Grating

About: Grating is a research topic. Over the lifetime, 54667 publications have been published within this topic receiving 651016 citations. The topic is also known as: grid & metal grid.

Electromagnetic theory of gratings

Abstract: 1 A Tutorial Introduction- 11 Preliminaries- 111 General Notations- 112 Time-Harmonic Maxwell Equations- 113 Boundary Conditions- 114 Electromagnetism and Distribution Theory- 115 Notations Used in the Description of a Grating- 12 The Perfectly Conducting Grating- 121 Generalities- 122 The Diffracted Field- 123 The Rayleigh Expansion and the Grating Formula- 124 An Important Lemma- 125 The Reciprocity Theorem- 126 The Conservation of Energy- 127 The Littrow Mounting- 128 The Determination of the Coefficients Bn by the Rayleigh Method- 129 An Integral Expression of ud in P Polarization- 1210 The Integral Method in P Polarization- 1211 The Integral Method in S Polarization- 1212 Modal Expansion Methods- 1213 Conical Diffraction- 13 The Dielectric or Metallic Grating- 131 General i ti es- 132 The Diffracted Field Outside the Groove Region- 133 Maxwell Equations and Distributions- 134 The Principle of the Differential Method (in P Polarization)- 14 Miscellaneous- References- Appendix A: The Distributions or Generalized Functions- AI Preliminaries- A2 The Function Space R- A3 The Space R1- A31 Definitions- A32 Examples of Distributions- A4 Derivative of a Distribution- A5 Expansion with Respect to the Basis ej(x) =exp [i (nK+k sine) x] = exp (i?n x)- A51 Theorem- A 52 Proof- A53 Application to deltaR- A6 Convolution- A61 Memoranda on the Product of Convolution in D'1- A62 Convolution in R1- 2 Some Mathematical Aspects of the Grating Theory- 21 Some Classical Properties of the Helmholtz Equation- 22 The Radiation Condition for the Grating Problem- 23 A Lemma- 24 Uniqueness Theorems- 241 Metallic Grating, with Infinite Conductivity- 242 Dielectric Grating- 25 Reciprocity Relations- 26 Foundation of the Yasuura Improved Point-Matching Method- 261 Definition of a Topological Basis- 262 The System of Rayleigh Functions is a Topological Basis- 263 The Convergence of the Rayleigh Series A Counterexample- References- 3 Integral Methods- 31 Development of the Integral Method- 32 Presentation of the Problem and Intuitive Description of an Integral Approach- 321 Presentation of the Problem- 322 Intuitive Description of an Integral Approach- 33 Notations, Mathematical Problem and Fundamental Formulae- 331 Notations and Mathematical Formulation- 332 Basic Formulae of the Integral Approach- 34 The Uncoated Perfectly Conducting Grating- 341 The TE Case of Polarization- 342 The TM Case of Polarization- 35 The Uncoated Dielectric or Metallic Grating- 351 The Mathematical Boundary Problem- 352 Vital Importance of the Choice of a Well-Adapted Unknown Function- 353 Mathematical Definition of the Unknown Function and Determination of the Field and Its Normal Derivative Above P- 354 Expression of the Field in M2 as a Function of ?- 355 Integral Equation- 356 Limit of the Equation when the Metal Becomes Perfectly Conducting- 36 The Multiprofile Grating- 37 The Grating in Conical Diffraction Mounting- 38 Numerical Application- 381 A Fundamental Preliminary Choice- 382 Study of the Kernels- 383 Integration of the Kernels- 384 Particular Difficulty Encountered with Materials of High Conductivity- 385 The Problem of Edges- 386 Precision on the Numerical Results- References- 4 Differential Methods- 41 Introductory Remarks- 411 Historical Survey- 412 Definition of Problem- 42 The E,, Case- 421 The Reflection and Transmission Matrices- 422 The Computation of Transmission and Reflection Matrices- 423 Numerical Algorithms- 424 Al ternative Matching Procedures for Some Grating Profiles- 425 Field of Application- 43 The H Case- 431 The Propagation Equation- 432 Numerical Treatment- 433 Field of Application- 44 The General Case (Conical Diffraction Case)- 441 The Reflection