SIMPLE ANALYTICAL METHOD OF CAVITY DESIGN FOR ASTIGMATISM-COMPENSATEDKERR-LENS MODE-LOCKED RING LASERS AND ITS APPLICATIONS

An analytical method based on a renormalized q parameter for Gaussian- beam propagation and properly matched self-consistent complex q parame ters is proposed to aid in the design of arbitrary-astigmatism-compens ated Kerr-lens mode-locked ring cavity lasers. The q parameters throug hout the ring cavity can be calculated by solution of an algebraically quadratic equation for an arbitrarily thick Kerr medium when the intr acavity laser power is less than the self-trapping power. The Kerr-len s mode-locking strength at the curved mirror was calculated over the s table range. The results indicate that the astigmatism is best compens ated so that the stable range of x and y directions have optimal overl apping. Although to maximize the hard-aperturing effect the curved mir ror separation must be at the far edge of the stable range, pump and c avity field matching inside the Kerr medium is also necessary. In addi tion, the insertion of a vertical slit is more effective than insertio n of a horizontal slit. A spiking phenomenon is found in the intracavi ty z scan curve, which can be observed only with thick Kerr materials and a high laser power.