Analysis of one-third harmonic generation in waveguides
Perry, Shum Ping
Date of Issue2014
School of Electrical and Electronic Engineering
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 Γ that is determined by U0, θ0, and the overlap integrals, where U0 and θ0 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 Γ is larger than a specific value Γc, called a critical value. A Γc provides a relation between U0 and θ0. So a set of critical conditions of U0 and θ0 is obtained. A highly efficient conversion may be supported if U0 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.
DRNTU::Science::Physics::Optics and light
Journal of the optical society of America B
© 2014 Optical Society of America. This paper was published in Journal of the Optical Society of America B and is made available as an electronic reprint (preprint) with permission of Optical Society of America. The paper can be found at the following official DOI: [http://dx.doi.org/10.1364/JOSAB.31.002142]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.