Fresnel equations and transmission line analogues for diffraction gratings

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A simple and intuitive formalism is presented to describe diffraction in multi-layered periodic structures. We use the well known results from scalar analysis (wave propagation in homogeneous layered media) and show that they can be generalized rather readily to vector problems such as diffraction analysis. Specifically, we derive: (1) generalized Fresnel equations appropriate for reflection and transmission from an infinitely thick grating, (2) a generalized Airy formula for thin-film to describe reflection and transmission of light through a lamellar grating and (3) a matrix propagation method akin to that used for multi-layer thin film analysis. The results developed here complement ... continued below

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12 p.

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Kaushik, S. August 1, 1995.

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This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 62 times . More information about this article can be viewed below.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

A simple and intuitive formalism is presented to describe diffraction in multi-layered periodic structures. We use the well known results from scalar analysis (wave propagation in homogeneous layered media) and show that they can be generalized rather readily to vector problems such as diffraction analysis. Specifically, we derive: (1) generalized Fresnel equations appropriate for reflection and transmission from an infinitely thick grating, (2) a generalized Airy formula for thin-film to describe reflection and transmission of light through a lamellar grating and (3) a matrix propagation method akin to that used for multi-layer thin film analysis. The results developed here complement the recent work on R-matrix and S-matrix propagation algorithms that have been used in connection with modal and differential grating theories. These algorithms have proven to be numerically stable for calculating diffraction efficiencies from deep groove gratings. The formalism developed here expands upon the earlier literature by providing important details that are hitherto unavailable.

Physical Description

12 p.

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OSTI as DE95016739

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  • 40. annual meeting of the Society of Photo-Optical Instrumentation Engineers, San Diego, CA (United States), 9-14 Jul 1995

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  • Other: DE95016739
  • Report No.: SAND--95-1891C
  • Report No.: CONF-950793--23
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 100032
  • Archival Resource Key: ark:/67531/metadc622144

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  • August 1, 1995

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  • June 16, 2015, 7:43 a.m.

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  • April 13, 2016, 1:55 p.m.

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Kaushik, S. Fresnel equations and transmission line analogues for diffraction gratings, article, August 1, 1995; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc622144/: accessed June 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.