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I have two lasers with different intensity distributions (shown below) — one is Gaussian and the other one is rectangular (having the shape of a Fresnel diffraction pattern at the target).

I am trying to compare the efficacy of the two lasers for burning a certain material (I am really comparing their wavelengths). But the two lasers have different total powers. I was told that the only way I can get a more direct comparison is to adjust the spot sizes so that the two have similar "intensities", i.e.,

$$\frac{P_{\text{Gaussian}}}{A_{\text{Gaussian}}}\approx\frac{P_{\text{Rectangular}}}{A_{\text{Rectangular}}}.$$

In many places, I have encountered people stating an intensity value in this way (dividing the total power of the beam by the beam cross-sectional area: ##I=P/A##). However, to me, it seems that this only works if you have a constant intensity distribution.

In fact, in optics textbooks, the intensity of a Gaussian beam is evaluated as the intensity of a

$$I(x,y,z)=I_{0}\left[\frac{w_{0}}{w(z)}\right]^{2}\exp\left[-2\frac{\left(x^{2}+y^{2}\right)}{w(z)^{2}}\right].$$

where ##w(z)## is the radius of the beam at a distance ##z##. The concept seems to be only applicable to a given point — we can't really speak about the intensity of a beam spot as a whole. So does the usage of ##I=P/A## have any validity?

Is there any way I can get a more like-for-like comparison when the distributions of the lasers are different?

Any suggestions would be greatly appreciated.

I am trying to compare the efficacy of the two lasers for burning a certain material (I am really comparing their wavelengths). But the two lasers have different total powers. I was told that the only way I can get a more direct comparison is to adjust the spot sizes so that the two have similar "intensities", i.e.,

$$\frac{P_{\text{Gaussian}}}{A_{\text{Gaussian}}}\approx\frac{P_{\text{Rectangular}}}{A_{\text{Rectangular}}}.$$

In many places, I have encountered people stating an intensity value in this way (dividing the total power of the beam by the beam cross-sectional area: ##I=P/A##). However, to me, it seems that this only works if you have a constant intensity distribution.

In fact, in optics textbooks, the intensity of a Gaussian beam is evaluated as the intensity of a

*single point*within the x-y plane (power transferred per unit area):$$I(x,y,z)=I_{0}\left[\frac{w_{0}}{w(z)}\right]^{2}\exp\left[-2\frac{\left(x^{2}+y^{2}\right)}{w(z)^{2}}\right].$$

where ##w(z)## is the radius of the beam at a distance ##z##. The concept seems to be only applicable to a given point — we can't really speak about the intensity of a beam spot as a whole. So does the usage of ##I=P/A## have any validity?

Is there any way I can get a more like-for-like comparison when the distributions of the lasers are different?

Any suggestions would be greatly appreciated.