The dissertation presents theoretical and experimental studies on the physical origin of the signal in photothermal microscopy of single particles. This noninvasive optical far field microscopy scheme allows the imaging and detection of single absorbing nanoparticles. Based on a heat-induced pertur- bation in the refractive index in the embedding medium of the nanoscopic absorber, a corresponding probe beam modification is measured and quantified. The method is well established and has been applied since its first demonstration in 2002 to the imaging and characterization of various absorbing particle species, such as quantum dots, single molecules and nanoparticles of different shapes. The extensive theoretical developments presented in this thesis provide the first quantitative assess- ment of the signal and at the same time enlarge its phenomenology and thereby its potential. On the basis of several approximation schemes to the Maxwell equations, which fundamentally gov- ern the interaction of light with inhomogeneities, several complementing models are devised which describe the photothermal signal both qualitatively and quantitatively. In succession an interdepen- dent and self-consistent set of theoretical descriptions is given and allows important experimental consequences to be drawn. In consequence, the photothermal signal is shown to correspond to the action of a nanoscopic (thermal) lens, represented by the spherically symmetric refractive index pro- file n(r) which accompanies the thermal expansion of the absorber’s environment. The achieved quantification allows the direct measurement of absorption cross-sections of nanoparticles. Further, a qualitatively new phenomenology of the signal is unraveled and experimentally demonstrated. The separate roles of the probing and the heating beams in photothermal microscopy is dismantled and the influence of their relative alignment shown to allow for a controlled adjustment of the effective detection volume. For the first time, both positive and negative signals are demonstrated to occur and to be the characteristic signature of the lens-like action on the probe beam. The detection of the probe beam’s modification is also shown to sensitively depend on the aperture used in the detection chan- nel, and a signal optimization is shown to be feasible. Also, a generalization of the detectable signal via the use of a quadrant photodiode is achieved. Specifically, measuring the far field beam deflec- tion the result of the beam passing the lens off-center manifests in a laterally split detection volume. Hereby, finally each classical photothermal spectroscopic techniques has been shown to possess its microscopic counterpart. Central to the understanding of this generalized and new phenomenology is a scalar wave-optical model which draws an analogy between the scattering of a massive particle wave-packet by a Coulomb potential and the deflection of a focused beam by a photonic potential connected with the thermal lens. The significance of the findings is demonstrated by its methodological implications on photother- mal correlation spectroscopy in which the diffusion dynamics of absorbing colloidal particles can be studied. The unique split focal detection volumes are shown to allow the sensitive measurement of a deterministic velocity field. Finally, the method is supplemented by a newly introduced sta- tistical analysis method which is capable of characterizing samples containing a heterogeneous size distribution.

Orientador: Carlos Lenz Cesar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física "Gleb Wataghin" / Made available in DSpace on 2018-08-18T09:30:54Z (GMT). No. of bitstreams: 1 Moreira_WendelLopes_D.pdf: 1772489 bytes, checksum: 3d4e37a805f4c66c447aea58b93692b8 (MD5) Previous issue date: 2010 / Resumo: Desde 1908, quando Mie apresentou expressões analíticas para os campos espalhados por uma partícula esférica sob incidência de uma onda eletromagnética plana, generalizações para esta expansão têm se mostrado incompletas. Isto se deve à presença de certos termos com dependência radial nos coe cientes de forma do feixe quando expandido em termos de funções de onda esféricas vetoriais. Aqui mostramos pela primeira como cancelar estes termos, permitindo expressões analíticas para os coe cientes para um campo