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 selfphase 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
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.
perfectly constant during the pulse.
frequency remains
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
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.
Result: High intensity sharply peaked soliton pulse
changes neither its shape nor its spectrum as it
travels along the fiber.
Hence, provided pulse energy is sufficiently strong, pulse
shape is maintained.
23. Soliton Pulses
Zero dispersion point = 1320 nm
For wavelengths shorter than 1320 nm ß2 is
+ive
For longer wavelengths ß2 is -ive
Thus ,soliton operation is limited
to the region greater than 1320 nm.
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.
1.
2.
3.
First term represents GVD effects of fiber
2nd term denote the fact that refractive index of
fiber depends on light intensity. Though SPM, this
phenomenon broadens the frequency spectrum of
a pulse .
3rd 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
dφnonlin = u(t)2 dz = sech2(t)dz …….(3)
For dispersion effect
Dφdis = [1/2- sech2(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
1.
Normalized Time T0
2.
Normalized distance or
Dispersion length Ldis
It is measure of period of soliton
3.
Soliton peak power Ppeak
T0 = 0.567 Ts
Ts = soliton pulse
31. Soliton Parameters
Ldis =2 πc T0 /
Soliton peak power Ppeak =
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 Ldis
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-tozero format. This condition constrain the achivable
bit rate.
33. Soliton Width & Spacing
If TB = width of bit slot
B = bit rate , soliton half max. width = Ts
Then,
B = 1/ TB = 1/ 2s0To
Where the factor 2s0 = TB / 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/soli
tons.html
