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Journal of Applied Mathematics
Volume 2014, Article ID 621751, 6 pages
Research Article

The Coupled Nonlinear Schrödinger Equations Describing Power and Phase for Modeling Phase-Sensitive Parametric Amplification in Silicon Waveguides

1School of Science, Xi’an University of Post & Telecommunications, Xi’an 710121, China
2Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China

Received 16 June 2014; Revised 13 August 2014; Accepted 14 August 2014; Published 24 August 2014

Academic Editor: Ray K.L. Su

Copyright © 2014 Xuefeng Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The coupled nonlinear Schrödinger (NLS) equations describing power and phase of the optical waves are used to model phase-sensitive (PS) parametric amplification in a width-modulated silicon-on-insulator (SOI) channel waveguide. Through solving the coupled NLS equations by the split-step Fourier and Runge-Kutta integration methods, the numerical results show that the coupled NLS equations can perfectly describe and character the PS amplification process in silicon waveguides.