The Electromagnetic Radiation of Periodically Polarized Piezoelectric Superlattice Plate
Date Issued
2010
Date
2010
Author(s)
Shih, Chih-Hua
Abstract
This thesis studies the behavior of polaritons in a periodically polarized Lithium Niobate plate. The polarization of the plate is in the thickness direction. Periodically polarized piezoelectric structures enable strong coupling of acoustic waves and electromagnetic waves. The governing equations of such coupled waves have to take care of both Newton’s second law and Maxwell’s equations simultaneously. Plane wave expansion method is adopted to study the characteristics of this periodically polarized structure. Two-dimensional plane waves in the general piezoelectric one-dimensional superlattice were solved first. Then the general wave solutions of a Lithium Niobate plate that is modulated periodically in the wave propagation direction were found. The particular solutions have to satisfy the boundary conditions on the plate-vacuum interface. For a plate has symmetry with respect to the middle plane, the solutions can be decoupled into symmetric and antisymmetric modes. The symmetric or antisymmetric particular solution that composed of general solutions must satisfy the boundary conditions to fulfill the dispersion relation. A new concept of even and odd function decomposition that results from the positive-negative periodically varied material coefficients was proposed. The vanishing of even term Fourier coefficients of the periodically varied piezoelectric constant leads to a decomposition of even term displacement couples odd term electric field and odd term displacement couples even term electric field, the EUOE and OUEE modes. Both the general solutions and boundary conditions can be decomposed into EUOE and OUEE modes. Waves in the plate can be grouped into four kinds of modes, the combinations between one of symmetric and antisymmetirc, and one of EUOE and OUEE. Dispersion curves were then plotted, and the field pattern and energy distribution were computed to investigate the acoustic-electromagnetic coupling phenomenon and the electromagnetic waves in vacuum. The even and odd function decomposition separates the folding of the dispersive curves at the Brillouin zone boundary, but the waves still possess the characteristics of periodic structures. Electromagnetic waves in vacuum possess very long attenuation distances for strong coupling cases, that is, the signal can be detected far away from the plate.
Subjects
polariton
piezoelectric superlattice plate
plane wave expansion
dispersion curve
Type
thesis
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