Huygens' principle is derived for short wavelengths in inhomogeneous, isotropic media from considerations of Green's second theorem and the solution to the time-independent wave-equation for a point-source in an inhomogeneous, isotropic medium. This principle leads to an integral equation for the field distribution on optical resonator mirrors, whose parameters depend only upon the geometrical-optics ABCD-matrices. The resonator parameters F, GI, G2, the resonance and stability conditions as well as the spot size of the fundamental mode at the mirrors are given as functions of A, B, C, D, for the special case of a rotationally symmetric optical system between square mirrors. The resonator parameters, F, GI, G2, are calculated by this new method for a case familiar from the literature.
The propagation of light near the axis of astigmatic optical systems may be described by the geometrical-optics approximation with the aid of ray-matrices. The application of the theory of diffraction to the propagation of light in such systems leads to integrals containing essentially the elements of the ray-matrices as parameters. The ABCD-law is derived by evaluating these integrals for gaussian beams. Integral equations applicable to astigmatic optical resonators, having nearly vanishing diffraction losses, are set up. They are only valid under certain conditions, which are comprehensively discussed. The eigensolutions and the eigenvalues of these integral equations are given. The spot-sizes at the resonator mirrors are derived from the eigensolutions, and the eigenvalues lead to the resonance condition. Spot-sizes and resonance condition appear as functions of the elements of the characteristic resonator matrices. The methods described here are applied to the propagation of gaussian beams through gas-lenses and to a resonator containing an internal gas-lens.1. Introduction H. Kogelnik [1] indicated that the geometrical optics ray-matrices (ABCD-matrices) are formally connected with the propagation of gaussian beams. By analogy he was led to the derivation of the ABCD-law joining the curvature of the phase front and the spot-size at two different cross sections of the gaussian beam. However, the elements of the ray-matrices appear likewise in the diffraction integrals describing the propagation of light of arbitrary field distribution through astigmatic lens-like systems. These integrals result from Huygens' principle in inhomogeneous, isotropic media for short wavelength [2]. The ABCD-Iaw will be shown to follow from them in a simple manner, if the field distribution is expanded in Hermite-Gauss-functions. At the same time the transformation of gaussian beams by astigmatic lens-like systems is obtained. The integral equations for the field distributions at the mirrors of astigmatic optical resonators in the limit of vanishing diffraction losses will be solved by applying this transformation.
A YAG: Nd laser system is described which supplies giant pulses which are within 3% constant in shape and size and do not depend on the pump energy and the shape of the pumping pulses. A LiNbO3 crystal cut at the Brewster angle is used as a Q switch. Since the oscillation of the laser in the off state is used to open the Q switch, a definite inversion always occurs within the laser rod at the instant the switch opens that is due to the threshold of the off state and depends solely on the cavity characteristics. The height of the giant pulses is moreover easily controlled by varying the voltage applied to the LiNbO3 crystal.
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