FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2286016710> ?p ?o ?g. }

• W2286016710 endingPage "1224" @default.
• W2286016710 startingPage "1220" @default.
• W2286016710 abstract "The problem of wave difiraction on a multilayer grating is considered. Numerical technique based on a combination of the incomplete Galerkin method and scattering matrix method is applied. The problem of scattering matrix singularity in the case when a new difiraction order appears is treated in detail and the singularity-free expressions for the scattering matrix are introduced. 1. INTRODUCTION Difiraction grating problems, particularly those for multilayer difiraction gratings, require rig- orous stable methods, which can provide fast and e-cient computations of the grating proper- ties. One of the most e-cient numerical techniques is based on a combination of the incomplete Galerkin method (1) and matrix formalism such as transfer matrix method, scattering matrix method etc. (2,3). Within this approach a grating is approximated by a set of inhomogeneous layers irrespective of the grating groove shape. The structure can also include a stack of homo- geneous layers. The difiracted wave fleld is decomposed into discrete set of plane waves, each of them corresponding to a certain difiraction order. The set of Maxwell equations is reduced to one second-order or a system of two flrst-order matrix difierential equations. The layered structure of the grating makes it reasonable to apply matrix methods. Being rather convenient in implementation, transfer matrix method turns out to be numerically unstable due to possible over∞ows during computations (2,3). The existence of evanescent difiraction orders results in large positive arguments of exponents for thick gratings or for metallic structures, and the calculations are therefore impossible. Scattering matrix approach (3) was suggested as a stable alternative method instead of transfer matrix technique. By implementing the scattering matrix formalism numerical over∞ows are avoided. However, scattering matrix method has some problems connected with singularity of a scattering matrix in the case when a new difiraction order appears in one of the grating layers, in the incident medium or in the substrate. The wave vector for this difiraction order is exactly parallel to the layer interface and has zero component in the direction perpendicular to the interface. Treated directly this requires inversion of the propagation matrix, which has a zero eigenvalue. In this paper, we suggest a rigorous and physically consistent approach to avoid the singularities of this type. Speciflc expressions for the scattering matrix are given, which are free of difiraction order singularity. Generalizations for lossy gratings are also discussed. The paper is organized as follows. In Section 2, we present the physical and mathematical description of a multilayer difiraction grating. In Section 3, we describe the numerical algorithm based on incomplete Galerkin method and scattering matrix method. In Section 4, we present particular expressions for a scattering matrix, which are free of difiraction order singularity. In Section 5, we discuss the physical consistency of the algorithm and the case of lossy gratings. Section 6 gives conclusions. 2. PROBLEM STATEMENT" @default.
• W2286016710 created "2016-06-24" @default.
• W2286016710 creator A5024095829 @default.
• W2286016710 creator A5031518632 @default.
• W2286016710 creator A5077357364 @default.
• W2286016710 date "2012-01-01" @default.
• W2286016710 modified "2023-09-24" @default.
• W2286016710 title "Avoiding Difiraction Order Singularity in Scattering Matrix Approach Used for Grating Modelling" @default.
• W2286016710 cites W1666853924 @default.
• W2286016710 cites W1995367634 @default.
• W2286016710 cites W2018890340 @default.
• W2286016710 hasPublicationYear "2012" @default.
• W2286016710 type Work @default.
• W2286016710 sameAs 2286016710 @default.
• W2286016710 citedByCount "0" @default.
• W2286016710 crossrefType "proceedings-article" @default.
• W2286016710 hasAuthorship W2286016710A5024095829 @default.
• W2286016710 hasAuthorship W2286016710A5031518632 @default.
• W2286016710 hasAuthorship W2286016710A5077357364 @default.
• W2286016710 hasConcept C106487976 @default.
• W2286016710 hasConcept C11413529 @default.
• W2286016710 hasConcept C120665830 @default.
• W2286016710 hasConcept C121332964 @default.
• W2286016710 hasConcept C122890649 @default.
• W2286016710 hasConcept C134306372 @default.
• W2286016710 hasConcept C158622935 @default.
• W2286016710 hasConcept C159985019 @default.
• W2286016710 hasConcept C16171025 @default.
• W2286016710 hasConcept C186899397 @default.
• W2286016710 hasConcept C191486275 @default.
• W2286016710 hasConcept C192562407 @default.
• W2286016710 hasConcept C2777813233 @default.
• W2286016710 hasConcept C31972630 @default.
• W2286016710 hasConcept C33923547 @default.
• W2286016710 hasConcept C41008148 @default.
• W2286016710 hasConcept C45374587 @default.
• W2286016710 hasConcept C62520636 @default.
• W2286016710 hasConceptScore W2286016710C106487976 @default.
• W2286016710 hasConceptScore W2286016710C11413529 @default.
• W2286016710 hasConceptScore W2286016710C120665830 @default.
• W2286016710 hasConceptScore W2286016710C121332964 @default.
• W2286016710 hasConceptScore W2286016710C122890649 @default.
• W2286016710 hasConceptScore W2286016710C134306372 @default.
• W2286016710 hasConceptScore W2286016710C158622935 @default.
• W2286016710 hasConceptScore W2286016710C159985019 @default.
• W2286016710 hasConceptScore W2286016710C16171025 @default.
• W2286016710 hasConceptScore W2286016710C186899397 @default.
• W2286016710 hasConceptScore W2286016710C191486275 @default.
• W2286016710 hasConceptScore W2286016710C192562407 @default.
• W2286016710 hasConceptScore W2286016710C2777813233 @default.
• W2286016710 hasConceptScore W2286016710C31972630 @default.
• W2286016710 hasConceptScore W2286016710C33923547 @default.
• W2286016710 hasConceptScore W2286016710C41008148 @default.
• W2286016710 hasConceptScore W2286016710C45374587 @default.
• W2286016710 hasConceptScore W2286016710C62520636 @default.
• W2286016710 hasLocation W22860167101 @default.
• W2286016710 hasOpenAccess W2286016710 @default.
• W2286016710 hasPrimaryLocation W22860167101 @default.
• W2286016710 hasRelatedWork W1609640382 @default.
• W2286016710 hasRelatedWork W1675109722 @default.
• W2286016710 hasRelatedWork W1972662638 @default.
• W2286016710 hasRelatedWork W1994284298 @default.
• W2286016710 hasRelatedWork W1998334200 @default.
• W2286016710 hasRelatedWork W2004449328 @default.
• W2286016710 hasRelatedWork W2010818986 @default.
• W2286016710 hasRelatedWork W2021402065 @default.
• W2286016710 hasRelatedWork W2021440297 @default.
• W2286016710 hasRelatedWork W2158607830 @default.
• W2286016710 hasRelatedWork W2185082504 @default.
• W2286016710 hasRelatedWork W2185834811 @default.
• W2286016710 hasRelatedWork W2203567914 @default.
• W2286016710 hasRelatedWork W2488296216 @default.
• W2286016710 hasRelatedWork W2600059457 @default.
• W2286016710 hasRelatedWork W2807701596 @default.
• W2286016710 hasRelatedWork W2916226678 @default.
• W2286016710 hasRelatedWork W293125764 @default.
• W2286016710 hasRelatedWork W2941483290 @default.
• W2286016710 hasRelatedWork W606764347 @default.
• W2286016710 isParatext "false" @default.
• W2286016710 isRetracted "false" @default.
• W2286016710 magId "2286016710" @default.
• W2286016710 workType "article" @default.