In
an optical fibre, different
rays travel different paths along the fibre,
leading to different travel times.
This causes a light pulse to spread out as it
travels along the fibre, resulting in information loss.
The delay time should be minimised in
designing a fibre. Consider
a ray that travels a distance L along a fibre axis and another that
is reflected, at the critical angle, as
it travels to the same distance as the first.
(a) We have to show that the difference
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Solution: Click For PDF Version We will refer to the problem 602, particularly to the figure in it for answering this problem.
As the
refractive index of core of the fibre cable is
As the
refractive index of the cladding is
A pulse that moves inside the fibre by total internal reflection covers a distance L along the axis by travelling distance
Therefore, the travel time for the pulse that moves inside the cable through total internal reflections will be
Hence, the
time difference
(b)
We calculate
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in the time of arrivals is given by
is the index of refraction of the core and
is the index of refraction of the cladding.
(b) We have to evaluate
and
,
with
.
is given by
