FIBER OPTICS. Prof. R.K. Shevgaonkar. Department of Electrical Engineering. Indian Institute of Technology, Bombay. Lecture: 36

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1 FIBER OPTICS Prof. R.K. Shevgaonkar Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture: 36 Solitonic Communication Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 1

2 Continuing with the preceding discussion on Optical Solitons, we arrived at an expression for the differential equation containing the time varying function V (as given in equation (35.23)) which is given below: (36.1) In this section, we shall begin with the solution to the above equation. We suggested that, in order to solve the equation, we use an intuitive approach by multiplying both sides by and then integrating both sides w.r.t.. Therefore, the expression modifies to: ( ) ( ) (36.2) The term C in the above equation is an arbitrary constant of integration which has to be solved by using boundary conditions. When, then the envelope remains unchanged i.e. and also. Substituting this boundary condition in equation (36.2) we obtain C=0. Applying the normalized condition: i.e. V=1 and at which represents the peak of the normalized pulse amplitude, we obtain the value of K=0.5. Hence, we can re-write equation (36.2) as: (36.3) Solving the above differential equation by integration, we obtain: (36.4) Combining the above amplitude function and the phase function from equation (35.22), we obtain a solution of the NLS as: (36.5) The above solution has an important significance- the fundamental soliton (N=1) can only be generated when the pulse has a shape is given by. That is, the cancellation of the dispersion and the non-linearity regimes on an optical fiber, with nonlinearity length equal to dispersion length, would take place only when the pulse has a hyperbolic secant shape. The exponent in the above solution is simply, the phase that the hyperbolic secant pulse accumulates with distance as it moves along the optical fiber. The above pulse shape is, hence, known as the Fundamental Soliton shape. Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 2

3 The above analysis, thus, suggests that if we can generate a fundamental soliton shape, then this shape would travel undistorted along the optical fiber provided that the balancing between the non-linearity and the dispersion is maintained. The spontaneous question that comes to the mind is that- what would happen to an arbitrary pulse shape launched into the optical fiber in the presence of non-linearity and dispersion? Would this arbitrary pulse form a soliton? It is very interesting to know that there is some kind of a non-linear phenomenon which does a re-shaping of the pulse in the presence of dispersion. If the non-linearity effect is sufficiently strong, any arbitrary pulse, naturally, gets re-shaped into a hyperbolic secant in the presence of non-linearity and dispersion. The amount of pulse energy that does not fit into the hyperbolic secant shape is dispersed. It is this secant which then propagates along the optical fiber. The following simulated result shows the pulse evolution that takes place during re-shaping of the arbitrary pulse. Figure 36.1: Pulse re-shaping to form soliton A super-gaussian pulse having the following distribution has been launched as an input to the fiber simulator. [ ( ) ] (36.6) It is also ensured that the power in the super-gaussian pulse is more than what is needed into the fundamental soliton. This is done by taking the pulse power such that L NL <L D. The above diagram shows how the initial super-gaussian pulse naturally evolves into a hyperbolic secant pulse with distance in the presence of sufficiently strong nonlinearity. Thus it is not necessary to generate a hyperbolic secant to generate a fundamental soliton. Any arbitrary pulse with appropriate power can be launched into the optical fiber in the presence of sufficiently strong non-linearity which would the naturally be re-shaped into a hyperbolic secant by the non-linearity. This re-shaped pulse would then propagate along the optical fiber. The amount of pulse energy that does not fit into the Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 3

4 fundamental soliton gets dispersed. The above simulation has been performed for different values of the exponent m and the amounts of pulse energy retained into the soliton are calculated. The results are shown in the following table: Table 36.1: Simulation results Input Pulse Shape Energy retained in soliton (%) Gaussian (m=1) 99 Super-Gaussian (m=3) 92 Rectangular (m ) 86 Transmission of data via Solitonic propagation involves multiple solitons to be transmitted along the fiber. Also, in WDM type applications, there may be multiple solitons transmitted simultaneously on the optical fiber. The question that comes to an inquisitive mind is that- is the Solitonic propagation affected by presence of multiple solitons? The answer to this question is Yes. The solitons, inside an optical fiber, behave analogous to charged particles. Following simulation shows the manner in which the simultaneous propagation of two solitons takes place inside an optical fiber: Figure 36.2: Interaction between two solitons Interaction between solitons is similar to the attraction and repulsion between charged particles. For the above simulation we consider two identical Gaussian pulses, each with a standard deviation of T 0. These two pulses are separated by distance 3T 0. As shown in above figure, as the two pulses move along the optical fiber, the distance between them starts to decrease and the two pulses merge into each other in a gradual manner to form a single pulse with higher amplitude. This single pulse then starts to reseparate out, as it moves further along the optical fiber, to form two identical pulses which recombine to the single pulse. This trend of separation and recombination takes place repeatedly as the pulses move along the optical fiber. Thus, there is some sort of periodic behaviour that takes place in the pulse interactions inside the optical fiber with distance. That is, if we look at any arbitrary point along the length of the optical fiber, depending on the distance, we may see a single pulse or two pulses. Even with three pulses, we do have Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 4

