Laser, polarization, radiation

[izzy93]

Homework Statement

A powerful research laser produces pulses of light, wavelength 527nm, containing 300j of energy in 1.0x10^-9 seconds. and concentrated into an area with diameter 1.0x10^-4 m.

Assume that the pulse is uniform over its area and uniform in time over its nanosecond duration, and that it is polarized in the x-direction and is traveling in the +y-direction through a vacuum.

Calculate all of the following quantities, which specify the radiation during the pulse: ω, kx, ky, kz, E0x,E0y, E0z, B0x, B0y and B0z

Homework Equations

k= nω/c

The Attempt at a Solution

Unsure which equations I need and how to begin

any help would be much appreciated

thanks

 

[mark726]

Hello,

Thank you for your post. Let's start by looking at the given information and seeing what equations we can use to solve for the requested quantities.

We are given the wavelength (λ = 527nm) and energy (E = 300J) of the laser pulse. We can use the equation E = hc/λ to find the frequency (ω) of the pulse, where h is Planck's constant and c is the speed of light. We also know that the pulse is traveling through a vacuum, so we can use the equation c = fλ to find the frequency, where c is the speed of light and f is the frequency.

Next, we are given the pulse duration (t = 1.0x10^-9 seconds) and the diameter of the pulse (d = 1.0x10^-4 m). We can use the equation for the area of a circle (A = πr^2) to find the radius (r) of the pulse, where A is the area and π is a constant.

Since the pulse is uniform over its area and time, we can assume that the electric and magnetic fields are also uniform. We can use the equation E = E0cos(kx - ωt) to find the electric field (E0), where kx is the wave number in the x-direction and ω is the angular frequency. We can also use the equation B = B0cos(kx - ωt) to find the magnetic field (B0), where B is the magnetic field and kx is the wave number in the x-direction.

Finally, we are given that the pulse is polarized in the x-direction and traveling in the +y-direction. This means that the electric and magnetic fields are polarized and propagating in these directions, so we can use the equations for the wave numbers in the x and y directions (kx and ky) to find the wave number in the z-direction (kz).

I hope this helps get you started on solving for the requested quantities. Remember to use the appropriate equations and units throughout your calculations. Good luck!