STUDY OF DISPERSION CURVES IN M-TYPE TRIPLE CLAD SINGLE MODE OPTICAL FIBER

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1 INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) International Journal of Electronics and Communication Engineering & Technology (IJECET) ISSN ISSN (Print) ISSN (Online) Volume 6 Issue 4 April (2015) pp IAEME: Journal Impact Factor (2015): (Calculated by GISI) IJECET I A E M E STUDY OF DISPERSION CURVES IN M-TYPE TRIPLE CLAD SINGLE MODE OPTICAL FIBER 1 Deepika Prajapati 2 Dhyanendra Parashar 12 SR Group of Institutions Gwalior Road Jhansi U. P. (INDIA) ABSTRACT In this paper the dispersion curves of M-type triple clad (4-layer) single mode optical fiber is analytically studied. Here in the presented work modal analysis of this fiber is done. Firstly the eigen value equation is derived for triple clad single mode fiber using Maxwell s equation for electromagnetic and by applying boundary conditions (LP approximation method) and then it is shown that how the single mode operation is dependent upon the order of the modes. Using numerical evaluation of the presented analytical relations normalized frequency and normalized propagation constant are calculated. Then using these parameters dispersion curves are drawn. Finally it is seen that all the curves have standard expected shape which means that the standard shifted M-type circular waveguide does not change in the standard shape of dispersion curve. 1. INTRODUCTION Optical fiber is an important element for optical communication. Attenuation and dispersion are two main mechanisms which affects the information carrying capacity of a fiber. Today low-loss optical fibers are available in some specified wavelengths such as 1.55 where the attenuation is minimum with minimum dispersion. This type of optical fiber is known as dispersion shifted fiber (DS). Dispersion has critical effect for large channel dense wavelength division multiplexing (DWDM) systems. Recently high bandwidth applications are requested in optical system. For this purpose dispersion curves of triple clad (4-layer) single mode optical fiber is studied. In this direction some papers are published and we have tried to review some of these papers. In [1] authors analyzed the chromatic dispersion. Chromatic dispersion is pulse spreading that takes place within a single mode. However in this paper they could not calculate waveguide dispersion and also the effect of system geometrical and optical parameters is not be included in the analysis based on the presented method. In [2] theoretical analysis of coaxial optical fibers was presented. But the effect of dispersion and system parameters were not included. 28

2 International Journal of Electronics and Communication Engineering & Technology (IJECET) ISSN In [3] authors designed an optical fiber including flat mode field in core for increasing mode field diameter concluding to low non-linear effect. But again the effects of the optical geometrical parameter on dispersion behaviour have not been studied. Also author has published papers [4 5 6] but in these papers complete analytical formulation for dispersion were not provided. In [7] authors presented analytical relation for incorporating dispersion behaviour of the proposed structure. Based on developed analytical relations zero-dispersion wavelengths can be controlled by geometrical and optical parameters. The effect of system parameters on dispersion characteristics was investigated. Based on the proposed relations optimum structures can be developed for optimum dispersion treatment. In this paper we consider M-type triple clad single mode optical fiber. Here in the presented work dispersion analysis of this structure is investigated. Modal analysis of triple clad single mode fiber is done. Using numerical evaluation normalized frequency and normalized propagation constant are calculated and then using these parameters dispersion curves are drawn accordingly. The organization of the paper is as follows. In section 2 mathematical modelling for complete analytical formulation is presented. Calculated results and dispersion curves of the analysis are discussed in section 3 and finally the paper ends with a short conclusion. 2. MATHEMATICAL MODELLING In this section the structure of triple-clad single mode fiber is studied (Fig.1). All layers are assumed to be lossless linear isotropic homogenous and non-magnetic. The outer cladding is assumed to extend to infinity in the radial direction. The width of the first second and third layer is and respectively. And the radius of the first second and third layer is a b c respectively. Here the width or radius of fourth (last) layer is assumed to be infinity. The relation between radius and width is given as follows: a = b = a+ c = b+ The corresponding refractive index distribution function is defined as follows: n(r) = (2.1) Where r is the radius position. Effective refractive index is given by = where is the propagation wave vector of guided modes and is the wave number in vaccum. The proposed structure of M-type can be divided into three regions which is defined as follows- I II III < < < < < < Here we are considering only the (I) region 29