and Transmission Matrices- 442 The Differential System- 443 Matching with Rayleigh Expansions- 444 Field of Application- 45 Stratified Media- 451 Stack of Gratings- 452 Plane Interfaces Between Homogeneous Media- 46 Infinitely Conducting Gratings: the Conformai Mapping Method- 461 Method- 462 Determination of the Conformai Mapping- 463 Field of Application- References- 5 The Homogeneous Problem- 51 Historical Summary- 52 Plasmon Anomalies of a Metallic Grating- 521 Reflection of a Plane Wave on a Plane Interface- 522 Reflection of a Plane Wave on a Grating- 53 Anomalies of Dielectric Coated Reflection Gratings Used in TE Polarization- 531 Determination of the Leaky Modes of a Dielectric Slab Bounded by Metal on One of Its Sides- 532 Reflection of a Plane Wave on a Dielectric Coated Reflection Grating Used in TE Polarization- 54 Extension of the Theory- 541 Anomalies of a Dielectric Coated Grating Used in TM Polarization- 542 Plasmon Anomalies of a Bare Grating Supporting Several Spectral Orders- 543 General Considerations on Anomalies of a Grating Supporting Several Spectral Orders- 55 Theory of the Grating Coupler- 551 Description of the Incident Beam- 552 Response of the Structure to a Plane Wave- 553 Response of the Structure to a Limited Beam- 554 Determination of the Coupling Coefficient- 555 Application to a Limited Incident Beam- References- 6 Experimental Verifications and Applications of the Theory- 61 Experimental Checking of Theoretical Results- 611 Generalities- 612 Microwave Region- 613 On the Determination of Groove Geometry and of the Refractive Index- 614 Infrared- 615 Visible Region- 616 Near and Vacuum UV- 617 XUV Domain- 618 X-Ray Domain- 62 Systematic Study of the Efficiency of Perfectly Conducting Gratings- 621 Systematic Study of Echelette Gratings in -1 Order Littrow Mount- 622 An Equivalence Rule Between Ruled, Holographic, and Lamel1ar Gratings- 623 Systematic Study of the Efficiency of Holographic Gratings in -1 Order Littrow Mount- 624 Systematic Study of the Efficiency of Symmetrical Lamellar Gratings in -1 Order Littrow Mount- 625 Influence of the Apex Angle- 626 Influence of a Departure from Littrow- 627 Higher Order Use of Gratings- 63 Finite Conductivity Gratings- 631 General Rules- 632 Typical Efficiency Curves in the Visible Region- 633 Influence of Dielectric Overcoatings in Vacuum UV- 634 The Use of Gratings in XUV and X-Ray Regions (?<1000 A)- 635 Conical Diffraction Mountings- 64 Some Particular Applications- 641 Simultaneous Blazing in Both Polarizations- 642 Spectrometers with Constant Efficiency- 643 Grating Bandpass Filter- 644 Reflection Grating Polarizer for the Infrared- 645 Transmission Gratings as Masks in Photolithography- 646 Gratings Used as Beam Sampling Mirrors for High Power Lasers- 647 Gratings as Wavelength Selectors in Tunable Lasers- 648 Transmission Dielectric Gratings used as Color Filters- Concluding Remarks- References- 7 Theory of Crossed Gratings- 71 Overview- 72 The Bigrating Equation and Rayleigh Expansions- 73 Inducti ve Gri ds- 731 Grids with Rectangular Apertures- 732 Numerical Tests and Applications- 733 Inductive Grids with Circular Apertures- 74 Capacitive and Other Grid Geometries- 741 High-Pass Filters- 742 Low-Pass Filters- 743 Bandpass Filters- 744 Bandstop Filters- 75 Spatially Separated Grids or Gratings- 751 The Crossed Lamellar Transmission Grating- 752 The Double Grating- 753 Symmetry Properties of Double Gratings- 754 Multielement Grating Interference Filters- 76 Finitely Conducting Bigratings- 761 A Short Description of the Method- 762 The Coordinate Transformation- 763 Integral Equation Form- 764 Iterative Solution of the Integral Equations- 765 Total Absorption of Unpolarized Monochromatic Light- 766 Reduction of Metallic Reflectivity: Plasmons and Moth-Eyes- 767 Equivalence Formulae Linking Crossed and Classical Gratings- 768 Coated Bigratings- References- Additional References with Titles

