Neste trabalho propomos o estudo da Espectrometria de Lente Térmica, sua teoria e aplicações, visto ser uma técnica de alta sensibilidade e que permite a medida das propriedades termo-ópticas dos materiais, como a difusividade térmica (D), a condutividade térmica (k), desvio do caminho óptico pela temperatura (ds/dT) - para materiais sólidos - ou a variação do índice de refração em relação à temperatura (dn/dT) - para líquidos e gases. Para isso inicialmente fizemos um estudo da teoria da difração. Valendo-se da Integral de Difração de Fresnel Kirchhoff obtivemos a expressão analítica da intensidade de um feixe de laser, difratado por diversos elementos ópticos (aberturas e obstáculos circular e retangular, por exemplo), tanto para o regime da difração de Fresnel, quanto da difração de Fraunhofer. Ainda no estudo da difração propusemos um arranjo experimental muito simples, utilizando-se um laser pointer sem a lente colimadora, permitindo que se obtenha, com grande facilidade, os padrões de difração no campo próximo, o que é difícil nas montagens tradicionais. Na seqüência fizemos uma revisão dos modelos de Lente Térmica tradicionalmente utilizados, modelos parabólico e aberrante. E, na comparação que realizamos entre eles, verificamos que pelos resultados obtidos através de simulações, com o modelo parabólico se apresenta em grande desacordo (>50%) com os obtidos com o modelo aberrante. Desta forma, concluímos que os dados da literatura obtidos na década de 70 e que ainda são utilizados, merecem ser revistos. Por fim, notamos na literatura um crescente interesse em lasers de alta potência, principalmente pelos bombeados por lasers de diodo. Desta forma fizemos um estudo valendo-se do modelo aberrante de Lente Térmica sob o regime de q grande, no qual procuramos verificar o limite de validade dos modelos de L.T. utilizados, observando o surgimento de fenômeno da aberração esférica, juntamente com as estruturas de anéis. / In this work we have proposed the study of Thermal Lens Spectrometry, its theory and applications, because it is a highly sensitive technique that allows the measure of the thermo-optical properties of the materials, as the thermal diffusivity (D), the thermal conductivity (k), the change of optical path length with temperature (ds/dT), for solid materials or the change of refractive index with temperature (dn/dT), for liquids and gases. Initially we studied the diffraction theory. We utilized the Fresnel Kirchhoff Diffraction Integral to obtain the analytic expression of the beam laser intensity, whose was diffracted for several optical elements, so much for the regime of the Fresnel diffraction as the regime of the Fraunhofer diffraction. Continuing in the study of the diffraction we proposed a very simple experimental apparatus where we used a laser pointer without the collimator lens, allowing that it was obtained with great facility the Fresnel diffraction patterns, which are difficult to observe in the common experimental apparatus. In the sequence, we made a revision of the models of Thermal Lens traditionally used, parabolic and aberrant models. And, in the comparison that we accomplished among them, we verified that for the results obtained through simulations, with the parabolic model it comes in great disagreement (>50%) with obtained them with the aberrant model. This way, we concluded that literature’s data obtained in the 70ths and they are still used, they must be reviewed. Finally, we noticed in the literature a growing interest in high power lasers. This way we made a study where we used the aberrant model of Thermal Lens under the regime of great q, in which we look for to verify the limit of validity of the used models, observing the appearance of the spherical aberration together with the rings structure.

