Topics in Current Physics

1. A Tutorial Introduction..- 1.1 Preliminaries.- 1.1.1 General Notations.- 1.1.2 Time-Harmonic Maxwell Equations.- 1.1.3 Boundary Conditions.- 1.1.4 Electromagnetism and Distribution Theory.- 1.1.5 Notations Used in the Description of a Grating.- 1.2 The Perfectly Conducting Grating.- 1.2.1 Generalities.- 1.2.2 The Diffracted Field.- 1.2.3 The Rayleigh Expansion and the Grating Formula.- 1.2.4 An Important Lemma.- 1.2.5 The Reciprocity Theorem.- 1.2.6 The Conservation of Energy.- 1.2.7 The Littrow Mounting.- 1.2.8 The Determination of the Coefficients Bn by the Rayleigh Method.- 1.2.9 An Integral Expression of ud in P Polarization.- 1.2.10 The Integral Method in P Polarization.- 1.2.11 The Integral Method in S Polarization.- 1.2.12 Modal Expansion Methods.- 1.2.13 Conical Diffraction.- 1.3 The Dielectric or Metallic Grating.- 1.3.1 General i ti es.- 1.3.2 The Diffracted Field Outside the Groove Region.- 1.3.3 Maxwell Equations and Distributions.- 1.3.4 The Principle of the Differential Method (in P Polarization).- 1.4 Miscellaneous.- References.- Appendix A: The Distributions or Generalized Functions.- A.I Preliminaries.- A.2 The Function Space R.- A.3 The Space R1.- A.3.1 Definitions.- A.3.2 Examples of Distributions.- A.4 Derivative of a Distribution.- A.5 Expansion with Respect to the Basis ej(x) =exp [i (nK+k sine) x] = exp (i?n x).- A.5.1 Theorem.- A. 5.2 Proof.- A.5.3 Application to R.- A.6 Convolution.- A.6.1 Memoranda on the Product of Convolution in D'1.- A.6.2 Convolution in R1.- 2. Some Mathematical Aspects of the Grating Theory.- 2.1 Some Classical Properties of the Helmholtz Equation.- 2.2 The Radiation Condition for the Grating Problem.- 2.3 A Lemma.- 2.4 Uniqueness Theorems.- 2.4.1 Metallic Grating, with Infinite Conductivity.- 2.4.2 Dielectric Grating.- 2.5 Reciprocity Relations.- 2.6 Foundation of the Yasuura Improved Point-Matching Method.- 2.6.1 Definition of a Topological Basis.- 2.6.2 The System of Rayleigh Functions is a Topological Basis.- 2.6.3 The Convergence of the Rayleigh Series; A Counterexample.- References.- 3. Integral Methods.- 3.1 Development of the Integral Method.- 3.2 Presentation of the Problem and Intuitive Description of an Integral Approach.- 3.2.1 Presentation of the Problem.- 3.2.2 Intuitive Description of an Integral Approach.- 3.3 Notations, Mathematical Problem and Fundamental Formulae.- 3.3.1 Notations and Mathematical Formulation.- 3.3.2 Basic Formulae of the Integral Approach.- 3.4 The Uncoated Perfectly Conducting Grating.- 3.4.1 The TE Case of Polarization.- 3.4.2 The TM Case of Polarization.- 3.5 The Uncoated Dielectric or Metallic Grating.- 3.5.1 The Mathematical Boundary Problem.- 3.5.2 Vital Importance of the Choice of a Well-Adapted Unknown Function.- 3.5.3 Mathematical Definition of the Unknown Function and Determination of the Field and Its Normal Derivative Above P.- 3.5.4 Expression of the Field in M2 as a Function of ?.- 3.5.5 Integral Equation.- 3.5.6 Limit of the Equation when the Metal Becomes Perfectly Conducting.- 3.6 The Multiprofile Grating.- 3.7 The Grating in Conical Diffraction Mounting.- 3.8 Numerical Application.- 3.8.1 A Fundamental Preliminary Choice.- 3.8.2 Study of the Kernels.- 3.8.3 Integration of the Kernels.- 3.8.4 Particular Difficulty Encountered with Materials of High Conductivity.- 3.8.5 The Problem of Edges.- 3.8.6 Precision on the Numerical Results.- References.- 4. Differential Methods.- 4.1 Introductory Remarks.- 4.1.1 Historical Survey.- 4.1.2 Definition of Problem.- 4.2 The E,, Case.- 4.2.1 The Reflection and Transmission Matrices.- 4.2.2 The Computation of Transmission and Reflection Matrices.- 4.2.3 Numerical Algorithms.- 4.2.4 Al ternative Matching Procedures for Some Grating Profiles.- 4.2.5 Field of Application.- 4.3 The H Case.- 4.3.1 The Propagation Equation.- 4.3.2 Numerical Treatment.- 4.3.3 Field of Application.- 4.4 The General Case (Conical Diffraction Case).- 4.4.1 The Reflection and Transmission Matrices.- 4.4.2 The Differential System.- 4.4.3 Matching with Rayleigh Expansions.