Saito Shinichi
Center for Exploratory Research Laboratory, Research & Development Group, Hitachi, Ltd., 1-280 Higashi-Koigakubo, Kokubunji, 185-8601, Tokyo, Japan.
Heliyon. 2024 Mar 21;10(7):e28367. doi: 10.1016/j.heliyon.2024.e28367. eCollection 2024 Apr 15.
Spin is a fundamental degree of freedom, which was discovered by Dirac for an electron in his relativistic quantum mechanics, known as the Dirac equation. The origin of spin for a photon is unclear because Maxwell's equations in a vacuum are Lorentz invariant without introducing the concept of spin. Here, the propagation of coherent rays of photons in a graded-index optical fibre is considered to discuss the origin of polarisation for photons using exact solutions of the Laguerre-Gauss and Hermite-Gauss modes. The energy spectrum is massive, and the effective mass is a function of the confinement and orbital angular momentum. The propagation is described by the one-dimensional (1) non-relativistic Schrödinger equation, which is equivalent to the 2 space-time Klein-Gordon equation by a unitary transformation. The probabilistic interpretation and the conservation law require the factorisation of the Klein-Gordon equation, leading to the 2 Dirac equation with spin. The spin expectation values of photons correspond to the polarisation state on the Poincaré sphere. As an application of the theory, a polarisation interferometer is proposed, whose energy spectrum shows a Dirac cone in the Stokes parameter space.
自旋是一种基本自由度，它由狄拉克在其相对论量子力学中针对电子发现，该理论即狄拉克方程。光子自旋的起源尚不清楚，因为真空中的麦克斯韦方程组在不引入自旋概念的情况下就是洛伦兹不变的。在此，考虑光子相干光束在渐变折射率光纤中的传播，以利用拉盖尔 - 高斯模和厄米 - 高斯模的精确解来讨论光子偏振的起源。能谱是大量子数的，有效质量是限制和轨道角动量的函数。传播由一维（1）非相对论薛定谔方程描述，通过幺正变换它等同于二维时空克莱因 - 戈登方程。概率解释和守恒定律要求克莱因 - 戈登方程因式分解，从而得到带有自旋的二维狄拉克方程。光子的自旋期望值对应于庞加莱球面上的偏振态。作为该理论的一个应用，提出了一种偏振干涉仪，其能谱在斯托克斯参数空间中呈现狄拉克锥。
