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fourier-factorization
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Artifact-free analysis of highly conducting binary gratings by using the legendre polynomial expansion method
, Article Journal of the Optical Society of America A: Optics and Image Science, and Vision ; Volume 26, Issue 6 , 2009 , Pages 1467-1471 ; 10847529 (ISSN) ; Mehrany, K ; Sharif University of Technology
OSA - The Optical Society
2009
Abstract
Analysis of highly conducting binary gratings in TM polarization has been problematic as the Fourier factorization fails and thus unwanted numerical artifacts appear. The Legendre polynomial expansion method (LPEM) is employed here, and the erroneous harsh variations attributed to the violation of the inverse rule validity in applying the Fourier factorization are filtered out. In this fashion, stable and artifact-free numerical results are obtained. The observed phenomenon is clearly demonstrated via several numerical examples and is explained by inspecting the transverse electromagnetic field profile. © 2009 Optical Society of America
Analysis and Design of Optical Devices by Colloidal Nano-Structures
, M.Sc. Thesis Sharif University of Technology ; Akbari, Mahmood (Supervisor)
Abstract
The colloidal crystals are formed of spherical particles and can be fabricated using simple and low-cost chemical methods. Optical properties of colloidal crystals should be recognized properly in order to design optical devices based on these nano-structures. Reflection and transmission coefficients of these multilayer structures are very important for understanding their properties. Semi-analytical methods like Fourier Modal method (FMM) can be very useful to obtain their reflection and transmission properties of these multilayer structures. In this thesis, we try to implement Matched Coordinate (MC) and Adaptive Spatial Resolution (ASR) techniques in the FMM. These techniques increase...
Analysis of Special Periodic Structures with Differential Method
, M.Sc. Thesis Sharif University of Technology ; Mehrany, Khashayar (Supervisor) ; Rashidian, Bizhan (Supervisor)
Abstract
In this thesis, the Maxwell's equations are transformed into a set of ordinary differential equations and then solved in periodic structures by using the differential method (DM). The periodic structures considered in this thesis are carved in linear anisotropic, nonlinear isotropic and nonlinear anisotropic media. Different numerical issues, e.g. stability and convergence rate, are addressed by following the conventional methods, e.g. S- and R- matrix formalism, and Fourier factorization. In addition, an algorithm is proposed for fast and efficient analysis of periodic structures with identical layers. Binary gratings and photonic crystals are examples of such structures. In this algorithm,...
Modal Analysis of Space-Time Periodic Diffraction Gratings
, M.Sc. Thesis Sharif University of Technology ; Mehrany, Khashayar (Supervisor) ; Khavasi, Amin (Supervisor)
Abstract
Over the past few years, time-periodic and space-time-periodic media have garnered a considerable amount of attention, thanks to their exotic and unique interactions with electromagnetic phenomena. These media do not generally comport with Lorentz's reciprocity theorem, thus can be utilized in order to implement non-reciprocal amplification and frequency transformation. One class of such media, that have been the subject of less discussion and interest, are space-time periodic diffraction gratings.In this thesis, we aim to develop a series of semi-analytical methods in order to analyze such structures. Our focus will be on a subset of methods which make use of the modal expansion of fields...
Highly accurate and east convergent diffractive interface theory for fast analysis of metasurfaces
, Article IEEE Journal of Quantum Electronics ; Volume 52, Issue 7 , 2016 ; 00189197 (ISSN) ; Khavasi, A ; Akbari, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
Abstract
Recently, an approximate formalism [Opt. Express 23, 2764, (2015)] called diffractive interface theory has been reported for the fast analysis of the optical response of metasurfaces, subwavelength two-dimensional periodic arrays. In this method, the electromagnetic boundary conditions are derived using the susceptibility distribution of the metasurface, such that the analysis of metasurface is possible without solving any eigenvalue equation inside the grating layer. In this paper, we modify the boundary conditions to achieve more accurate results. In addition, in this paper, correct Fourier factorization rules are also applied leading to faster convergence rate. The obtained results are...
Fast convergent Fourier modal method for the analysis of periodic arrays of graphene ribbons
, Article Optics Letters ; Volume 38, Issue 16 , 2013 , Pages 3009-3012 ; 01469592 (ISSN) ; Sharif University of Technology
2013
Abstract
Li's Fourier factorization rules [J. Opt. Soc. Am. A 13, 1870 (1996)] should be applied to achieve a fast convergence rate in the analysis of diffraction gratings with the Fourier modal method. I show, however, that Li's inverse rule cannot be applied for periodic patterns of graphene when the conventional boundary condition is used. I derive an approximate boundary condition in which a nonzero but sufficiently small height is assumed for the boundary. The proposed boundary condition enables us to apply the inverse rule, leading to a significantly improved convergence rate. A periodic array of graphene ribbons is in fact a special type of finite-conductivity strip grating, and thus the...