Analysis of 3D inhomogeneous optical systems via the Lorentzian formalism

IF 2.3 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physics Letters A Pub Date : 2025-05-07 DOI:10.1016/j.physleta.2025.130606

Angel García-Botella , Manuel Gutiérrez

{"title":"Analysis of 3D inhomogeneous optical systems via the Lorentzian formalism","authors":"Angel García-Botella , Manuel Gutiérrez","doi":"10.1016/j.physleta.2025.130606","DOIUrl":null,"url":null,"abstract":"<div><div>The application of Lorentz geometry to the study of homogeneous media nonimaging optical systems was introduced successfully in <span><span>[1]</span></span>, see also <span><span>[2]</span></span>, based on the analogy between lightlike cones and the cone of edge rays. Recently, we applied this technique to the study of 2D inhomogeneous optical systems <span><span>[3]</span></span>. In the present paper, we generalize previous studies to stationary 3D inhomogeneous optical systems. We obtain and provide some solutions to the systems of nonlinear partial differential equations in cartesian and spheric coordinates in three dimensions. We study optical systems with exponential refraction index. The solutions provide the geometrical vector flux <strong>J</strong> at any point of these 3D optical systems. From this Lorentzian formalism, we have obtained irradiance patterns of these stationary inhomogeneous optical systems and we have compared it with irradiance patterns obtained by raytrace simulations. Finally a study of the physical interpretation of eigenvalues of the Gram matrix of the Lorentzian metric <strong>G</strong> is presented.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"551 ","pages":"Article 130606"},"PeriodicalIF":2.3000,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics Letters A","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S037596012500386X","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

The application of Lorentz geometry to the study of homogeneous media nonimaging optical systems was introduced successfully in [1], see also [2], based on the analogy between lightlike cones and the cone of edge rays. Recently, we applied this technique to the study of 2D inhomogeneous optical systems [3]. In the present paper, we generalize previous studies to stationary 3D inhomogeneous optical systems. We obtain and provide some solutions to the systems of nonlinear partial differential equations in cartesian and spheric coordinates in three dimensions. We study optical systems with exponential refraction index. The solutions provide the geometrical vector flux J at any point of these 3D optical systems. From this Lorentzian formalism, we have obtained irradiance patterns of these stationary inhomogeneous optical systems and we have compared it with irradiance patterns obtained by raytrace simulations. Finally a study of the physical interpretation of eigenvalues of the Gram matrix of the Lorentzian metric G is presented.

查看原文本刊更多论文

三维非均匀光学系统的洛伦兹形式分析

基于类光锥与边缘射线锥的类比，在[1]中成功地介绍了洛伦兹几何在均匀介质非成像光学系统研究中的应用，参见[2]。最近，我们将该技术应用于二维非均匀光学系统[3]的研究。本文将以往的研究推广到固定式三维非均匀光学系统。得到并给出了三维直角坐标系和球面坐标系下非线性偏微分方程组的若干解。我们研究具有指数折射率的光学系统。该解决方案提供了这些三维光学系统任意点的几何矢量通量J。从这个洛伦兹形式中，我们得到了这些静止非均匀光学系统的辐照度图，并将其与射线追踪模拟得到的辐照度图进行了比较。最后对洛伦兹度量G的格拉姆矩阵特征值的物理解释进行了研究。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Physics Letters A 物理-物理：综合

CiteScore

5.10

自引率

3.80%

发文量

493

审稿时长

30 days

期刊介绍： Physics Letters A offers an exciting publication outlet for novel and frontier physics. It encourages the submission of new research on: condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathematical and computational physics, general and cross-disciplinary physics (including foundations), atomic, molecular and cluster physics, plasma and fluid physics, optical physics, biological physics and nanoscience. No articles on High Energy and Nuclear Physics are published in Physics Letters A. The journal''s high standard and wide dissemination ensures a broad readership amongst the physics community. Rapid publication times and flexible length restrictions give Physics Letters A the edge over other journals in the field.