A Simple Analytical Method to Calculate Bending Loss in Dielectric Rectangular Waveguides
Keywords:Analytical method, attenuation constant, bending loss, perturbation theory, propagation constant, rectangular waveguides
We present a simple analytical method to compute attenuation in bent dielectric rectangular waveguides. An approximate formulation for the attenuation constant is first derived by determining the ratio of average power loss per unit length to the average power propagating along the waveguide. Since the waveguide has been simplified into a slab in the process of derivation, losses at the four edges of the structure have been neglected. To account for these losses, the perturbation theory has been employed. The total loss is found to agree closely with that obtained via the Finite Element Method (FEM). Unlike the FEM which requires considerable computational time and power to solve, we demonstrate that the analytical method proposed here can easily be applied and it gives sufficiently accurate result.
D. K. Cheng, Field and Wave Electromagnetics. 2nd ed., Addison Wesley Inc., 1989.
R. E. Collin, Field Theory of Guided Waves. 2nd ed., IEEE Press, New York, 1991.
E. A. J. Marcatili, “Bends in optical dielectric guides,” The Bell System Technical Journal, vol. 48, no. 9, pp. 2103-2132, 1969.
Y. Cai, T. Mizumoto, and Y. Naito, “Improved perturbation feedback method for the analysis of rectangular dielectric waveguides,” Journal of Lightwave Technology, vol. 9, no. 10, pp. 1231- 1237, 1991.
P. R. Young and R. J. Collier, “Solution of lossy dielectric waveguides using dual effective-index method,” Electronics Letters, vol. 33, no. 21, pp. 1788-1789, 1997.
E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” The Bell System Technical Journal, vol. 48, no. 9, pp. 2071-2102, 1969.
K. H. Yeap, K. H. Teh, K. C. Yeong, K. C. Lai, and M. C. Loh, “Propagation in dielectric rectangular waveguides,” Optica Applicata, vol. 46, no. 2, pp. 317-330, 2016.
D.-P. Cai, S.-C. Nien, H.-K. Chiu, C.-C. Chen, and C.-C. Lee, “Electrically tuneable liquid crystal waveguide attenuators,” Optics Express, vol. 19, no. 12, pp. 11890-11896, 2011.
H.-K. Chiu, F.-L. Hsiao, C.-H. Chan, and C.-C. Chen, “Compact and low-loss bent hollow waveguides with distributed Bragg reflector,” Optics Express, vol. 16, no. 19, pp. 15069-15073, 2008.
S.-S. Lo, C.-C. Chen, S.-C. Hsu, and C.-Y. Liu, “Fabricating a hollow optical waveguide for optical communication applications,” Journal of Microelectromechanical Systems, vol. 15, no. 3, pp. 584-587, 2006.
S.-S. Lo, M.-S. Wang, and C.-C. Chen, “Semiconductor hollow optical waveguides formed by omni-directional reflectors,” Optics Express, vol. 22, no. 26, pp. 6589-6593, 2004.
D. Marcuse, “Bending losses of the asymmetric slab waveguide,” The Bell System Technical Journal, vol. 50, no. 8, pp. 2551-2563, 1971.
R. T. Deck, M. Mirkov, and B. G. Bagley, “Determination of bending losses in rectangular waveguides,” Journal of Lightwave Technology, vol. 16, no. 9, pp. 1703-1714, 1998.
P. I. Somlo and J. D. Hunter, “On the TE10 mode cutoff frequency in lossy-walled rectangular waveguides,” IEEE Transactions on Instrumentation and Measurement, vol. 45, pp. 301-304, 1996.
T. K. Hong, “Analysis of Loss in Dielectric Waveguides,” Universiti Tunku Abdul Rahman, Malaysia, B.Eng., 2014.
B. M. Kolundžija and A. R. Djordjević, Field Integral Equations. In: Electromagnetic Modeling of Composite Metallic and Dielectric Structure, Artech House, Massachusetts, pp. 181-182, 2002.