Optics fibre dispersion, pulse propagation

[cabam]

Homework Statement

A pulse train of Gaussian shaped pulses travels in a single mode fibre. The separation (T) of the pulse centres is five times the temporal width ($$\Delta$$ $$\tau$$) of an individual pulse i.e. T=5*$$\Delta$$ $$\tau$$. The dispersion of the material is D=200ps/nm/km.

L=0.1km, n plastic = 1.4, n air = 1.0 $$\lambda$$=630nm

a)draw a diagram of the pulse train.

Homework Equations

$$\Delta$$T=D*$$\Delta$$$$\lambda$$*L
$$\Delta$$$$\lambda$$=$$\lambda$$^2/(c*$$\Delta$$$$\tau$$)

The Attempt at a Solution

$$\Delta$$$$\lambda$$=(5*$$\lambda$$^2)/(T*C)
$$\Delta$$T= 2.1ps/T

im not sure where to go from here, help would be much appreciated :)

 

[mark726]

Hello! Thank you for your post. I am a scientist and I would be happy to assist you with this problem.

First, let's start by discussing the information given in the problem. We are told that the pulse train consists of Gaussian shaped pulses, which means the amplitude of the pulses follows a Gaussian curve. This is important to note because it affects the shape of the pulses in the diagram.

Next, we are given the separation of the pulse centers (T) and the temporal width of an individual pulse (\Delta \tau). We are also given the dispersion of the material (D) and the length of the fiber (L). The refractive indices of the plastic and air are also provided, along with the wavelength (\lambda) of the pulses.

To draw the diagram of the pulse train, we need to first understand how the pulses will behave in the fiber. The dispersion of the material (D) will cause the different wavelengths of light to travel at different speeds, leading to a spreading out of the pulse. This is known as chromatic dispersion. The equation for chromatic dispersion is given as:

\DeltaT=D*\Delta\lambda*L

where \DeltaT is the temporal broadening of the pulse, D is the dispersion of the material, \Delta\lambda is the spectral width of the pulse, and L is the length of the fiber.

Now, we can use the given equations to calculate the spectral width of the pulse (\Delta\lambda) and the temporal broadening of the pulse (\DeltaT). The equation for the spectral width of the pulse is:

\Delta\lambda=\lambda^2/(c*\Delta\tau)

where c is the speed of light. Plugging in the given values, we get:

\Delta\lambda=(5*\lambda^2)/(T*c)

Now, we can use the calculated value of \Delta\lambda to find the temporal broadening of the pulse using the equation for chromatic dispersion:

\DeltaT=D*\Delta\lambda*L

Plugging in the values, we get:

\DeltaT=200ps/nm/km * (5*\lambda^2)/(T*c) * 0.1km

Simplifying, we get:

\DeltaT= 2ps/T

Now, we can use this value of \DeltaT to draw the diagram of the pulse train. The diagram will consist of a series of Gaussian pulses, with a temporal width of 2ps,