This paper investigates one-third harmonic generation (OTHG) by analytical methods with a nondepletion approximation and with an exact solution in continuous wave conditions. The nondepletion method shows that OTHG with a small initial power is confined in a very small range except that the overlapping integrals of the pump and signal follow a certain relation. The efficiency depends only on the initial conditions. Increasing pump power only shortens the interaction length to reach the maximum conversion. Furthermore, we exactly explore OTHG by the elliptic functions whose expressions depend on the types of roots derived from the integral and the initial power. We find that the output power level is limited by the initial conditions and the structure of the waveguide, while the pump power only determines the period. There is a constant value that is determined by , , and the overlap integrals, where and are the initial power of the signal and the initial phase difference between pump and signal, respectively. We found that a highly efficient conversion only occurs when is larger than a specific value , called a critical value. A provides a relation between and . So a set of critical conditions of and is obtained. A highly efficient conversion may be supported if is larger than the power in this set. We investigated some typical structure parameters and found the minimum initial power supporting high conversion efficiency. In OTHG, the variation curve has a sharp peak pattern, which means that a variation of the initial phase difference leads to a great change of the conversion. We established a way to get the smallest initial power with a large phase tolerance. Finally, we find a relation among the overlapping integrals and phase mismatching that can support a high conversion efficiency with a small initial power. This study gives valuable suggestions on the experimental design.
© 2014 Optical Society of AmericaFull Article | PDF Article
OSA Recommended Articles
Tianye Huang, Xuguang Shao, Zhifang Wu, Timothy Lee, Yunxu Sun, Huy Quoc Lam, Jing Zhang, Gilberto Brambilla, and Shum Ping
Opt. Express 21(23) 28403-28413 (2013)
Jianyu Zhang, Yunxu Sun, and Qinghai Song
Opt. Express 23(13) 17407-17420 (2015)
Daniel Hartley, M. A. Lohe, T. M. Monro, and Shahraam Afshar V.
J. Opt. Soc. Am. B 32(3) 379-387 (2015)