2ND HARMONIC-GENERATION WITH FOCUSED BROAD-BAND AND HIGH-ORDER TRANSVERSE-MODE LASERS

A theoretical study on the optimum conditions of second-harmonic generation with focused high-order transverse-mode and broadband longitudinal-mode lasers is presented. It is shown that the ratio of second-harmonic intensities for TEM//0//0, TEM//1//0, and TEM//1//1 modes are 1:3/4:9/64, indicating that the deviation from phase matching beyond the focus for high-order-mode lasers is catastrophic. Phase coherence of each longitudinal mode of a broadband laser yields a higher parametric generation than a randomly distributed laser. Line-width narrowing and the acceptance-angle widening of the output wave become pronounced as the bandwidth and the fundamental mode number increase.