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QUESTION:
A light pulse with wavelength 850 nm passes through a single-mode silica fiber.
For Silica Use d^2n/dx^2 =3×10^10m-2
(a) Determine the time spread of the pulse per unit length due to material dispersion if the spectral width is 20 nm.
(b) Repeat if the spectral width is 2 nm.
ANSWER:
a) Time spread is 0.00051 per meter
b) Time spread is 0.000051 per meter
EXPLANATION: Time spread is the time it takes the pulse to spread out to a distance, which is in relation with the dispersion of the material.
Tm = Dm × L × ∆x ............(1)
Tm = Time spread
Dm = material dispersion coefficient
L = wavelength of the fiber
∆x = Spectra width
STEP 1: CALCULATE DISPERSION COEFFICIENT (Dm) OF SILICA FIBER;
Dm = (-x/c) ( d^2n/dx^2).......(2)
Period= -x/c..........(3)
x is the wavelength
c is the speed of the wave
Since period is a constant in this question, and -x/c is the period
For Silica:
d^2n/dx^2 = 3×10^10 m-2
therefore using equation 2
Dm = d^2n/dx^2
Dm = 3e10m-2
(a) Find Tm when ∆x = 20nm.
Using equation 1
L = 850nm = 8.5e-7m
Dm = 3e10m-2
∆x = 20nm = 2e-8m
Using equation 1
Tm = 3e10 × 8.5e-7 × 2e-8 = 0.00051
Tm = 5.1e-4/m
(b) Find Tm where ∆x = 2nm
Using equation 1
L = 850nm = 8.5e-7m
Dm = 3e10m-2
∆x = 2nm = 2e-9m
Using equation 1
Tm = 3e10 × 8.5e-7 × 2e-9 = 0.000051
Tm = 5.1e-5/m