eletromagnético completamente arbitrário. Damos tambem vários exemplos deste novo método, que também é muito apropriado para cálculos numéricos. Obtemos deste modo, expressões analíticas para feixes de Bessel e para os modos de guias de onda metálicos retangulares e cilíndricos. Estes resultados são extremamente relevantes para o incremento na velocidade de cálculo das forças de radiação atuando sobre uma partícula esférica, colocada em um campo eletromagnético arbitrário, com por exemplo, em pinças ópticas / Abstract: Since 1908, when Mie reported analytical expressions for the elds scattered by a spherical particle upon incidence of an electromagnetic plane-wave, generalizing his analysis to the case of an arbitrary incident wave has proved elusive. This is due to the presence of certain radially-dependent terms in the equation for the beam-shape coecients of the expansion of the electromagnetic elds in terms of vector spherical wave functions. Here we show for the rst time how these terms can be canceled out, allowing analytical expressions for the beam shape coecients to be found for a completely arbitrary incident eld. We give several examples of how this new method, which is well suited to numerical calculation, can be used. Analytical expressions are found for Bessel beams and the modes of rectangular and cylindrical metallic waveguides. The results are highly relevant for speeding up calculation of the radiation forces acting on spherical particles placed in an arbitrary electromagnetic eld, such as in optical tweezers / Doutorado / Física / Doutor em Ciências

En la exploración de nuevos métodos para el mejoramiento de la eficiencia y rendimiento del motor diésel, es claro que un gran esfuerzo debe estar enfocado en el proceso de inyección de combustible. La eficiencia de la combustión y las emisiones, se ven muy afectadas por el proceso de atomización, y se ha demostrado que incrementos en presiones de inyección conllevan un gran potencial para mejorar el ahorro de combustible, producir mejores mezclas de aire y combustible, y por tanto menor generación de emisiones contaminantes. Últimamente, las presiones de inyección han aumentado de alrededor de 50 MPa en los años 70 hasta 250 MPa en los días actuales. Presiones de inyección muy altas (250-300 MPa) o incluso ultra altas (> 300 MPa) vienen siendo materia de investigación con el fin de ser implementadas de manera comercial en un futuro próximo. La estructura y desarrollo del spray diésel pueden ser caracterizados desde un punto de vista microscópico por medio de la medición del tamaño de gotas del spray y sus velocidades. En condiciones no-evaporativas, técnicas como el PDPA (Phase Doppler Particle Analyzer) vienen siendo utilizadas para la obtención de perfiles de diámetros y velocidades de gota con una alta resolución temporal. Desde el punto de vista macroscópico, existen parámetros específicos que permiten caracterizar a un chorro diésel, estos son: la penetración de vapor y líquida junto con el ángulo de apertura del chorro. La penetración líquida es un indicador claro de la capacidad de evaporación del combustible utilizado, mientras que la penetración de vapor, por su parte, es indicativo del proceso de mezcla y la probabilidad de colisión con las paredes de la cámara de combustión; factores claves a la hora de la generación de emisiones contaminantes. En esta tesis se estudia la influencia de presiones bajas, medias y muy altas presiones inyección, sobre un amplio espectro de condiciones y diagnósticos experimentales, y desde el punto de vista macroscópico y microscópico. Se realizaron experimentos para tres diferentes inyectores, 2 solenoides y un piezo eléctrico, este último con la capacidad de alcanzar presiones de inyección cercanas a 270 MPa. Las medidas incluyen una caracterización hidráulica, compuesta por tasa de inyección; una visualización de alta velocidad del chorro líquido isotermo; una visualización de alta velocidad del chorro inerte evaporativo, con captura simultánea de las fases líquida y vapor; y finalmente, una caracterización microscópica por medio de la obtención de distribución de tamaño de gotas y sus velocidades. Con respecto a los ensayos microscópicos, se desarrolló una metodología para el aislamiento y alineación de sprays con un error de medición muy bajo de 0,22°. Se llevaron