Solitons _+23929042873nxjsj938292 and explanation

Solitons

1. Suwetha.s , b.tech ece , Acet. Solitons in Optical Fiber Communication

2. Contents Introduction Solitons in Fiber-Optics History of solitons in OFC In OFC, Solitons Soliton Pulses Soliton Parameters Soliton Width & Spacing

3. Introduction A solitary wave is a wave that retains its shape, despite dispersion and nonlinearities. A soliton is a pulse that can collide with another similar pulse and still retain its shape after the collision, again in the presence of both dispersion and nonlinearities.

4. Soliton First observation of Solitary Waves in 1838 John Scott Russell (1808-1882) Scottish engineer at Edinburgh

5. Resulting water wave was of great height and traveled rapidly and unattenuated over a long distance. After passing through slower waves of lesser height, waves emerge from the interaction undistorted, with their identities unchanged.

6. Solitons in Fiber-Optics – Why ? Data transfer capabilities - copper telephone wires ~ 2 dozen conversations - mid-1980's pair of fibers ~12,000 conversations (equivalent to ~ 9 television channels) - early 1990's solitons in fibers ~ 70 TV channels (transmission rate of 4 Gb/s) Increase transmission rate, and distance between repeater stations Solitons' inherent stability make long-distance transmission possible without the use of repeaters, and could potentially double transmission capacity as well

7. History of solitons in OFC In 1973, Akira Hasegawa of AT&T Bell Labs was the first to suggest that solitons could exist in optical fibers , due to a balance between self-phase modulation and dispersion. Solitons in a fiber optic system are described by the Manakov equations. In 1987 the first experimental observation of the propagation of a solution, in an optical fiber was made In 1988, soliton pulses over 4,000 kilometers were transmitted using a phenomenon called the Raman effect

8. History of solitons in OFC In 1991, a Bell Labs research team transmitted solitons error-free at 2.5 gigabits per second over more than 14,000 kilometers, using erbium optical fiber amplifiers In 1998, combining of optical solitons of different wavelengths was done, a data transmission of 1 terabit per second was demonstrated In 2001, the practical use of solitons became a reality

9. In OFC, Solitons Soliton is very narrow, high intensity optical pulses. Retain their shape through the interaction of balancing pulse dispersion with non linear properties of an optical fiber. GVD causes most pulses to broaden in time, but soliton takes advantage of non-linear effects in silica (SPM) resulting from Kerr nonlinearity, to over come the pulse broadening effects of GVD

10. All wave phenamenon :A beam spreads in time and space on propagation SPACE:BROADENING BY DIFFRACTION TIME: BROADENING BY GVD

11. Broadening + Narrowing Via a Nonlinear Effect = Soliton (Self-Trapped beam Spatial/Temporal Soliton

12. In OFC, Solitons Depending on the particular shape chosen, the pulse either does not change its shape as it propagate, or it undergoes periodically repeating change in shape. The family of pulse that do not change in shape are called Fundamental Soliton . The family of pulse that undergo periodic shape change are called Higher order soliton.

13. In OFC, Solitons On the left there is a standard Gaussian pulse, that's the envelope of the field oscillating at a defined frequency. frequency remains perfectly constant during the pulse.

14. In OFC, Solitons Now we let this pulse propagate through a fiber with D > 0, it will be affected by group velocity dispersion. The higher frequency components will propagate a little bit faster than the lower frequencies , thus arriving before at the end of the fiber. The overall signal we get is a wider pulse ,

15. Effect of self-phase modulation on frequency At the beginning of the pulse the frequency is lower, at the end it's higher. After the propagation through ideal medium, we will get a chirped pulse with no broadening

16. In OFC, Solitons two effects introduce a change in frequency in two different opposite directions. It is possible to make a pulse so that the two effects will balance each other . Considering higher frequencies, linear dispersion will tend to let them propagate faster, while nonlinear Kerr effect will slow them down. The overall effect will be that the pulse does not change while propagating

17. Soliton Pulses No optical pulse is monochromatic.. Since the medium is dispersive the pulse will spread in time with increasing distance along the fiber.

