By Dr. rer. nat. Norman Hodgson, Prof. Dr. Ing. Horst Weber (auth.)
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Extra info for Optical Resonators: Fundamentals, Advanced Concepts and Applications
Example text
B - ----<-l'! Fig. 6 Imaging with a biconvex focusing lens. In order to get more experience and confidence in the utilization of ray transfer matrices the reader should first go through the two examples presented below. After this we will proceed with a more generalized presentation of ray matrix properties. Imaging with a focusing lens We are looking for the imaging condition for a focusing lens. 22) A ray starting on the left plane with parameters XJ,a. J=O), as depicted in Fig. 6, and a second ray emerging from the same point but going through the center of the lens (a.
J. :J. 40) REAL SPACE X 11 f, X2 Q2 ~ Z1 Zj Z2 Z PHASE SPACE x Fig. 11 Imaging by means of a focusing lens and the corresponding phase space presentation. 41) The condition on the determinant also arises since energy conservative optical systems are reversible. 41) holds for its ray transfer matrix. Thus it is not possible to build an optical funnel which transforms a large diameter divergent beam into a collimated thin ray . /4 (product of the beam radius and the half angle of divergence). g.
8) since it is an important optical element in resonator physics. All laser media can be described in a first approach as a thick lens due to a refractive power induced by the pumping process. We utilize the ray matrix of a thick lens presented in Fig. 5 and first calculate the ray transfer matrix for the propagation from the input to the output plane as shown in Fig. 8. The resulting ray transfer matrix reads: M = (1 o (1 +h/f Ln/n (1 g) b) 1 1 2) -11f h2-b I-hIlf nl L- + -- f n2 1 + 0 1 h b(l --) g(1 l f with -1 f .