Abstract
We present an improved variational effective index method for reduction of 2-D Bragg grating problems to 1-D and show significant improvements particularly at smaller wavelengths. The method is based on the optimal variational (Vopt) method, which we have earlier used successfully for conventional waveguides. A 1-D transverse profile along with a longitudinal index variation are reduced to a 1-D longitudinal distribution, reflection and transmission spectra of which have been studied for both the TE and TM modes by transfer matrix methods. An accurate modeling for the out of plane scattering losses has been presented which occur when a guided wave propagating in a conventional waveguide impinges on a photonic crystal waveguide. Taking these losses into account brings the results pretty close to those of a rigorous 2-D Helmholtz solver QUEP, improving them remarkably over the variational EIM (vEIM) results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Benson T.M., Bozeat R.J., Kendall P.C.: Rigorous effective index method for semiconductor rib waveguides. IEE Proc. J. 139(1), 67–70 (1992)
Bindal P., Sharma A.: Modelling of Ti:LiNbO3 waveguide directional couplers. IEEE Photon. Technol. Lett. 4(7), 728–731 (1992)
Bindal, P., Sharma, A.: Improved variational effective index approximation for photonic crystal slabs. In: 18th International Workshop on Optical Waveguide Theory and Numerical Modeling 9th–10th. April 2010, Cambridge, UK (2010)
Cryan M.J. et al.: Calculation of losses in 2D photonic crystal membrane waveguides using the 3D FDTD method. IEEE Photon. Technol. Lett. 17(1), 58–60 (2005)
Foresi J.S., Villeneuve P.R., Ferrera J., Thoen E.R., Steinmeyer G., Fan S., Joannopoulos J.D., Kimerling L.C., Smith H.I, Ippen E.P.: Microcavities in optical waveguides. Nature 390, 143–145 (1997)
Ghatak A., Thyagarajan K.: Introduction to Fiber Optics. Cambridge university press, Cambridge, UK (1998)
Hammer M.: Quadridirectional eigenmode expansion scheme for 2-D modeling of wave propagation in integrated optics. Opt. Commun. 235, 285–303 (2004)
Hammer M., Ivanova O.V.: Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment. Opt. Quantum Electron 41, 267–283 (2009)
Kok, A., Geluk, E.J., Docter, B., Van der Tol, J., Notzel, R., Smit, M.: Transmission of pillarbased photonic crystal waveguides in InP technology. Appl. Phys. Lett. 91:201109 (1-3)(2007)
Krauss T.F., Rue R.M.D.L., Brand S.: Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths. Nature 383, 699–702 (1996)
Lalanne P., Benisty H.: Out-of-plane losses of two-dimensional photonic crystals waveguides: electromagnetic analysis. J. Appl. Phys. 89(2), 1512–1514 (2001)
Prather D.W., Shi S., Murakowski J., Schneider G.J., Sharkawy A., Chen C., Miao B.: Photonic crystal structures and applications: perspective, overview, and development. IEEE J. Sel. Top. Quantum Electron 12(6), 1416–1437 (2006)
Sharma A.: On approximate theories of single-mode rectangular waveguides. Opt. Quantum Electron 21, 517–520 (1989)
Sharma A., Bindal P.: An accurate variational analysis of single-mode diffused channel waveguides. Opt. Quantum Electron 24, 1359–1371 (1992)
Thyagarajan K., Diggavi S., Ghatak A.K.: Analytical investigations of leaky and absorbing structures. Opt. Quantum Electron 19, 131–137 (1987)
Yeh C.: Optical waves in layered media. Wiley, New York (1988)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bindal, P., Sharma, A. Modelling of photonic crystal waveguides: a simple and accurate approach. Opt Quant Electron 42, 435–446 (2011). https://doi.org/10.1007/s11082-010-9431-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11082-010-9431-x