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Universität Tübingen

1. Dommermuth, Marius Hermann. Theory on the local electromagnetic field in crystalline dielectrics .

Degree: 2019, Universität Tübingen

URL: http://hdl.handle.net/10900/91938

Starting from the microscopic Maxwell equations, a self-contained theory of the local electromagnetic field in crystalline dielectrics and its relation to macroscopic electrodynamics is established. Applying the Helmholtz decomposition theorem to the microscopic Maxwell equations, two independent sets of equations determining the solenoidal (transverse) and irrotational (longitudinal) contributions of the local electromagnetic field are initially identified. This enables to restate the microscopic Maxwell equations in terms of equivalent inhomogeneous integral equations, where the entire matter and its response to the local electromagnetic field is fully taken into account by the current density. Implementing a phenomenological material model into this current density, where the local electric field is assumed to polarize individual atoms/ions or subunits of the material in reaction to an externally applied electric field, the inhomogeneous integral equation determining the local electric field is specified first with respect to crystalline dielectrics, solely with the crystal structure and the individual polarizabilities as an input into the theory. Afterwards, it is solved exactly by making use of a newly discovered orthonormal and complete system of non-standard Bloch eigenfunctions of the crystalline translation operator. The propagable modes within the dielectric crystal as well as their dispersion relations ω_{n} ≤ ft(\mathbf{q}))
, also called photonic band structure, are then obtained from the corresponding solvability condition of the associated homogeneous integral equation. Additionally, the impact of radiation damping and of a static external magnetic induction field on ω_{n} ≤ ft(\mathbf{q}))
is elucidated, followed by a discussion on the characteristics of the local electromagnetic field in crystalline dielectrics. Subsequently, the macroscopic electromagnetic field is consistently derived from the local electromagnetic field by applying a spatial low-pass filter to the latter one to eliminate all spatial variations that occur on length scales comparable to the lattice constant. The same filtering procedure is then deployed to the microscopic polarization, so that the dielectric tensor ε_{Λ} ≤ ft(\mathbf{q},ω))
can be introduced in a tried and tested way as that quantity that relates the low-pass filtered microscopic polarization with the macroscopic electric field. Next, the differential equations satisfied by the longitudinal and transverse parts of the macroscopic electric field describing electric field screening or wave propagation are deduced in terms of the longitudinal and transverse dielectric tensor ε^{ ≤ ft({L}))} ≤ ft(\mathbf{q},ω))
and ε^{ ≤ ft({T}))} ≤ ft(\mathbf{q},ω))
respectively, followed by a comparison of the local and macroscopic radiation field in dielectric crystals. Finally, the dielectric tensor and its transverse counterpart are discussed. It is shown, that…
*Advisors/Committee Members: Schopohl, Nils (Prof. Dr.) (advisor).*

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APA (6^{th} Edition):

Dommermuth, M. H. (2019). Theory on the local electromagnetic field in crystalline dielectrics . (Thesis). Universität Tübingen. Retrieved from http://hdl.handle.net/10900/91938

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Dommermuth, Marius Hermann. “Theory on the local electromagnetic field in crystalline dielectrics .” 2019. Thesis, Universität Tübingen. Accessed September 19, 2019. http://hdl.handle.net/10900/91938.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Dommermuth, Marius Hermann. “Theory on the local electromagnetic field in crystalline dielectrics .” 2019. Web. 19 Sep 2019.

Vancouver:

Dommermuth MH. Theory on the local electromagnetic field in crystalline dielectrics . [Internet] [Thesis]. Universität Tübingen; 2019. [cited 2019 Sep 19]. Available from: http://hdl.handle.net/10900/91938.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Dommermuth MH. Theory on the local electromagnetic field in crystalline dielectrics . [Thesis]. Universität Tübingen; 2019. Available from: http://hdl.handle.net/10900/91938

Not specified: Masters Thesis or Doctoral Dissertation