volume | PIER Journals

Abstract

The mathematical model elaborated in this paper is based on the concept of intrinsic modes in order to analyze and synthesize optical wave propagation along a non-uniform optical structure which is used in integrated optics communication as tapered optical coupler. The new mathematical model is simply developed by introducing modifications to the intrinsic integral, and its numerical evaluation illustrate the electromagnetic field distribution inside a taper thin film and also outside the waveguide constituted by the substrate and the cladding of lower refractive index. The proposed method permits efficiently tracking the behaviour of the optical waves both inside and outside of the optical waveguide, and quantifying the radiation and optical coupling occurring from the taper thin film of higher refractive index to adjacent mediums until a total energy transfer; this happens at thicknesses lower than waveguide cutoff thickness of each mode. The new model can be applied to all types of tapered optical coupler, having a high or low contrast of the refractive indexes, and different wedge angles formed by the different mediums of the waveguide.

1. Lifante, G., Integrated Photonics: Fundamentals, John Willey & Sons Ltd., 2003.
doi:10.1002/0470861401

2. Boudrioua, A., Photonic Waveguides Theory and Applications, ISTE Ltd, 2009.
doi:10.1002/9780470611142

3. Bacha, M. and A. Belghoraf, "Evaluation of optical propagation and radiation in optical waveguide using a numerical method," Chinese Optics Letters, Vol. 12, No. 7, 070801-4, 2014.
doi:10.3788/COL201412.070801

4. Luyssaert, B., et al. "Efficient nonadiabatic planar waveguide tapers," Journal of Lightwave Technology, Vol. 23, No. 8, 2462-2468, 2005.
doi:10.1109/JLT.2005.850795

5. Debnath, K., et al. "Low-loss silicon waveguides and grating couplers fabricated using anisotropic wet etching technique," Frontiers in Materials, Vol. 3, 1-7, Article 10, 2016.

6. Subbaraman, H., et al. "Recent advances in silicon-based passive and active optical interconnects," Optics Express, Vol. 23, No. 3, 2487-2510, 2015.
doi:10.1364/OE.23.002487

7. Yoo, K. and J.-H. Lee, "Design of a high-efficiency fiber-to-chip coupler with reflectors," EIE Transactions on Smart Processing and Computing, Vol. 5, No. 2, 123-128, 2016.
doi:10.5573/IEIESPC.2016.5.2.123

8. Okamoto, K., Fundamentals of Optical Waveguides, Elsevier Inc., 2006.

9. Whang, A. J., et al. "Innovative coupler design based on a tapered light pipe with lens," Chinese Optics Letters, Vol. 11, No. 12, 1222011-1222014, 2013.

10. Kamel, A. and L. B. Fielsen, "Spectral theory of sound propagatin in an ocean channel with weakly sloping bottom," J. Acoust. Soc. Am., Vol. 73, No. 4, 1120, 1983.
doi:10.1121/1.389282

11. Arnold, J. and A. Ansbro, "Intrinsic modes in wedge shaped oceans," Journal de Physique Colloques, Vol. 51, No. C2, C2-953-C2-956, 1990.

12. Arnold, J. M., A. Belghoraf, and A. Dendane, "Intrinsic mode theory of tapered optical waveguide," IEE Proceedings, Vol. 132, No. 6, 314-318, 1985.

13. Dendane, A. and J. M. Arnold, "Beam radiation from tapered waveguides," IEEE Journal of Quantum Electrons, Vol. 22, No. 9, 1551-1556, 1986.
doi:10.1109/JQE.1986.1073156

14. Belghoraf, A., "A simplified approach to analysing non uniform structure in integrated optics," A.M.S.E. Periodicals: Modelling, Measurement and Control. A, Vol. 74, No. 5, 61-71, 2001.

15. Belghoraf, A., "Numerical comparison between intrinsic and adiabatic modes for tapered optical waveguide in optical communication," A.M.S.E. Periodicals: Modelling, Measurement and Control. A, Vol. 45, No. 4, 21-42, 1992.

16. Cada, M., et al. "Intrinsic modes in tapered optical waveguides," IEEE Journal of Quantum Electronics, Vol. 24, No. 5, 1988.
doi:10.1109/3.191

17. Cada, M., et al. "A substantially improved treatment of intrinsic modes in tapered optical waveguides," IEEE Journal of Quantum Electronics, Vol. 25, No. 5, 1989.
doi:10.1109/3.27983

18. Prajzler, V., H. Tuma, J. Spirkova, et al. "Design and modeling of symmetric three branch polymer planar optical power dividers," Radioengineering, Vol. 22, No. 1, 233-239, 2013.

19. Kawano, K. and T. Kitoh, Introduction to Optical Waveguide Analysis, John Willey & Sons Ltd., 2001.
doi:10.1002/0471221600.ch6

20. Yip, G. L., "Simulation and design of integrated optical waveguide devices by the BPM," Integrated Optical Circuits SPIE, Vol. 1583, 240-248, 1991.
doi:10.1117/12.50894

21. Han, Y. T., J. U. Shin, D. J. Kim, et al. "A rigorous 2D approximation technique for 3D waveguide structures for BPM calculations," ETRI Journal, Vol. 25, No. 6, 535-537, 2003.
doi:10.4218/etrij.03.0203.0020

22. Ismail, M. M. and M. N. Shah Zainuddin, "Numerical method approaches in optical waveguide modelling," Applied Mechanics and Materials, Vol. 52-54, 2133-2137, 2011.
doi:10.4028/www.scientific.net/AMM.52-54.2133

23. Bacha, M. and A. Belghoraf, "Analysis of electromagnetic Wave propagation along optical waveguide," Int. Rev. on Mod. and Simul. (I.RE.MO.S), Vol. 6, 1624, 2013.

24. Belghoraf, A. and M. Bacha, "Mathematical model for analysing a tapered optical coupler," International Research Journal of Engineering and Technology (IRJET), Vol. 3, No. 5, 3049-3052, 2016.

25. Tien, P. K., G. Smolinsky, and R. J. Martin, "Radiation fields of a tapered film and a novel film-to-fiber coupler," IEEE Trans. Microwave Theory Tech., Vol. 23, 79-85, 1975.
doi:10.1109/TMTT.1975.1128507

26. Rumao, T., X. Wang, H. Xiao, et al. "Coherent beam combination of fiber lasers with a strongly confined tapered self-imaging waveguide: Theoretical modelling and simulation," Photon. Res., Vol. 1, No. 4, 2013.

27. Olver, F. W. J., Asymptotic and Special Functions, Academic, 1974.

28. Liu, J.-M., Photonic Devices, Cambridge University Press, 2005.
doi:10.1017/CBO9780511614255

Mr. Mansour Bacha

Dr. Abderrahmane Belghoraf