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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Multiple-prism dispersion theory ： ウィキペディア英語版 Multiple-prism dispersion theory The first description of multiple-prism arrays, and multiple-prism dispersion, was given by Newton in his book ''Opticks''.〔I. Newton, ''Opticks'' (Royal Society, London, 1704).〕 Prism pair expanders were introduced by Brewster in 1813.〔D. Brewster, ''A Treatise on New Philosophical Instruments for Various Purposes in the Arts and Sciences with Experiments on Light and Colours'' (Murray and Blackwood, Edinburgh, 1813).〕 A modern mathematical description of the single-prism dispersion was given by Born and Wolf in 1959.〔M. Born and E. Wolf, ''Principles of Optics'', 7th Ed. (Cambridge University, Cambridge, 1999).〕 The generalized multiple-prism dispersion theory was introduced by Duarte and Piper〔F. J. Duarte and J. A. Piper, "Dispersion theory of multiple-prism beam expanders for pulsed dye lasers", ''Opt. Commun.'' 43, 303–307 (1982).〕〔F. J. Duarte and J. A. Piper, "Generalized prism dispersion theory", ''Am. J. Phys.'' 51, 1132–1134 (1982).〕 in 1982. ==Generalized multiple-prism dispersion equations== The generalized mathematical description of multiple-prism dispersion, as a function of the angle of incidence, prism geometry, prism refractive index, and number of prisms, was introduced as a design tool for multiple-prism grating laser oscillators by Duarte and Piper,〔〔 and is given by :$(\backslash partial\backslash phi\_/\backslash partial\backslash lambda)\; =\; H\_\; (\backslash partial\; n\_m/\backslash partial\backslash lambda)\; +\; (k\_k\_)^\backslash bigg(H\_(\backslash partial\; n\_m/\backslash partial\backslash lambda)\; \backslash pm\backslash \; (\backslash partial\backslash phi\_/\backslash partial\backslash lambda)\backslash bigg)$ which can also be written as :$\backslash nabla\_\backslash phi\_\; =\; H\_\backslash nabla\_n\_m\; +\; (k\_k\_)^\backslash bigg(H\_\backslash nabla\_n\_m\; \backslash pm\; \backslash nabla\_\backslash phi\_\backslash bigg)$ using :$\backslash nabla\_=\; \backslash partial/\backslash partial\; \backslash lambda$ Also, :$\backslash ,k\_=cos\backslash psi\_/cos\backslash phi\_$ :$\backslash ,k\_=cos\backslash phi\_/cos\backslash psi\_$ :$\backslash ,H\_=(tan\backslash phi\_)/n\_m$ :$\backslash ,H\_=(tan\backslash phi\_)/n\_m$ Here, $\backslash phi\_$ is the angle of incidence, at the ''m''th prism, and $\backslash psi\_$ its corresponding angle of refraction. Similarly, $\backslash phi\_$ is the exit angle and $\backslash psi\_$ its corresponding angle of refraction. The two main equations give the first order dispersion for an array of ''m'' prisms at the exit surface of the ''m''th prism. The plus sign in the second term in parentheses refers to a positive dispersive configuration while the minus sign refers to a compensating configuration.〔〔 The ''k'' factors are the corresponding beam expansions, and the ''H'' factors are additional geometrical quantities. It can also be seen that the dispersion of the ''m''th prism depends on the dispersion of the previous prism (''m'' - 1). These equations can also be used to quantify the angular dispersion in prism arrays, as described in Isaac Newton's book ''Opticks'', and as deployed in dispersive instrumentation such as multiple-prism spectrometers. A comprehensive review on practical multiple-prism beam expanders and multiple-prism angular dispersion theory, including explicit and ready to apply equations (engineering style), is given by Duarte.〔 More recently, the generalized multiple-prism dispersion theory has been extended to include positive and negative refraction.〔F. J. Duarte, Multiple-prism dispersion equations for positive and negative refraction, ''Appl. Phys. B'' 82, 35-38 (2006).〕 Also, higher order phase derivatives have been derived using a Newtonian iterative approach.〔(F. J. Duarte, Generalized multiple-prism dispersion theory for laser pulse compression: higher order phase derivatives, ''Appl. Phys. B'' 96, 809-814 (2009) ).〕 This extension of the theory enables the evaluation of the Nth higher derivative via an elegant mathematical framework. Applications include further refinements in the design of prism pulse compressors and nonlinear optics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Multiple-prism dispersion theory」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.