Open AccessA MATRIX THEORY FOR OPTICAL PASSIVE RESONATORS (IN CYLINDRICAL COORDINATES) (II)——CALCULATION FOR AXIAL SYMMETRIC STABLE RESONATORS
Author(s) -
Li Xian-Shu,
Gao Yan-Qiu,
Chen Zhi-Tian,
Feng Zeng-Ye
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.32.1002
Subject(s) - resonator , matrix (chemical analysis) , physics , basis (linear algebra) , mathematical analysis , characteristic equation , matrix difference equation , mode (computer interface) , order (exchange) , optics , mathematics , geometry , computer science , differential equation , materials science , composite material , riccati equation , finance , economics , operating system
Attempts are made to explore the way of solving the problem of calculating modes in optical passive resonators on the basis of the matrix equation in the previous papers, and to determine the superior limits of calculation errors resulting from truncating the matrix equation. For convenience of comparison between the results of ours and those obtained previously by other methods in literatures, we have calculated the characteristics of the modes in various stable resonators with two symmetric reflectors for Fresnel numbers N ≤ 1, and have determined the superior limits of the calculation errors using both the trial method of mathematics (the matrix has been truncated into various order to solve the matrix equation) and the rigorous formulae derived in the previous paper in general. It is shown that the superior limits followed from these formulae are resonable for all modes, including high order modes, but they are far larger than real errors. So that a new formula, which is more suitable for determining the superior limits of errors in our calculation than the previous one, has been adopted.Some new characteristics of the modes are obtained.It is obvious that, by means of the matrix equation, all modes in a resonator, whose losses are not very close to unity, with various radial mode numbers p and an arbitrary given angular mode number l can be caculated at a time, It has been found that a satisfactory accuracy can be achieved for the modes in resonators 0 ≤g≤0.95 in our calculation,provided the matrix equation is truncated into (N + 1) order, where N≥ 8N(1+g)1/2-l/2.