Perfectly matched absorbing layers for the paraxial equations
A new absorbing boundary technique for the paraxial wave equations is proposed and analyzed. Numerical results show the efficiency of the method. 15 refs., 8 figs., 4 tabs.
Extending the general approach for first-order hyperbolic systems developed in [D. Appeloe, T. Hagstrom, G. Kreiss, Perfectly matched layers for hyperbolic systems: general formulation, well-posedness and stability, SIAM J. Appl. Math., 2006, to appear], we construct PML equations for the mixed-type system governing propagation of optical wave packets in both 1D and 2D Bragg resonant photonic waveguides with a cubic nonlinearity, i.e. the coupled mode equations. We prove that in the linear case the layer equations are absorbing and perfectly matched. We also prove they are stable for constant parameters. A number of numerical experiments are performed to assess the layer's performance in both the linear and nonlinear regimes.
Dohnal, Tomas, and Hagstrom, Thomas. Perfectly matched layers in photonics computations: 1D and 2D nonlinear coupled mode equations. United States: N. p., 2007.
Web. doi:10.1016/j.jcp.2006.10.002.
Dohnal, Tomas, & Hagstrom, Thomas. Perfectly matched layers in photonics computations: 1D and 2D nonlinear coupled mode equations. United States. doi:10.1016/j.jcp.2006.10.002.
Dohnal, Tomas, and Hagstrom, Thomas. Tue .
"Perfectly matched layers in photonics computations: 1D and 2D nonlinear coupled mode equations". United States.
doi:10.1016/j.jcp.2006.10.002.
@article{osti_20991576,
title = {Perfectly matched layers in photonics computations: 1D and 2D nonlinear coupled mode equations},
author = {Dohnal, Tomas and Hagstrom, Thomas},
abstractNote = {Extending the general approach for first-order hyperbolic systems developed in [D. Appeloe, T. Hagstrom, G. Kreiss, Perfectly matched layers for hyperbolic systems: general formulation, well-posedness and stability, SIAM J. Appl. Math., 2006, to appear], we construct PML equations for the mixed-type system governing propagation of optical wave packets in both 1D and 2D Bragg resonant photonic waveguides with a cubic nonlinearity, i.e. the coupled mode equations. We prove that in the linear case the layer equations are absorbing and perfectly matched. We also prove they are stable for constant parameters. A number of numerical experiments are performed to assess the layer's performance in both the linear and nonlinear regimes.},
doi = {10.1016/j.jcp.2006.10.002},
journal = {Journal of Computational Physics},
number = 2,
volume = 223,
place = {United States},
year = {Tue May 01 00:00:00 EDT 2007},
month = {Tue May 01 00:00:00 EDT 2007}
}