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FFT literature has been mostly concerned with minimizing the number of floating-point operations performed by an algorithm. Unfortunately, on present-day microprocessors this measure is far less important than it used to be, and interactions with the processor pipeline and the memory hierarchy have a larger impact on performance. Consequently, one must know… (More)
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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)
This paper describes FFTW, a portable C package for computing the one-and multidimen-sional complex discrete Fourier transform (DFT). FFTW is typically faster than all other publicly available DFT software, including the well-known FFTPACK and the code from Numerical Recipes. More interestingly, FFTW is competitive with or better than proprietary ,… (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)
This note is intended as a brief introduction to the theory and practice of per fectly matched layer (PML) absorbing boundaries for wave equations, intended for future use in the courses 18.369 and 18.336 at MIT. It focuses on the complex stretched-coordinate viewpoint, and also discusses the limitations of PML.