349 research outputs found
On the Simulation of Electromagnetic Wave Scattering by Periodic and Randomly Rough Layered Structures based on the Reduced Rayleigh Equations: Theory, numerical analysis and applications
No full textA great number of natural phenomena that we observe, as well as numerous man-made objects we use in our everyday life, are made possible thanks to the interaction between light and matter. In particular, when light is interacting with a surface between two homogeneous media, light may be scattered either diffusely or with specific diffraction properties depending on the level of roughness and geometrical structure of the surface. From one extreme to the other, a perfectly smooth surface will reflect a laser beam only along the specular direction according to the well known Snell-Descartes law of reflection. If the surface is a grating and possesses periodic undulations whose period is of the order of a few wavelength, the laser beam will be diffracted into a set of well defined directions. Now if the undulations on the surface are random and do not exhibit any periodicity, and the level of roughness is comparable to the wavelength, the laser beam will be scattered broadly and become diffuse.
The present thesis deals with the scattering of light by structured and randomly rough surfaces. The study is carried out within the theoretical framework of the so-called reduced Rayleigh equations. This framework is particularly well adapted to the study of weakly rough surfaces and allows for simple approximations which are easy to implement, fast to compute and can give physical insights into some phenomena observed in the diffusely scattered light.
Two such phenomena, the Yoneda ring phenomenon and the Brewster scattering phenomenon, have been observed experimentally and numerically for decades but were lacking clear physical explanations. The work presented in this thesis shed new light on these effects and provides a clear physical interpretation. The Yoneda ring is a ring of enhanced intensity in the diffusely scattered light observed in the medium of highest refractive index. The Brewster scattering phenomenon is the observation of minima, or near zero, of intensity in the diffuse scattered light for polarized light. The proposed theory explains these two phenomena respectively in terms of coupled progressive-evanescent modes and in terms of the dipole radiation from the microscopic scatterers in the materials (atoms, molecules). In the latter, the fundamental role of Snell-conjugate waves is discussed and a simple but powerful geometrical interpretation is presented. Two new phenomena were also predicted by the theory for light scattering under total internal reflection: (i) what we have called the s-black-out phenomenon for which the diffusely scattered light is purely p-polarized independently of the scattering direction, and which occurs exactly at the critical incidence for total internal reflection and is associated with the alignment of the elementary oscillating dipoles along the axis normal to the average surface plane; (ii) a linearly to circularly polarized Brewster scattering effect for incidences beyond the total internal reflection incidence which was shown to be caused by a regime in which dipoles in the materials are no longer oscillating but rotating.
After the study of the scattering by a single rough surface, the scattering by a film whose interfaces are rough was analyzed. In particular, we have been interested in a case where the film thickness is of the order of a few wavelength such that interference rings in the diffuse scattered light, known as Selényi rings, could be observed. We have demonstrated theoretically that, in a single scattering regime, the cross-correlation between the two-rough surfaces of the dielectric film induces a selective intensity enhancement and attenuation of the Selényi rings. This is a clear example of correlation induced interference, an effect of fundamental interest here, but which may be useful for surface characterization and for the design of disordered optical material by engineering correlation.
Finally, we have demonstrated a powerful technique for parameter retrieval, or inverse scattering of surfaces, based on the reduced Rayleigh equations. The method was applied successfully to a plasmonic photonic surface based on experimental Mueller matrix ellipsometry measurements, with a demonstrated accuracy of a couple of nanometers and a speed-up factor of a hundred compared with the use of a commercial the finite element software. The method based on the reduced Rayleigh equations has, however, a limited range of validit
Theoretical and computational studies of the scattering of light from randomly rough dielectric surfaces
No full textWe are surrounded by light being scattered from surfaces all around us, both natural and man-made. Improving our understanding of exactly how light (and more generally, electromagnetic waves) interacts with and scatters from or through surfaces, such as a solar cell, a telescope mirror, paint or a glass window, is of value and importance to both industry and society as a whole. It gives us a better understanding of the world around us and how we perceive it, and it can also enable us to develop new technologies and improve upon existing ones.
