We investigate the electromagnetic properties of a two-dimensional (2-D) photonic-crystal array of vertical cavities for use in nonlinear optical image processing. We determine the 2-D photonic band structure of the array, and we discuss how it is influenced by the degree of interaction between cavities. We study the properties of defects in the 2-D lattice and show that neighboring cavities interact through their overlapping wave functions. This interaction can be used to produce nearest-neighbor nonlinear Boolean functions such as and, or, and xor, which are useful for optical image processing. We demonstrate the use of 2-D photonic bandgap structures for image processing by removing noise from a sample image with a nearest-neighbor and function.
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