Generalized Virtual Source Theory of Unstable Laser Resonators within an Extended Fresnel Approximation
Unstable resonators are now widely used in high-directionality laser systems in which large-volume active media with good mode control and automatic output coupling are required.1 The resonator modes have been studied using Fox-Li-type numerical methods2 and the asymptotic treatment within a Fresnel approximation (FA).3,4 In this paper, a generalized virtual source theory with an extended Fresnel approximation (EFA) is developed for the analyses of resonator modes. A uniform asymptotic treatment will be used to obtain an analytic expression of the Kirchhoff integral for a strip resonator. The periodic feature of the eigenvalue is analyzed and compared with the numerical results. Finally, the optimum condition for the effective Fresnel number providing good beam quality and the effects of the spatial dependence of the diffraction loss, derived from an unloaded resonator, on the threshold lasing condition of a loaded resonator are discussed.
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