This thesis is a collection of work where we have tried to better understand a few of these interactions through the use of theory, experimental results and computer simulations.
We have investigated the scattering of polarized light from two-dimensional randomly rough dielectric interfaces, in order to look for scattering patterns of interest in the angular intensity distributions of the diffusely scattered light. The basis for our investigations has been the reduced Rayleigh equations and their numerical solutions. Our overall contribution is towards an increased understanding of diffuse scattering from randomly rough surfaces, especially for three-dimensional systems where we allow for cross-polarized scattering. This can be useful in a wide range of optical systems, since the non-invasive method of surface characterization through the analysis of scattering data is interesting for both industry and research.
When light is scattered diffusely in either reflection or transmission from or through a weakly rough interface, two phenomena of interest can be observed in the scattering intensity distributions. These are the Yoneda phenomenon, relatable to the idea of total internal reflection from a planar interface, and the Brewster scattering phenomenon, relatable to the polarizing angle observed for a planar interface. These scattering phenomena have only partially been investigated in the past, and their study has been the core of this thesis. We investigate these phenomena thoroughly through perturbative and non-perturbative numerical and theoretical work, also with the aid of new experimental results. We show, describe, explain and predict the behavior of both phenomena based on a lowest non-zero order perturbative approach, and as such we conclude that they are so-called single-scattering phenomena. We also investigate the physical mechanisms that underpin these phenomena, and attempt to describe them in terms of simple notions such as scalar waves, oscillating and rotating dipoles and geometrical arguments.
If you let sunlight reflect from the layer of water vapor hovering some micrometers above the reflective surface of your morning cup of tea, you might observe some colored rings of light when you look into the reflection. These rings are a variety of Selenyi rings, an interesting interference effect that emerges when light is scattered diffusely by thin dielectric films. We investigate this effect thoroughly in this thesis, and describe the Selenyi phenomenon theoretically and numerically.
Lastly, when medium interfaces are randomly rough, it is of value if we can infer the statistical properties of the roughness along with the properties of the scattering media based purely on the non-invasive scattering of light. Through the use of numerical phase perturbation theory based on the reduced Rayleigh equations, we investigate the reconstruction of such properties through a minimization method based on the reflected intensity distributions
Plasmonic response of supported and interacting spherical nanoparticles
No full textPartikkelvekst er vanlig i vitenskap og diverse industrier. De optiske egenskapene til nanopartikler dyrket på et substrat er nyttige når det gjelder overvåking av tykkelsen og sammensetningen til den tynne filmen. Programvarepakken GranFilm implementert av I. Simonsen and R. Lazzari er basert på arbeidet til D. Bedeaux og J. Vlieger, som antar den kvasistatiske approksimasjonen. Den beregner lineære optiske koeffisienter for sfærer og sfæroider trunkert av et substrat. Programvaren tar i betraktning samspillet med substratet og de andre partiklene. Den tillater høy orden i multipolutviklingen som omhandler samspillet med substratet, men er begrenset til kvadrupol orden i multipolutviklingen som omhandler samspillet mellom partiklene. En pythonkode er skrevet for hele sfærer over et substrat og tar dermed høy orden i betraktning av samspillet mellom partiklene. Fra sammenligning er grensen for hvor kvadrupolapproksimasjonen bryter ned funnet til å være en overflatetetthet på 55% for et Al2O3 substrat og 45% for et TiO2 substrat. Resonansen til de optiske koeffisientene er studert sammen med nærfeltsberegningene. Lavere høyder over substratet induserer rødforskyvninger av energiposisjonene til resonansene for alle retninger for det innkommende elektriske feltet, og den største rødforskyvningen oppnås for innkommende elektrisk felt parallelt med z-aksen. Kortere avstander mellom nabosfærer induserer en