Asimetrik Bir Dielektrik Dilim Dalga Kılavuzunun Etkin Kırılma İndisinin Teorik Olarak Hesaplanması

Yıl 2009, Cilt: 22 Sayı: 2, 125 - 137, 31.12.2009

Çiğdem Harmankuyu Ali Çetin

Öz

Bu çalışmada bir asimetrik dilim dalga kılavuzunun etkin kırılma indisini tespit etmek

için hem analitik yöntem hem de bir yaklaşım yöntemi olan sonlu farklar yöntemi kullanılmıştır.

Dalga kılavuzunda diyot lazerin etkin yayılımının sağlanması için etkin indis değeri

hesaplanmıştır. Analitik yöntemle elde edilen sonuçla sonlu farklar yöntemi ile elde edilen

sonuçların kullanılacak kılavuz türü için geçerliliği karşılaştırılmıştır.

Anahtar Kelimeler

Optik dilim dalga kılavuzu, analitik yöntem, sonlu farklar yöntemi, etkin kırılma indisi, elektromanyetik dalga

Theoretical Calculation Of Effective Refractive Index Of An Asymmetrical Dielectric Slab Waveguide

Öz

In this paper, we use both analytical method and finite difference method to determine effective refractive index of an asymmetrical slab waveguide. Effective index value is

calculated to efficient propagation of diod laser in slab waveguide. The validity of the obtained

values by both of methods are compared for using waveguide type.

Anahtar Kelimeler

Optical slab waveguide, analytical method, finite difference method, effective refractive index, electromagnetic wave.

Kaynakça

• [1] T. B. Koch, J. B. Davides, D. Wickramasinghe, “Finite Element/Finite Difference Propagation Algorithm For Integrated Optical Device”, Electronics Letters, Vol. 25 No.8., pp. 514-516, 1989.
• [2] C. L. Xu, W.P. Huang, “Finite-Difference Beam Propagation Method For Guide Wave Optics”, Progress In Electromagnetics Research, PIER, vol. 11, pp. 1-49, 1995.
• [3] Ahmed A. Abou El-Fadl, “An Optimal Method To Study The Propagation Characterics Of Rectangular Optical Waveguides”, Fifteen National Radio Science Conference, Feb. 24-26, 1998, Helvan, Cairo, Egypt.
• [4] M. D. Feit, J. A. Fleck, Jr, “Computation Of Mode Eigenfunctions In Graded Index Optical Fibers By The Propagating Beam Method”, Applied Optics, Vol. 19 No.13, pp. 2240-2246, 1980.
• [5] M. D. Feit, J. A. Fleck, Jr, “Computation Of Mode Properties In Optical Fiber Waveguides By A Propagating Beam Method”, Applied Optics, Vol. 19, No.7, pp. 1154-1164, 1980.
• [6] M. D. Feit, J. A. Fleck, Jr, “Calculation Of Dispersion For Two Optical Fiber Profiles By The Propagating Beam Technique”, Applied Optics, Vol. 19, No.7, pp. 326-329, 1980.
• [7] Y. Chung, N. Dağlı, “An Assessment Of Finite Difference Beam Propagation Method”, IEE Journal Of Quantum Electronics, Vol. 26 No. 8, pp. 1335-1338, 1990.
• [8] D. Marcuse, ‘‘Theory Of Dielectric Optical Waveguides’’, Academic Press, Boston, 1991. [9] M. S. Stern, “Semivectorial Polarised Finite Difference Method For Optical Waveguides With Arbitrary Index Profiles” . IEE Proc. J., Vol. 135, No. 1, pp. 56-63. 1988.
• [10] M. S. Stern, “Semivectorial Polarised H Field Solutions For Dielectric Waveguides With Arbitrary Index Profiles”. IEE Proc. J. Vol. 135, No. 5, pp. 333-338, 1988.
• [11] A. S. M. Supa’at, A. B. B. Mohammad, N. M. Kassim, R. Omar, “Analysis Of Mode Fields In Optical Waveguides”, Proceedings Of IEEE, TENCON, pp. 829-832, 2002.
• [12] M. A. Matin, M. T. Benson, P. C. Kendall, M. S. Stern, “New Technique For Finite Difference Analysis Of Optical Waveguide Problems”, International Journal Of Numerical Modelling: Electronic Networks, Devices And Fields, Vol. 7, pp. 25-33, 1994.
• [13] N. M. Kassım, A. B. Mohammad, M. H. İbrahim, “Optical Waveguide Modelling Based On Scalar Finite Difference Scheme” Jurnal Teknologi, Vol. 42 (D), pp. 41-54, 2005.
• [14] K. Kawano, T. Kitoh, “Introduction To Optical Waveguide Analysis”, John Wiley & Sons, New York, 2001.
• [15] M. Khalaj-Amirhosseini, “Analysis of Lossy Inhomogeneous Planar Layers Using Taylor’s Series Expansion”, IEEE Transactions On Antennas And Propagation, Vol. 54, No. 1, pp. 130-135, 2006.
• [16] Y. Won-Young, C. Wenwu, T. S. Chung, J. Morris, “Applied Numerical Methods Using Matlab”, John Wiley & Sons, New Jersey, 2005.
• [17] M. M. Spühler, D. Wiesmann, P. Freuler, M. Diergardt, “Direct Computation Of Higher- Order Propagation Modes Using The Imaginary-Distance Beam Propagation Method”, Optical And Quantum Electronics, Vol. 31. pp. 751-761, 1999.
• [18] K. Jaan, “Numerical Methods In Engineering With Matlab”, Cambridge University Press, England, 2006.
• [19] V. A. Popescu, N. N. Puscas, “Determination Of Normalized Propagation Constants For The Double-Clad Planar Nd:YAG and Yb:YAG Waveguide Lasers”, Journal Of Optoelectronics And Advanced Materials, Vol. 8, No. 3, pp. 1262–1266, 2006.