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We describe a fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy (birefringence) or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis. Favorable scaling with the system size(More)
Recent results by Van Buskirk have broken the record set by Yavne in 1968 for the lowest exact count of real additions and multiplications to compute a power-of-two discrete Fourier transform (DFT). Here, we present a simple recursive modification of the split-radix algorithm that computes the DFT with asymptotically about 6% fewer operations than Yavne,(More)
Citation Oskooi, Ardavan F. et al. " Meep: A flexible free-software package for electromagnetic simulations by the FDTD method. " The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract This paper describes Meep, a popular free implementation of the finite-difference time-domain (FDTD)(More)
We describe an all-angle negative refraction effect that does not employ a negative effective index of refraction and involves photonic crystals. A few simple criteria sufficient to achieve this behavior are presented. To illustrate this phenomenon, a microsuperlens is designed and numerically demonstrated. Negative refraction of electromagnetic waves in(More)
Linear waveguides in photonic-crystal slabs, two-dimensionally periodic dielectric structures of finite height, are fundamentally different from waveguides in two-dimensional photonic crystals. The most important distinctions arise from the fact that photonic-crystal slab waveguides must be index-confined in the vertical direction ͑while a band gap confines(More)
We prove that an adiabatic theorem generally holds for slow tapers in photonic crystals and other strongly grated waveguides with arbitrary index modulation, exactly as in conventional waveguides. This provides a guaranteed pathway to efficient and broad-bandwidth couplers with, e.g., uniform waveguides. We show that adiabatic transmission can only occur,(More)