Two-dimensional photonic band gap crystals

Citation

Anderson, Cheryl Marie (1999) Two-dimensional photonic band gap crystals. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/17mm-qm12. https://resolver.caltech.edu/CaltechETD:etd-02082008-170050

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. A photonic crystal is a periodic dielectric structure that possesses a band of frequencies in which propagating electromagnetic waves are forbidden. Two- dimensional photonic crystals exhibit a band gap for waves traveling in the crystal plane, a property that offers promise for improved operation of optoelectronic devices including semiconductor lasers, light-emitting diodes, and frequency filters. A theoretical investigation of two-dimensional photonic band gap crystals has been performed. The plane-wave expansion method is used to solve Maxwell's equations for the electromagnetic frequency bands in several square (Lane group 4mm) and triangular (Laue group 6mm) crystal structures. The size of absolute band gaps is often limited by band degeneracies at lattice symmetry points. By reducing the lattice symmetry, these degeneracies can be lifted to increase the size of existing photonic band gaps, or to create new gaps where none existed for the more symmetric structure. Symmetry analysis also offers a rational approach for exploring and designing new photonic crystal structures. Gap maps for several important crystal structures are presented as a useful reference guide for experimentalists. The utility of photonic crystals for many applications is enhanced through the introduction of a defect into the crystal structure, which creates localized frequency states within the photonic band gap. Defect modes in two-dimensional square photonic crystal structures were studied using a supercell approach. By changing the radius of a single rod, several defect modes with complex electromagnetic field patterns appear within the photonic band gap. The mode frequencies can be tuned by varying the size of the defect rod. The double-rod square structure has two rod types per unit cell, yielding different defect characteristics depending on which rod is altered. In addition, anisotropic etching of patterned silicon has been investigated experimentally using a hyperthermal neutral fluorine atom beam generated by laser- induced detonation of [...]. The detrimental effects of surface charging are eliminated by the use of charge-neutral etch species; however, inelastic scattering of energetic reactive species has a significant effect on the development of the etch profiles, especially at high aspect ratios. Etch profile anomalies including microtrenching and undercutting are observed.

Thesis Files