investigated by solving the coupled differential rate and signal propagation equations. A numerical algorithm has been suggested to solve these equations. As far as we are concerned, a broadband optically pumped QD-RSOA that can operate as a filter has been introduced.
The outbreak of the COVID-19 virus has faced the world with a new and dangerous challenge due to ... more The outbreak of the COVID-19 virus has faced the world with a new and dangerous challenge due to its contagious nature. Hence, developing sensory technologies to detect the coronavirus rapidly can provide a favorable condition for pandemic control of dangerous diseases. In between, because of the nanoscale size of this virus, there is a need for a good understanding of its optical behavior, which can give an extraordinary insight into the more efficient design of sensory devices. For the first time, this paper presents an optical modeling framework for a COVID-19 particle in the blood and extracts its optical characteristics based on numerical computations. To this end, a theoretical foundation of a COVID-19 particle is proposed based on the most recent experimental results available in the literature to simulate the optical behavior of the coronavirus under varying physical conditions. In order to obtain the optical properties of the COVID-19 model, the light reflectance by the str...
Physica A: Statistical Mechanics and its Applications, 2005
Volatility features of the Nordic day ahead power spot market for a 12-year period up till May 20... more Volatility features of the Nordic day ahead power spot market for a 12-year period up till May 2004 are studied. The daily logarithmic volatility was measured for this period to be about 16%. This level is well above what is observed for most other well-studied financial markets. Volatility clustering, log-normal distribution, and long-range correlations are found to be striking features of the volatility of power markets. In addition, a cyclic behavior of the time-dependent volatility can be observed for the Nordic power market. Furthermore, the volatility shows a dependence on the price level, and this is pronounced mostly when the spot price is low. The correlation in volatility is consistent with an inverse power-law decay, t Àn , superposed on an oscillating term. The numerical value of the exponent n is similar to what has been reported previously for stock markets.
The scattering of light from a weakly rough random silver surface characterized by a double recta... more The scattering of light from a weakly rough random silver surface characterized by a double rectangular power spectrum is studied by numerical simulations. This power spectrum can support both the enhanced back and forward scattering phenomena, which for weakly rough surfaces, are both related to the excitation of surface plasmon polaritons. Here we review these phenomena and present new results from a numerical study of the dependence of the diffuse scattering on the amplitudes (γi, i = 1, 2) of the two rectangular portions of the power spectrum. It is found that there exist an optimal range of ratios, γ2/γ1, over which forward scattering peaks can be observed. By just changing the correlations along the interface, while keeping all other parameters like roughness, polarization, and angle of incidence unchanged, the fraction of the incident light that is scattered diffusely can be as large as 16%, while for other parameters as small as 1%. Moreover, a change in the correlation function only, can result in a 3.5 times increase in the amount of light that is absorbed at the weakly rough metal interface (σ = 10 nm).
No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depen... more No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field of rough surface scattering of electromagnetic waves is addressed. This topic has implications and practical applications in fields as diverse as observational astronomy and the electronics industry. This article reviews the theoretical and computational foundation and methods used in the study of rough surface scattering. Furthermore, it presents and explains the physical origin of a series of multiple scattering surface phenomena. In particular what is discussed are: the enhanced backscattering and satellite peak phenomena, coherent effects in angular intensity correlation functions and second harmonic generated light (a non-linear effect).
Mask-based pattern generation is a crucial step in microchip production. The next-generation extr... more Mask-based pattern generation is a crucial step in microchip production. The next-generation extreme-ultraviolet-(EUV) lithography instruments with a wavelength of 13.5 nm is currently under development. In principle, this should allow patterning down to a resolution of a few nanometers in a single exposure. However, there are many technical challenges, including those due to the very high energy of the photons. Lithography with metastable atoms has been suggested as a cost-effective, less-complex alternative to EUV lithography. The great advantage of atom lithography is that the kinetic energy of an atom is much smaller than that of a photon for a given wavelength. However, up till now no method has been available for making masks for atom lithography that can produce arbitrary, high resolution patterns. Here we present a solution to this problem. First, traditional binary holography is extended to near-field binary holography, based on Fresnel diffraction. By this technique, we demonstrate that it is possible to make masks that can generate arbitrary patterns in a plane in the near field (from the mask) with a resolution down to the nanometer range using a state of the art metastable helium source. We compare the flux of this source to that of an established EUV source (ASML, NXE:3100) and show that patterns can potentially be produced at comparable speeds. Finally, we present an extension of the grid-based holography method for a grid of hexagonally shaped subcells. Our method can be used with any beam that can be modeled as a scalar wave, including other matter-wave beams such as helium ions, electrons or acoustic waves.
