## Analysis of diffraction gratings by using an edge element method

JOSA A, Vol. 22, Issue 2, pp. 278-288 (2005)

http://dx.doi.org/10.1364/JOSAA.22.000278

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### Abstract

Typically the grating problem is formulated for TE and TM polarizations by using, respectively, the electric and magnetic fields aligned with the grating wall and perpendicular to the plane of incidence, and this leads to a one-field-component problem. For some grating profiles such as metallic gratings with a triangular profile, the prediction of TM polarization by using a standard finite-element method experiences a slower convergence rate, and this reduces the accuracy of the computed results and also introduces a numerical polarization effect. This discrepancy cannot be seen as a simple numerical issue, since it has been observed for different types of numerical methods based on the classical formulation. Hence an alternative formulation is proposed, where the grating problem is modeled by taking the electric field as unknown for TM polarization. The application of this idea to both TE and TM polarizations leads to a two-field-component problem. The purpose of the paper is to propose an edge finite-element method to solve this wave problem. A comparison of the results of the proposed formulation and the classical formulation shows improvement and robustness in the new approach.

© 2005 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(050.1960) Diffraction and gratings : Diffraction theory

**Citation**

Kokou Dossou, Muthukumaran Packirisamy, and Marie Fontaine, "Analysis of diffraction gratings by using an edge element method," J. Opt. Soc. Am. A **22**, 278-288 (2005)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-2-278

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### References

- E. Popov and M. Nevière, "Grating theory: new equations in Fourier space leading to fast converging results for TM polarization," J. Opt. Soc. Am. A 17, 1773-1784 (2000).
- G. Bao, D. C. Dobson, and J. A. Cox, "Mathematical studies in rigorous grating theory," J. Opt. Soc. Am. A 12, 1029-1042 (1995).
- T. Delort and D. Maystre, "Finite-element method for gratings," J. Opt. Soc. Am. A 10, 2592-2601 (1993).
- A. Delage and K. Dossou, "Polarisation dependent loss calculation in echelle gratings using finite element method and Rayleigh expansion," Opt. Quantum Electron. 36, 223-238 (2004).
- R. Petit, ed., Electromagnetic Theory of Gratings , Vol. 22 of Topics in Current Physics (Springer-Verlag, New York, 1980).
- J.-C. Nédélec, "Mixed finite elements in R3," Numer. Math. 35, 315-341 (1980).
- J.-C. Nédélec, "A new family of mixed finite elements in R3," Numer. Math. 50, 57-81 (1986).
- M. Koshiba, S. Maruyama, and K. Hirayama, "A vector finite element method with the high-order mixed-interpolation-type triangular elements for optical waveguiding problems," J. Lightwave Technol. 12, 495-502 (1994).
- L. Demkowicz and L. Vardapetyan, "Modeling of electromagnetic absorption/scattering problems using hp-adaptive finite elements," Comput. Methods Appl. Mech. Eng. 152, 103-124 (1998).
- K. Dossou and M. Fontaine, "A high order isoparametric finite element method for the computation of waveguide modes," Comput. Methods Appl. Mech. Eng. 194 , 837-858 (2005).
- L. Li, J. Chandezon, G. Granet, and J.-P. Plumey, "Rigorous and efficient grating-analysis method made easy for optical engineers," Appl. Opt. 38, 304-313 (1999).
- S. Janz, A. Balakrishnan, S. Charbonneau, P. Cheben, M. Cloutier, A. Delage, K. Dossou, L. Erickson, M. Gao, P. Krug, B. Lamontagne, M. Packirisamy, M. Pearson, and D.-X. Xu, "Planar waveguide echelle gratings in silica-on-silicon," IEEE Photonics Technol. Lett. 16, 503-505 (2004).
- D. Chowdhuri, "Design of low-loss and polarization-insensitive reflection grating-based planar demultiplexers," IEEE J. Sel. Top. Quantum Electron. 6, 233-239 (2000).
- P. Clemens, G. Heise, R. Marz, H. Michel, A. Reichelt, and H. Schneider, "8-channel optical demultiplexer realized as SiO2/Si flat-field spectrograph," IEEE Photonics Technol. Lett. 6, 1109-1111 (1994).
- J.-J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, and E. Koteles, "Monolithic integrated wavelength demultiplexer based on a waveguide Rowland circle grating in InGaAsP/lnP," J. Lightwave Technol. 16, 631-638 (1998).
- E. Loewen, D. Maystre, E. Popov, and L. Tsonev, "Echelles: scalar, electromagnetic, and real-groove properties," Appl. Opt. 34, 1707-1727 (1995).

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