Daffodil International University Institutional Repository Proceedings of NCCIS November 007 007-11-4 Analysis of Dispersion of Single Mode Optical Fiber Hossen, Monir Daffodil International University http://hdl.handle.net/0.500.11948/76 Downloaded from http://dspace.library.daffodilvarsity.edu.bd, Copyright Daffodil International University Library
National Conference on Communication and Information Security, NCCIS 007 Daffodil International University, Dhaka, Bangladesh, 4 November 007 Analysis of Dispersion of Single Mode Optical Fiber Monir Hossen, Md. Asaduzzaman, Gour Chand Sarkar Dept. of Electronics &Communication Engineering, KUET, Khulna E-mail: (mnrhossen;asad_ece_006;leon_ece_08)@yahoo.com Abstract: This paper addresses some of the fundamental problems which have to be solved in order for optical networks to utilize the full bandwidth of optical fibers. It discusses some of the premises for signal processing in optical fibers. It gives a short historical comparison between the development of transmission techniques for radio and microwaves to that of optical fibers. There is also a discussion of bandwidth with a particular emphasis on what physical interactions limit the speed in optical fibers. Finally, there is a section on line codes and some recent developments in optical encoding of wavelets. Keywords: Dispersion, Absorption, Non-linear Optical Interaction, Zero Dispersion Slop (ZDS), Singlemode Optical Fiber (SMF), SONET, WDM, TDM. 1. Introduction When Claude Shannon developed the mathematical theory of communication [1] he knew nothing about lasers and optical fibers. What he was mostly concerned with wire communication channels using radio and microwaves. Inherently, these channels have a narrower bandwidth than do optical fibers because of the lower carrier frequency (longer wavelength).recently there was no real need for any advanced signal processing in optical fiber communications systems. This has all changed over the last few years with the development of the internet. Optical fiber communication became an economic reality in the early 1970s when absorption of less than 0 db/km was achieved in optical fibers and lifetimes of more than 1 million hours for semiconductor lasers were accomplished. Both of these breakthroughs in material science were related to minimizing the number of defects in the materials used. For optical fiber glass, it is absolutely necessary to have less than 1 parts per billion (ppb) of any defect or transition metal in the glass in order to obtain necessary performance. For the last thirty years, optical fibers have in many ways been a system engineer s dream. They have had, literally, an infinite bandwidth and as mentioned above, a stable and reproducible noise floor. So no wonder it s been sufficient to use intensity pulse-code modulation, also known as on-off keying (OOK), for transmitting information in optical fibers. The bit-rate distance product for optical fibers has grown exponentially over the last 30 years. (Using bandwidth time s length as a measurement makes sense, since any medium can transport a huge bandwidth if the distance is short enough. For this growth to occur, several fundamental and technical problems had to be overcome. In this paper we will limit ourselves to three fundamental processes; absorption, dispersion and nonlinear optical interactions. These three processes are undoubtedly the most researched physical processes in optical glass fibers, which is one reason for discussing them. Another reason, of great importance to mathematicians, is that recent developments in time/frequency and wavelet analysis have introduced novel line coding schemes which seem to be able to drastically reduce. Fig. 1 Electromagnetic spectrum of importance or communication. Frequencies are given in Hertz.. Signal Processing in Optical Fibers The spectrum of electromagnetic waves of interest for different kinds of communication is shown in Figure1. A typical communications system for using these waves to convey information is shown in Figure This system assumes digitized information but is otherwise completely transparent to any type of physical medium used for the channel. Any electromagnetic wave is completely characterized by its amplitude and phase: E(r; t) = A(r; t) exp Á(r; t)...1 143
