Calculating Nd-YAG Laser Parameters: Beam Size, Power Density, and Peak Power

[joslaz90]

Hey guys!

I am currently working on some tasks to improve and expand my skills,
but I can not go on with the following task

An Nd-YAG laser (D=5mm diameter) is focussed with a lens (f = 200mm).

I: How big is the laser beam at its waist? (Solved)

II: What is the largest bundle behind the lens occurring in the optical axis (beam axis)? (Solved)

III: How long is the zone around the waist in which the beam is smaller than 0.2mm? (Solved)

IV: What is the average power density? (P= 3 Watt)

V: What is the peak power when the laser delivers the 3 watts in the form of 10000 pulses per second, each of which is 20 ns long?

Already identified solutions

To I:

(1060nm wavelength)

With
d= 2,44 α x f / D
I get as size for the laser beam at a waist of 1.035x10^-4m

((2,44x1.06x10^-6m x 2 x 10^-1m)/5x10^-3m)

To II:

tan α = 0,5D - 0,5 d /f

= 2,5 x 10^-3m - 0,5 x 1.035 x 10 ^-4m / 2 x 10 ^-1m
= 0,01225
tan ^-1(0,01225)=0,702
α = 0,7°

To III:

tan α = 0,2mm / a
a = 0,2mm / tan α
=16,3mm

To IV:
I = P / A =

P = 3 W

I= 3W / 0,5 x 1.035 x 10^-4m²Pi

Am I right with these considerations / approaches?

Can you help me with the last two tasks?

 

[anathema]

Hi there!

As a fellow scientist, I would be happy to help you with the last two tasks. Here are my solutions:

IV: To calculate the average power density, we need to first calculate the area of the laser beam at its waist. We can use the formula for the area of a circle, A=πr^2, where r is the radius of the beam at its waist. Plugging in the value we calculated for the beam size at its waist (1.035x10^-4m), we get an area of 3.35x10^-8m^2.

Now, we can calculate the average power density using the formula I=P/A, where P is the power (3 watts) and A is the area we just calculated. This gives us an average power density of 8.96x10^7 watts/m^2.

V: To calculate the peak power, we need to first determine the energy of each pulse. We can use the formula E=Pt, where P is power (3 watts) and t is time (20 nanoseconds or 20x10^-9 seconds). This gives us an energy of 6x10^-8 joules per pulse.

Now, we can calculate the peak power using the formula P= E/t, where E is the energy per pulse and t is the time between pulses (1/10000 seconds or 1x10^-4 seconds). This gives us a peak power of 6x10^-4 watts.

I hope this helps and let me know if you have any further questions or need clarification on anything. Good luck with your tasks!