a cabo mediciones de velocidad de gotas, cuyos resultados mostraron buen ajuste con perfiles teóricos de velocidad. De igual manera, una correlación para el tamaño de gota SMD se obtuvo mostrando un alto nivel de ajuste y siendo representativa para todo el rango de presiones de inyección estudiados. En el caso de la caracterización macroscópica del chorro isotermo, se han detectado variaciones macroscópicas en el desarrollo del chorro con propiedades de gas, inclusive en condiciones de motor comunes. Para estimar estos efectos y otros que las presiones de inyección muy altas tendrían sobre la estructura del chorro, se incentivó la aparición de ondas de choque controlando la velocidad del sonido del ambiente. Se usaron tres gases ambientales (SF6 N2 y CO2) con diferentes velocidades de sonido, promoviendo de esta manera chorros supersónicos en determinados casos. Al comparar ensayos con mismas densidades y diferentes gases ambientales, se encontró que todas las tendencias cercanas al estado transónico (0.8 <M <1.2) tenían una mayor penetración y menor ángulo de chorro. / En l'exploració de nous mètodes per al millorament de l'eficiència i rendiment del motor dièsel, és clar que un gran esforç s'ha enfocar en el procés d'injecció de combustible. L'eficiència de la combustió i les emissions, es veuen molt afectades pel procés d'atomització, i s'ha demostrat que increments en pressions d'injecció comporten un gran potencial per a millorar l'estalvi de combustible, produir millors mescles d'aire i combustible, i per tant menor generació d'emissions contaminants. Últimament, les pressions d'injecció han augmentat d'al voltant de 50 MPa en els anys 70 fins a 250 MPa en els dies actuals. Pressions d'injecció molt altes (250-300 MPa) o inclús ultra altes (> 300 MPa) vénen sent matèria d'investigació a fi de ser implementades de manera comercial en un futur pròxim. L'estructura i desenrotllament de l'esprai dièsel poden ser caracteritzats des d'un punt de vista microscòpic per mitjà del mesurament de la grandària de gotes de l'esprai i les seues velocitats. En condicions no-evaporatives, tècniques com el PDPA (Phase doppler particle analyzer) vénen sent utilitzades per a l'obtenció de perfils de diàmetres i velocitats de gota amb una alta resolució temporal. Des del punt de vista macroscòpic, hi ha paràmetres específics que permeten caracteritzar a un doll dièsel, estos són: la penetració de vapor i la penetració líquida junt amb l'angle d'obertura del doll. La penetració líquida és un indicador clar de la capacitat d'evaporació del combustible utilitzat, mentres que la penetració de vapor, per la seua banda, és indicatiu del procés de mescla i la probabilitat de col·lisió amb les parets de la cambra de combustió; factors claus a l'hora de la generació d'emissions contaminants. En esta tesi s'estudia la influència de pressions d' injecció baixes, mitges i molt altes, sobre un ampli espectre de condicions i diagnòstics experimentals, i des del punt de vista macroscòpic i microscòpic. Es van realitzar experiments per a tres injectors diferents, 2 solenoides i un piezo elèctric, este últim amb la capacitat d'aconseguir pressions d'injecció pròximes a 270 MPa. Les medides inclouen una caracterització hidràulica, composta per taxa d'injecció; una visualització d'alta velocitat del doll líquid isoterm; una visualització d'alta velocitat del doll inert evaporativo, amb captura simultània de les fases líquida i vapor; i finalment, una caracterització microscòpica per mitjà de l'obtenció de distribució de grandària de gotes i les seues velocitats. Respecte als assajos microscòpics, es va desenrotllar una metodologia per a l'aïllament i alineació d'esprais amb un error de mesurament molt davall de 0,22°. Es van dur a terme mesuraments de velocitat de gotes, els resultats van mostrar bon ajust amb perfils teòrics de velocitat. De la mateixa manera, una correlació per a la grandària de gota SMD es va obtindre mostrant un alt nivell d'ajust i sent representativa per a tot el rang de pressions d'injecció estudiats. En el cas de la caracterització macroscòpica del doll isoterm, s'han detectat variacions macroscòpiques en el desenrotllament del doll amb propietats de gas, inclusivament en condicions de motor comú. Per a estimar estos efectes i altres que altes pressions d'injecció tindrien sobre