- 4.4.4 Field of Application.- 4.5 Stratified Media.- 4.5.1 Stack of Gratings.- 4.5.2 Plane Interfaces Between Homogeneous Media.- 4.6 Infinitely Conducting Gratings: the Conformai Mapping Method.- 4.6.1 Method.- 4.6.2 Determination of the Conformai Mapping.- 4.6.3 Field of Application.- References.- 5. The Homogeneous Problem.- 5.1 Historical Summary.- 5.2 Plasmon Anomalies of a Metallic Grating.- 5.2.1 Reflection of a Plane Wave on a Plane Interface.- 5.2.2 Reflection of a Plane Wave on a Grating.- 5.3 Anomalies of Dielectric Coated Reflection Gratings Used in TE Polarization.- 5.3.1 Determination of the Leaky Modes of a Dielectric Slab Bounded by Metal on One of Its Sides.- 5.3.2 Reflection of a Plane Wave on a Dielectric Coated Reflection Grating Used in TE Polarization.- 5.4 Extension of the Theory.- 5.4.1 Anomalies of a Dielectric Coated Grating Used in TM Polarization.- 5.4.2 Plasmon Anomalies of a Bare Grating Supporting Several Spectral Orders.- 5.4.3 General Considerations on Anomalies of a Grating Supporting Several Spectral Orders.- 5.5 Theory of the Grating Coupler.- 5.5.1 Description of the Incident Beam.- 5.5.2 Response of the Structure to a Plane Wave.- 5.5.3 Response of the Structure to a Limited Beam.- 5.5.4 Determination of the Coupling Coefficient.- 5.5.5 Application to a Limited Incident Beam.- References.- 6. Experimental Verifications and Applications of the Theory.- 6.1 Experimental Checking of Theoretical Results.- 6.1.1 Generalities.- 6.1.2 Microwave Region.- 6.1.3 On the Determination of Groove Geometry and of the Refractive Index.- 6.1.4 Infrared.- 6.1.5 Visible Region.- 6.1.6 Near and Vacuum UV.- 6.1.7 XUV Domain.- 6.1.8 X-Ray Domain.- 6.2 Systematic Study of the Efficiency of Perfectly Conducting Gratings.- 6.2.1 Systematic Study of Echelette Gratings in -1 Order Littrow Mount.- 6.2.2 An Equivalence Rule Between Ruled, Holographic, and Lamel1ar Gratings.- 6.2.3 Systematic Study of the Efficiency of Holographic Gratings in -1 Order Littrow Mount.- 6.2.4 Systematic Study of the Efficiency of Symmetrical Lamellar Gratings in -1 Order Littrow Mount.- 6.2.5 Influence of the Apex Angle.- 6.2.6 Influence of a Departure from Littrow.- 6.2.7 Higher Order Use of Gratings.- 6.3 Finite Conductivity Gratings.- 6.3.1 General Rules.- 6.3.2 Typical Efficiency Curves in the Visible Region.- 6.3.3 Influence of Dielectric Overcoatings in Vacuum UV.- 6.3.4 The Use of Gratings in XUV and X-Ray Regions (?<1000 A).- 6.3.5 Conical Diffraction Mountings.- 6.4 Some Particular Applications.- 6.4.1 Simultaneous Blazing in Both Polarizations.- 6.4.2 Spectrometers with Constant Efficiency.- 6.4.3 Grating Bandpass Filter.- 6.4.4 Reflection Grating Polarizer for the Infrared.- 6.4.5 Transmission Gratings as Masks in Photolithography.- 6.4.6 Gratings Used as Beam Sampling Mirrors for High Power Lasers.- 6.4.7 Gratings as Wavelength Selectors in Tunable Lasers.- 6.4.8 Transmission Dielectric Gratings used as Color Filters.- Concluding Remarks.- References.- 7. Theory of Crossed Gratings.- 7.1 Overview.- 7.2 The Bigrating Equation and Rayleigh Expansions.- 7.3 Inducti ve Gri ds.- 7.3.1 Grids with Rectangular Apertures.- 7.3.2 Numerical Tests and Applications.- 7.3.3 Inductive Grids with Circular Apertures.- 7.4 Capacitive and Other Grid Geometries.- 7.4.1 High-Pass Filters.- 7.4.2 Low-Pass Filters.- 7.4.3 Bandpass Filters.- 7.4.4 Bandstop Filters.- 7.5 Spatially Separated Grids or Gratings.- 7.5.1 The Crossed Lamellar Transmission Grating.- 7.5.2 The Double Grating.- 7.5.3 Symmetry Properties of Double Gratings.- 7.5.4 Multielement Grating Interference Filters.- 7.6 Finitely Conducting Bigratings.- 7.6.1 A Short Description of the Method.- 7.6.2 The Coordinate Transformation.- 7.6.3 Integral Equation Form.- 7.6.4 Iterative Solution of the Integral Equations.- 7.6.5 Total Absorption of Unpolarized Monochromatic Light.- 7.6.6 Reduction of Metallic Reflectivity: Plasmons and Moth-Eyes.- 7.6.7 Equivalence Formulae Linking Crossed and Classical Gratings.- 7.6.8 Coated Bigratings.- References.- Additional References with Titles.