større rødforskyvning enn tilsvarende minking av høyde, men kun for innkommende felt parallelt med en kort gittervektor. Ellers vil kortere avstander indusere en svak blåforskyvning som følge av symmetriske potensialøkninger istedenfor antisymmetriske, og Coulombkraften vil da fungere som en gjenopprettende kraft. Til slutt er multipolutviklingsmetoden sammenlignet med den diskrete dipolapproksimasjonsprogramvaren DDSCAT med gode overenstemmelser med unntak av området i nærheten av resonansene. Diskretiseringen på 523 305 punktdipoler er utilstrekkelig for nøyaktige resultater når feltøkningene er på deres største.Particle growth is common in various industries and sciences. The optical properties of nanoparticles grown on a substrate are useful when trying to monitor the layer thickness or the composition of the thin film. The software package GranFilm implemented by I. Simonsen and R. Lazzari is based on the work of D. Bedeaux and J. Vlieger, which assumes the quasi-static approximation. It computes linear optical coefficients for truncated spheres and spheroids by a substrate, taking account for the interaction with the substrate and other particles. The software package allows for high order in the multipole expansion regarding interaction with the substrate, but is limited to quadrupole order for the multipole expansion regarding interaction between the particles. A python code is written for full spheres above the substrate taking high order interaction between particles into account. By comparison, the quadrupole approximation breaks down for a surface density of 55% for an Al2O3 substrate and 45% for a TiO2 substrate. The resonances of the optical coefficients are studied along with the near field calculations. Lower heights above the substrate induce red shifts of the energy positions of the resonances for any direction of the incident electric field, and the largest red shift is obtained for incident electric field parallel to the z-axis. Shorter distances between neighbouring spheres induce a larger red shift than the corresponding decrease in height, but only if the incident field is parallel to a short lattice vector. Otherwise, the shorter distances induce a slight blue shift due to the potential enhancements being symmetric rather than anti-symmetric, and the Coulomb force is hence acting as a restoring force. Lastly, the multipole expansion method is compared to the discrete dipole approximation software DDSCAT with great agreement except in the region near the resonances. The discretisation at 523 305 point dipoles is insufficient for obtaining accurate results where the field enhancements are at their largest
Plasmonic response of supported and interacting spherical nanoparticles
No full textPartikkelvekst er vanlig i vitenskap og diverse industrier. De optiske egenskapene til nanopartikler dyrket på et substrat er nyttige når det gjelder overvåking av tykkelsen og sammensetningen til den tynne filmen. Programvarepakken GranFilm implementert av I. Simonsen and R. Lazzari er basert på arbeidet til D. Bedeaux og J. Vlieger, som antar den kvasistatiske approksimasjonen. Den beregner lineære optiske koeffisienter for sfærer og sfæroider trunkert av et substrat. Programvaren tar i betraktning samspillet med substratet og de andre partiklene. Den tillater høy orden i multipolutviklingen som omhandler samspillet med substratet, men er begrenset til kvadrupol orden i multipolutviklingen som omhandler samspillet mellom partiklene. En pythonkode er skrevet for hele sfærer over et substrat og tar dermed høy orden i betraktning av samspillet mellom partiklene. Fra sammenligning er grensen for hvor kvadrupolapproksimasjonen bryter ned funnet til å være en overflatetetthet på 55% for et Al2O3 substrat og 45% for et TiO2 substrat. Resonansen til de optiske koeffisientene er studert sammen med nærfeltsberegningene. Lavere høyder over substratet induserer rødforskyvninger av energiposisjonene til resonansene for alle retninger for det innkommende elektriske feltet, og den største rødforskyvningen oppnås for innkommende elektrisk felt parallelt med z-aksen. Kortere avstander mellom nabosfærer induserer en større rødforskyvning enn tilsvarende minking av høyde, men kun for innkommende felt parallelt med en kort gittervektor. Ellers vil kortere avstander indusere en svak blåforskyvning som følge av symmetriske potensialøkninger istedenfor antisymmetriske, og Coulombkraften vil da fungere som en gjenopprettende kraft. Til slutt er multipolutviklingsmetoden sammenlignet med den diskrete dipolapproksimasjonsprogramvaren DDSCAT med gode overenstemmelser med unntak av området i nærheten av resonansene. Diskretiseringen på 523 305 punktdipoler er utilstrekkelig for nøyaktige resultater når feltøkningene er på deres største
