Abstract
For any photonic device simulation, the accuracy of the numerical solution not only depends on the methods being used but also on the discretization parameters used in that numerical method. In this work, Finite Element Method and Finite Difference Time Domain Method based on Maxwell’s equations were used to simulate optical waveguides and directional couplers. As the solution accuracy may also depend on the index contrast used in such photonic devices, the characteristics of low-index contrast Germanium doped Silica and high-index contrast Silicon Nanowire Waveguides were analyzed, evaluated and benchmarked. Numerical results to benchmark Directional Couplers are also reported in this paper.
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References
Berenger, J.P.: A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114(2), 185–200 (1994)
Bierwirth, K., Schulz, N., Arndt, F.: Finite-difference analysis of rectangular dielectric waveguide structures. IEEE Trans. Microw. Theory Tech. 34(11), 1104–1114 (1986)
Chiang, K.S.: Analysis of optical fibers by the effective-index method. Appl. Opt. 25(3), 348–354 (1986)
Chiang, K.S.: Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides. Opt. Quantum Electron. 26(3), S113–S134 (1994)
Chiang, K.S., Lo, K.M., Kwok, K.S.: Effective-index method with built-in perturbation correction for integrated optical waveguides. J. Lightwave Technol. 14(2), 223–228 (1996)
Chung, Y., Dagli, N., Thylen, L.: Explicit finite difference vectorial beam propagation method. Electron. Lett. 27(23), 2119–2121 (1991)
Davies, J.B., Muilwyk, C.A.: Numerical solution of uniform hollow waveguides with boundaries of arbitrary shape. In: Proceedings of the Institution of Electrical Engineers, vol. 113, pp. 277–284. IET (1966)
de Electroniagnetisnio, G., de Cieiicias, F., de Granada, U.: Time-domain integral equation methods for transient analysis. IEEE Antennas Propag. Mag. 34(3), 15–23 (1992)
Feit, M., Fleck, J.: Computation of mode properties in optical fiber waveguides by a propagating beam method. Appl. Opt. 19(7), 1154–1164 (1980)
Garcia, S.G., Lee, T.W., Hagness, S.C.: On the accuracy of the ADI-FDTD method. IEEE Antennas Wirel. Propag. Lett. 1(1), 31–34 (2002)
Hagness, S., Taflove, A., Bridges, J.: Wideband ultralow reverberation antenna for biological sensing. Electron. Lett. 33(19), 1594–1595 (1997)
Huang, W.P., Xu, C., Chaudhuri, S.K.: A finite-difference vector beam propagation method for three-dimensional waveguide structures. IEEE Photonics Technol. Lett. 4(2), 148–151 (1992a)
Huang, W.P., Xu, C.: A wide-angle vector beam propagation method. IEEE Photonics Technol. Lett. 4(10), 1118–1120 (1992b)
Itoh, T.: Numerical Techniques for Microwave and Millimeter-Wave Passive Structures. Wiley, New York (1989)
Knox, R., Toulios, P.: Integrated circuits for the millimeter through optical frequency range. In: Proceedings of Symposium Submillimeter Waves, vol. 20, pp. 497–515. Polytechnic Press of Polytechnic Institute of Brooklyn (1970)
Luebbers, R.: Three-dimensional cartesian-mesh finite-difference time-domain codes. IEEE Antennas Propag. Mag. 36(6), 66–71 (1994)
Marcatili, E.A.: Dielectric rectangular waveguide and directional coupler for integrated optics. Bell Syst. Tech. J. 48(7), 2071–2102 (1969)
März, R.: Integrated Optics: Design and Modeling. Artech House on Demand, Boston (1995)
Obayya, S.A., Rahman, B.M.A., El-Mikati, H.: New full-vectorial numerically efficient propagation algorithm based on the finite element method. J. Lightwave Technol. 18(3), 409–415 (2000)
Rahman, B.M.A., Agrawal, A.: Finite Element Modeling Methods for Photonics. Artech House, Boston (2013)
Rahman, B.M.A., Davies, J.B.: Finite-element solution of integrated optical waveguides. J. Lightwave Technol. 2(5), 682–688 (1984)
Rahman, B.M.A., Davies, J.B.: Vector-H finite element solution of GaAs/GaAlAs rib waveguides. IEE Proc. J. Optoelectron. 132(6), 349–353 (1985)
Taflove, A., Hagness, S.C.: Computational Electrodynamics. Artech House, Boston (2005)
Tsuji, Y., Koshiba, M.: A finite element beam propagation method for strongly guiding and longitudinally varying optical waveguides. J. Lightwave Technol. 14(2), 217–222 (1996)
Yee, K.S.: Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14(3), 302–307 (1966)
Acknowledgments
Authors acknowledge, numerical simulations by Dr. Ajanta Bahr, IIT Delhi, India, Mr. Jitendra K. Mishra, ISM, Dhanbad, India, Mr. Yousaf Omar Azabi, City University London, UK, Md. Enayetur Rahman, City University London, UK, and Mr. James Pond, Ph.D., Lumerical Solutions, Inc., Canada.
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This article is part of the Topical Collection on Optical Wave & Waveguide Theory and Numerical Modelling, OWTNM’ 15.
Guest edited by Arti Agrawal, B. M. A. Rahman, Tong Sun, Gregory Wurtz, Anibal Fernandez and James R. Taylor.
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Hada, S.L., Rahman, B.M.A. Rigorous analysis of numerical methods: a comparative study. Opt Quant Electron 48, 309 (2016). https://doi.org/10.1007/s11082-016-0579-x
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DOI: https://doi.org/10.1007/s11082-016-0579-x