Analysis the Path of the Light in the Optical Waveguide with Quadratic Graded Index by Using Simple Approximation Method

Ali Çetin, Serel Ozmen Akyol, Eyyup Gulbandilar


Optical waveguides are photonic circuit elements where the light is guided inside. These photonic elements require a transparent medium that the refractive index of the layer is higher than that of the surrounding material. Optical waveguides usually consist of two parts. The inside part is called as core has high refractive index The second part is called as cladding with lower refractive index surrounded the core. Guiding property of optical waveguides are based on the principle of total reflection of light from planar dielectric interfaces. This property of optical waveguides is defined by some structure parameters. Since the refractive index of optical waveguides decreases from the core center to cladding gradually, the refractive index changing of optical waveguides with graded index should be taken into consideration. In this study, behavior of light is analyzed by the parameter changing of optical waveguides. Eikonal equation is used to determine the trajectory of the light. Determination of the trajectory of the light is useful for the explanation of guiding in these waveguides. 


Optical waveguides, refractive index, light trajectory, approximation technique, Eikonal equation

Full Text:



Lifante, Integrated Photonics: Fundamentals, John Wiley & Sons, West Sussex, 2003.

Peter W. Milonni, Joseph H. Eberly, Laser Physics, John Wiley & Sons, 2010.

A. Çetin and Kiliçkaya M. S. "Investigation of the Transverse Electromagnetic Modes in an Embedded Optical Waveguide," Advanced Studies in Theoretical Physics, vol. 9, no.15, pp. 723-735, 2015.

A. K. Thander and B. Sucharita, "Study of Optical Waveguide Using HOC Scheme," Applied Mathematical Sciences, vol. 8, no. 79, pp. 3931-3938, 2014.

A. K. Thander and B. Sucharita, "Optical Confinement Study of Different Semiconductor Rib Waveguides Using Higher Order Compact Finite Difference Method," Optik, vol. 127, no. 4, pp. 2116-2120, 2016.

A. Nerukh, H. Semenova, and N. Sakhnenko. "Alternative Calculations of Initial Value Problem for Electromagnetic Field in Dielectric Waveguide," Optical and Quantum Electronics, vol. 40, no. 11-12, pp. 943-956, 2008.

P. Roy Chaudhuri and S. Roy, "Analysis of Arbitrary Index Profile Planar Optical Waveguides and Multilayer Nonlinear Structures: A Simple Finite Difference Algorithm," Optical and Quantum Electronics, vol. 39, no. 3, pp. 221-237, 2007.

Y. Ding, Z. Q. Cao and Q. S. Shen. "Determination of Optical Waveguide Refractive-Index Profiles With the Inverse Analytic Transfer Matrix Method," Optical and Quantum Electronics, vol. 36, no. 6, pp. 489-497, 2004.

W. Yan, Y. Tang, Q. Ji, X. Yan and H. Zhanget, "The Transmission Characteristics of a Subwavelength Metal Slab Waveguide," Optik, vol. 185, pp. 151-155, 2019.

M. Jelínek, "Progress in Optical Waveguiding Thin Films," Czechoslovak Journal of Physics, vol. 53, no. 5, pp. 365-377, 2003.

M, Najafi-Hajivar and M. Hosseini-Farzad, "Broadband Polarization-Insensitive Amplitude and Phase Modulators Based on Graphene-Covered Buried and Ridge Silicon Waveguides," Optics Communications, vol. 125860, 2020.

C. S. Hsiao, Y. J. Chiang, Likarn Wang and L. Wen-Wei, "A Semi-Analytic Method for Solving Rib-Type Waveguide Problems," Journal of Modern Optics, vol. 55, no. 8, pp. 1315-1329, 2008.

D. W. Nkemzi and N. D. Nguti, "A Uniform Approximation for the Eigenmodes of a Planar Dielectric Waveguide," Optics communications, vol. 281, no. 9, pp. 2485-2490, 2008.

A. Çetin Ali, E. Uçgun and M. S. Kilickaya, "Determining the Effective Refractive Index of Algaas-GaAs Slab Waveguide Based on Analytical and Finite Difference Method, " Journal of Physical Science and Application, vol. 2, no. 9, pp. 381, 2012.

S. P. Mohanty, S. K. Sahoo, A. Panda and G. Palai, "FDTD Method to Photonic Waveguides for Application of Optical Demultiplexer at 3-Communication Windows, " Optik, vol. 185, pp. 146-150, 2019.

L. Vázquez, S, Jiménez and A. B. Shvartsburg, "The Wave Equation: From Eikonal to Anti-Eikonal Approximation," Modern Electronic Materials, vol. 2, no. 2, pp. 51-53, 2016.

M. D. Malykh, N. E. Nikolaev and L. A. Sevastianov, "The Geometrical Description of Electromagnetic Radiation," Journal of Electromagnetic Waves and Applications, vol. 30, no.15, pp. 2055-2066, 2016.

J. H. Stosch, T. Kühler and E. Griese, "Analysis and Optimisation of Bidirectional Optical Couplers in PCBs," Optical and Quantum Electronics, vol. 50, no. 2, p. 109, 2018.

] Z. Cao, J. Jiang, Q. Shen, X. Dou and Y. Chen, "Exact Analytical Method for Planar Optical Waveguides with Arbitrary Index Profile," JOSA A, vol. 16, no. 9, pp. 2209-2212, 1999.. Tichi, Electronic Hearth: Creating an American Television Culture, Oxfool.rd University Press, 1991.

A. W. Snyder and J. Love, Optical Waveguide Theory, Springer Science & B.



  • There are currently no refbacks.

Copyright (c) 2020 Ali Çetin

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.