@Article{CiCP-10-57,
author = {Gang Bao, Zhengfu Xu and Jianhua Yuan},
title = {Continuation Finite Element Simulation of Second Harmonic Generation in Photonic Crystals},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {1},
pages = {57--69},
abstract = {<p style="text-align: justify;">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&#39;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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.150710.290910a},
url = {http://global-sci.org/intro/article_detail/cicp/7434.html}
}