Mario Henrique Simonsen
No full textO AUTOR inicia o artigo efetuando uma breve revisão da literatura nacional que analisa as contribuições de Mario Henrique Simonsen à teoria econômica. Em seguida, detalham-se quatro pontos não abordados nos trabalhos revistos. Em particular, sua derradeira contribuição, referente à literatura sobre os custos de bem-estar da inflação, pesquisa que deu origem recentemente, cinco anos após o seu falecimento, a um artigo publicado no prestigioso Journal of Money, Credit and Banking.THE AUTHOR starts the article by presenting a short a review of the Brazilian literature concerning the academic contributions of Mario Henrique Simonsen. In a subsequent step, four points not included in the works surveyed are detailed. Particularly, his last contribution, related to the welfare costs of inflation, which lead to an article published in February of 2001, five years after his death, in the prestigious Journal of Money Credit and Banking
Mario Henrique Simonsen
No full textO AUTOR inicia o artigo efetuando uma breve revisão da literatura nacional que analisa as contribuições de Mario Henrique Simonsen à teoria econômica. Em seguida, detalham-se quatro pontos não abordados nos trabalhos revistos. Em particular, sua derradeira contribuição, referente à literatura sobre os custos de bem-estar da inflação, pesquisa que deu origem recentemente, cinco anos após o seu falecimento, a um artigo publicado no prestigioso Journal of Money, Credit and Banking.THE AUTHOR starts the article by presenting a short a review of the Brazilian literature concerning the academic contributions of Mario Henrique Simonsen. In a subsequent step, four points not included in the works surveyed are detailed. Particularly, his last contribution, related to the welfare costs of inflation, which lead to an article published in February of 2001, five years after his death, in the prestigious Journal of Money Credit and Banking
Numerical Simulations of Scattering of Light from Two-Dimensional Rough Surfaces Using the Reduced Rayleigh Equation
No full textA formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation (RRE) for the scattering of light from two-dimensional penetrable rough surfaces. Implementation and performance issues of the method, and various consistency checks of it, are presented and discussed. The proposed method is found, within the validity of the Rayleigh hypothesis, to give reliable results. For a non-absorbing metal surface the conservation of energy was explicitly checked, and found to be satisfied to within 0.03%, or better, for the parameters assumed. This testifies to the accuracy of the approach and a satisfactory discretization. As an illustration, we calculate the full angular distribution of the mean differential reflection coefficient for the scattering of p- or s-polarized light incident on two-dimensional dielectric or metallic randomly rough surfaces defined by (isotropic or anisotropic) Gaussian and cylindrical power spectra. Simulation results obtained by the proposed method agree well with experimentally measured scattering data taken from similar well-characterized, rough metal samples, or to results obtained by other numerical methods.Copyright © 2013 Nordam, Letnes and Simonsen. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these term
Electromagnetic Wave Scattering from Rough Surfaces on Uniaxial Media
No full textDenne tesen utvikler teorien om elektromagnetisk bølgespredning fra tilfeldig ujevne overflater på partikulært orienterte uniaksiale medier. Dispersjonsrelasjonene for overflate-plasmon-polaritoner (SPP) og overflate-magnon-polaritoner (SMP) utledes for denne typen overflater, og det vises at SPP- og SMP-eksitasjoner støttes basert på henholdsvis permittiviteten og permeabiliteten i overflateplanet. De fullstendige elektromagnetiske spredningsligningene utvikles ved bruk av Rayleigh-hypotesen, og det vises at valg av testfunksjoner muliggjør at den reduserte Rayleigh-ligningen (RRE) kan utledes for spredning fra ujevne overflater på disse uniaksiale mediene. Både de fullstendige spredningsligningene og RRE implementeres numerisk ved hjelp av Julia, og de gir sammensvarende resultater.
