Open AccessA MATRIX THEORY FOR OPTICAL PASSIVE RESONATORS (IN CYLINDRICAL COORDINATES) (I)——MATRIX EQUATION OF THE SELF-CONSISTENT FIELD
Author(s) -
Li Xian-Shu
Publication year - 1983
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.32.990
Subject(s) - eigenvalues and eigenvectors , matrix (chemical analysis) , basis (linear algebra) , resonator , field (mathematics) , physics , finite element method , symmetry (geometry) , mathematical analysis , mathematics , quantum mechanics , optics , geometry , pure mathematics , materials science , composite material , thermodynamics
In this paper, we discuss the matrix equation of the self-consistent field in an optical passive resonator, which was proposed in the previous paper on the basis of a matrix theory for the light propagation. A new understanding of the self-consistent field, the concept of the transform of element modes and the method of analysis of the element mode structure of the self-consistent field are presented here. It has been proved in general that the above mentioned matrix equation can be truncated into finite order so as to be solved approximately. The rigorous formula used to determine the superior limits of the errors of the eigenvalues followed from using the finite order matrix equation is given in general, and some other formulae, which are more convenient than it, are also given.It is shown that the matrix theory for optical passive resonators is very suitable for calculating modes containing the high-order modes whose diffraction losses are very close to unity. The author believe that this theory should also be suitable to analysis and design of complicated resonators.On account of the coordinates used, the theory presented here is only suited to systems with ideal axial symmetry.