## Fast and accurate modeling of waveguide grating couplers

JOSA A, Vol. 17, Issue 9, pp. 1565-1572 (2000)

http://dx.doi.org/10.1364/JOSAA.17.001565

Enhanced HTML Acrobat PDF (188 KB)

### Abstract

A boundary variation method for the analysis of both infinite periodic and finite aperiodic waveguide grating couplers in two dimensions is introduced. Based on a previously introduced boundary variation method for the analysis of metallic and transmission gratings [J. Opt. Soc. Am. A 10, 2307, 2551 (1993)], a numerical algorithm suitable for waveguide grating couplers is derived. Examples of the analysis of purely periodic grating couplers are given that illustrate the convergence of the scheme. An analysis of the use of the proposed method for focusing waveguide grating couplers is given, and a comparison with a highly accurate spectral collocation method yields excellent agreement and illustrates the attractiveness of the proposed boundary variation method in terms of speed and achievable accuracy.

© 2000 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(050.0050) Diffraction and gratings : Diffraction and gratings

(050.1960) Diffraction and gratings : Diffraction theory

**History**

Original Manuscript: March 16, 2000

Revised Manuscript: May 30, 2000

Manuscript Accepted: May 30, 2000

Published: September 1, 2000

**Citation**

P. G. Dinesen and J. S. Hesthaven, "Fast and accurate modeling of waveguide grating couplers," J. Opt. Soc. Am. A **17**, 1565-1572 (2000)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-9-1565

Sort: Year | Journal | Reset

### References

- T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985). [CrossRef]
- B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 1592–1598 (1994). [CrossRef]
- K. Hirayama, E. N. Glytsis, T. K. Gaylord, D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996). [CrossRef]
- D. W. Prather, S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A 16, 1131–1141 (1999). [CrossRef]
- K. H. Dridi, A. Bjarklev, “Optical electromagnetic vector-field modeling for the accurate analysis of finite diffractive structures of high complexity,” Appl. Opt. 38, 1668–1676 (1999). [CrossRef]
- J. S. Hesthaven, P. G. Dinesen, J.-P. Lynov, “Spectral collocation time-domain modeling of diffractive optical elements,” J. Comput. Phys. 155, 287–306 (1999). [CrossRef]
- O. P. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries,” J. Opt. Soc. Am. A 10, 1168–1175 (1993). [CrossRef]
- O. P. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. II. Finitely conducting gratings, Padé approximants, and singularities,” J. Opt. Soc. Am. A 10, 2307–2316 (1993). [CrossRef]
- O. P. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. III. Doubly periodic gratings,” J. Opt. Soc. Am. A 10, 2551–2562 (1993). [CrossRef]
- S. Ramo, J. R. Whinnery, T. van Duzer, Fields and Waves in Communications Electronics, 3rd ed. (Wiley, New York, 1993).
- O. Bruno, F. Reitich, “Solution of a boundary value problem for Helmholtz equation via variation of the boundary into the complex domain,” Proc. R. Soc. Edinburgh, Sect. A: Math. 122, 317–340 (1992). [CrossRef]
- S. A. Schelknuoff, “Some equivalence theorems of electromagnetics and their application to radiation problems,” Bell Syst. Tech. J. 15, 92–112 (1936). [CrossRef]
- P. G. Dinesen, J. S. Hesthaven, J. P. Lynov, L. Lading, “Pseudo-spectral method for the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 26, 1124–1130 (1999). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.