Ciattoni Alessandro, Palma Claudio
Dipartimento di Fisica, Università Roma Tre, 1-00146 Rome, Italy.
J Opt Soc Am A Opt Image Sci Vis. 2003 Nov;20(11):2163-71. doi: 10.1364/josaa.20.002163.
We describe monochromatic light propagation in uniaxial crystals by means of an exact solution of Maxwell's equations. We subsequently develop a paraxial scheme for describing a beam traveling orthogonal to the optical axis. We show that the Cartesian field components parallel and orthogonal to the optical axis are extraordinary and ordinary, respectively, and hence uncoupled. The ordinary component exhibits a standard Fresnel behavior, whereas the extraordinary one exhibits interesting anisotropic diffraction dynamics. We interpret the anisotropic diffraction as a composition of two spatial geometrical affinities and a single Fresnel propagation step. As an application, we obtain the analytical expression of the extraordinary Gaussian beam. We then derive the first nonparaxial correction to the paraxial beam, thus giving a scheme for describing slightly nonparaxial fields. We find that nonparaxiality couples the Cartesian components of the field and that the resultant longitudinal component is greater than the correction to the transverse component orthogonal to the optical axis. Finally, we derive the analytical expression for the nonparaxial correction to the paraxial Gaussian beam.
我们通过麦克斯韦方程组的精确解来描述单轴晶体中的单色光传播。随后，我们开发了一种傍轴方案来描述垂直于光轴传播的光束。我们表明，与光轴平行和垂直的笛卡尔场分量分别是非常光分量和寻常光分量，因此它们是解耦的。寻常光分量表现出标准的菲涅耳行为，而非常光分量则表现出有趣的各向异性衍射动力学。我们将各向异性衍射解释为两种空间几何亲和性和一个单一菲涅耳传播步骤的组合。作为应用，我们得到了非常光高斯光束的解析表达式。然后，我们推导了傍轴光束的一阶非傍轴修正，从而给出了一种描述略微非傍轴场的方案。我们发现，非傍轴性会耦合场的笛卡尔分量，并且由此产生的纵向分量大于对垂直于光轴的横向分量的修正。最后，我们推导了傍轴高斯光束的非傍轴修正的解析表达式。
