Ortega-Vidals Paula, de Jesús Cabrera-Rosas Omar, Espíndola Ramos Ernesto, Juárez Reyes Salvador Alejandro, Julían Macías Israel, Silva-Ortigoza Gilberto, Silva-Ortigoza Ramón, Sosa-Sánchez Citlalli Teresa
J Opt Soc Am A Opt Image Sci Vis. 2017 Sep 1;34(9):1670-1678. doi: 10.1364/JOSAA.34.001670.
The aim of the present work is to obtain an integral representation of the field associated with the refraction of a plane wave by an arbitrary surface. To this end, in the first part we consider two optical media with refraction indexes n and n separated by an arbitrary interface, and we show that the optical path length, ϕ, associated with the evolution of the plane wave is a complete integral of the eikonal equation in the optical medium with refraction index n. Then by using the k function procedure introduced by Stavroudis, we define a new complete integral, S, of the eikonal equation. We remark that both complete integrals in general do not provide the same information; however, they give the geometrical wavefronts, light rays, and the caustic associated with the refraction of the plane wave. In the second part, using the Fresnel-Kirchhoff diffraction formula and the complete integral, S, we obtain an integral representation for the field associated only with the refraction phenomena, the geometric field approximation, in terms of secondary plane waves and the k-function introduced by Stavroudis in solving the problem from the geometrical optics point of view. We use the general results to compute: the wavefronts, light rays, caustic, and the intensity associated with the refraction of a plane wave by an axicon and plano-spherical lenses.
本工作的目的是获得与平面波被任意表面折射相关的场的积分表示。为此，在第一部分中，我们考虑由任意界面分隔的两种折射率分别为(n)和(n')的光学介质，并表明与平面波演化相关的光程(\phi)是折射率为(n)的光学介质中程函方程的一个完全积分。然后，通过使用斯塔夫鲁迪斯引入的(k)函数方法，我们定义了程函方程的一个新的完全积分(S)。我们注意到，一般来说，这两个完全积分并不提供相同的信息；然而，它们给出了与平面波折射相关的几何波前、光线和焦散。在第二部分中，利用菲涅耳 - 基尔霍夫衍射公式和完全积分(S)，我们从几何光学的角度出发，以二次平面波和斯塔夫鲁迪斯引入的(k)函数，获得了仅与折射现象相关的场的积分表示，即几何场近似。我们使用这些一般结果来计算：平面波被圆锥透镜和平凸 - 平凸透镜折射时的波前、光线、焦散和强度。
