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Main Question or Discussion Point
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 crosssectional 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 xy 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 likeforlike 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 crosssectional 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 xy 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 likeforlike comparison when the distributions of the lasers are different?
Any suggestions would be greatly appreciated.
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