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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Roger Petit |

ISBN: | 9783642815003 3642815006 9783642815027 3642815022 |

OCLC Number: | 858930725 |

Description: | 1 online resource. |

Contents: | 1. A Tutorial Introduction. -- 1.1 Preliminaries -- 1.2 The Perfectly Conducting Grating -- 1.3 The Dielectric or Metallic Grating -- 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 [delta]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 -- 2.5 Reciprocity Relations -- 2.6 Foundation of the Yasuura Improved Point-Matching Method -- References -- 3. Integral Methods -- 3.1 Development of the Integral Method -- 3.2 Presentation of the Problem and Intuitive Description of an Integral Approach -- 3.3 Notations, Mathematical Problem and Fundamental Formulae -- 3.4 The Uncoated Perfectly Conducting Grating -- 3.5 The Uncoated Dielectric or Metallic Grating -- 3.6 The Multiprofile Grating -- 3.7 The Grating in Conical Diffraction Mounting -- 3.8 Numerical Application -- References -- 4. Differential Methods -- 4.1 Introductory Remarks -- 4.2 The E, Case -- 4.3 The H Case -- 4.4 The General Case (Conical Diffraction Case) -- 4.5 Stratified Media -- 4.6 Infinitely Conducting Gratings: the Conformai Mapping Method -- References -- 5. The Homogeneous Problem -- 5.1 Historical Summary -- 5.2 Plasmon Anomalies of a Metallic Grating -- 5.3 Anomalies of Dielectric Coated Reflection Gratings Used in TE Polarization -- 5.4 Extension of the Theory -- 5.5 Theory of the Grating Coupler -- References -- 6. Experimental Verifications and Applications of the Theory -- 6.1 Experimental Checking of Theoretical Results -- 6.2 Systematic Study of the Efficiency of Perfectly Conducting Gratings -- 6.3 Finite Conductivity Gratings -- 6.4 Some Particular Applications -- 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 -- 7.4 Capacitive and Other Grid Geometries -- 7.5 Spatially Separated Grids or Gratings -- 7.6 Finitely Conducting Bigratings -- References -- Additional References with Titles. |

Series Title: | Topics in Current Physics, 22; Topics in current physics, 22. |

Responsibility: | edited by Roger Petit. |

### Abstract:

When I was a student, in the early fifties, the properties of gratings were generally explained according to the scalar theory of optics. Indeed those grating properties, we can call optical properties, were taught'in a satisfac- tory manner and the students were able to clearly understand the diffraction and dispersion of light by gratings.
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