5 aperiodic merging and re-separation with distance inside the optical fiber as suggested by the simulation results for three identical pulses in the figure below: Figure 36.3: Interaction between three pulses The above phenomenon of merging and separation of pulses (solitons) with distance is, certainly not, a desirable phenomenon as far as data transmission on optical fiber is concerned because if the data bits merge into each other, the data cannot be recovered. Thus, though a soliton appears to be a promising distortion-free pulse that could travel large distances, in presence of multiple solitons, the above proposition does not hold. A spontaneous question based on the soliton-charged particle analogy is- what is the minimum practical distance of separation between the two solitons to stop the occurrence of merging? Simulations show that the pulses must be separated about 8-10 times T 0. Thus the pulse train looks like: Figure 36.4: Solitonic Pulse train One observation that is very clear from the above figure is that the pulse scheme to be used in Solitonic propagation has to be Return-to-zero (RZ) scheme. Secondly, the duty cycle of the pulse should only be 10-20%. If it is more than this, the pulses would start Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 5

6 to interact as there would not be enough separation between them. Thus, Solitonic propagation is realizable only when the above two basic conditions are met. It is thus clear that the bandwidth required for the Solitonic propagation is several orders of magnitude higher than the data rate. This requirement limits the maximum possible data rate achievable in Solitonic propagation to about 10Gbps. One of the important and rather inherent requirements of Solitonic propagation is the maintenance of strong non-linear conditions throughout the transmission so the balancing between dispersion and non-linearity prevails. If at any point of time or length, the non-linearity goes weaker, the dispersion would quickly take over and then the game is lost. So it is utterly necessary to ensure that at every point during transmission, the nonlinearity length remains smaller than dispersion length. But if we take into account the loss on the optical fiber, the non-linearity length tends to increase due to the drop in the power level due to attenuation. Thus, the power of the input pulse to the fiber has to be such that even after the loss in the optical fiber, the characteristic non-linearity remains less than the dispersion length on the optical fiber. But, increasing the power in the pulse leads to a decrease in the non-linearity length L NL which, in turn, leads to generation of higher order solitons (N>1) as suggested by equation (35.18). Higher order solitons (N>1) have shapes different from that of a fundamental soliton and are often complicated. For example, the second order soliton (N=2) has a pulse shape given by: { } (36.7) It is clear from the above expression of a pulse shape that, even for N=2, the soliton assumes a shape that is quite complicated. This further complicates the use of this pulse in transmission of data through the optical fiber. Therefore excitation of higher order solitons is strongly prohibited in data transmission. In other words, arbitrary increase of input pulse power is not a solution for sustained non-linearity in an optical fiber. This limitation points out that we, in deed, are in search of some sort of a mechanism of distributed compensation for the power loss in the optical fiber along its length rather than a lumped amplification of pulse power at a single location. This mechanism should also take care that the power at any location does not exceed the limit at which there emerges the possibility of generation higher order solitons. In other words, we are looking for a distributed amplification mechanism which provides exact compensation for the power loss in the optical fiber at every location so that the power of the pulse remains almost constant throughout the optical fiber. In such a mechanism, under no circumstances does the value of N reach 2 but always remains well below that. Such a distributed amplification mechanism is provided by Raman Amplification. This amplification scheme is based on Raman Scattering, which is also a non-linear effect in an optical fiber. Raman Scattering and the construction of a Raman Amplifier based on Raman Scattering shall be discussed in subsequent discussions. Propagation of optical solitons has also been experimentally demonstrated in the laboratory by considering loops of optical fibers to emulate long distance communication links. Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 6