18. Soliton Pulses In a fiber a pulse is affected by both GVD and Kerr nonlinearity. When high intensity optical pulse is coupled to fiber, optical power modulates the refractive index This induces phase fluctuations in the propagating waves, thereby producing chirping effect in the pulse. Result: Front of the pulse has lower frequencies and the back of the pulse has higher frequencies than the carrier frequency.

19. Soliton Pulses 1.Medium with Positive GVD Leading part of the pulse is shifted toward lower frequencies , so the speed in that portion increases. In trailing half, the frequency rises so the speed decreases. This causes trailing edge to be further delayed. Also energy in the centre of pulse is dispersed to either side, and pulse takes on a rectangular wave shape. These effects will severely limit high speed long distance transmission if the system is operated in this condition

20. Soliton Pulses

21. Soliton Pulses 2.Medium with Negative GVD GVD counteracts the chirp produced by SPM. GVD retards the low frequencies in the front end of pulse and advances the high frequencies at the back. Hence, provided pulse energy is sufficiently strong, pulse shape is maintained. Result: High intensity sharply peaked soliton pulse changes neither its shape nor its spectrum as it travels along the fiber.

22. Soliton Pulses

23. Soliton Pulses Zero dispersion point = 1320 nm For wavelengths shorter than 1320 nm ß 2 is +ive For longer wavelengths ß 2 is -ive Thus ,soliton operation is limited to the region greater than 1320 nm.

24. Soliton Pulses Nonlinear Schrödinger (NLS) equation

25. Soliton Pulses Here, u(z,t) = pulse envelope function z = propagation distance along the fiber N = order of soliton α = coefficient of energy gain per unit length Negative Value of α representing energy Loss

26. Soliton Pulses For 3 RHS terms in NLS eqn. First term represents GVD effects of fiber 2 nd term denote the fact that refractive index of fiber depends on light intensity. Though SPM, this phenomenon broadens the frequency spectrum of a pulse . 3 rd term represents the effect of energy loss or gain.

27. Soliton Pulses For N = 1 the solution of the equation is simple and it is the fundamental soliton For N ≥ 2 It does change its shape during propagation, but it is a periodic function of z . Solution of NLS Eqn. for fundamental soliton is given by U(z,t) = sech(t)exp(jz/2)………..(2) where sech(t) is hyperbolic secent function. This is a bell shaped pulse

28. Soliton Pulses In NLS eqn. first order effects of dispersive and non linear terms are just complimentary phase shifts given by-- For nonlinear process d φ nonlin = u(t) 2 dz = sech 2 (t)dz …….(3) For dispersion effect D φ dis = [1/2- sech 2 (t) ] dz ………(4) Plot of these terms & their sum is a constant. Upon integration, sum simply gives a phase shift of z/2,common to entire pulse. Since such a phase shift do not change shape of pulse, soliton remains completely non dispersive.

29. Soliton Parameters Normalized Time T Normalized distance or Dispersion length L dis It is measure of period of soliton Soliton peak power P peak T = 0.567 T s T s = soliton pulse

30. Soliton Parameters

31. Soliton Parameters L dis =2 π c T 0 / Soliton peak power P peak = For N >1, soliton pulse experiences periodic changes in its shape & spectrum as it propagate through fiber. It resume its initial shape at multiple distances of soliton period ,given by L = π /2 L dis

32. Soliton Width & Spacing Soliton solution to the NLS eqn. holds valid when individual pulses are well separated. To ensure it ,soliton width must be small fraction of bit slot. To ensure this, the soliton width must be small fraction of bit slot. So for eliminating this we use the Non-return-to-zero format. This condition constrain the achivable bit rate.

33. Soliton Width & Spacing If T B = width of bit slot B = bit rate , soliton half max. width = Ts Then, B = 1/ T B = 1/ 2s To Where the factor 2s = T B / To is normalized separation b/w neighboring soliton.

34. References Optical Fiber Communication By Gerd Keiser,Third edition Soliton (optics) From Wikipedia.com http://www.ma.hw.ac.uk/solitons/ http://people.deas.harvard.edu/~jones/solitons/solitons.html

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