Over the last decade, an enormous interest and activity in complex networks have been witnessed w... more Over the last decade, an enormous interest and activity in complex networks have been witnessed within the physics community. On the other hand, diffusion and its theory, have equipped the toolbox of the physicist for decades. In this paper, we will demonstrate how to combine these two seemingly different topics in a fruitful manner. In particular, we will review and develop further, an auxiliary diffusive process on weighted networks that represents a powerful concept and tool for studying network (community) structures. The working principle of the method is the observation that the relaxation of the diffusive process towards the stationary state is non-local and fastest in the highly connected regions of the network. This can be used to acquire non-trivial information about the structure of clustered and non-clustered networks.
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichl... more The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of the diffracted Bragg beams. From the results of these calculations the diffraction efficiencies of several of the lowest order diffracted beams are calculated as functions of the polar and azimuthal angles of incidence. The angular dependencies of the diffraction efficiencies display features that can be identified as Rayleigh anomalies for both types of surfaces. In the case of a Neumann surface additional features are present that can be attributed to the existence of surface waves on such surfaces. Some of the results obtained through the use of the Rayleigh equation are validated by comparing them with results of a rigorous Green's function numerical calculation.
In recent publications, the authors have considered inverse statistics of the Dow Jones Industria... more In recent publications, the authors have considered inverse statistics of the Dow Jones Industrial Averaged (DJIA) [1, 2, 3]. Specifically, we argued that the natural candidate for such statistics is the investment horizons distribution. This is the distribution of waiting times needed to achieve a predefined level of return obtained from detrended historic asset prices. Such a distribution typically goes through a maximum at a time coined the optimal investment horizon, τ ρ , which defines the most likely waiting time for obtaining a given return ρ. By considering equal positive and negative levels of return, we reported in [2, 3] on a quantitative gain/loss asymmetry most pronounced for short horizons. In the present paper, this gain/loss asymmetry is re-visited for 2/3 of the individual stocks presently in the DJIA. We show that this gain/loss asymmetry established for the DJIA surprisingly is not present in the time series of the individual stocks. The most reasonable explanatio...
2017 International Applied Computational Electromagnetics Society Symposium - Italy (ACES), 2017
We show how to design a one-dimensional randomly rough interface between two dielectric media tha... more We show how to design a one-dimensional randomly rough interface between two dielectric media that, when illuminated at normal incidence by a Gaussian beam, produces a transmitted beam whose spectral density in the mean interface has a Gaussian form, while its spectral degree of coherence in this plane has a nearly arbitrary form.
An approach is presented for the inversion of experimental in-plane, co-polarized light scatterin... more An approach is presented for the inversion of experimental in-plane, co-polarized light scattering data in p and s polarization to obtain the normalized surface-height autocorrelation function and the rms-roughness of a two-dimensional randomly rough metal surface. The approach is based on an expression, obtained on the basis of second-order phase perturbation theory, for the contribution to the mean differential reflection coefficient from the light scattered diffusely by the rough surface. The inversion scheme is validated by using several sets of computer generated scattering data for rough silver surfaces defined by Gaussian surface height correlation functions. The reconstructions obtained by this approach are found to be rather accurate for weakly rough surfaces illuminated by pand s-polarized incident light; this is also true in cases where the contributions to the input data from multiple scattering of surface plasmon polaritons is not insignificant. Finally, the inversion s...
