几何光学中的光线传输矩阵课件幻灯片.pptVIP

§2.2 共轴球面腔的稳定性条件 光线传输矩阵(optical ray matrices or ABCD matrices) 腔内光线往返传播的矩阵表示 共轴球面腔的稳定性条件 常见的几种稳定腔、非稳腔、临界腔 稳区图 一 光线传输矩阵 腔内任一傍轴光线在某一给定的横截面内都可以由两个坐标参数来表征：光线离轴线的距离r、光线与轴线的夹角?。规定：光线出射方向在腔轴线的上方时， ?为正；反之，为负。 光线在自由空间行进距离L时所引起的坐标变换为 球面镜对傍轴光线的变换矩阵为（R为球面镜的曲率半径） 球面镜对傍轴光线的反射变换与焦距为f=R/2的薄透镜对同一光线的透射变换是等效的。 用一个列矩阵描述任一光线的坐标，用一个二阶方阵描述入射光线和出射光线的坐标变换。 该矩阵称为光学系统对光线的变换矩阵。 Ray optics---by which we mean the geometrical laws for optical ray propagation, without including diffraction---is a topic that is not only important in its own right, but also very useful in understanding the full diffractive propagation of light waves in optical resonators and beams. Ray matrices or paraxial ray optics provide a general way of expressing the elementary lens laws of geometrical optics, or of spherical-wave optics, leaving out higher-order aberrations, in a form that many people find clearer and more convenient. Ray optics and geometrical optics in fact contain exactly the same physical content, expressed in different fashion. Ray matrices or “ABCD matrices” are widely used to describe the propagation of geometrical optical rays through paraxial optical elements, such lenses, curved mirrors, and “ducts”. These ray matrices also turn out to be very useful for describing a large number of other optical beam and resonator problems, including even problems that involve the diffractive nature of light. Since a ray is, by definition, normal to the optical wavefront, an understanding of the ray behavior makes it possible to trace the evolution of optical waves when they are passing through various optical elements. We find that the passage of a ray (or its reflection) through these elements can be described by simple 2x2 matrices. Furthermore, these matrices will be found to describe the propagation of spherical waves and of Gaussian beams such as those which are characteristics of the output of lasers. Ray propagation through cascaded elements: A single 4-element ray matrix equal to the ordinary matrix pro