Optical and dispersion forces experienced by spherical objects

  • We study electromagnetic forces exerted on spherical objects, which either arise from quantum and thermal fluctuations of the electromagnetic field or from an externally applied field. The former effect is known as Casimir interaction, while the latter is utilised in optical tweezer applications. The first part of this thesis deals with the trapping of spherical objects in a vortex beam. We studied the trapping of spherical objects with a tightly focused Laguerre-Gaussian beam. The force field is calculated from a surface integral over the time-averaged Maxwell stress tensor, where the surface encloses the spherical particle under consideration. The field entering the stress tensor consists of the incident and scattered fields. For spherical objects, the scattered field is determined by employing the Mie theory. We apply a Debye-type non-paraxial model of the focused beam to account for the tightly focusing with a high numerical aperture lens, used in most optical tweezerWe study electromagnetic forces exerted on spherical objects, which either arise from quantum and thermal fluctuations of the electromagnetic field or from an externally applied field. The former effect is known as Casimir interaction, while the latter is utilised in optical tweezer applications. The first part of this thesis deals with the trapping of spherical objects in a vortex beam. We studied the trapping of spherical objects with a tightly focused Laguerre-Gaussian beam. The force field is calculated from a surface integral over the time-averaged Maxwell stress tensor, where the surface encloses the spherical particle under consideration. The field entering the stress tensor consists of the incident and scattered fields. For spherical objects, the scattered field is determined by employing the Mie theory. We apply a Debye-type non-paraxial model of the focused beam to account for the tightly focusing with a high numerical aperture lens, used in most optical tweezer experiments. To obtain an even better description of real experimental setups, we include optical aberrations, like spherical aberration and astigmatism. The optical force components can be calculated analytically and are given in terms of a multipole expansion, which we evaluated numerically. Vortex beams carry orbital angular momentum in addition to spin angular momentum associated with the polarization of the beam. Thus, the torque experienced by a trapped particle is enhanced. It is known that the torque is sensitive to the properties of the trapped particle, and this sensitivity becomes stronger for vortex beams. In collaboration with Kaina et al., we developed an experimental method based on this torque that allows for the precise measurement of the radius of trapped beads. We apply our numerical method to fit the experimental data obtained by Kaina et al. to determine unknown system parameters like the sphere radius and even optical aberration parameters. The second part of this thesis concerns the Casimir interaction between two spherical objects, including the limiting case of a sphere and a planar surface. We studied the two-sphere system in various limiting cases and for different materials by applying the scattering approach to the Casimir free energy. Firstly, we examine the Casimir interaction for the experimentally relevant cases of metallic spheres in vacuum and dielectric spheres in an electrolytic solution. In both cases, we studied the high-temperature limit, where the origin of the Casimir interaction becomes entropic, and the dimensionless Casimir free energy becomes a universal function of the geometrical parameters. Based on the scattering approach, we were able to derive an analytical expression for the Casimir free energy of the system with metallic spheres modelled by the Drude model. The universality of this system arises from the diverging dielectric function of the spheres in the static limit. Our calculations are based on a relation between the scattering process between the spheres and a combinatorial problem of bicoloured integer partitions. The final result can be expressed in terms of a special type of Lambert series, which also allows for an analytical calculation of the short-distance limit. The other system we analysed at high temperatures consists of dielectric spheres in an electrolytic solution. While we were not able to find a complete analytical solution in this case, we were able to derive a result for the single-round-trip term of the Casimir free energy. Together with the approximate conformal character of the dimensionless free energy, we were able to define a semi-analytical approximation of the Casimir free energy, which is applicable over the whole distance range between the spheres. We also discuss the relevance of our result for biological and colloidal systems, where the Casimir interaction might lead to relevant long-range interaction. Furthermore, we explored the Casimir interaction between specific kinds of polarisation-mixing materials, namely bi-isotropic spheres. Based on previous calculations done for dielectric spheres, we examined the Casimir interaction in the short-distance limit. From an asymptotic expansion for large sphere radii, we obtained the so-called proximity force approximation to the Casimir free energy. Particularly, we explored the Casimir interaction for an idealised case of bi-isotropic materials, namely perfect electromagnetic conductor (PEMC) spheres. PEMCs interpolate between a perfect electric and magnetic conductor. Earlier results at zero temperature and for two plates revealed that the Casimir force vanishes for a specific PEMC configuration. We extended this study to two PEMC spheres at finite temperatures. Our analysis showed that the vanishing of the force depends on the system's geometry and temperature.show moreshow less

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Metadaten
Author:Tanja SchogerORCiD
URN:urn:nbn:de:bvb:384-opus4-1148070
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/114807
Advisor:Gert-Ludwig Ingold
Type:Doctoral Thesis
Language:English
Year of first Publication:2024
Publishing Institution:Universität Augsburg
Granting Institution:Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät
Date of final exam:2024/07/09
Release Date:2024/09/12
Tag:Optical tweezers; Vortex beam; Casimir effect; Perfect electromagnetic conductor
GND-Keyword:Casimir-Effekt; Quantenfluktuation; Kugel
Pagenumber:192
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik / Lehrstuhl für Theoretische Physik I
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Licence (German):CC-BY-NC 4.0: Creative Commons: Namensnennung - Nicht kommerziell (mit Print on Demand)