Second harmonic generation with focused broadband 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 the second-harmonic intensities for TEM/sub 00/, TEM/sub 10/, and TEM/sub 11/, 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.<>