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The design of high quality factor (Q) optical cavities in two dimensional photonic crystal (PC) slab waveguides based upon a momentum space picture is presented. The results of a symmetry analysis of defect modes in hexagonal and square host photonic lattices are used to determine cavity geometries that produce modes which by their very symmetry reduce the vertical radiation loss from the PC slab. Further improvements in the Q are achieved through tailoring of the defect geometry in Fourier space to limit coupling between the dominant momentum components of a given defect mode and those momentum components which are either not reflected by the PC mirror or which lie within the radiation cone of the cladding surrounding the PC slab. Numerical investigations using the finite-difference time-domain (FDTD) method predict that radiation losses can be significantly suppressed through these methods, culminating with a graded square lattice design whose total Q approaches 10;5 with a mode volume of approximately 0.25 cubic half-wavelengths in vacuum.
Srinivasan et al. (Mon,) studied this question.