Script Fundamentals of Modern Optics, FSU Jena, Prof. T. Pertsch, FoMO_Script_2014-10-24s.docx 1 Script Fundamentals of Modern Optics, FSU Jena, Prof. T. Pertsch, FoMO_Script_2014-10-24s.docx 2 Fundamentals of Modern Optics 2.6 (The Kramers-Kronig relation, covered by lecture Structure of Matter) ......... 100 3. Diffraction theory .................................................................................. 104 Winter Term 2014/2015 3.1 Interaction with plane masks .......................................................................... 104 3.2 Propagation using different approximations ................................................... 105 Prof. Thomas Pertsch 3.2.1 The general case - small aperture .................................................................. 105 Abbe School of Photonics 3.2.2 Fresnel approximation (paraxial approximation) ............................................ 105 3.2.3 Paraxial Fraunhofer approximation (far field approximation) ......................... 106 Friedrich-Schiller-Universität Jena 3.2.4 Non-paraxial Fraunhofer approximation ......................................................... 108 3.3 Fraunhofer diffraction at plane masks (paraxial) ............................................ 108 3.3.1 Fraunhofer diffraction pattern ......................................................................... 108 3.4 Remarks on Fresnel diffraction ...................................................................... 113 Table of content 4. Fourier optics - optical filtering .............................................................. 114 0. Introduction ............................................................................................... 4 4.1 Imaging of arbitrary optical field with thin lens ............................................... 114 4.1.1 Transfer function of a thin lens ....................................................................... 114 1. Ray optics - geometrical optics (covered by lecture Introduction to Optical 4.1.2 Optical imaging ............................................................................................... 115 Modeling) ............................................................................................... 16 4.2 Optical filtering and image processing ........................................................... 117 1.1 Introduction ....................................................................................................... 16 4.2.1 The 4f-setup .................................................................................................... 117 1.2 Postulates ......................................................................................................... 16 4.2.2 Examples of aperture functions ...................................................................... 119 1.3 Simple rules for propagation of light ................................................................. 17 4.2.3 Optical resolution ............................................................................................ 120 1.4 Simple optical components............................................................................... 17 5. The polarization of electromagnetic waves .......................................... 123 1.5 Ray tracing in inhomogeneous media (graded-index - GRIN optics) .............. 21 5.1 Introduction ..................................................................................................... 123 1.5.1 Ray equation ..................................................................................................... 21 5.2 Polarization of normal modes in isotropic media ............................................ 123 1.5.2 The eikonal equation ........................................................................................ 23 5.3 Polarization states .......................................................................................... 124 1.6 Matrix optics ...................................................................................................... 24 1.6.1 The ray-transfer-matrix ..................................................................................... 24 6. Principles of optics in crystals ............................................................... 126 1.6.2 Matrices of optical elements ............................................................................. 24 6.1 Susceptibility and dielectric tensor ................................................................. 126 1.6.3 Cascaded elements .......................................................................................... 25 6.2 The optical classification of crystals ............................................................... 128 6.3 The index ellipsoid .......................................................................................... 129 2. Optical fields in dispersive and isotropic media ...................................... 26 6.4 Normal modes in anisotropic media ............................................................... 130 2.1 Maxwell’s equations ...................................................................................... 26 6.4.1 Normal modes propagating in principal directions ......................................... 131 2.1.1 Adaption to optics ............................................................................................. 26 6.4.2 Normal modes for arbitrary propagation direction .......................................... 132 2.1.2 Temporal dependence of the fields .................................................................. 31 6.4.3 Normal surfaces of normal modes ................................................................. 136 2.1.3 Maxwell’s equations in Fourier domain ............................................................ 31 6.4.4 Special case: uniaxial crystals ........................................................................ 138 2.1.4 From Maxwell’s equations to the wave equation ............................................. 32 2.1.5 Decoupling of the vectorial wave equation ....................................................... 33 7. Optical fields in isotropic, dispersive and piecewise homogeneous media 2.2 Optical properties of matter .............................................................................. 34 ............................................................................................................. 141 2.2.1 Basics ............................................................................................................... 34 7.1 Basics ............................................................................................................. 141 2.2.2 Dielectric polarization and susceptibility ........................................................... 37 7.1.1 Definition of the problem ................................................................................. 141 2.2.3 Conductive current and conductivity ................................................................ 39 7.1.2 Decoupling of the vectorial wave equation ..................................................... 142 2.2.4 The generalized complex dielectric function .................................................... 40 7.1.3 Interfaces and symmetries ............................................................................. 143 2.2.5 Material models in time domain ........................................................................ 44 7.1.4 Transition conditions ....................................................................................... 143 2.3 The Poynting vector and energy balance ......................................................... 46 7.2 Fields in a layer system matrix method ..................................................... 144 2.3.1 Time averaged Poynting vector ........................................................................ 46 7.2.1 Fields in one homogeneous layer .................................................................. 144 2.3.2 Time averaged energy balance ........................................................................ 47 7.2.2 The fields in a system of layers ...................................................................... 146 2.4 Normal modes in homogeneous isotropic media ............................................. 49 7.3 Reflection – transmission problem for layer systems ..................................... 148 2.4.1 Transversal waves ............................................................................................ 50 7.3.1 General layer systems .................................................................................... 148 2.4.2 Longitudinal waves ........................................................................................... 51 7.3.2 Single interface ............................................................................................... 154 2.4.3 Plane wave solutions in different frequency regimes ....................................... 52 7.3.3 Periodic multi-layer systems - Bragg-mirrors - 1D photonic crystals ............. 161 2.4.4 Time averaged Poynting vector of plane waves .............................................. 58 7.3.4 Fabry-Perot-resonators .................................................................................. 168 2.5 Beams and pulses - analogy of diffraction and dispersion ............................... 58 7.4 Guided waves in layer systems ...................................................................... 174 2.5.1 Diffraction of monochromatic beams in