l'estructura del doll, es va incentivar l'aparició d'ones de xoc controlant la velocitat del so de l'ambient. Es van usar tres gasos ambientals (SF6, N2 i CO2) amb diferents velocitats de so, promovent d'esta manera dolls supersònics en determinats casos. Al comparar assajos amb mateixes densitats i diferents gasos ambientals, es va trobar que totes les tendències pròximes a l'estat transónic (0.8 < M < 1.2) tenien una major penetració i menor angle de doll. Respecte al doll evaporatiu, per a pressions d'injecció molt altes com 270MPa, els efectes dels paràmetres ambientals i d'injecció van romandre iguals respecte a totes les carac / In the exploration of new methods for improving the efficiency and performance of the diesel engine, it is clear that a great effort should be focused on the fuel injection process. The efficiency of combustion and emissions are greatly affected by the atomization process, and it is considered that injection pressures increments have a great potential to improve fuel economy, produce better air and fuel mixtures, and thus low generation of polluting emissions. Lately, injection pressures have increased from around 50 MPa in the 70's to 250 MPa in the current days, even very high injection pressures (250-300 MPa) or ultra high pressures (> 300 MPa) have been the subject of the scientific community in order to be implemented in future injection systems. The structure and development of the diesel spray can be characterized from a microscopic point of view by means of estimation of droplets size and velocities. At non-evaporative conditions, techniques such as PDPA (Phase Doppler Particle Analyzer) are being used to obtain diameters and velocity profiles a with high temporal resolution. From the macroscopic point of view, there are specific parameters that allow characterizing the diesel spray, these are: the liquid and vapor penetration along with the spray angle. The liquid penetration is a clear indicator of the evaporation capacity of the fuel used, whilst the vapor penetration, on the other hand, is an indicative of the mixing process and the probability of collision with the combustion chamber walls; key factors when generating polluting emissions. In this thesis the influence of low and very high injections pressures over the macro and micro characteristics of the diesel spray is studied, over a wide spectrum of conditions and experimental diagnoses. Experiments were carried out for three different injectors, two solenoids and one piezoelectric, the latter with the capacity to reach injection pressures close to 270MPa. The measurements include a hydraulic characterization; a high speed visualization of the liquid spray at isothermal conditions; a high-speed visualization of the evaporative spray, with simultaneous capture of the liquid and vapor phases; and finally, a microscopic characterization. Regarding the microscopic tests, a methodology was developed for the spray isolation and alignment with a very low measurement error of 0.22° Droplets velocity measurements were carried out, the results showed good adjustment with theoretical velocity profiles. Similarly, a correlation for SMD droplet size was obtained showing a high level of adjustment and being representative for the entire range of injection pressures studied. In the case of the macroscopic characterization of the isothermal spray, variations have been detected in the development of the jet with gas properties, even at common engine injection conditions. To estimate these effects and others that very high injection pressures would have on the spray structure, the apparition of shock waves was enhanced by controlling the speed of sound of the environment using three ambient gases with different speed of sound (SF6, N2 and CO2). When comparing tests with same densities and different ambient gases, it was found that all the tendencies near the transonic state (0.8 <M <1.2) had a higher penetration and lower spray angle. With respect to the evaporative jet, for very high injection pressures like 270MPa, the effects of the environmental and injection parameters remained the same with respect to all the macroscopic characteristics. / Giraldo Valderrama, JS. (2018). Macroscopic and microscopic characterization of non-reacting diesel sprays at low and very high injection pressures [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/113643 / TESIS

