In this dissertation, photonic crystals were studied theoretically and great attention was paid to the metallic three-dimensional (3-D) photonic crystals. Woodpile structures and spiral structures are especially studied. First, the infrared propagation character of metallic woodpile photonic crystals made of gold in the direction was studied. The bandgap in metallic woodpile was found to be interrupted by a new propagating mode far beyond the waveguide cutoff. Studies of surface plasmons within the structure showed that 3-D metallic photonic crystals can expand the propagating mode far beyond waveguide cutoff.;Second, based on this propagating mode, this dissertation details the design and simulation of an inconspicuous photonic paint that can be applied onto an object for anticounterfeit and tag, track, and locate (TTL) applications. The paint consists of three-dimensional metallic tilted woodpile photonic crystals embedded into a visible and infra-red transparent polymer film, which can be applied to almost any surface. The tilted woodpile photonic crystals are designed with a specific pass band detectable at nearly all incident angles of light. When painted onto a surface, these crystals provide a unique reflective infra-red optical signature that can be easily observed and recorded to verify the location or contents of a package.;Finally, the optical properties of a gold spiral photonic crystal (PC) were studied theoretically and a full three-dimensional (3-D) band gap at near infrared wavelengths was found. This band gap, ranging from 1.2µm to 1.8µm in wavelength, covers all the second and third telecom windows used in optical fiber communications. Chiral and other optical properties were also discussed. There is a very high absorption at the band gap edge due to the retarded speed of light and an abnormal high transmission outside the band gap contributed by surface plasmon polaritons. Both right circular polarized (RCP) and left circular polarized (LCP) light are studied, and great diversities were found in certain regions of the spectrum. These optical properties maintain within large incident angles. All these studies will give a deeper insight to the complex metallic 3-D photonic crystals.
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