Den midlere differensielle refleksjonskoeffisienten (MDRC) og den midlere differensielle transmisjonskoeffisienten (MDTC) beregnes for ulike uniaksiale materialer, herunder dobbeltbrytende (birefraktive) krystaller, uniaksiale metaller, hyperbolske materialer av type I og II, og venstrehendte materialer. Yoneda-topper og -daler vises å bli transmittert ved to forskjellige vinkler i dobbeltbrytende krystaller. I reflekterende, uniaksiale materialer påvirker graden av anisotropi amplituden av den forsterkede tilbakespredningstoppen som oppstår fra utkoblingen av SPP-er. I hyperbolske medier av type II viser utkoblingen av SPP-er uvanlig oppførsel i form av amplitude-"skuldre" utenfor den teoretiske maksimale utkoblingsvinkelen for SPP-er i en tilfeldig ujevn overflate med West-O'Donnell-korrelasjonsfunksjonen. Ved å bruke teorien etablert for SPP- og SMP-eksitasjon, ble det utført simuleringer på et venstrehendt materiale som kunne støtte både SPP-er og SMP-er. Dette viste forsterkede spredningstopper på grunn av utkoblingen av SPP-er i p-polarisert lys og SMP-er i s-polarisert lys, både i MDRC og MDTC, noe som viser at den forsterkede tilbakespredningseffekten har en tilsvarende transmisjonseffekt i et venstrehendt medium, lignende andre resultater for forsterket tilbakespredning og transmisjon i tynne metallfilmer.In this thesis, the theory regarding electromagnetic wave scattering from randomly rough surfaces on particularly aligned uniaxial media is developed. The dispersion relations for the surface plasmon polariton (SPP) and surface magnon polariton (SMP) are derived for this type of interface and it is shown that SPP and SMP excitations are supported based on the surface plane permittivity and permeability, respectively. The full set of electromagnetic scattering equations are developed using the Rayleigh hypothesis and it is shown that the choice of testing functions allow for the reduced Rayleigh equation (RRE) to be found for scattering from rough surfaces on these uniaxial media. Both the full scattering equations and the RRE are implemented numerically using Julia and they yield consistent results.
The mean differential reflection coefficient (MDRC) and the mean differential transmission coefficient (MDTC) are calculated for various uniaxial materials, including birefringent crystals, uniaxial metals, hyperbolic materials of type I and II, and left-handed materials. Yoneda peaks and valleys are shown to be transmitted at two different angles in birefringent crystals. In reflective, uniaxial materials, the level of anisotropy affects the amplitude of the enhanced backscattering peak resulting from the outcoupling of SPPs. In hyperbolic media of type II supporting SPPs, the indirect scattering pattern shows unusual behavior in the form of amplitude ``shoulders'' outside of the theoretical maximum outcoupling angle for SPPs in a randomly rough surface with the West-O'Donnell correlation function. Using the theory established for SPP and SMP excitation, simulation was performed on a left-handed material which could support both SPPs and SMPs. This showed enhanced scattering peaks due to the outcoupling of SPPs in p-polarized light and SMPs in s-polarized light. These effects were present in both the MDRC and MDTC, showing that the enhanced backscattering effect has an equivalent transmission effect in a left-handed medium. This is similar to results for thin metallic films showing enhanced backscattering with an equivalent transmission effect
Reflection of diffuse light from two-dimensional rough surfaces & The light scattering properties of Gaussian-cosine correlated surfaces
No full textI denne oppgaven studeres reflektansen til 2D tilfeldig rue overflater opplyst av diffust lys, sammen med sprednings- og de polarimetriske egenskaper til Gaussisk-cosinus korrelerte overflater, gjennom resultater oppnådd fra tunge numeriske simuleringer. Simuleringene var basert på en ikke-perturbativ direkte løsning av den todimensjonale reduserte Rayleigh-ligningen for refleksjon.
Reflektiviteten og reflektansen for både diffust- og rettningsbelyste Gaussisk korrelerte glassflater er presentert og sammenlignet med tidligere oppnådde resultater for 1D overflater. Reflektansen for s-polarisert, p-polarisert og upolarisert diffus belysning er funnet å enten øke eller avta, avhengig av overflatens ruhet. Flere forskjeller er funnet i oppførselen til reflektansen mellom 1D og 2D overflater, avhengig av den karakteristiske lengden på uregelmessighetene, når ruheten økes systematisk.
