Achromatic phase matching (APM), a favorable method in increasing phase matching bandwidth, is explored for second harmonic generation of ultrashort pulses based on a typical grating telescope system. A set of coupled equations incorporating angular dispersion is constructed in the space–time domain. An analytic solution with a pump of tilting pulsed Gaussian beam to the equations is given under the undepleted pump approximation. With the aid of matrix formalism, some properties of the conversion are demonstrated. Though a maximal phase matching bandwidth is obtained, angular dispersion makes the conversion active only around the geometrical focus. Theory shows that APM does not require an overall pulse-front matching in the conversion process.
© 2013 Optical Society of America
Original Manuscript: September 20, 2012
Manuscript Accepted: December 5, 2012
Published: January 23, 2013
Jin Jer Huang, Liu Yang Zhang, Wen Chao Zhang, Shi Rong Yan, Shao Zhi Pu, and Wei Xin Ren, "Theory of second harmonic generation of ultrashort pulses for collinear achromatic phase matching," J. Opt. Soc. Am. B 30, 431-438 (2013)