Raul Donangelo, ∗ Mogens H. Jensen, † Ingve Simonsen, 4, ‡ and Kim Sneppen § Instituto de Fisica ... more Raul Donangelo, ∗ Mogens H. Jensen, † Ingve Simonsen, 4, ‡ and Kim Sneppen § Instituto de Fisica da UFRJ, Caixa Postal 68528, 21941-972 Rio de Janeiro, Brazil The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark Department of physics, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark (Dated: February 2, 2008)
An approach is introduced for the non-parametric reconstruction of the statistical properties of ... more An approach is introduced for the non-parametric reconstruction of the statistical properties of penetrable, isotropic randomly rough surfaces from in-plane, co-polarized light scattering data. Starting from expressions within the Kirchhoff approximation for the light scattered diffusely by a two-dimensional randomly rough surface, an analytic expression for the normalized surface height correlation function is obtained as an integral over the in-plane and co-polarized scattering data with the introduction of only a couple of additional approximations. The inversion approach consists of two main steps. In the first step the surface roughness is estimated. Next, this value is used to obtain the functional form of the surface height correlation function without initially assuming any particular form for this function (non-parametric inversion). The input data used in validating this inversion approach consist of in-plane and co-polarized scattering data obtained for different forms of the correlation function by either computer simulations or by experiments for two-dimensional randomly rough dielectric or metallic surfaces. Good agreement was obtained between the correlation function and surface roughness obtained during the reconstruction and the corresponding quantities assumed when generating the input scattering data; this was the case for both dielectric and metallic surfaces, for both p-and s-polarized light, and for different polar angles of incidence. The proposed inversion approach provides an accurate, efficient, robust and contact-less method based on in-plane and co-polarized scattering data for the non-parametric characterization of the statistical properties of isotropic two-dimensional randomly rough dielectric and metallic surface.
International Journal of Antennas and Propagation, 2018
By the use of phase perturbation theory we show that if a single realization of a one-dimensional... more By the use of phase perturbation theory we show that if a single realization of a one-dimensional randomly rough interface between two dielectric media is illuminated at normal incidence from either medium by a broadband Gaussian beam, it produces a scattered field whose differential reflection coefficient closely matches the result produced by averaging the differential reflection coefficient produced by a monochromatic incident beam over the ensemble of realizations of the interface profile function.
Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces is studied for th... more Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces is studied for the purpose of using the intensity scattered from them to obtain the Hurst exponent and topothesy that characterize the self-affine roughness. By the use of the Kirchhoff approximation a closed form mathematical expression for the angular dependence of the mean differential reflection coefficient is derived under the assumption that the surface is illuminated by a plane incident wave. It is shown that this quantity can be expressed in terms of the isotropic, bivariate (α-stable) Lévy distribution of a stability parameter that is two times the Hurst exponent of the underlying surface. Features of the expression for the mean differential reflection coefficient are discussed, and its predictions compare favorably over large regions of parameter space to results obtained from rigorous computer simulations based on equations of scattering theory. It is demonstrated how the Hurst exponent and the topothesy of the self-affine surface can be inferred from scattering data it produces. Finally several possible scattering configurations are discussed that allow for an efficient extraction of these self-affine parameters.
By the use of both perturbative and non-perturbative solutions of the reduced Rayleigh equation, ... more By the use of both perturbative and non-perturbative solutions of the reduced Rayleigh equation, we present a detailed study of the scattering of light from two-dimensional weakly rough dielectric films. It is shown that for several rough film configurations, Selényi interference rings exist in the diffusely scattered light. For film systems supported by dielectric substrates where only one of the two interfaces of the film is weakly rough and the other planar, Selényi interference rings are observed at angular positions that can be determined from simple phase arguments. For such single-rough-interface films, we find and explain by a single scattering model that the contrast in the interference patterns is better when the top interface of the film (the interface facing the incident light) is rough than when the bottom interface is rough. When both film interfaces are rough, Selényi interference rings exist but a potential cross-correlation of the two rough interfaces of the film can be used to selectively enhance some of the interference rings while others are attenuated and might even disappear. This feature may in principle be used in determining the correlation properties of interfaces of films that otherwise would be difficult to access.
By the use of the Rayleigh method we have calculated the angular dependence of the reflectivity a... more By the use of the Rayleigh method we have calculated the angular dependence of the reflectivity and the efficiencies of several other diffracted orders when the periodically corrugated surface of an isotropic elastic medium is illuminated by a volume acoustic wave of shear horizontal polarization. These dependencies display the signatures of Rayleigh and Wood anomalies, usually associated with the diffraction of light from a metallic grating. The Rayleigh anomalies occur at angles of incidence at which a diffracted order appears or disappears; the Wood anomalies here are caused by the excitation of the shear horizontal surface acoustic waves supported by the periodically corrugated surface of an isotropic elastic medium. The dispersion curves of these waves in both the nonradiative and radiative regions of the frequency-wavenumber plane are calculated, and used in predicting the angles of incidence at which the Wood anomalies are expected to occur.
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Papers by Ingve Simonsen