Den fulle vinkelfordelingen av den gjennomsnittlige differensielle refleksjonskoeffisienten og Mueller-matrisen for lysspredning fra både isotrope og anisotrope Gaussisk-cosinus korrelerte sølvflater er presentert og diskutert i detalj. Disse størrelsene beskriver sprednings- og den polariserende oppførselen til de tilfeldig rue overflatene. Resultatene er samenlignet med tilsvarenede størrelsene som har blitt regnet ut for Gaussisk korrelerte overflater, som representerer det klassiske eksemplet på en ru overflate. Det observeres at de Gaussisk-cosinus korrelerte overflatene har interessante spredningsegenskaper, for eksempel en forsterkning av p-polarisert spredt lys, en nær spekulær undertrykkelse og høy reflektans. Noen av egenskapene er vist å avhenge sterkt av den karakteristiske størrelsen på uregelmessighetene og tilstedeværelsen av overflate plasmon polaritoner. Disse funnene kan være av interesse i ulike bransjer og felt, for eksempel solcelleindustrien, hvor disse egenskapene er ettertraktet.In this thesis the reflectance of 2D randomly rough surfaces illuminated by diffuse light, along with the scattering and polametric properties of Gaussian-cosine correlated surfaces, is studied through results obtained from rigorous numerical simulations. The simulations were based on a non-perturbational direct solution of the two-dimensional reduced Rayleigh equation for reflection.
The reflectivity and reflectance for both the directional and diffuse illumination of Gaussian correlated glass surfaces is presented and compared to previously obtained results for 1D surfaces. The reflectance for s-polarized, p-polarized and unpolarized diffuse illumination is found to either increase or decrease, depending on the nature of the surface roughness. Several differences are found in the behavior of the reflectance between 1D and 2D surfaces, depending on the characteristic length of the irregularities, when the roughness is systematically increased.
The full angular distribution of the mean differential reflection coefficient and the Mueller matrix for light scattering from both isotropic and anisotropic Gaussian-cosine correlated silver surfaces is presented and discussed in detail. These quantities describe the scattering and polarizing behavior of the randomly rough surfaces. The results are contrasted with the same quantities obtained for Gaussian correlated surfaces, which represent the classically studied example of a rough surface. It is observed that the Gaussian-cosine correlated surfaces have interesting scattering properties, such as an enhancement of p-polarized scattered light, a near specular suppression and a high reflectance. Some of the properties are shown to depend strongly on the characteristic size of the irregularities and the presence of surface plasmon polaritons. These findings could be of interest in various industries, such as the solar cell industry, where these properties are sought after
Scattering of Electromagnetic Waves from Randomly Rough Surfaces with Skewed Height Distributions
No full textResearch on the scattering of electromagnetic waves from rough surfaces has greatly advanced in the past decades through the access to rigorous numerical simulations. However, most of the research has focused on surfaces with a Gaussian height distribution. In this thesis, the effect of the skewness of the surface height distribution on the scattering process is qualitatively examined. This is accomplished through rigorous numerical simulations of an electromagnetic field incident on rough surfaces with different values for the surface height skewness. Both the reflection from opaque materials and transmission from transparent materials are studied. For the reflected field, strongly skewed surface heights were found to induce more scattered intensity in the forward direction, both for positive and negative values of the skewness. For negative values, there was an additional increase in the scattered intensity for large angles in the forward direction. A negative correlation was found between the surface height skewness and the size of the enhanced backscattering peak. For non-normal angles of incidence, the intensity in large angle backward directions was found to have a negative correlation with the surface height skewness. For absorbing materials, the absorption rate did not seem to be affected by the surface height skewness. The coherent component of the scattered field from weakly rough surfaces appeared to be slightly larger both for large positive and large negative values of the surface height skewness. For the transmitted field from transparent materials, the effects of positive and negative values of the surface height skewness were the same, and only the magnitude had an effect. For a normal angle of incidence, larger magnitudes of the surface height skewness induced less diffusion, while for oblique angles of incidence the effect was opposite. The transmittance seemed to be independent of the surface height skewness. Plausible explanations of the effects are given by modelling a surface with strongly skewed surface heights as a relatively flat surface with a few of tall peaks or deep pits
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