volume | PIER Journals

Abstract

In this paper a novel approach based on Asymptotic Iteration Method (AIM) is presented to solve analytically the light propagation through one-dimensional inhomogeneous slab waveguide. Practically implemented optical slab waveguides based on traditional techniques are usually inhomogeneous and numerical methods are used to obtain guided wave characteristics. In this work, we develop analytical method for modal analysis includes Eigen modes (electric and magnetic fields distribution) and Eigen values (guided wave vector) using AIM. The developed method is applied to some especial examples.

1. Motavali, H. and A. Rostami, "Exactly modal analysis of inhomogeneous slab waveguide using Nikiforov-Uvarov method," Journal of Electromagnetic Waves and Applications, Vol. 22, 681, 2008.
doi:10.1163/156939308784159507

2. Nikiforov, A. F. and V. B. Uvarov, Special Functions of Mathematical Physics, Birkhauser, 1988.

3. Egrifes, H. and R. Sever, "Bound state of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method," Phys. Lett. A, Vol. 344, 117, 2005.
doi:10.1016/j.physleta.2005.06.061

4. Aktas, M. and R. Sever, "Exact supersymmetric solution of Schrodinger equation for central confining potentials by using the Nikiforov-Uvarov method," J. Mol. Struct. (Theochem), Vol. 710, 223, 2004.
doi:10.1016/j.theochem.2004.09.011

5. Berkdemir, C., A. Berkdemir, and R. Sever, "Systematical approach to the exact solutions of the Dirac equation for a deformed form of the Woods-Saxon potential," J. Phys. A: Math. Gen., Vol. 39, 13455, 2006.
doi:10.1088/0305-4470/39/43/005

6. Yasuk, F., A. Durmus, and I. Boztosun, "Exact analytical solution to the relativistic Klein-Gordon equation with non-central equal scalar and vector potentials," J. Math. Phys., Vol. 47, 082302, 2006.
doi:10.1063/1.2227258

7. Simsek, M. and H. Egrifes, "The Klein-Gordon equation for the generalized Hulthen potential in complex quantum mechanics," J. Phys. A: Math. Gen., Vol. 37, 4379, 2004.
doi:10.1088/0305-4470/37/15/007

8. Ciftci, H., R. L. Hall, and N. Saad, "Asymptotic iteration method for eigenvalue problems," J. Phys. A: Math. Gen., Vol. 36, 11807, 2003.
doi:10.1088/0305-4470/36/47/008

9. Ciftci, H., R. L. Hall, and N. Saad, "Perturbation theory in a framework of iteration methods," Phys. Lett. A, Vol. 346, 381, 2005.
doi:10.1016/j.physleta.2005.08.090

10. Bender, C. M. and Q. Wang, "A class of exactly-solvable eigenvalue problems," J. Phys. A, Vol. 34, 9835, 2001.
doi:10.1088/0305-4470/34/46/307

11. Bayrak, O. and I. Boztosun, "Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method," J. Phys. A: Math. Gen., Vol. 39, 6955, 2006.
doi:10.1016/j.theochem.2006.09.006

12. Bayrak, O and I. Boztosun, "Analytical solution to the Hulthen and Morse potentials by using the asymptotic iteration method," J. Mol. Struct. (Theochem), Vol. 802, 17, 2007.
doi:10.1142/S0218301306004788

13. Durmus, A., F. Yasuk, and I. Boztosun, "Exact analytical solution of the Kline-Gordon equation for the pionic atom by asymptotic iteration method," Int. J. Mod. Phys. E (IJMPE), Vol. 15, 1243, 2006.

14. Rostami, A. and S. K. Moayedi, "Exact solution for light propagation through inhomogeneous media," Indian J. Phys. B, Vol. 75, 357, 2001.
doi:10.1088/1464-4258/5/4/313

15. Rostami, A. and S. K. Moayedi, "TM mode in inhomogeneous slab waveguide as an exactly solvable oscillator-like Hamiltonian," J. Opt. A: Pure and Applied Optics, Vol. 5, 380, 2003.
doi:10.1140/epjb/e2003-00354-5

16. Moayedi, S. K. and A. Rostami, "PT-invariant Helmholtz optics and its applications to slab waveguides," Eur. Phys. J. B, Vol. 36, 359, 2003.

17. Rostami, A. and S. K. Moayedi, "Exactly modal analysis of inhomogeneous slab waveguides using similarity transformed harmonic-oscillator algebra," IL Nuovo Cimento B, Vol. 120, 285, 2005.