[pt] Neste trabalho foi feito o estudo do espalhamento da luz realizado por partículas esféricas dielétricas, pelo uso do método dos elementos finitos, através do software COMSOL Multiphysics 5.6, sendo considerado o comportamento da luz tanto como onda quanto como partícula. Este estudo visa, no futuro, a compreensão do laser aleatório em sistemas com centros espalhadores de diferentes geometrias. Considerando o comportamento ondulatório da luz, foi estudada a teoria sobre as séries de Mie. Esta, por sua vez, é uma solução que, dado o campo de incidência, pode-se calcular os campos espalhados e absorvidos por partículas esféricas. Foram calculados os valores da seção de choque de espalhamento e a média do cosseno do ângulo de espalhamento para uma partícula de raio (r) maior que um décimo do comprimento de onda (Comprimento de onda) da luz (raio maior que um décimo do comprimento de onda) e uma com (raio menor que um décimo do comprimento de onda). Neste último caso, também foi estudada a variação da intensidade da luz espalhada em função do ângulo de espalhamento. Os resultados das partículas pequenas corresponderam ao regime de Rayleigh. As partículas esféricas consideradas foram a rutila, TiO2, e a alumina, Al2O3. Foi estudado também o espalhamento de luz realizado por duas partículas idênticas. Para esse caso, obteve-se uma luz espalhada mais intensa na região entre as partículas em comparação a outras regiões. Ademais, ao comparar com o espalhamento feito por uma única partícula, foi notado que a luz espalhada por duas partículas, na região entre as duas, também era mais intenso. Além disso, ao estudar o confinamento de luz entre duas e três partículas de r = 230 nm, viu-se que o espectro do campo espalhado apresentava mais de um pico, como há em lasers aleatórios coerentes. No que concerne ao comportamento corpuscular da luz, foi considerada a equação de difusão de fótons, onde o espectro de emissão da fluorescência de R6G incidindo em uma concentração da ordem de 1010 cm−3 partículas foi simulado e, posteriormente, comparou-se o resultado obtido com o comportamento de um sistema de laser aleatório incoerente. / [en] In this work, the study of light scattering performed by dielectric spherical particles was carried out, using the finite element method, through the COMSOL Multiphysics 5.6 software, considering the behavior of light both as a wave and as a particle. This study aims, in the future, to understand the random laser in systems with scatter centers with different geometries. Considering the wave behavior of light, the theory of the Mie series was studied. This is a solution that, given the incidence field, makes it possible to calculate the fields scattered and absorbed by the spherical particles. The values of the scattering cross section and the mean of the cosine of the scattering angle were calculated for a particle with radius (r) bigger than one tenth of the light wavelength (wave length) (radius greater than one tenth of the wave length) and one with (radius less than one tenth of the wave length). In the latter case, the variation of the scattered light intensity as a function of the scattering angle was also studied. The small particle results corresponded to the Rayleigh regime. The spherical particles considered were rutile, TiO2, and aluminium oxide, Al2O3. The scattering of light performed by two identical particles was also studied. For this case, a more intense scattered light was obtained in the region between the particles compared to other regions. Furthermore, when comparing with the scattering done by a single particle, it was noticed that the light scattered by two particles, in the region between the two, was also more intense. Furthermore, when studying the confinement of light between two and three particles with r = 230 nm, it was seen that the spectrum of the scattered field showed more than one peak, as one has in coherent random lasers. Concerning the corpuscular behavior of light, the photon diffusion equation was considered, where the emission spectrum of the fluorescence of R6G incident on a concentration of the order of 1010 cm−3 particles was simulated and, later, the result obtained was compared with the behavior of an incoherent random laser system.

