Wave Number Range: 633nm Laser & 100MHz Radio

[Winzer]

Homework Statement

A 1ns pulse of electromagnetic waves would be 30cm long.
a) Consider such a pulse of 633 nm wavelength laser light. Find its central wavenumber and the range of wave numbers it is comprised of.
b) Repeat a except for a 1ns pulse of 100MHz radio
waves.

Homework Equations

$$k=\frac{2\pi}{\lambda}$$

The Attempt at a Solution

I got the central wavenumber with the above equation. But I am at a lost on where to go from there.

 

[Winzer]

Do I have to deal with the gaussian wave packet & fouier transform?

 

[Moetasim]

The central wavenumber for the 633nm laser light would be 9.95 x 10^6 m^-1. To find the range of wave numbers, we need to consider the frequency range of the pulse. Since it is a 1ns pulse, the frequency would be 1 GHz (1/1ns). Using the relation v=fλ, we can find the wavelength range to be 0.3m to 300m. Plugging these values into the wavenumber equation, we get a range of 3.33 x 10^6 m^-1 to 3.33 x 10^9 m^-1. This means that the pulse of 633nm laser light is comprised of a range of wave numbers from 3.33 x 10^6 m^-1 to 3.33 x 10^9 m^-1.

For the 1ns pulse of 100MHz radio waves, the central wavenumber would be 3 x 10^8 m^-1 (using the equation k=\frac{2\pi}{\lambda}). The frequency range for this pulse would be 100MHz to 100GHz, giving a wavelength range of 3m to 3 x 10^4 m. Plugging these values into the wavenumber equation, we get a range of 3.33 x 10^7 m^-1 to 3.33 x 10^11 m^-1. This means that the pulse of 100MHz radio waves is comprised of a range of wave numbers from 3.33 x 10^7 m^-1 to 3.33 x 10^11 m^-1.