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Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

Baczewski, Andrew D.; Miller, Nicholas C.; Shanker, Balasubramaniam S.

Here, the analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require Ο(Ν2) operations, Ν being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in Ο(Ν) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.

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Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein-Gordon potentials

Journal of Computational Physics

Baczewski, Andrew D.; Vikram, Melapudi V.; Shanker, Balasubramaniam S.; Kempel, Leo K.

Diffusion, lossy wave, and Klein–Gordon equations find numerous applications in practical problems across a range of diverse disciplines. The temporal dependence of all three Green’s functions are characterized by an infinite tail. This implies that the cost complexity of the spatio-temporal convolutions, associated with evaluating the potentials, scales as O(Ns2Nt2), where Ns and Nt are the number of spatial and temporal degrees of freedom, respectively. In this paper, we discuss two new methods to rapidly evaluate these spatio-temporal convolutions by exploiting their block-Toeplitz nature within the framework of accelerated Cartesian expansions (ACE). The first scheme identifies a convolution relation in time amongst ACE harmonics and the fast Fourier transform (FFT) is used for efficient evaluation of these convolutions. The second method exploits the rank deficiency of the ACE translation operators with respect to time and develops a recursive numerical compression scheme for the efficient representation and evaluation of temporal convolutions. It is shown that the cost of both methods scales as O(NsNtlog2Nt). Furthermore, several numerical results are presented for the diffusion equation to validate the accuracy and efficacy of the fast algorithms developed here.

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Electron transport in zinc-blende wurtzite biphasic gallium nitride nanowires and GaNFETs

Nanotechnology

Jacobs, Benjamin W.; Ayres, Virginia A.; Stallcup, Richard S.; Hartman, Alan H.; Tupta, Mary A.; Baczewski, Andrew D.; Crimp, Martin C.; Halpern, Joshua H.; He, Maoqi H.; Shaw, Harry S.

Two-point and four-point probe electrical measurements of a biphasic gallium nitride nanowire and current–voltage characteristics of a gallium nitride nanowire based field effect transistor are reported. The biphasic gallium nitride nanowires have a crystalline homostructure consisting of wurtzite and zinc-blende phases that grow simultaneously in the longitudinal direction. There is a sharp transition of one to a few atomic layers between each phase. Here, all measurements showed high current densities. Evidence of single-phase current transport in the biphasic nanowire structure is discussed.

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Results 176–178 of 178
Results 176–178 of 178