Mode Matching calculation for green beam - Yarm

After measuring the beam radius out from the Faraday for the green, I made the calculation to match the green beam mode with the IR mode inside the arm.

The beam waist after the Faraday is elliptical, and I found the following value for the waist:

w0x = 3.55e-5 m @ z0x = -0.042 m

w0y = 2.44e-5 m @ z0y = -0.036 m

(the origin of the z axis is the output of the Faraday, so the waist is inside the Faraday itself)

I did the calculation using a la mode, using as beam waist and its position the following values:

w0 = sqrt(w0x*w0y) = 2.943e-5 m @ z0 = (z0x+z0y)/2 = -0.039 m

The results are shown in the attached plots.

                      Focal length (m)             position (m)

lens1            0.125                                0.1416

lens2            0.100                                0.5225

L                    1.000                                1.5748 (fixed lens used to focus transmitted beam)

As the first plot shows, the green beam size on the ETMY is about 6mm. My concern is that it could be too big.

The third plot shows the X and Y section of the beam. It is strongly elliptical, but nevertheless the coupling factor calculated with Koji's formula  gives C=0.936 for the astigmatic beam, and C=0.985 for the non astigmatic beam, so it seems to be still ok.