This letter describes an approach for recording three-dimensional ͑3D͒ periodic structures in a photosensitive polymer using a single diffraction element mask. The mask has a central opening surrounded by three diffraction gratings oriented 120°relative to one another such that the three first order diffracted beams and the nondiffracted laser beam give a 3D spatial light intensity pattern. Structures patterned in this polymer using 1.0 and 0.56 m grating periods have hexagonal symmetry with micron-to submicron-periodicity over large substrate area. Band structure calculations of these low index contrast materials predict photonic gaps in certain high symmetry directions.
Lattice dynamical theory of thermal expansion and mode Grüneisen parameters in cubic boron monophosphide is reported in the quasiharmonic approximation within the framework of a second-neighbor rigid-ion model. In this scheme, we optimized the involved force constants by using nonlinear least-squares procedures with constrained parameters and weighting of the available data on critical-point phonons and elastic and lattice constants. Theoretical results of the phonon dispersion curves along high-symmetry directions ͑both at ambient and 89 kbar pressures͒, mode Grüneisen parameters, and thermal expansion coefficient ͕␣(T)͖ are compared and discussed with the existing experimental and ab initio calculations. Consistent with x-ray data, our calcualtion for the variation of ␣(T) with temperature in BP is found to be remarkably similar to that of -SiC, and unlike most other III-V-compounds, it does not attain negative values at lower temperatures.
We introduce a method of gradient-based optimization that continuously deforms a periodic dielectric distribution to generate photonic structures that possess any desired figure of merit expressible in terms of the electromagnetic eigenmodes. As an example, we generate forbidden regions between specified bands at extremely low dielectric contrast.
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