Question

A light pulse with wavelength 850 nm passes through a single-mode silica fiber.

Answer 1

Answer:

Answer for the question:

A light pulse with wavelength 850 nm passes through a single-mode silica fiber.

(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.

is explained in the attachment.

Explanation:

Answer 2

Your question is incomplete, as you have not provided all the information needed, please let me assume this to be your question;

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