Analysis of one-third harmonic generation in waveguides

Sun, Yunxu, Shao, Xuguang, Huang, Tianye, Wu, Zhifang, Lee, Timothy, Perry, Shum Ping and Brambilla, Gilberto (2014) Analysis of one-third harmonic generation in waveguides. Journal of the Optical Society of America B, 31 (9), 2142-2149. (doi:10.1364/JOSAB.31.002142).

Abstract

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 Gamma that is determined by U[0], theta[0], and the overlap integrals, where U[0] and Gamma[0] 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 Gamma is larger than a specific value Gamma[c], called a critical value. A Gamma[c] provides a relation between U[0] and theta[0]. So a set of critical conditions of U[0] and theta[0] is obtained. A highly efficient conversion may be supported if U[0] 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.

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Contributors

Author: Timothy Lee

Author: Gilberto Brambilla

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