How to Calculate Peak Power Density for a Nd:YAG Pulsed Laser?

[dark_knight3]

Hi

I have a power meter that measures a Nd:YAG laser intensity with 20 pulses per second as 200 mW. The pulsewidth is 5 ns and I have information relating to the diameter and wavelength of the beam as 3mm and 216 nm, respectively. I also have an expression the intensity or power of the beam as a function of time i.e. I(t) = C exp(-t/pulsewidth), where C is the peak power density.

I have used the equations of E = Pavg(average power)/PRR(pulse repetition rate) to get the power of each pulse.

For the calculation of the peak power density i.e. the C -term in the function representing intensity as a function of time, I need to find that value of I, which corresponds to a peak power value of the beam during it's pulsing. So for peak power, I think it's Pmax = Pavg/DC(duty cycle). So with this max intensity value, I should be able to obtain the peak power density by substituting into I = Cf(t) but what value do I use for time in the expression and since it's peak power density in W.m-2, I suppose the 3mm diameter of the beam gets factored in somehow ?? Do I also need to use the wavelength of the laser in the calculations ?

 

[Jhero]

Hi there,

Thank you for sharing your setup and equations. It seems like you have a good understanding of the basic concepts involved in calculating the peak power density of your Nd:YAG laser. Let's break down the different components and how they relate to the final calculation.

First, let's define some terms. Peak power is the maximum power output of a single pulse, while average power is the total power output over a given time period. Pulse repetition rate is the number of pulses per second. Duty cycle is the ratio of the pulse width to the period between pulses. In your case, the duty cycle would be 5 ns/50 ms = 1x10^-7.

Now, let's look at your equation for intensity as a function of time, I(t) = C exp(-t/pulsewidth). Here, C is the peak power density, so in order to solve for it, we need to find the value of I at the peak power time. This will give us the peak power density in W.m^-2.

To find the peak power time, we can use the equation t = pulsewidth * ln(1/DC). In your case, the pulsewidth is 5 ns and the duty cycle is 1x10^-7, so the peak power time is approximately 5.00000005 ns.

Now, we can substitute this value into your equation for intensity and solve for C. This will give us the peak power density in W.m^-2.

As for factoring in the diameter and wavelength of the beam, these values are important for determining the total power output of the laser, but they are not directly related to the peak power density. The peak power density is a measure of the intensity of the beam at a specific point in time, so the diameter and wavelength are not directly involved in the calculation.

I hope this helps clarify the process for calculating the peak power density of your laser. Let me know if you have any further questions or concerns. Best of luck with your research!