3 International Journal of Electronics and Communication Engineering & Technology (IJECET) ISSN n (r) III II I II III IV I r a b c Fig.1 Refractive index profile of proposed M-type structure with parameter defined. According to the wave equation the boundary conditions of electromagnetic field and under the LP approximation the characteristics equations in region (I) can be obtained as follows!" # $!" # $%!"" # 0!"'''# %!"''' ' # "!" # $"!" # $" %!" # 0 ''' "!"'''# "'''%!"'''# $!" # $%!" # 0!"'''# %!"'''# $!/ # =0 (2.2) $"!" # $" %!" # 0 "'''!"'''# "'''%!"'''# $/!/ # Where % ( are the Bessel and modified Bessel functions. The parameters used in the above matrix are defined as follows: " = a)!* $ # " = a)!* $ # " = b)!* $ # / = c)! $ * # (2.3) (2.4) "''' = + " "''' = " + (2.5) Where P and Q are the geometrical parameters defined as follows: P = Q = (2.6) Optical parameters are defined as: - =. - =... (2.7) 30

4 International Journal of Electronics and Communication Engineering & Technology (IJECET) ISSN For evaluating of the index of refraction difference between core and cladding the following definition is done =.. (2.8) Normalized frequency is V = * 2) $ (2.9) Normalized propagation constant is B =!3 4 5#.. (2.10) 3. CALCULATED RESULTS AND ANALYSIS In this section dispersion analysis based on derived relations in previous sections is done. The total dispersion relation for the introduced single mode fiber is as follows: D = $ !<=# Where A = $ B = >$?!<=# 8= (3.1) is the group index of the outer cladding. Now the modes are calculated for the equation (2.2) with the help of MATLAB. Here the dispersion curves are drawn for an operating wavelength B = 1.55 m and various values of dimensional parameter in regular increasing order. The value of other parameter is: = 0.5 = 0.5 = = = = Fig. 2. Normalized propagation constant (B) vs. Normalized frequency (V) for m=0 31

5 International Journal of Electronics and Communication Engineering & Technology (IJECET) ISSN Fig. 3. Normalized propagation constant (B) vs. Normalized frequency (V) for m=1 Fig. 2.Normalized propagation constant (B) vs. Normalized frequency (V) for m=2 Fig. 3. Normalized propagation constant (B) vs. Normalized frequency (V) for m=3 32

6 International Journal of Electronics and Communication Engineering & Technology (IJECET) ISSN Table 1. Cut-off frequencies values) for some lower order modes in M-type four layer waveguide for first inner cladding with width = 1.5 Cut-off (@ )value m=0 m=1 m= C D E F CONCLUSION In this paper dispersion analysis for the proposed M-type fiber has been done. Here we have analyzed the dispersion behavior of the proposed structure. With the help of normalized frequency and normalized propagation constant dispersion curves are drawn.we have concluded that in the range of 0 to 20 of the normalized frequency there are 7 modes for m=0 6 modes for m=1 6 modes for m=2 and 5 modes for m=3. Hence we can say that the total number of modes decreases as the order of modes increases. REFERENCES 1. H.T. Hattori A. Safaei-Jazi Applied Optics 37 (1998) F.D. Nunes C.A. de Souza Melo Applied Optics 35 (1996) R.K. Varhsney A.K. Ghatak I.C. Goyal S.C.AntonyOptical Fiber Technology 9 (2003) X. Tian X. Zhang Optics Communication 230 (2004) X. Zhang X. Tian Optics & Laser Technology 35 (2003) X. Zhang X. Wang Optics & Laser Technology 37 (2003) A. Ghatak K.Thyagrajan Introduction to Fiber Optics Cambridge University press A. Rostumi M. Savadi-Oskouei investigation of dispersion characteristics in MI and MII-type single mode optical fibers Optics Coomunication 271 (2007) S.K Mohapatra R. Bhojray and S.K Mandal Analog and Digital Modulation Formats of Optical Fiber Communication within and beyond 100 Gb/S: A Comparative Overview International journal of Electronics and Communication Engineering &Technology (IJECET) Volume 4 Issue pp ISSN Print: ISSN Online: Elham Jasim Mohammad and Gaillan H. Abdullah Soliton Optical Fibers Super continuum Generation Near The Zero Dispersion International Journal of Industrial Engineering Research and Development (IJIERD) Volume 4 Issue pp ISSN Online: ISSN Print: