# Photonic band gap structure simulator

## Abstract

A system and method for designing photonic band gap structures. The system and method provide a user with the capability to produce a model of a two-dimensional array of conductors corresponding to a unit cell. The model involves a linear equation. Boundary conditions representative of conditions at the boundary of the unit cell are applied to a solution of the Helmholtz equation defined for the unit cell. The linear equation can be approximated by a Hermitian matrix. An eigenvalue of the Helmholtz equation is calculated. One computation approach involves calculating finite differences. The model can include a symmetry element, such as a center of inversion, a rotation axis, and a mirror plane. A graphical user interface is provided for the user's convenience. A display is provided to display to a user the calculated eigenvalue, corresponding to a photonic energy level in the Brilloin zone of the unit cell.

- Inventors:

- Publication Date:

- Research Org.:
- Massachusetts Institute of Technology, Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1175926

- Patent Number(s):
- 7,117,133

- Application Number:
- 10/171,725

- Assignee:
- Massachusetts Institute of Technology (Cambridge, MA) OSTI

- DOE Contract Number:
- FG02-95ER40919

- Resource Type:
- Patent

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Chen, Chiping, Shapiro, Michael A., Smirnova, Evgenya I., Temkin, Richard J., and Sirigiri, Jagadishwar R.
```*Photonic band gap structure simulator*. United States: N. p., 2006.
Web.

```
Chen, Chiping, Shapiro, Michael A., Smirnova, Evgenya I., Temkin, Richard J., & Sirigiri, Jagadishwar R.
```*Photonic band gap structure simulator*. United States.

```
Chen, Chiping, Shapiro, Michael A., Smirnova, Evgenya I., Temkin, Richard J., and Sirigiri, Jagadishwar R. Tue .
"Photonic band gap structure simulator". United States. https://www.osti.gov/servlets/purl/1175926.
```

```
@article{osti_1175926,
```

title = {Photonic band gap structure simulator},

author = {Chen, Chiping and Shapiro, Michael A. and Smirnova, Evgenya I. and Temkin, Richard J. and Sirigiri, Jagadishwar R.},

abstractNote = {A system and method for designing photonic band gap structures. The system and method provide a user with the capability to produce a model of a two-dimensional array of conductors corresponding to a unit cell. The model involves a linear equation. Boundary conditions representative of conditions at the boundary of the unit cell are applied to a solution of the Helmholtz equation defined for the unit cell. The linear equation can be approximated by a Hermitian matrix. An eigenvalue of the Helmholtz equation is calculated. One computation approach involves calculating finite differences. The model can include a symmetry element, such as a center of inversion, a rotation axis, and a mirror plane. A graphical user interface is provided for the user's convenience. A display is provided to display to a user the calculated eigenvalue, corresponding to a photonic energy level in the Brilloin zone of the unit cell.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Oct 03 00:00:00 EDT 2006},

month = {Tue Oct 03 00:00:00 EDT 2006}

}