Όταν ηλεκρομαγνητική (ΗΜ) ακτινοβολία, προερχόμενη από κάποια πηγή, προσπίπτει σε σύνολο από σωμάτια τότε λαμβάνουν χώρα δύο φαινόμενα. Πρώτον, ασκούνται δυνάμεις στα σωμάτια οι οποίες οφείλονται αποκλειστικά στην σκέδαση της ΗΜ ακτινοβολίας της πηγής από αυτά. Οι δυνάμεις αυτές ονομάζονται Optical Trapping Forces. Δεύτερον, τα ίδια τα σωμάτια σκεδάζοντας την ΗΜ ακτινοβολία της πηγής, λειτουργούν και αυτά ως πηγές ακτινοβολίας. Έτσι ασκούν δυνάμεις το ένα στο άλλο. Οι δυνάμεις αυτές ονομάζονται Optical Binding Forces. H παράλληλη δράση των δύο αυτών ειδών δυνάμεων έχει ως αποτέλεσμα την δημιουργία ευσταθών δομών από τα σωμάτια. Προκειμένου την θεωρητική πρόβλεψη των δομών που αναπτύσσονται, χρειαζόμαστε έναν ταχύτατο αλγόριθμο υπολογισμού των δυνάμεων. Ο πιο ταχύς αλγόριθμος θα είναι το αποτέλεσμα της εύρεσης ενός αναλυτικού τύπου υπολογισμού των δυνάμεων. Η κατασκευή και η παρουσίαση του αναλυτικού τύπου αυτού είναι και το περιεχόμενο της εργασίας που ακολουθεί. / When the electromagnetic radiation, originating from a source, meets an ensemble of particles, there are two phenomena which take place. First, there are forces acting on these particles due exclusively to the scattering of the electromagnetic radiation from the particles. These are the so-called “Optical Trapping Forces”. Second, particles themselves act as sources of radiation since they scatter the radiation, and they exert forces one to another. These are the so-called “Optical Binding Forces”. The coexistence of these two different forces results in the creation of stable structures where the particles are self-organized. To achieve the theoretical prediction of these structures, we need a very efficient algorithm to calculate the forces. The fastest possible and thus more efficient algorithm originates from the analytical formula of the forces. The construction and the solution of the forces analytical formula is the content of this research work.

This study is a presentation of an instantaneous and simultaneous velocity and concentration measurement technique and its applications on car park fire scenarios. <p>In this actual chapter 1 general introduction is given to each chapter. Chapter 2 is dedicated to a detailed description of the instantaneous and simultaneous velocity and concentration measurement technique and its associated error assessment methodology. The name of the new technique is derived from the names of the acquired parameters (VELocity and COncentration) and shall be hereafter referred to as VELCO. After having validated and performed an error assessment of this technique, it is applied to an investigation of full-scale car park (30 m x 30 m x 2.6 m – Gent / WFRGENT) fire cases in chapter 3. The measurements were carried out with the financial support of IWT-SBO program. In the full-scale measurements only the velocity part is applied of VELCO, yet it can be considered as its application since the special data treating was developed and implemented in the Rabon (see: §2.1.2) program, which is the software of the new technique along with Tucsok (see: §2.1.1) and they will be both discussed in the related chapter. Here it is enough to mention that the concentration and velocity information can be obtained independently as well. During the full-scale measurements, beyond of VELCO the smoke back-layering distances (SBL) are also derived from the temperature values, which were measured by thermocouples under the ceiling in the midline of the car park. The critical velocity, which is an important measure of fire safety, can be obtained from the SBL results. In chapter 4, isothermal fire modeling is surveyed in order to present how full-scale fires are modeled in small-scale. In this part of the study the theory of fire related formulae and an isothermal model are described. Here it is important to stress the fact that the fire modeling is not directly related to the VELCO technique. However it connects the full-scale to the small-scale measurements, which the technique is applied on. Chapter 5 discusses small-scale measurements (1:25 – Rhode Saint Genese / VKI) on the car park introduced in chapter 3 and their validation. After the validation, more complex car parks scenarios are also investigated due to the easy to change layout in the small-scale model with respect to the full-scale car park. In this chapter the smoke back-layering distances are obtained by VELCO. Finally, in chapter 6 important conclusions are drawn with the objective of increasing fire safety. <p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

