Advanced numerical methods in diffractive optics and applications to periodic photonic nanostructures [Elektronische Ressource] / von Sabine Essig

Advanced Numerical Methods inDiffractive OpticsandApplications toPeriodic Photonic NanostructuresZur Erlangung des akademischen Grades einesDoktors der Naturwissenschaftenvon der Fakult¨at fur¨ Physik desKarlsruher Instituts fur¨ Technologie (KIT)genehmigteDissertationvonDiplom-Physikerin Sabine Essigaus Baden-BadenTag der mundlic¨ hen Prufung:¨ 4. Februar 2011Referent: Prof.Dr.Kurt BuschKorreferent: Prof.Dr.Martin WegenerContents1. Introduction 12. Basic Principles of Classical Optics 52.1. Maxwell’s Equations ............................ 52.2.ConstitutiveRelations......... 62.2.1.OrdinaryDielectrics...... 72.2.2.AnisotropicDielectrics............ 82.2.3.DispersiveMaterials................. 92.3.ReductiontoTwoDimensions..... 122.4.WaveEquation.................... 122.5.Poynting’sTheorem 132.6. Electromagnetic Waves at Boundaries ............ 142.7. Maxwell’s Equations in Covariant Formulation.............. 182.7.1. Curvilinear Coordinates .... 182.7.2. Maxwell’s Equations ...... 202.8.OpticsinPeriodicSystems......................... 212.8.1.BlochTheorem......... 232.8.2.Diffraction............ 232.9.RescaledVariables....... 253. Numerical Methods in Diffractive Optics 273.1.HistoricalReview.............................. 273.2.FourierModalMethod......... 293.2.1.System... 293.2.2.IncidentPlaneWave............. 303.2.3.StructuredRegion.................. 313.2.4.HomogeneousRegions..... 343.2.5.ScateringMatrix............... 353.2.