volume | PIER Journals

Abstract

We characterize the alpha power and chirped types of refractive index profile planar slab waveguide in terms of TE/TM mode study, waveguide dispersion study, mode profile properties, power confinement factor and universal b-V graph. Our own developed finite element method has been efficiently applied to analyze the symmetric planar slab waveguide having a complicated refractive index profile. There is a requirement for a high accuracy of numerical technique to analyze the arbitrary refractive index waveguide, as at some frequency the TE and TM modes are smeared on each other, and it is difficult to distinguish them while analyzing. This paper successfully demonstrates the different TE/TM modes supported by the waveguide with respect to alpha-power and linearly chirped types of refractive index profile. The main contribution of our work is to identify the TE/TM mode numerically for a complex refractive index planar slab waveguide and to characterize them in terms of their performance parameters. Then we apply the mode propagation concept to estimate the propagation phenomena in alpha-power and chirped types of refractive index profile waveguide. All the results presented in this paper are simulated in MATLAB only. Our study reveals that waveguide dispersion and number of allowed guided modes are small while for the case of triangular index profile followed by chirped profile and maximum for step index profile case. Hence triangular and chirped types of refractive index profile waveguide seem to be more efficient for long haul optical communication systems.

1. Zheludev, N. I., "Photonic-plasmonic devices: A 7-nm light pen makes its mark," Nat. Nanotechnol., Vol. 5, 10-11, 2010.
doi:10.1038/nnano.2009.460 Google Scholar

2. Politano, A. and G. Chiarello, "Quenching of plasmons modes in air-exposed grapheme-Ru contacts for plasmonic devices," Appl. Phy. Lett., Vol. 102, 201608, 2013.
doi:10.1063/1.4804189 Google Scholar

3. He, X. Y., Q. J. Wang, and S. F. Yu, "Numerical study of gain-assisted terahertz hybrid plasmonic waveguide," Plasmonics, Vol. 7, 571-577, 2012.
doi:10.1007/s11468-012-9344-6 Google Scholar

4. Baqir, M. A. and P. K. Choudhary, "Dispersion characteristics of optical fibers under PEMC twist," Journal of Electromagnetic Wave and Application, Vol. 28, No. 17, 2124-2134, 2014.
doi:10.1080/09205071.2014.971974 Google Scholar

5. Li, Z., K. Bao, Y. Fang, Y. Huang, P. Nordlander, and H. Xu, "Correlation between incident and emission polarization in nanowire surface plasmons waveguide," Nano. Lett., Vol. 10, 1831-1835, 2010.
doi:10.1021/nl100528c Google Scholar

6. Politano, A. and G. Chiarello, "Unravelling suitable grapheme-metal contacts for grapheme-based plasmonic device," Nanoscale, Vol. 5, 8251-8220, 2013.
doi:10.1039/c3nr02027d Google Scholar

7. Raghuwanshi, S. K. and S. Kumar, "Waveguide dispersion characteristics of graded/linearly chirp type’s refractive index profile of planar slab optical waveguide by using the modified finite element method," Journal of Optics, Springer, Aug. 12, 2014, Doi: 10.1007/s12596-014-0220-y. Google Scholar

8. Mussina, R., D. R. Selviah, F. A. Fernnandez, A. G. Tijhuis, and B. P. D. Hon, "A rapid accurate technique to calculate the group delay dispersion and dispersion slop of arbitrary radial refractive index profile weakly-guiding optical fibers," Progress In Electromagnetics Research, Vol. 145, 99-113, 2014. Google Scholar

9. Walpita, L. M., "Solution for planar optical waveguide equation by selecting zero elements in a characteristics matrix," Journal of the Optical Society of America, Vol. A2, 592-602, 1985. Google Scholar

10. Rahman, B. M. A., "Finite element analysis of optical waveguides," Progress In Electromagnetics Research, Vol. 10, 187-216, 1995. Google Scholar

11. Honkis, T. H., "Analysis of optical waveguide with arbitrary index profile using an immersed interface method," International Journal of Modern Physics C, Vol. 22, No. 7, 687-710, 2011.
doi:10.1142/S0129183111016543 Google Scholar

12. Okoshi, T. and K. Okamoto, "Analysis of wave propagation in inhomogeneous optical fibers using a varational method," IEEE Trans. on Microwave Theory and Tech., Vol. 22, No. 11, 938-945, 1974.
doi:10.1109/TMTT.1974.1128389 Google Scholar

13. Popescu, V. A., "Determination of normalized propagation constant for optical waveguide by using second order variational method," Journal of Optoelectronics and Advanced Mat., Vol. 7, No. 5, 2783-2786, 2005. Google Scholar

