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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 N-slit interferometric equation ： ウィキペディア英語版 N-slit interferometric equation Quantum mechanics was first applied to optics, and interference in particular, by Paul Dirac.〔P. A. M. Dirac, ''The Principles of Quantum Mechanics'', 4th Ed. (Oxford, London, 1978).〕 Feynman, in his lectures, uses Dirac's notation to describe thought experiments on double-slit interference of electrons.〔R. P. Feynman, R. B. Leighton, and M. Sands, ''The Feynman Lectures on Physics'', Vol. III (Addison Wesley, Reading, 1965).〕 Feynman's approach was extended to N-slit interferometers for either single-photon illumination, or narrow-linewidth laser illumination, that is, illumination by indistinguishable photons, by Duarte.〔F. J. Duarte and D. J. Paine, Quantum mechanical description of N-slit interference phenomena, in ''Proceedings of the International Conference on Lasers '88'', R. C. Sze and F. J. Duarte (Eds.) (STS, McLean, Va, 1989) pp. 42-47.〕〔F. J. Duarte, Dispersive dye lasers, in ''High Power Dye Lasers'', F. J. Duarte (Ed.) (Springer-Verlag, Berlin, 1991) Chapter 2.〕 The ''N''-slit interferometer was first applied in the generation and measurement of complex interference patterns.〔〔 In this article the generalized ''N''-slit interferometric equation, derived via Dirac's notation, is described. Although originally derived to reproduce and predict ''N''-slit interferograms,〔〔 this equation also has applications to other areas of optics. ==Probability amplitudes and the N-slit interferometric equation== In this approach the probability amplitude for the propagation of a photon from a source (''s'') to an interference plane (''x''), via an array of slits (''j''), is given using Dirac's bra–ket notation as〔 :$\backslash langle\; x\; |\; s\; \backslash rangle\; =\; \backslash sum\_^\backslash N\backslash ,\; \backslash langle\; x\; |\; j\; \backslash rangle\; \backslash langle\; j\; |\; s\; \backslash rangle$ This equation represents the probability amplitude of a photon propagating from ''s'' to ''x'' via an array of ''j'' slits. Using a wavefunction representation for probability amplitudes,〔 and defining the probability amplitudes as〔〔〔F. J. Duarte, On a generalized interference equation and interferometric measurements, ''Opt. Commun.'' 103, 8-14 (1993).〕 :$\backslash langle\; j\; |\; s\; \backslash rangle\; =\; \backslash Psi(r\_)\; e^$ :$\backslash langle\; x\; |\; j\; \backslash rangle\; =\; \backslash Psi(r\_)\; e^$ where $\backslash theta\; \_j$ and $\backslash phi\; \_j$ are the incidence and diffraction phase angles, respectively. Thus, the overall probability amplitude can be rewritten as :$\backslash langle\; x\; |\; s\; \backslash rangle\; =\; \backslash sum\_^\backslash N\backslash ,\; \backslash Psi(r\_j)\; e^$ where :$\backslash Psi(r\_j)\; =\; \backslash Psi(r\_)\; \backslash Psi(r\_)$ and :$\backslash Omega\_j\; =\; \backslash theta\_j+\backslash phi\_j$ after some algebra, the corresponding probability becomes〔〔〔 :$|\backslash langle\; x\; |\; s\; \backslash rangle|^2\backslash \; =\; \backslash sum\_^\backslash N\backslash ,\backslash Psi(r\_j)^2\backslash \; +2\; \backslash sum\_^\backslash N\backslash ,\backslash Psi(r\_j)\backslash bigg(\backslash sum\_^\backslash N\backslash ,\backslash Psi(r\_m)\backslash cos(\backslash Omega\_m-\backslash Omega\_j)\backslash bigg)$ where N is the total number of slits in the array, or transmission grating, and the term in parentheses represents the phase that is directly related to the exact path differences derived from the geometry of the N-slit array (''j''), the intra interferometric distance, and the interferometric plane ''x''.〔 In its simplest version, the phase term can be related to the geometry using :$\backslash cos(\backslash Omega\_m-\backslash Omega\_j)\; =\; \backslash cos\; k\; |L\_-L\_|$ where $k$ is the wave number, and $L\_$ and $L\_$ represent the exact path differences. Here it should be noted that the Dirac–Duarte (DD) ''interferometric equation'' is a probability distribution that is related to the intensity distribution measured experimentally.〔(F. J. Duarte, Comment on "reflection, refraction, and multislit interfernce," ''Eur. J. Phys.'' 25, L57-L58 (2004). )〕 The calculations are performed numerically.〔 The(DD) interferometric equation applies to the propagation of a single photon, or the propagation of an ensemble of indistinguishable photons, and enables the accurate prediction of measured N-slit interferometric patterns continuously from the near to the far field.〔〔 Interferograms generated with this equation have been shown to compare well with measured interferograms for both even (N = 2, 4, 6...) and ''odd'' (N = 3, 5, 7...) values of N from 2 to 1600.〔〔F. J. Duarte, (Tunable Laser Optics'', 2nd Edition (CRC, New York, 2015) ).〕 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「N-slit interferometric equation」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.