National Conference on Communication and Information Security, NCCIS 007 Daffodil International University, Dhaka, Bangladesh, 4 November 007 where A is the amplitude and Á(r; t) is the phase. The variations can be in either analog or digital form. The advantage in using analog transmission is that it takes up less bandwidth than a digital transmission with the same information content. The first optical fiber systems in the 1970s used timedivision multiplexing (TDM), each individual channel was multiplexed onto a trunk line using protocols called T1-T5, where T1-T5 refers to particular bit rates; see Figure 3 Each individual channel was in turn encoded with the users digital information. TDM is still the most common scheme used for sending information down an optical fiber. Today, we are using a multiplexing protocol called SONET which uses the acronyms OC48, OC96, etc., where OC48 corresponds to a bit rate of 565 Mbits/sec and each doubling of the OC-number corresponds to a doubling of the bit rate. SIGNAL PROSESING IN OPTICAL FIBERS Source Voice Data User Voice Data attention. In a TDM system each bit is an optical pulse, for WDM system each bit can either be a pulse or a continuous wave (CW). WDM systems rely on the fact that light of different wavelengths do not interfere with each other (in the linear regime); see Figure 4 Signal processing in optical fibers has, historically, been separated into two distinct areas: pulse propagation and signal processing. To introduce these areas we will keep with tradition and describe them separately, however please bear in mind that the area in which mathematicians may play the most important role in future signal processing is to understand the physical limitations imposed by basic processes that are part of the pulse propagation and invent new signal processing schemes which oppose these deleterious effects. A pulse propagating in an optical fiber can be expressed by E(x; y; z; t) = ˆxEx(x; y; z; t)+ˆyey(x; y; z; t) + ˆzEz(x; y; z; t);... Where z is the direction of propagation and x, y are in the transversal plane. Encoding Modulation Optical Fiber Wireless Demodulation Decoding Fig. 4 Wavelength-division multiplexing. Transmitter Channel Receiver Fig. Typical block diagram of a digital communications system. Fig. 3 Time-division multiplexing. The increase in speed has been made possible by the dramatic improvement of electronic circuits and the shift from multi-mode fibers to dispersion-compensated single-mode fibers. Several large national labs are testing, in the laboratory, time-multiplexed systems up to 100 Gbits/sec, commercially most systems are still.5 Gbits/sec. As industry is preparing for an ever growing demand of bandwidth it is clear that electronics cannot keep up with the optical bandwidth, which is estimated to be 30 Tbits/sec for optical fibers. Because of this wavelength-division multiplexing (WDM) has attracted a lot of Fig. 5 Optical fiber geometry 3. Problem of Signal Processing in Optical Fibers The bit-rate distance product for optical fibers has grown exponentially over the last 30 years. (Using bandwidth times length as a measurement makes sense, since any medium can transport a huge bandwidth if the distance is short enough. For this growth to occur, several fundamental and technical problems had to be overcome. In this paper we will limit ourselves to three fundamental 144
National Conference on Communication and Information Security, NCCIS 007 Daffodil International University, Dhaka, Bangladesh, 4 November 007 processes; dispersion, absorption and nonlinear optical interactions. (a) Dispersion Material dispersion Waveguide dispersion Intermodal dispersion (b) Absorption Intrinsic absorption. Extrinsic absorption. (c) Non-Linear Optical Interaction Non-linear effects in optical fibers are due to either change in the reflection index (RI) of the medium with optical power or scattering phenomena. [-4] 4. Dispersion In Single-Mode Fibers and simulation result The pulse broadening in single-mode fibers results almost entirely from intramodal dispersion as only a single-mode is allowed to propagate. Hence the bandwidth is limited by the finite spectral width of the source. The transit time or specific group delay τ g for a light pulse propagating along a unit length of a single-mode fiber may be given, following as [3] 1 dβ τ g = 4.1 c dκ Where c is the velocity of the light in a vacuum, β is the propagation constant for mode within the fiber core of refractive index n 1 and k is the propagation constant for the mode in a vacuum. The total first order dispersion parameter of a single-mode fiber, D T, is given by the derivative of the specific group delay with respect to the vacuum wavelength λ as: [3] dτ D = g.4. T In common with the material dispersion parameter it is usually expressed in units of ps nm -1 km -1. when the variable λ is replaced by ω, then the total dispersion parameter becomes:[3] ω dτ g ω d β DT = =.4.3 The fiber exhibits intramodal dispersion when β varies nonlinearly with wavelength and may be expressed in terms of the relative refractive index