Neste trabalho propomos o estudo da Espectrometria de Lente Térmica, sua teoria e aplicações, visto ser uma técnica de alta sensibilidade e que permite a medida das propriedades termo-ópticas dos materiais, como a difusividade térmica (D), a condutividade térmica (k), desvio do caminho óptico pela temperatura (ds/dT) - para materiais sólidos - ou a variação do índice de refração em relação à temperatura (dn/dT) - para líquidos e gases. Para isso inicialmente fizemos um estudo da teoria da difração. Valendo-se da Integral de Difração de Fresnel Kirchhoff obtivemos a expressão analítica da intensidade de um feixe de laser, difratado por diversos elementos ópticos (aberturas e obstáculos circular e retangular, por exemplo), tanto para o regime da difração de Fresnel, quanto da difração de Fraunhofer. Ainda no estudo da difração propusemos um arranjo experimental muito simples, utilizando-se um laser pointer sem a lente colimadora, permitindo que se obtenha, com grande facilidade, os padrões de difração no campo próximo, o que é difícil nas montagens tradicionais. Na seqüência fizemos uma revisão dos modelos de Lente Térmica tradicionalmente utilizados, modelos parabólico e aberrante. E, na comparação que realizamos entre eles, verificamos que pelos resultados obtidos através de simulações, com o modelo parabólico se apresenta em grande desacordo (>50%) com os obtidos com o modelo aberrante. Desta forma, concluímos que os dados da literatura obtidos na década de 70 e que ainda são utilizados, merecem ser revistos. Por fim, notamos na literatura um crescente interesse em lasers de alta potência, principalmente pelos bombeados por lasers de diodo. Desta forma fizemos um estudo valendo-se do modelo aberrante de Lente Térmica sob o regime de q grande, no qual procuramos verificar o limite de validade dos modelos de L.T. utilizados, observando o surgimento de fenômeno da aberração esférica, juntamente com as estruturas de anéis. / In this work we have proposed the study of Thermal Lens Spectrometry, its theory and applications, because it is a highly sensitive technique that allows the measure of the thermo-optical properties of the materials, as the thermal diffusivity (D), the thermal conductivity (k), the change of optical path length with temperature (ds/dT), for solid materials or the change of refractive index with temperature (dn/dT), for liquids and gases. Initially we studied the diffraction theory. We utilized the Fresnel Kirchhoff Diffraction Integral to obtain the analytic expression of the beam laser intensity, whose was diffracted for several optical elements, so much for the regime of the Fresnel diffraction as the regime of the Fraunhofer diffraction. Continuing in the study of the diffraction we proposed a very simple experimental apparatus where we used a laser pointer without the collimator lens, allowing that it was obtained with great facility the Fresnel diffraction patterns, which are difficult to observe in the common experimental apparatus. In the sequence, we made a revision of the models of Thermal Lens traditionally used, parabolic and aberrant models. And, in the comparison that we accomplished among them, we verified that for the results obtained through simulations, with the parabolic model it comes in great disagreement (>50%) with obtained them with the aberrant model. This way, we concluded that literature’s data obtained in the 70ths and they are still used, they must be reviewed. Finally, we noticed in the literature a growing interest in high power lasers. This way we made a study where we used the aberrant model of Thermal Lens under the regime of great q, in which we look for to verify the limit of validity of the used models, observing the appearance of the spherical aberration together with the rings structure.

Micro-cylinders with the diameters spanning the 1-20 μm range are growing in importance, for realizing devices with new functionalities. For custom functionalities, their device-designs impose, tolerance-related constraints on their critical dimension. To meet the challenges for the associated online micro-metrology, new methods for the micro-cylinder diameter measurement, are currently receiving considerable attention. „Optical diffraction under Fraunhofer Approximation‟ is one of the most viable experimental techniques for cylinder diameter measurement, in the laboratory as well as Industrial environment. In 1-20 μm diameter range, however, the cylinder-diffraction is not well understood. The reliability of the current models/formulations for this range is far from satisfactory in respect of speed, accuracy, resolution etc., and need a re-examination. The present thesis concerns with a few investigations on the „Optical Diffraction by Micro-Cylinder‟. It highlights both the theoretical and the experimental aspects of the investigations on micro-cylinders with diameters in the range of 1-50 μm. The results of the investigation are organized into two categories. The first of them details a pair of new analytical models obtained from the principles of „Geometrical Theory of Micro-Cylinder Diffraction‟ while the second category highlights another pair of new analytical models obtained from the principles of the „Customary Fraunhofer Theory of Micro-Cylinder Diffraction‟. The model from the „geometrical theory‟ is based on the hypothesis that the ‘ray-paths relevant to the location of ‘diffraction minima’, facilitate to construct, a geometrically-equivalent triangle’. The solution of such a triangle provides the new formulation for the micro-cylinder diffraction. The model from the „customary Fraunhofer theory‟, instead, relies on the on the fact that „the diffraction pattern for a micro-cylinder is essentially, a chirped-interference pattern modulated by a diffraction envelope’. The functional form of the formulation depends upon, the type of triangle constructed for geometrical theory and the type of illumination used in the customary Fraunhofer theory. The thesis highlights, four new formulations (two from each of the approaches) to describe the micro-cylinder diffraction. The principal conclusions of the investigations are as under. - All the new formulations for the micro-cylinder diffraction facilitate, enhanced diameter inversion accuracy, in the hitherto esoteric diameter range of 1-20 μm. For the reported experimental data on 3 μm diameter micro-cylinder, the models proposed in the present investigation improve the accuracy of diameter-estimation from 16.5% known from earlier models to less than 1%. - The investigation also brings out for the first time, the hitherto unnoticed difference between slit-diffraction and the micro-cylinder diffraction: When the micro-cylinder diameter approaches the wavelength of the illumination, the first order diffraction angle approaches nearly 200. It may be noted that for a slit of same width, the corresponding diffraction angle approaches 900. When the critical dimension of the cylinder and the slit decreases from λ to 5λ, the difference in the corresponding diffraction angles reduce from nearly 700 to nearly 1.50. - The investigation also highlights that in the micro-cylinder diffraction for the said range of interest, the absolute intensity at the zero-order interference- maximum provides a new signature for the distance of separation between the diffraction minima. The consequence of this new finding is a considerable simplification in the apparatus and algorithm for diameter inversion from a diffraction experiment. The function of an array detector can be replaced by a point detector at a fixed point for all the diameters in the range of interest. - The two formulations proposed from the geometrical theory are suited for diffraction- minima search based algorithm, while those from customary Fraunhofer theory are well suited for intensity minima search based method for diameter inversion.

Vad karaktäriserar en kristall? Svaret på denna till synes enkla fråga blir kanske att det är en anordning av atomer uppradade i periodiska mönster. Så ordnade strukturer kan studeras genom att det uppträder så kallade Braggtoppar i röntgendiffraktionsmönstret. Om frågan gäller elektrontäthetsfördelningen, kanske svaret blir att denna är periodisk och grundar sig på elektronvågor som genomtränger hela kristallen. I och med att nya typer av ordnade system, så kallade kvasikristaller, upptäcks och framställs på artificiell väg blir svaren på dessa frågor mer intrikata. En kristall behöver inte bestå av enheter upprepade periodiskt i rummet, och den klassiska metoden att karaktärisera strukturer via röntgendiffraktionsmönstret kanske inte alls är den allena saliggörande. I denna avhandling visas att ett ordnat gitter vars röntgendiffraktionsmönster saknar inre struktur, dvs är av samma diffusa typ som vad ett oordnat material uppvisar, fortfarande kan ha elektronerna utsträckta över hela strukturen. Detta implicerar att det inte finns något enkelt samband mellan diffraktionsmönstret från gittret och dess fysikaliska egenskaper såsom t ex lokalisering av vågfunktionerna. Man talar om lokalisering när en vågfunktion är begränsad inom en del av materialet och inte utsträckt över hela dess längd, vilket är av betydelse när man vill avgöra huruvida ett material är en isolator, halvledare eller ledare. Det vittnar samtidigt om behovet av att söka efter andra karakteristika när man försöker beskriva skillnaden mellan ett ordnat och ett oordnat material, där den senare kategorin kan uppvisa lokalisering. Resultaten utgör en klassificering av det svåröverskådliga området aperiodiska gitter i en dimension. Det leder till hypotesen att ideala kvasikristaller, genererade med bestämda regler, har kontinuerligt energispektrum av fraktal natur. I reella material spelar korrelation en viktig roll. Vid icke-linjär återkoppling till gittret kan man erhålla intrinsiskt lokaliserade vågor, som i många avseenden beter sig som partiklar, solitoner, vilka har visat sig ha viktiga tillämpningar inom bl a optisk telekommunikation. Sådana vågors roll for lagring och transport av energi har undersökts i teoretiska modeller for optiska vågledare och kristaller där ljuset har en förmåga att manipulera sig självt. / Spectral and dynamical properties of electrons, phonons, electromagnetic waves, and nonlinear coherent excitations in one-dimensional modulated structures with long-range correlations are investigated from a theoretical point of view. First a proof of singular continuous electron spectrum for the tight-binding Schrödinger equation with an on-site potential, which, in analogy with a random potential, has an absolutely continuous correlation measure, is given. The critical behavior of such a localization phenomenon manifests in anomalous diffusion for the time-evolution of electronic wave packets. Spectral characterization of elastic vibrations in aperiodically ordered diatomic chains in the harmonic approximation is achieved through a dynamical system induced by the trace maps of renormalized transfer matrices. These results suggest that the zero Lebesgue measure Cantor-set spectrum (without eigenvalues) of the Fibonacci model for a quasicrystal is generic for deterministic aperiodic superlattices, for which the modulations take values via substitution rules on finite sets, independent of the correlation measure. Secondly, a method to synthesize and analyze discrete systems with prescribed long-range correlated disorder based on the conditional probability function of an additive Markov chain is effectively implemented. Complex gratings (artificial solids) that simultaneously display given characteristics of quasiperiodic crystals and amorphous solids on the Fraunhofer diffraction are designated. A mobility edge within second order perturbation theory of the tight-binding Schrödinger equation with a correlated disorder in the dichotomic potential realizes the success of the method in designing window filters with specific spectral components. The phenomenon of self-localization in lattice dynamical systems is a subject of interest in various physical disciplines. Lattice solitons are studied using the discrete nonlinear Schrödinger equation with on-site potential, modeling coherent structures in, for example, photonic crystals. The instability-induced dynamics of the localized gap soliton is found to thermalize according to the Gibbsian equilibrium distribution, while the spontaneous formation of persisting intrinsic localized modes from the extended out-gap soliton reveals a phase transition of the solution.

This discourse deals with a theoretical study of the radiation passage through a diffraction screen with non-zero size in the propagation direction of the radiation, i.e. the radiation passage through a three-dimensional object. Without any loss of generality, we solve the problem for cylindrical cavity in metal. The task exceeds evidently standard scalar theory of diffraction, thus we solve the problem using a waveguiding theory. Following the principles of the electromagnetic theory, we derive required formulae to determine mode distribution at the entry of the cavity. Further, we solve numerically the radiation propagation through the cavity, then we actually seek for radiation distribution at the very end of the cavity. This yields, with a help of the discrete Fourier transform, an intensity distribution of Fraunhofer diffraction pattern, consequently compared with an intesity distribution of the radiation pattern of Fraunhofer diffraction on infinitely thin circular opening having the radius of the cylinder cavity under study. A comparison of such patterns results to a conclusion, that the cavity length has a significatn influence on the diffraction pattern and more importantly, that the scalar diffraction theory appears incorrect for a coherent light passage through cavities longer than their radius squared. Similarly, the same conclusion is inversely proportional to a wavelength of the interacting radiation. Finally, we mention an existence of the so called "focal regime", when the radiation repeatedly exhibits roughly one order increased intensity on the symmetry axis of the cavity.