194 research outputs found

    The Decoupled Potential Integral Equation for Time-Harmonic Electromagnetic Scattering

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    We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A,ϕ{\bf A},\phi in the Lorenz gauge, we establish boundary conditions on the potentials themselves, rather than on the field quantities. This permits the development of a well-conditioned second kind Fredholm integral equation which has no spurious resonances, avoids low frequency breakdown, and is insensitive to the genus of the scatterer. The equations for the vector and scalar potentials are decoupled. That is, the unknown scalar potential defining the scattered field, ϕSc\phi^{Sc}, is determined entirely by the incident scalar potential ϕIn\phi^{In}. Likewise, the unknown vector potential defining the scattered field, ASc{\bf A}^{Sc}, is determined entirely by the incident vector potential AIn{\bf A}^{In}. This decoupled formulation is valid not only in the static limit but for arbitrary ω≥0\omega\ge 0.Comment: 33 pages, 7 figure

    Mie Scattering in the Time Domain. Part I. The Role of Surface Waves

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    We computed the Debye series p = 1 and p = 2 terms of the Mie scattered intensity as a function of scattering angle and delay time for a linearly polarized plane wave pulse incident on a spherical dielectric particle and physically interpreted the resulting numerical data. Radiation shed by electromagnetic surface waves plays a prominent role in the scattered intensity. We determined the surface wave phase and damping rate and studied the structure of the p = 1, 2 surface wave glory in the time domain. (C) 2011 Optical Society of Americ

    Photothermal Single Particle Detection in Theory & Experiments

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    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 Bibliograph

    Laser Beam Interaction with Spheroidal Droplets: Computation and Measurement

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    Sprays and droplets are involved in numerous industrial processes and in nature, e.g. fuel injection in combustion chambers, painting, spray cooling, spray coating, chemical engineering, cloud physics, etc. The understanding of the light scattering features from the droplets, or particles in general, lays the foundation for extending existing techniques or devising novel techniques for particle characterization. The optical techniques are clearly advantageous over sampling, because of their non-intrusiveness and immediacy of results. Typical particle characteristics of interest include refractive index, size, velocity, and especially for non-spherical particles, some information regarding shape or form and orientation. However, most of existing optical techniques are only available for the measurement of spherical particles. In this thesis, the light scattering from a spheroid is studied and the generalized rainbow technique is proposed for droplet non-sphericity measurement. First, the vector ray tracing (VRT) model is employed to simulate the optical caustic structures in the primary rainbow region of oblate spheroidal droplets, which includes the rainbow and hyperbolic umbilic (HU) fringes. The location of cusp caustic is calculated by use of the VRT simulation and compared with that calculated by using analytic solution, exhibiting excellent agreement. Furthermore, the evolution process of the optical caustic structures is consistent with the experimental observation. It reveals that the optical caustic structures in the primary rainbow region can be used to measure the non-sphericity of oblate droplets. The VRT model can also be used to simulate and predict the optical caustic structures observed in higher-order rainbows. As a further validation, the cusp location and optical caustic structures in the secondary rainbow region also have been studied using the VRT method. The secondary rainbow fringe, as well as the location and opening rate of the cusp caustic provide a further avenue for non-sphericity measurement of oblate droplets. Then the character of the generalized rainbow pattern from a spheroidal water droplet is investigated experimentally. In the experiment, light scattering from spheroidal water droplets in the vicinity of the primary rainbow region has been observed to contain a variety of characteristic interference patterns which are the generalization of the rainbow from a sphere. These patterns start from being a fold rainbow, change to transverse cusp caustics and then to hyperbolic umbilic catastrophe as the aspect ratio of the droplet increases. A comparison of the intensity distribution of the observed rainbow patterns in the horizontal equatorial plane with those of Airy simulation reveals that these patterns can be used for characterizing droplets, in particular for determining the refractive index and the diameter of the spheroidal droplet in the equatorial plane. According to the generalized rainbow patterns and Airy approximation, the refractive index and equatorial diameter of water droplets can be inverted from the corresponding generalized rainbow patterns. A comparison of the refractive indices inverted from the corresponding generalized rainbow patterns with that of pure water shows good agreement with absolute errors less than 0.5x10-4. The water droplet diameters in the horizontal equatorial plane are calculated from the generalized rainbow patterns and compared to that measured by direct imaging. It is shown that the relative errors of droplet diameters associated with the generalized rainbow patterns lie between -5% and 5%; hence reliable diameter estimations of droplets can be obtained from the generalized rainbow patterns. The curvatures of simulated rainbow fringes are compared with observed ones from the generalized rainbow patterns, in which good agreement is also shown. Since for a given type of droplet, the curvatures of the rainbow fringes are only a function of the aspect ratios, the non-sphericity (in terms of aspect ratio) of water droplets are inferred from the relevant generalized rainbow patterns. The relative errors of aspect ratios calculated from the generalized rainbow pattern lie between -1% and 1%. Accordingly, the complete informations of a spheroidal water droplet in terms of geometric and optical properties are obtained. Then, the evolution of the optical caustic structures for tilted spheroidal droplets is investigated. The rainbow fringes are tilted counterclockwise as the spheroidal droplet is tilted counterclockwise and vice versa. The changes of the fringes depend on the aspect ratio and tilt angle. A preliminary experiment for tilted spheroidal droplet is shown. Furthermore, Mobius’s approximation is modified to calculate the deviation between the geometrical rainbow angle for an ellipse and that for a sphere. And the vector ray tracing model is also used to compute the rainbow angle deviation for an ellipse, which agrees with modified Mobius equation for small eccentricity. Moreover, the application range of Mobius’s approximation is also investigated. It is demonstrated that, for small eccentricity (0.95≤a/c ≤1.05), the Mobius approximation can predict the rainbow angle difference of ellipse

    Mie scattering in the time domain. Part 1. The role of surface waves,”

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    We computed the Debye series p ÂĽ 1 and p ÂĽ 2 terms of the Mie scattered intensity as a function of scattering angle and delay time for a linearly polarized plane wave pulse incident on a spherical dielectric particle and physically interpreted the resulting numerical data. Radiation shed by electromagnetic surface waves plays a prominent role in the scattered intensity. We determined the surface wave phase and damping rate and studied the structure of the p ÂĽ 1; 2 surface wave glory in the time domain
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