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Continuation Finite Element Simulation of Second Harmonic Generation in Photonic Crystals

Published online by Cambridge University Press:  20 August 2015

Gang Bao*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, China Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Zhengfu Xu*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Jianhua Yuan*
Affiliation:
Department of Mathematics, Beijing University of Posts and Telecommunications, Beijing 100876, China
*
Corresponding author.Email:yuan_bupt@yahoo.com.cn
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Abstract

A computational study on the enhancement of the second harmonic generation (SHG) in one-dimensional (1D) photonic crystals is presented. The mathematical model is derived from a nonlinear system of Maxwell’s equations, which partly overcomes the shortcoming of some existing models based on the undepleted pump approximation. We designed an iterative scheme coupled with the finite element method which can be applied to simulate the SHG in one dimensional nonlinear photonic band gap structures in our previous work. For the case that the nonlinearity is strong which is desirable to enhance the conversion efficiency, a continuation method is introduced to ensure the convergence of the iterative procedure. The convergence of our method is fast. Numerical experiments also indicate the conversion efficiency of SHG can be significantly enhanced when the frequencies of the fundamental and the second harmonic wave are tuned at the photonic band edges. The maximum total conversion efficiency available reaches more than 50% in all the cases studied.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2011

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