# Accurate solution of the paraxial wave equation using Richardson extrapolation

## Abstract

Accurate analysis of guided wave devices such as waveguides and couplers is important for the development of optical integrated circuits. Richardson extrapolation is used along with the mid-step Euler finite difference method to solve the paraxial wave equation. Highly accurate solutions can be efficiently obtained using this combined approach. Numerical results are presented for wave propagation in a straight integrated optical waveguide and a Y-junction waveguide. Discretization errors in both the propagation and the transverse dimension can be systematically eliminated by using Richardson extrapolation. Accuracies on the order of 10[sup [minus]11] or better are obtained.

- Authors:

- (Univ. of Maryland, Baltimore, MD (United States). Dept. of Electrical Engineering)
- (Univ. of Maryland, Baltimore, MD (United States). Dept. of Electrical Engineering Univ. of Maryland, College Park, MD (United States). Lab. of Plasma Research)

- Publication Date:

- OSTI Identifier:
- 7228667

- Resource Type:
- Journal Article

- Journal Name:
- IEEE Photonics Technology Letters (Institute of Electrical and Electronics Engineers); (United States)

- Additional Journal Information:
- Journal Volume: 6:3; Journal ID: ISSN 1041-1135

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; WAVE EQUATIONS; NUMERICAL SOLUTION; WAVEGUIDES; WAVE PROPAGATION; INTEGRATED CIRCUITS; THEORETICAL DATA; DATA; DIFFERENTIAL EQUATIONS; ELECTRONIC CIRCUITS; EQUATIONS; INFORMATION; MICROELECTRONIC CIRCUITS; NUMERICAL DATA; PARTIAL DIFFERENTIAL EQUATIONS; 426000* - Engineering- Components, Electron Devices & Circuits- (1990-)

### Citation Formats

```
Chinni, V.R., Menyuk, C.R., and Wai, P.K.A.
```*Accurate solution of the paraxial wave equation using Richardson extrapolation*. United States: N. p., 1994.
Web. doi:10.1109/68.275502.

```
Chinni, V.R., Menyuk, C.R., & Wai, P.K.A.
```*Accurate solution of the paraxial wave equation using Richardson extrapolation*. United States. doi:10.1109/68.275502.

```
Chinni, V.R., Menyuk, C.R., and Wai, P.K.A. Tue .
"Accurate solution of the paraxial wave equation using Richardson extrapolation". United States. doi:10.1109/68.275502.
```

```
@article{osti_7228667,
```

title = {Accurate solution of the paraxial wave equation using Richardson extrapolation},

author = {Chinni, V.R. and Menyuk, C.R. and Wai, P.K.A.},

abstractNote = {Accurate analysis of guided wave devices such as waveguides and couplers is important for the development of optical integrated circuits. Richardson extrapolation is used along with the mid-step Euler finite difference method to solve the paraxial wave equation. Highly accurate solutions can be efficiently obtained using this combined approach. Numerical results are presented for wave propagation in a straight integrated optical waveguide and a Y-junction waveguide. Discretization errors in both the propagation and the transverse dimension can be systematically eliminated by using Richardson extrapolation. Accuracies on the order of 10[sup [minus]11] or better are obtained.},

doi = {10.1109/68.275502},

journal = {IEEE Photonics Technology Letters (Institute of Electrical and Electronics Engineers); (United States)},

issn = {1041-1135},

number = ,

volume = 6:3,

place = {United States},

year = {1994},

month = {3}

}

DOI: 10.1109/68.275502

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