14. Rostami, A. and H. Motavali, "Asymptotic iteration method: A power approach for analysis of inhomogeneous dielectric slab waveguide," Progress In Electromagnetics Research B, Vol. 4, 171-182, 2008.
doi:10.2528/PIERB08011701 Google Scholar

15. Chaudhuri, P. R. and S. Roy, "Analysis of arbitrary index profile planar optical waveguide and multilayer nonlinear structure: A simple finite differences algorithm," Opt. Quant. Electron., Vol. 39, 221-237, 2007.
doi:10.1007/s11082-007-9076-6 Google Scholar

16. Sadiku, M. N. O., Numerical Techniques in Electromagnetic, 2nd Ed., CRC Press LLC, 1992.

17. Booton, R. C., Computational Methods for Electromagnetic and Microwave, John Wiley and Sons, 1992.

18. Kasim, N. M., A. B. Mohammad, and M. H. Ibrahim, "Optical waveguide modeling based on scalar finite difference scheme," Journal Teknologi., Vol. 45(D), 181-194, 2006. Google Scholar

19. Gambling, W. A., D. N. Payne, and H. Matsumura, "Cut-off frequency in radically inhomogeneous single mode fiber," Electron. Letters, Vol. 13, No. 5, 130-140, 1977.
doi:10.1049/el:19770092 Google Scholar

20. Zhuangqi, C., Y. Jiang, and C. Yingli, "Analytical investigation of planar optical waveguide with arbitrary index profiles," Optical and Quant. Electronics, Vol. 31, 637-644, 1999. Google Scholar

21. Chiang, K. S., "Review of numerical and approximation methods for modal analysis of general dielectric waveguide," Opt. Quant. Electron., Vol. 26, 113-134, 1994.
doi:10.1007/BF00384667 Google Scholar

22. Xu, W., Z. H. Wang, and Z. M. Huang, "Propagation constant of a planar dielectric waveguide with arbitrary refractive index variation," Opt. Lett., Vol. 18, 805-807, 1993. Google Scholar

23. Okamoto, K., Fundamentals of Optical Waveguide, Academic Press, 2006.

24. Sharma, E. K., I. C. Goyal, and A. K. Ghatak, "Calculation of cut-off frequencies in optical fibers for arbitrary profiles using the matrix method," IEEE Journal of Quant. Electron., Vol. 17, No. 12, 2317-2320, 1981.
doi:10.1109/JQE.1981.1071045 Google Scholar

25. Okamoto, K. and T. Okoshi, "Analysis of wave propagation in optical fibers having core with α-power refractive distribution and uniform cladding," IEEE Trans. on Microwave Theory and Tech., Vol. 24, No. 7, 416-421, 1976.
doi:10.1109/TMTT.1976.1128869 Google Scholar

26. Raghuwanshi, S. K. and S. Kumar, "Analytical expression for dispersion properties of circular core dielectric waveguide without computing d²β/dk² numerically," I-manager’s Journal on Future Engineering & Technology, Vol. 7, No. 3, 26-34, 2012. Google Scholar

27. Raghuwanshi, S. K., S. Kumar, and A. Kumar, "Dispersion characteristics of complex refractive-index planar slab optical waveguide by using finite element method," Optik, Vol. 125, No. 20, 5929-5935, Elsevier, Oct. 2014.
doi:10.1016/j.ijleo.2014.05.049 Google Scholar

28. Ghatak, A. K. and K. Thyagarajan, Optical Electronics: Introduction to Fiber Optics, Cambridge Press, 1999.

29. Hotate, K. A. and T. Okoshi, "Formula giving single-mode limit of optical fiber having arbitrary refractive index profile," Electron. Letters, Vol. 14, No. 8, 246-248, 1978.
doi:10.1049/el:19780167 Google Scholar

30. Rostami, A. and S. K. Moyaedi, "Exact solution for the TM mode in inhomogeneous slab waveguides," Laser Physics, Vol. 14, No. 12, 1492-1498, 2004. Google Scholar

31. Survaiya, S. P. and R. K. Shevagaonkar, "Dispersion characteristics of an optical fiber having linear chirp refractive index profile," IEEE Journal of Lightwave Tech., Vol. 17, No. 10, 1797-1805, 1999.
doi:10.1109/50.793753 Google Scholar

32. Raghuwanshi, S. K. and S. Talabattula, "Dispersion and peak reflectivity analysis in a non-uniform FBG based sensors due to arbitrary refractive index profile," Progress In Electromagnetics Research B, Vol. 36, 249-265, 2012.
doi:10.2528/PIERB11081704 Google Scholar

33. Hadley, G. R., "Transparent boundary condition for beam propagation," Opt. Lett., Vol. 16, 624-626, 1991.
doi:10.1364/OL.16.000624 Google Scholar

Dr. Sanjeev Kumar Raghuwanshi

Dr. B. M. Azizur Rahman