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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 Jones vector ： ウィキペディア英語版 Jones calculus In optics, polarized light can be described using the Jones calculus, discovered by R. C. Jones in 1941. Polarized light is represented by a Jones vector, and linear optical elements are represented by ''Jones matrices''. When light crosses an optical element the resulting polarization of the emerging light is found by taking the product of the Jones matrix of the optical element and the Jones vector of the incident light. Note that Jones calculus is only applicable to light that is already fully polarized. Light which is randomly polarized, partially polarized, or incoherent must be treated using Mueller calculus. == The Jones vector == The Jones vector describes the polarization of light in free space or another homogeneous isotropic non-attenuating medium, where the light can be properly described as transverse waves. Suppose that a monochromatic plane wave of light is travelling in the positive ''z''-direction, with angular frequency ''ω'' and wavevector k = (0,0,''k''), where the wavenumber ''k'' = ''ω''/''c''. Then the electric and magnetic fields E and H are orthogonal to k at each point; they both lie in the plane "transverse" to the direction of motion. Furthermore, H is determined from E by 90-degree rotation and a fixed multiplier depending on the wave impedance of the medium. So the polarization of the light can be determined by studying E. The complex amplitude of E is written :$\backslash begin\; E\_x(t)\; \backslash \backslash \; E\_y(t)\; \backslash \backslash \; 0\backslash end$ = \begin E_ e^ \\ E_ e^ \\ 0\end =\begin E_ e^ \\ E_ e^ \\ 0\ende^ . Note that the physical E field is the real part of this vector; the complex multiplier serves up the phase information. Here $i$ is the imaginary unit with $i^2=-1$. The Jones vector is then :$\backslash begin\; E\_\; e^\; \backslash \backslash \; E\_\; e^\; \backslash end\backslash ;.$ Thus, the Jones vector represents the amplitude and phase of the electric field in the ''x'' and ''y'' directions. The sum of the squares of the absolute values of the two components of Jones vectors is proportional to the intensity of light. It is common to normalize it to 1 at the starting point of calculation for simplification. It is also common to constrain the first component of the Jones vectors to be a real number. This discards the overall phase information that would be needed for calculation of interference with other beams. Note that all Jones vectors and matrices on this article employ the convention that the phase of the light wave is given by $\backslash phi\; =\; kz\; -\; \backslash omega\; t$, a convention used by Hecht. Under this convention, increase in $\backslash phi\_x$ (or $\backslash phi\_y$) indicates retardation (delay) in phase, while decrease indicates advance in phase. For example, a Jones vectors component of $i$ ($=e^$) indicates retardation by $\backslash pi/2$ (or 90 degree) compared to 1 ($=e^$). Collett uses the opposite definition for the phase ($\backslash phi\; =\; \backslash omega\; t\; -\; kz$). The reader should be wary of the choice of convention when consulting references on the Jones calculus. The following table gives the 6 common examples of normalized Jones vectors. || $|H\backslash rangle$ |- | Linear polarized in the y-direction Typically called 'Vertical' || $\backslash begin\; 0\; \backslash \backslash \; 1\; \backslash end$ || $|V\backslash rangle$ |- | Linear polarized at 45° from the x-axis Typically called 'Diagonal' L+45 || $\backslash frac\; \backslash begin\; 1\; \backslash \backslash \; 1\; \backslash end$ || $|D\backslash rangle\; =\; \backslash frac\; (\; |H\backslash rangle\; +\; |V\backslash rangle\; )$ |- | Linear polarized at −45° from the x-axis Typically called 'Anti-Diagonal' L-45 || $\backslash frac\; \backslash begin\; 1\; \backslash \backslash \; -1\; \backslash end$ || $|A\backslash rangle\; =\; \backslash frac\; (\; |H\backslash rangle\; -\; |V\backslash rangle\; )$ |- | Right Hand Circular Polarized Typically called RCP or RHCP || $\backslash frac\; \backslash begin\; 1\; \backslash \backslash \; -i\; \backslash end$ || $|\; R\backslash rangle\; =\; \backslash frac\; (\; |H\backslash rangle\; -\; i\; |V\backslash rangle\; )$ |- | Left Hand Circular Polarized Typically called LCP or LHCP || $\backslash frac\; \backslash begin\; 1\; \backslash \backslash \; +i\; \backslash end$ || $|L\backslash rangle\; =\; \backslash frac\; (\; |H\backslash rangle\; +\; i\; |V\backslash rangle\; )$ |} A general vector that points to any place on the surface is written as a ket $|\backslash psi\backslash rangle$. When employing the Poincaré sphere (also known as the Bloch sphere), the basis kets ($|0\backslash rangle$ and $|1\backslash rangle$) must be assigned to opposing (antipodal) pairs of the kets listed above. For example, one might assign $|0\backslash rangle$ = $|H\backslash rangle$ and $|1\backslash rangle$ = $|V\backslash rangle$. These assignments are arbitrary. Opposing pairs are * $|H\backslash rangle$ and $|V\backslash rangle$ * $|D\backslash rangle$ and $|A\backslash rangle$ * $|R\backslash rangle$ and $|L\backslash rangle$ The polarization of any point not equal to $|R\backslash rangle$ or $|L\backslash rangle$ and not on the circle that passes through $|H\backslash rangle,\; |D\backslash rangle,\; |V\backslash rangle,\; |A\backslash rangle$ is known as elliptical polarization. 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「Jones calculus」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.