Abstract
An extension of the effective index method is proposed as a tool to investigate leakage losses in two-dimensional waveguides. The above method, referred to as the Extended Effective Index Method (EEIM), utilizes the Transfer Matrix Technique (TMT) for the calculation of the complex propagation constants. The results show that the EEIM can be applied to conventional rib leaky waveguides as well as to rib ARROW leaky waveguides. The results for rib ARROW waveguides show excellent agreement when compared to those obtained with Finite Element Method.
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M. Ohkawa, M. Izutsu and T. Sueta, “Integrated Optic Pressure Sensor on Silicon Substrate”, Appl. Opt., vol. 28,no. 23, pp. 5153–5157, December 1989.
K. Fischer, J. Muller, R. Hoffmann, F. Wasse and D. Salle, “Elastooptical Properties of SiON Layers in an Integrated Optical Inteferometer Used as a Pressure Sensor”, J. Lightwave Technol., vol. 12,no. 1, pp. 163–169, January 1994.
C. Wagner, J. Frankenberger, and P.P. Deimel, “Optical Pressure Sensor Based on a Mach-Zehnder Interferometer Integrated with a Lateral a-Si:H p-i-n Photodiode”, IEEE Photon. Technol. Lett., vol. 5,no. 10, pp. 1257–1259, October 1993.
P.K. Tien, “Integrated Optics and New Wave Phenomena in Optical Waveguides”, Rev. of Modern Phys., vol. 49,no. 2, pp. 361–420, April 1977.
T.L. Koch, E.G. Burkhardt, F.G. Storz, T.J. Bridges, and T. Sizer, “Vertically Grating-Coupled ARROW Structures for III–V Integrated Optics”, IEEE J.Quantum Electron., vol. QE-23,no. 6, pp. 889–896, June 1987.
T.L. Kock, P.J. Corvini, W.T. Tsang, U. Koren, and B.I. Miller, “Wavelength Selective Interlayer Directionally Grating-Coupled InP/InGaAsP Waveguide Photodetection”, Appl. Phys. Lett., vol. 51,no. 14, pp. 1060–1062, 5 October 1987.
W. Jiang, J. Chrostowski, and M. Fontane, “Analysis of Arrow Waveguides”, Optics Comm., vol. 72,no. 3–4, pp. 180–187, 15 July 1989.
R.A. Soref and K.J. Ritter, “Silicon Antiresonant Reflecting Optical Waveguides”, Opt. Lett., vol. 15,no. 14, pp. 792–794, 15 July 1990.
L.J. Mawst, D. Botez, C. Zmudzinski, C. Tu, “Antiresonant Reflecting Optical Waveguide-Type, Single-Mode Diode Lasers”, Appl. Phys. Lett., vol. 61,no. 5, pp. 503–505, 3 August 1992.
J.C. Grant, J.C. Beal, and N.J.P. Frenette, “Finite Element Analysis of the ARROW Leaky Optical Waveguide”, IEEE J. Quantum Electron., vol. 30,no. 5, pp. 1250–1253, May 1994.
I. Garcés, F. Villuendas, J.A. Vallés, C. Domíngues, and M. Moreno, “Analysis of Leakage Properties and Guiding Conditions of Rib Antiresonant Reflecting Optical Waveguides”, J. Lightwave Technol., vol. 14,no. 5, pp. 798–805, May 1996.
M. Moreno, C. Domínguez, J. Muñoz, J. Calderer, J.R. Morante, “Photosensor and Optical Waveguide Coupling in Silicon Technology”, Sensors and Actuators A, vol. 62, pp. 524–528, 1997.
M. Tabib-Azar, G. Beheim, “Modern Trends in Microstructures and Integrated Optics for Communication, Sensing, and Actuation”, Opt. Eng., vol 36,no. 5, pp. 1307–1318, May 1997.
K.-H. Schlereth, and M. Tacke, “The complex Propagation Constant of Multilayer Waveguides: An Algorithm for a Personal Computer”, IEEE J. Quantum Electron., vol. 26,no. 4, pp. 627–630, April 1990.
M.R. Ramadas, E. Garmire, A.K. Ghatak, K. Thyagarajan, and M.R. Shenoy, “Analysis of Absorbing and Leaky Planar Waveguides: a Novel Method”, Opt. Lett., vol. 14,no. 7, pp. 376–378, 1 April 1989.
S.-L. Lee, Y. Chung, L.A. Coldren, and N. Dagli, “On Leaky Mode Approximations for Modal Expansion in Multilayer Open Waveguides”, IEEE J. Quantum Electron., vol. 31,no. 10, pp. 1790–1802, October 1995.
G.M. Barry, S.V. Burky, J.M. Heaton, and D.R. Wight, “Analysis of Multilayer Semiconductor Rib Waveguides with High Refractive Index Substrates”, Electron. Lett., vol. 29,no. 22, pp. 1941–1942, 28 October 1993.
E.C.M. Pennings, R.J. Deri, and R.J. Hawkins, “Simple Method for Estimating Usable Bend Radii of Deeply Etched Optical Rib Waveguides”, Electron. Lett., vol. 27,no. 17, pp. 1532–1534, 15 August 1991.
W. h. Press, B. P. Flannery, S. A. Teukolsky e W. T. Vetterling, Numerical Recipes, London: Cambridge University Press, 1986.
R.J. Deri, E. Kapon, and L. M. Schiavone, “Scattering in Low-Loss GaAs / GaAlAs rib Waveguides”, Appl. Phys. Lett., 51(11), pp. 789–791, 14 September 1987.
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Borges, BH.V., Romero, M.A. & Cesar, A.C. An Extension of the Effective Index Method to Analyze Leakage Losses in Rib Type Waveguides. International Journal of Infrared and Millimeter Waves 20, 1783–1793 (1999). https://doi.org/10.1023/A:1021757530291
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DOI: https://doi.org/10.1023/A:1021757530291