Transmission Resonances on Metallic Gratings with Very Narrow Slits

Abstract: Transmission metallic gratings with very narrow and deep enough slits can exhibit transmission resonances for wavelengths larger than the period of the grating. By using a transfer matrix formalism and a quasianalytical model based on a modal expansion, we show that there are two possible ways of transferring light from the upper surface to the lower one: by the excitation of coupled surface plasmon polaritons on both surfaces of the metallic grating or by the coupling of incident plane waves with waveguide resonances located in the slits. Both mechanisms can lead to almost perfect transmittance for those particular resonances.

Coherent emission of light by thermal sources

Abstract: A thermal light-emitting source, such as a black body or the incandescent filament of a light bulb, is often presented as a typical example of an incoherent source and is in marked contrast to a laser. Whereas a laser is highly monochromatic and very directional, a thermal source has a broad spectrum and is usually quasi-isotropic. However, as is the case with many systems, different behaviour can be expected on a microscopic scale. It has been shown recently that the field emitted by a thermal source made of a polar material is enhanced by more than four orders of magnitude and is partially coherent at a distance of the order of 10 to 100nm. Here we demonstrate that by introducing a periodic microstructure into such a polar material (SiC) a thermal infrared source can be fabricated that is coherent over large distances (many wavelengths) and radiates in well defined directions. Narrow angular emission lobes similar to antenna lobes are observed and the emission spectra of the source depends on the observation angle--the so-called Wolf effect. The origin of the coherent emission lies in the diffraction of surface-phonon polaritons by the grating.

Theory and applications of guided-mode resonance filters

Abstract: The guided-mode resonance properties of planar dielectric waveguide gratings are presented and explained. It is shown that these structures function as filters that produce complete exchange of energy between forward- and backward-propagating diffracted waves with smooth line shapes and arbitrarily narrow filter linewidths. Simple expressions based on rigorous coupled-wave theory and on classical slab waveguide theory give a clear view and quantification of the inherent TE/TM polarization separation and the free spectral ranges of the filters. Furthermore, the resonance regimes, defining the parametric regions of the guided-mode resonances, can be directly visualized. It is shown that the linewidths of the resonances can be controlled by the grating modulation amplitude and by the degree of mode confinement (refractive-index difference at the boundaries). Examples presented of potential uses for these elements include a narrow-line polarized laser, a tunable polarized laser, a photorefractive tunable filter, and an electro-optic switch. The guided-mode resonance filter represents a basic new optical element with significant potential for practical applications.

Self-organized nanogratings in glass irradiated by ultrashort light pulses

Abstract: Periodic nanostructures are observed inside silica glass after irradiation by a focused beam of a femtosecond Ti:sapphire laser Backscattering electron images of the irradiated spot reveal a periodic structure of stripelike regions of ~20 nm width with a low oxygen concentration, which are aligned perpendicular to the laser polarization direction These are the smallest embedded structures ever created by light The period of self-organized grating structures can be controlled from ~140 to 320 nm by the pulse energy and the number of irradiated pulses The phenomenon is interpreted in terms of interference between the incident light field and the electric field of the bulk electron plasma wave, resulting in the periodic modulation of electron plasma concentration and the structural changes in glass