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We perform full 3D topology optimization (in which "every voxel" of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc (including diamond), bcc, and simple-cubic lattices. Even without imposing the constraints of any fabrication process, the(More)
In this paper, we show that bone piezoelectricity-a phenomenon in which bone polarizes electrically in response to an applied mechanical stress and produces a short-range electric field-may be a source of intense blast-induced electric fields in the brain, with magnitudes and timescales comparable to fields with known neurological effects. We compute the(More)
We prove, via an elementary variational method, one-dimensional ͑1D͒ and two-dimensional ͑2D͒ localiza-tion within the band gaps of a periodic Schrödinger operator for any mostly negative or mostly positive defect potential, V, whose depth is not too great compared to the size of the gap. In a similar way, we also prove sufficient conditions for 1D and 2D(More)
We derive a sufficient condition for the existence of index-guided modes in a very general class of dielectric waveguides, including photonic-crystal fibers (arbitrary periodic claddings, such as "holey fibers"), anisotropic materials, and waveguides with periodicity along the propagation direction. This condition provides a rigorous guarantee of(More)
We present analytical results that shed new light on the properties of photonic-crystal fibers (optical fibers with periodic structures in their cladding). First, we discuss a general theorem, applicable to any periodic cladding structure, that gives rigorous conditions for the existence of cutoff-free guided modes—it lets you look at a structure, in most(More)
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