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arXiv 1401.2472physics.optics
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光子轨道和自旋角动量的组合演算

Combined calculi for photon orbital and spin angular momenta

Nicholas M. Elias

摘要:

上下文波长、光子自旋角动量(PSAM)和光子轨道角动量(POAM)完全描述了光子或电场(光子系综)的状态。波长直接与能量和线动量有关,即相应的动能。PSAM和POAM本身是动力学量,通俗地分别称为偏振和光学涡旋。天体物理学来源发射携带这种信息的光子。目标。PSAM的电场(强度)特性用Jones(Stokes/Mueller)演算来描述。同样,我创建了演算来表示天体物理学背景下电场和强度的POAM特性。在所有这些演算中加入波长依赖性是微不足道的。接下来的逻辑步骤是:1)形成光子总角动量(PTAM = POAM + PSAM)演算; 2)使用算子和期望值证明它们的有效性; 3)表明仪器PSAM可以影响某些类型电场的测量POAM值。方法.将POAM演算与PSAM演算相结合,导出了电场和场强的PTAM演算。我展示了这些量如何从天球传播到像平面。我还形成了PTAM算子(POAM和PSAM算子之和),有和没有仪器PSAM,并计算相应的期望值。结果除了向量、矩阵、点积和直积符号外,PTAM和POAM演算在表面上看起来是相同的。我提供了所有可能形式的PTAM结石的表格。我证明了PTAM的期望值是正确的仪器和仪器PSAM。我还表明,POAM测量的“未分解”PTAM电场通过非零仪器圆形PSAM可以偏置。结论.组合的PTAM演算提供了如何对PTAM源进行数学建模以及校准POAM和PSAM引起的POAM测量误差的见解。

英文摘要:

Context. Wavelength, photon spin angular momentum (PSAM), and photon orbital angular momentum (POAM), completely describe the state of a photon or an electric field (an ensemble of photons). Wavelength relates directly to energy and linear momentum, the corresponding kinetic quantities. PSAMand POAM, themselves kinetic quantities, are colloquially known as polarization and optical vortices, respectively. Astrophysical sources emit photons that carry this information. Aims. PSAM characteristics of an electric field (intensity) are compactly described by the Jones (Stokes/Mueller) calculus. Similarly, I created calculi to represent POAM characteristics of electric fields and intensities in an astrophysical context. Adding wavelength dependence to all of these calculi is trivial. The next logical steps are to 1) form photon total angular momentum (PTAM = POAM + PSAM) calculi; 2) prove their validity using operators and expectation values; and 3) show that instrumental PSAM can affect measured POAM values for certain types electric fields. Methods. I derive the PTAM calculi of electric fields and intensities by combining the POAM and PSAM calculi. I show how these quantities propagate from celestial sphere to image plane. I also form the PTAMoperator (the sum of the POAMand PSAMoperators), with and without instrumental PSAM, and calculate the corresponding expectation values. Results. Apart from the vector, matrix, dot product, and direct product symbols, the PTAM and POAM calculi appear superficially identical. I provide tables with all possible forms of PTAM calculi. I prove that PTAM expectation values are correct for instruments with and without instrumental PSAM. I also show that POAM measurements of "unfactored" PTAM electric fields passing through non-zero instrumental circular PSAM can be biased. Conclusions. The combined PTAM calculi provide insight into how to mathematically model PTAM sources and calibrate POAMand PSAM- induced POAM measurement errors.

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