In this paper, a matrix theory for the propagation of a scalar wave in a system consisting of plane screens (in cylindrical coordinates) is proposed on the basis of [8]. The action matrices characterizing the diffraction by a plane filter close to a thin lens, the phase transform action of a lens, and the effect of a piece of free space are given. The diffraction by a common aperture in an opaque screen, the action of a reflection plane screen, the interference produced by a plane screen and so on, are naturally taken into account. The transform matrix describing the effect of changing the reference light field on the field distribution vector, and the method to write the light propagation matrices of various systems consisting of these plane screens are also given. But the action of a scattering screen has not been considered. The method to solve for the super limit of the error which results from truncatingthe action matrix to finite order is contained in the appendix of this paper.On account of the coordinates used, the matrix theory is mainly suited forsystems with ideally axial symmetry. The main significance of this matrix theoryis that some problems of light propagation in the system above mentioned, which israther difficult to treat in practice by means of the previous theory, can be treatedrather conveniently by virtue of the present theory.The theory is only valid for systems in which each plane screen is perpendicularto the propagation axis, and the diffraction formula and the approximate conditionspresented in section (2) of this paper are suited for the diffraction by each planescreen.As an example of application of this theory, the matrix equation of the mode inoptical resonator (passive) is obtained and discussed in the section (5) of this paper.It is compared with the well known integral equations obtained previously by Foxand Li. It is shown that the matrix equation has some important advantages ofpractical value.
下载:
