Rigorous Fourier Methods Based on Numerical Integration for the Calculation of Diffractive Optical Systems
| Autor: | Iff, Wolfgang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Elektromagnetisches Feld
pacs:42.79.Dj msc:45B05 msc:78Mxx Fredholm-Integralgleichung / Art 2 pacs:11.55.-m Randwertproblem Elektromagnetische Welle pacs:07.60.Ly pacs:41.20.-q Differentialgleichung msc:35F15 pacs:02.70.Jn msc:34B05 msc:65L10 pacs:03.50.De Maxwellsche Theorie ddc:535 pacs:42.15.Dp ddc:518 Naturwissenschaftliche Fakultät pacs:42.40.Jv pacs:42.40.Lx Elektromagnetische Streuung / Berechnung msc:65N22 pacs:03.65.Nk msc:65L04 pacs:42.25.Fx Fredholm-Integralgleichung pacs:02.60.Lj pacs:02.60.Nm Beugungstheorie |
| Popis: | Rigorous Fourier methods are methods for the rigorous calculation of the scattering of waves at gratings, which are based on Fourier expansions of the field and material distribution in the direction(s) of periodicity; they are of importance for the calculation of optical systems containing diffractive elements – e.g. interferometers. In the direction(s) of periodicity, the time-independent Maxwell equations are projected onto a Fourier basis. The remaining ordinary differential equation defines together with the boundary conditions at the homogeneous medium of incidence and transmission the boundary value problem, the subject of this thesis. Its solution is given by the scattering-matrix (S-matrix) to be calculated. The fulfillment of the boundary conditions is possible in different ways: The Conventional Differential Method is based on the Shooting Method. Its disadvantage is numerical integration along exponentially increasing functions (anti-evanescent waves). As naturally stable pendant to this, the Direct S-matrix Integration has been developed in the context of this thesis: It integrates the S-matrix directly by a differential equation derived for this. Both methods have O(N³)-complexity, with N the number of harmonics. Recently, alternative rigorous Fourier methods of merely O(N·ln(N))-complexity based on integral equations are emerging. Improvable points here are the number of iterations for the solution of the integral equation, the memory consumption and a lack of flexibility. One remedy to this developed in the context of this thesis is the S-vector algorithm. The presented methods are combined with polarization ray tracing as well as the angular spectrum of plane waves outside gratings. The specified examples show the need, applicability and merit of rigorous Fourier methods. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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