Browsing by Subject "Homogeneous materials"

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Open Access
Asymmetric transmission in prisms using structures and materials with isotropic-type dispersion
(Optical Society of America, 2015) Gundogdu, F. T.; Serebryannikov, A. E.; Cakmak, A. O.; Özbay, Ekmel
It is demonstrated that strong asymmetry in transmission can be obtained at the Gaussian beam illumination for a single prism based on a photonic crystal (PhC) with isotropic-type dispersion, as well as for its analog made of a homogeneous material. Asymmetric transmission can be realized with the aid of refraction at a proper orientation of the interfaces and wedges of the prism, whereas neither contribution of higher diffraction orders nor anisotropic-type dispersion is required. Furthermore, incidence toward a prism wedge can be used for one of two opposite directions in order to obtain asymmetry. Thus, asymmetric transmission is a general property of the prism configurations, which can be obtained by using simple geometries and quite conventional materials. The obtained results show that strong asymmetry can be achieved in PhC prisms with (nearly) circular shape of equifrequency dispersion contours, in both cases associated with the index of refraction 0 < n < 1 and n > 1. For the comparison purposes, results are also presented for solid uniform nonmagnetic prisms made of a material with the same value of n. It is shown in zero-loss approximation that the PhC prism and the ultralow-index material prism ( 0 < n < 1) can replace each other in some cases without affecting the scenario of asymmetric transmission. Moreover, the PhC prism and the solid dielectric prism can show the same scenario at n > 1. Possible contributions of scattering on the individual rods and diffraction on the wedge to the resulting mechanism are discussed. Analogs of unidirectional splitting and unidirectional deflection regimes, which are known from the studies of PhC gratings, are obtained in PhC prisms and solid uniform prisms, i.e. without higher diffraction orders. ©2015 Optical Society of America.
Open Access
On the optimality of the window method in computational homogenization
(2013) Temizer, I.; Wu, T.; Wriggers, P.
The window method, where the microstructural sample is embedded into a frame of a homogeneous material, offers an alternative to classical boundary conditions in computational homogenization. Experience with the window method, which is essentially the self-consistent scheme but with a finite surrounding medium instead of an infinite one, indicates that it delivers faster convergence of the macroscopic response with respect to boundary conditions of pure essential or natural type as the microstructural sample size is increased to ensure statistical representativeness. In this work, the variational background for this observed optimal convergence behavior of the homogenization results with the window method is provided and the method is compared with periodic boundary conditions that it closely resembles. © 2013 Elsevier Ltd. All rights reserved.