difference and the normalized propagation constant b as:[3] Β=kn 1 [1- (1-b)] 1/.4.4 The final expression may be separated into three composite dispersion components in such a way that one of the effects dominates each term. The dominating effects are as follows: 1. The material dispersion parameter D M defined by λ/c d n/ where n=n 1 or n for the core or cladding respectively.. The waveguide dispersion parameter D W, which may be expressed as n1 n d ( Vb) D W = V...4.5 λc dv Where V is the normalized frequency for the fiber. Since the normalized propagation constant b for specific fiber is only dependent on V, then the normalized waveguide dispersion coefficient d ( Vb ) V also dv depends on V. 3. A profile dispersion parameter D p which is proportional to d /. Strictly speaking, in single-mode fiber with a power law refractive index profile the composite dispersion terms should be employed. Nevertheless, it is useful to consider the total first order dispersion D T in a practical single-mode fiber as comprising: D T =D M +D W +D P (ps nm -1 km 1 )...4.5 Which is simply the addition of the D M,D W,D P components. For single-mode fibers optimized for operation at a wavelength of 1.3µm, the CCITT recommends that the maximum value of chromatic dispersion D T shall not exceed 3.5ps nm -1 km -1 in the wavelength range 1.85 to 1.330µm. The variation of the intermodal dispersion with wavelength is usually characterized by the second order dispersion parameter or dispersion slope S which may be written as:[3] dd d τ g S = T =...4.6 Whereas the first order dispersion parameter D T may be seen to be related only to the second derivative of the propagation constant β with respect to angular frequency ω, the dispersion slope can be shown to be related to both the second and third derivatives following:[3] ( πc) 3 d β 4πc d β S = + 4.7 4 3 3 145
National Conference on Communication and Information Security, NCCIS 007 Daffodil International University, Dhaka, Bangladesh, 4 November 007 It should be noted that although there is zero first order dispersion at λ o, these higher order chromatic effects impose limitations on the possible bandwidth that may be achieved with single-mode fibers. An important value of the dispersion slope S(λ) is obtained at the wavelength of minimum intermodal dispersion λ o such that :[3] S o = S(λ o ).4.8 Where So is called the zero dispersion slope which, is determine only by the third derivative of β. Typical values for the dispersion slope for slandered single mode fibers at λ o are in the region 0.085 to 0.09 ps nm - km -1. Moreover, for such fibers the CCITT has recently proposed that λ o lies in the range 1.95 to 1.3µm with a zero less than 0.095 ps nm - km -1. The chromatic dispersion at an arbitrary wavelength can be estimated when the two parameter λ o and S o are specified according to:[3].shown in figure 6. 4 λ S o λ o D ( λ ) = 1..4.9 T 4 λ In our analysis we observed the simulation result using the MATLAB code, where the total dispersion of single-mode fibers which is similar to the experimental result [3]. But if the dispersion slope is adjusted then the dispersion is reduced for the particular wavelength. So we can say by adjusting the dispersion slope the dispersion problem is improved then the experimental value. A wide variety of single-mode fiber refractive index profiles are capable of modification in order to tune the zero-dispersion wavelength point λ o to a specific wavelength within a region adjacent to the zero- materialdispersion (ZMD) point. The wavelength at point λ o could be shifted to longer wavelength by altering the material composition of the single-mode fiber [5]. Fig. 6 Total dispersion characteristics for singlemode fiber. 5. Conclusion In conclusion, dispersion greatly affects the single-mode fiber in the world of fiber optics technology. Although it is widely accepted that dispersion, which is measured in ps nm -1 km -1, occurs as a function of wavelength, researchers are still exploring new ways to decrease dispersion in fibers. Higher transmission speed and efficient long distance communication are the key qualities that have to be obtained in order for fiber optics to lead our world into the future. References [1] S. Haykin, Communication systems, 4th Edition, Wiley, New York, 001. [] JH Franz and VK Jain, Optical Communications Components and Systems, 15. [3] J. M. SENIOR Optical Fiber Communications Principles and Practice, nd Edition, 10-107. [4] D. Cotter et al., Nonlinear optics for high-speed digital information processing, Science 86 (1999), 153 158. [5] P. Bayvel, Future high-capacity optical telecommunication networks, Phil. Trans. R. Soc. Lond. ser. A 358 (000), 303 39. 146