The dissertation presents theoretical and experimental studies on the physical origin of the signal in photothermal microscopy of single particles. This noninvasive optical far field microscopy scheme allows the imaging and detection of single absorbing nanoparticles. Based on a heat-induced pertur- bation in the refractive index in the embedding medium of the nanoscopic absorber, a corresponding probe beam modification is measured and quantified. The method is well established and has been applied since its first demonstration in 2002 to the imaging and characterization of various absorbing particle species, such as quantum dots, single molecules and nanoparticles of different shapes. The extensive theoretical developments presented in this thesis provide the first quantitative assess- ment of the signal and at the same time enlarge its phenomenology and thereby its potential. On the basis of several approximation schemes to the Maxwell equations, which fundamentally gov- ern the interaction of light with inhomogeneities, several complementing models are devised which describe the photothermal signal both qualitatively and quantitatively. In succession an interdepen- dent and self-consistent set of theoretical descriptions is given and allows important experimental consequences to be drawn. In consequence, the photothermal signal is shown to correspond to the action of a nanoscopic (thermal) lens, represented by the spherically symmetric refractive index pro- file n(r) which accompanies the thermal expansion of the absorber’s environment. The achieved quantification allows the direct measurement of absorption cross-sections of nanoparticles. Further, a qualitatively new phenomenology of the signal is unraveled and experimentally demonstrated. The separate roles of the probing and the heating beams in photothermal microscopy is dismantled and the influence of their relative alignment shown to allow for a controlled adjustment of the effective detection volume. For the first time, both positive and negative signals are demonstrated to occur and to be the characteristic signature of the lens-like action on the probe beam. The detection of the probe beam’s modification is also shown to sensitively depend on the aperture used in the detection chan- nel, and a signal optimization is shown to be feasible. Also, a generalization of the detectable signal via the use of a quadrant photodiode is achieved. Specifically, measuring the far field beam deflec- tion the result of the beam passing the lens off-center manifests in a laterally split detection volume. Hereby, finally each classical photothermal spectroscopic techniques has been shown to possess its microscopic counterpart. Central to the understanding of this generalized and new phenomenology is a scalar wave-optical model which draws an analogy between the scattering of a massive particle wave-packet by a Coulomb potential and the deflection of a focused beam by a photonic potential connected with the thermal lens. The significance of the findings is demonstrated by its methodological implications on photother- mal correlation spectroscopy in which the diffusion dynamics of absorbing colloidal particles can be studied. The unique split focal detection volumes are shown to allow the sensitive measurement of a deterministic velocity field. Finally, the method is supplemented by a newly introduced sta- tistical analysis method which is capable of characterizing samples containing a heterogeneous size distribution.:Contents Bibliographic description Abbreviations 1 Introduction 2 Theoretical Background 2.1 The current literature on the subject of the photothermal signal 2.2 Thermal conduction, and the temperature field around heated nanoparticles 2.3 The linear thermo-refractive response and the thermal lens 2.4 MAXWELL equations and approximation schemes 2.4.1 The MAXWELL equations 2.4.2 HELMHOLTZ equations 2.4.3 Paraxial HELMHOLTZ equation for the field components 2.4.4 Geometrical optics and the eikonal ansatz 2.5 Diffraction and the optical resolution limit in far field microscopy 2.5.1 Transmission scanning microscopy 2.5.2 Point spread functions and aberrations 2.5.3 Scalar diffraction approximation for weakly focused beams 2.5.4 Vectorial diffraction for highly focused electromagnetic fields 2.5.5 Theoretical description of transmission signals 2.6 Elastic scattering of light 2.6.1 Overview of optical elastic scattering