Beam profile inside the resonator

We have fixed the cavity length to keep it stable. Now we will look in details at the beam profile inside the resonator.

We already know that the waist will be located on the plane mirror : the beam has to bounce back on itself.

Let us first determine the size of the beam on each mirror (w0 on the plane mirror and w1 on the spherical one), as well as the beam's divergence and the associated Rayleigh length ZR :

A simple approach is to work with the equivalent resonator (see above), with a length .

If z=0 is taken on the plane mirror, we can write that for z = d (that is on the spherical mirror) the radius of curvature of the laser beam is the same as the radius of curvature of the spherical mirror (to ensure that the beam bounces back on the same way). But we know how R varies with z (see course), so that we can write :

we then easily deduce that :

with d = L+l/n = 80+10/1,8 = 85,5 mm and R = 100 mm, we obtain :

ZR = 35,2 mm and w0 = 110 µm (the wavelength is 1064 nm)

The divergence is which is equal to 3 mrad.

To obtain the beam waist on the output coupler, we only need the following formula :

which leads for z=d to :

or w1 = 286 µm.

The beam profile inside the resonator is consequently depicted on figure 4 :