# Perfectly matched layers in photonics computations: 1D and 2D nonlinear coupled mode equations

## Abstract

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.

- Authors:

- Seminar for Applied Mathematics, ETH-Zentrum, CH-8092, Zuerich (Switzerland). E-mail: dohnal@math.ethz.ch
- Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131 (United States). E-mail: hagstrom@math.unm.edu

- Publication Date:

- OSTI Identifier:
- 20991576

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 223; Journal Issue: 2; Other Information: DOI: 10.1016/j.jcp.2006.10.002; PII: S0021-9991(06)00469-4; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCULATION METHODS; EQUATIONS; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PERFORMANCE; STABILITY; TWO-DIMENSIONAL CALCULATIONS; WAVE PACKETS; WAVEGUIDES

### Citation Formats

```
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}

}

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