Studies on Some Aspects of Light Beam Propagation Through ...

Temporal solitons
Another process in fibers which results in loss is due to Rayleigh scattering.
It is a fundamental loss mechanism occurring because of random
density fluctuations embedded in the fiber material. As a result there is
a local fluctuation in the index of refraction whlch scatters light in all directions.
The Rayleigh scattering loss is proportional to A -4 and hence,
it is dominant at short wavelength. This loss is intrinsic to any dielectric
medium. The intrinsic loss level is
3
(1.2)
where C is in the range 0.4-0.5dB/(km f.lm 4 ) depending on the constituent
of the fiber core. Successful fabrication of low loss fibers has resulted in
the wide use of fibers in optical communication. Data is sent using these
fibers. But after some distance, the pulse begins to disperse and the input
data is no longer available at the output. One needs to put repeaters
through out the transmission line for an effective data transfer.
When an electromagnetic wave interacts with the bound electrons of a
dielectric medium, the response of the medium depends upon the optical
frequency w. As a result, the refractive index depends upon the frequency
of light. This is known as chromatic dispersion. The origin of chromatic
dispersion is related to the characteristic resonance frequencies at which
the medium absorbs the electromagnetic radiation through oscillation of
bound electrons. The effect of fiber dispersion is accounted for by expanding
the mode propagation constant (J in a Taylor series about the frequency
Wo at which the pulse spectrum is centered and is written as
where
w 1 2
f3 (w) = n (w ) - = {3o + {31 (w - wo) + - {32 (w - wo) + ... , (1. 3)
c 2
drr!{3
{3n = (-)
dw n W=Wu
(m=O,l,2, ... ). (1.4)
The parameters {31 and {32 are related to the refractive index n and its
derivatives as
(1.5)
( 1.6)
where ny is the group index and Vg is the group velocity. The parameter
{32 is responsible for pulse broadening and is known as the group-velocity
dispersion parameter. The variation of {32 with wavc!ength is such that