18. Moayedi, S. K. and A. Rostami, "Exact treatment of light in inhomogeneous slab waveguides using supersymmetric quantum mechanics," IL Nuovo Cimento B, Vol. 118, 729, 2003.
doi:10.2528/PIER07071905

19. Liu, S. H., C. H. Liang, W. Ding, L. Chen, and W. T. Pan, "Electromagnetic wave propagation through a slab waveguide of uniaxially anisotropic dispersive metamaterial," Progress In Electromagnetics Research, Vol. 76, 467-475, 2007.
doi:10.2528/PIER06021802

20. Wang, Z. J. and J. F. Dong, "Analysis of guided modes in asymmetric left-handed slab waveguides," Progress In Electromagnetics Research, Vol. 62, 203-215, 2006.
doi:10.2528/PIER06071101

21. Singh, V., Y. Prajapati, and J. P. Saini, "Modal analysis and dispersion curves of a new unconventional Bragg waveguide using a very simple method," Progress In Electromagnetics Research, Vol. 64, 191-204, 2006.
doi:10.2528/PIER05110602

22. Attiya, A. M. and A. A. Kishk, "Modal analysis of a two-dimensional dielectric grating slab excited by an obliquely incident plane wave," Progress In Electromagnetics Research, Vol. 60, 221-243, 2006.
doi:10.2528/PIER03081801

23. Hu, F. G., C. F. Wang, Y. Xu, and Y. B. Gan, "Modal method analysis of multilayered coated circular waveguide using a modified characteristic equation," Progress In Electromagnetics Research, Vol. 45, 243-262, 2004.
doi:10.2528/PIER99052501

24. Liu, S., L. W. Li, M. S. Leong, and T. S. Yeo, "Rectangular conducting waveguide filled with uniaxial anisotropic media: A modal analysis and dyadic Green’s function," Progress In Electromagnetics Research, Vol. 25, 111-129, 2000.
doi:10.1016/j.cplett.2005.10.039

25. Berkdemir, A., C. Berkdemir, and J. Han, "Bound state solutions of the Schr¨odinger equation for modified Kratzer’s molecular potential," Chem. Phys. Lett., Vol. 417, 2006.
doi:10.2528/PIERB07121303

26. Hatamzadeh-Varmazyar, S. and M. Naser-Moghadasi, "New numerical method for determining the scattered electromagnetic fields from thin wires," Progress In Electromagnetics Research B, Vol. 3, 207-218, 2008.
doi:10.2528/PIER07122601

27. Banai, A. and A. Hashemi, "A hybrid multimode contour integral method for analysis of the H-plane waveguide discontinuties," Progress In Electromagnetics Research, Vol. 81, 167-182, 2008.
doi:10.2528/PIER08010303

28. Ho, M., F.-S. Lai, S.-W. Tan, and P.-W. Chen, "Numerical simulation of propagation of EM pulse through lossless non-uniform dielectric slab using characteristic-based method," Progress In Electromagnetics Research, Vol. 81, 197-212, 2008.
doi:10.2528/PIER07103105

29. Collino, F., F. Millot, and S. Pernet, "Boundary-integral methods for iterative solution of scattering problems with variable impedance surface condition," Progress In Electromagnetics Research, Vol. 80, 1-28, 2008.
doi:10.2528/PIER07100802

30. Carpentieri, B., "Fast iterative solution Methods in electromagnetic scattering," Progress In Electromagnetics Research, Vol. 79, 151-178, 2008.
doi:10.2528/PIER06071101

31. Singh, V., Y. Prajapati, and J. P. Saini, "Modal analysis and dispersion curves of a new unconventional Bragg waveguide using a very simple method," Progress In Electromagnetics Research, Vol. 64, 191-204, 2006.
doi:10.2528/PIER07030802

32. Khalaj-Amirhosseini, M., "Analysis of lossy inhomogeneous planar layers using equivalent sources method," Progress In Electromagnetics Research, Vol. 72, 61-73, 2007.
doi:10.2528/PIER07030806

33. Berginc, G. and C. Bourrely, "The small-slope approximation method applied to a three-dimensional slab with rough boundaries," Progress In Electromagnetics Research, Vol. 73, 131-211, 2007.
doi:10.2528/PIERB07103002

34. Kazemi, S., H. R. Hassani, G. Dadashzadeh, and F. Geran, "Performance improvement in amplitude synthesis of unequally spaced array using least mean square method," Progress In Electromagnetics Research B, Vol. 1, 135-145, 2008.
doi:10.2528/PIERL07111902

35. Samuel, E. P. and D. S. Patil, "Analysis of wavefunction distribution in quantum well biased laser diode using transfer matrix method," Progress In Electromagnetics Research Letters, Vol. 1, 119-128, 2008.

Prof. Ali Rostami

Dr. Hossein Motavali