## Beam Divergence and Distribution In Two Typical Lasers

### Version 1.0 of 23/10/2009-12:00 a.m.

Typical laser beams diverge at large distances. The beam divergence, is defined to be the angle φ on the figure below. Angle φ specifies the beam divergence

One can measure the divergence directly, using two photographs of the laser beam: One at a small distance and a second at a relatively large distance. Follow two pairs of photographs for two typical laser beams, at a reference distance on the left and at a distance of 9.6m on the right.  Beam divergence for typical 660nm red diode laser @9.6m  Beam divergence for typical 532nm green diode laser @9.6m

For the first pair, according to the first figure and considering the width of the beam up to the first diffraction ring, the divergence @9.6m, would be such that:

tan(φ)=AC/BC. With BC = 9.6m = 9600mm. For the first pair, the beam on the left side has a diameter of ~3mm, and on the right a diameter of ~12mm. Therefore the divergence of the red laser diode @9.6m is such that:

For the second pair, the beam on the left side has a diameter of ~2mm, and on the right a diameter of ~11mm. Therefore the divergence of the green laser diode @9.6m is such that:

Now let's measure the beam distribution of the second beam. For this, we slice the beam target with Iris at angles α(k)=2*k*π/n, with n=8, and k in {0,1,2,3,..7}. Because the slices are symmetric past k=3, it suffices to run k in {0,1,2,3}. Beam distribution slices at angles π/4  D(α(k)), k=0, 1.  D(α(k)), k=2, 3.

If we pick the first distribution, we can see that its profile is almost Gaussian G(x,σ,μ), but not quite: D(α(k)), k=0 and 16000*G(x,20,-5)

Because the slices are not symmetric, the green laser beam is then necessarily astigmatic, with respect to at least one angle α(k). 