theory 2.6.2 The integral equation of potential scattering and the BORN approximation 2.6.3 The generalized LORENZ-MIE theory 2.6.4 The electromagnetic fields 2.6.5 Description of the incident field: beam shape coefficients 2.6.6 Multilayered scatterers 2.6.7 POYNTING vector and field decomposition 2.6.8 Energy balance & total cross-sections 2.6.9 Optical theorem & the extinction paradox 2.6.10 Small particle scattering: the RAYLEIGH-limit 2.7 Optical properties of gold nanoparticles & Surface plasmon resonances 2.7.1 Dielectric function of gold 2.7.2 Total cross-sections of plasmonic nanoparticles properties of gold nanoparticles & Surface plasmon resonances 2.8 (Hot) BROWNian motion, diffusion and their statistical analysis 2.8.1 (Hot) BROWNian motion 2.8.2 Diffusion and correlation analysis 2.8.3 Methods regarding the signal statistics of diffusing tracer particles 2.9 RUTHERFORD scattering of charged particles 2.9.1 Classical RUTHERFORD scattering 2.9.2 Quantum mechanical COULOMB scattering 3 Experimental Setup 3.1 Sample preparation 3.2 Photothermal microscopy setup 4 Photothermal Imaging: Results and Discussion 4.1 MAXWELL equations: Exact treatment of the PT signal 4.1.1 Angularly resolved powers: Fractional cross-sections 4.1.2 Incident power and background normalization 4.1.3 Fractional scattering and extinction cross-sections (off-axis) 4.1.4 Fractional scattering and extinction cross-sections (on-axis) 4.1.5 Small particle approximation(on-axis) 4.1.6 General properties of transmission scans 4.1.7 The thermal lens n(r) in the MIE-scattering framework 4.1.8 The photothermal signal F in the MIE scattering framework 4.2 Geometrical optics: Photonic RUTHERFORD scattering (ray optics) 4.2.1 FERMAT’s principle for a thermal lens medium 4.2.2 Gaussian beam transformation by a thermal lens 4.2.3 Experiments using weakly focused, i.e. nearly Gaussian beams 4.3 HELMHOLTZ equation: Photonic RUTHERFORD scattering (wave optics) 4.3.1 Plane-wave scattering 4.3.2 Focused beam scattering 4.3.3 Connection to the far field 4.3.4 Photothermal Rutherford scattering microscopy 4.3.5 Photothermal half-aperture measurements 4.4 Paraxial HELMHOLTZ equation: FRESNEL diffraction by a thermal lens 4.4.1 The diffraction integral and the phase mask for a thermal lens 4.4.2 The photothermal signal expressed via the image plane field 4.4.3 Experimental demonstration of the signal inversion 4.4.4 Connection to photothermal RUTHERFORD scattering 4.5 Plane-wave extinction & scattering by a thermal lens 4.5.1 The BORN approximation for the ideal and time-dependent thermal lens 4.5.2 The eikonal approximation for the ideal thermal lens and x>>1 4.5.3 Lessons to be learned from plane-wave scattering by thermal lenses 4.6 What is a lens? And is n(r) a lens? 5 Methodological Applications of the Results 5.1 Generalized photothermal correlation spectroscopy (incl. twin-PhoCS) 5.2 Photothermal signal distribution analysis (PhoSDA) 6 Summary and Outlook 6.1 Summary of the results 6.2 Outlook 7 Appendix 7.1 Material parameters 7.2 Calculation parameters 7.3 Interactive simulation scripts (Processing) 7.4 Vectorial scattering in the BORN-approximation 7.5 Details regarding the scattering framework 7.5.1 Connection between Gmn,TE,TM of Ref.1 and gmn,TE,TM in the GLMT 7.5.2 Off-axis BSCs including aberration (single interface) 7.5.3 Details on the incidence power Pinc 7.5.4 Details on the incidence power Pinc for arbitrary beams 7.5.5 Explicit expressions for the spherical field components of Es,i and Hs,i 7.5.6 Note on the time-dependence and the corresponding sign-conventions in M 7.5.7 Recurrence relation for Pn and tn 7.5.8 Gaussian beam shape coefficients: Off-axis 7.5.9 Multilayered Scatterer 7.5.10 POYNTING-vector and energy flow fields 7.5.11 Convergence 7.5.12 Further evaluations in the GLMT framework 7.5.13 Diffraction model: Comparison of angular PT signal pattern to the GLMT 7.6 Details on geometrical optics models 7.6.1 Geometrical optics: Exact solution r(f) for |bx|<1 7.6.2 Correspondences in photonic and partile RUTHERFORD scattering 7.6.3 On the difference in the definition of optical energy 7.6.4 Ray-opticsphotothermalsignal 7.6.5 Thick lens raytracing and the equivalent lens shape for a given aberration 7.7 Thermal lens around a wire of radius R 7.8 Twin-PhoCS: Graphic illustration of the CCF integrand Curriculum Vitae Publications Declaration Acknowledgements List of Tables List of Figures Bibliography

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