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 on the figure below.

laser divergence
Angle 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.

red laser beam divergence close  red laser beam divergence far
Beam divergence for typical 660nm red diode laser @9.6m

green laser beam divergence close  green laser beam divergence far
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()=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:

tan()=(12/2-3/2)/9600 => ~ 0.000468749965 rad ~ 4.6 millirad@9.6m.

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:

tan()=(11/2-2/2)/9600 => ~ 0.0005208332862 rad ~ 5.2 millirad@9.6m.

Now let's measure the beam distribution of the second beam. For this, we slice the beam target with Iris at angles (k)=2*k*/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}.

laser beam distribution slices
Beam distribution slices at angles /4

Follow the distributions:

beam distribution slice 0  beam distribution slice 1
D((k)), k=0, 1.

beam distribution slice 2  beam distribution slice 3
D((k)), k=2, 3.

If we pick the first distribution, we can see that its profile is almost Gaussian G(x,,), but not quite:

beam distribution vs gaussian distribution
D((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 (k).

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