Since we're getting into the regime of higher power operations, we need to start thinking about TCS from a higher-order mode standpoint (higher than just spherical power/defocus). The current CO2 laser central heating and the ring heater provide almost 100% spherical power correction to the optic. The SELF heating, however, still produces a partly non-spherical lens from the absorption of the Gaussian beam.

These residual non-spherical lenses will increasingly cause problems as we go to higher power.

I've run a quick analysis of how much TEM00 is scattered AFTER the nominal spherical lens is corrected. This is purely for the substrate thermal lens (not for surface deformation, which is about 1/12th of the size).

For this model:

• I've assumed between 200ppb and 300ppb absorption for each optic.
• Power level in the arm:
  • O1: ~100kW
  • O2: ~170kW [check this]
• The total substrate lens (Optical Path Distortion [OPD]) was calculated in COMSOL
  • then scaled by the absorbed power and
  • scaled by a factor of 2 to account for the round-trip through the ITM.
• The OPD then has the nominal spherical power removed to yield a residual thermal lens.
• The TEM00 (beam radius = 54mm) scatter from the residual thermal lens was calculated.

The scatter is calculated in the following way:

w0 = 54E-3;

k = 2*pi/1064E-9;

E1 = exp(-(r/w0)^2)

OPD1 = uncompensated lens (dobule-passed)

S0 = best fit defocus (spherical power) to uncompensated lens

OPD2 = OPD1 - S0/2 * r^2   % the residual thermal lens after spherical power is removed

E2 = E1*exp(i*k*OPD2)

OL = sum(r*conj(E1)*E2)*sum(r*E1*conj(E2)) / [ sum(r*E2*conj(E2))*sum(r*conj(E1)*E1) ]   % overlap between pure gaussian and gaussian with residual thermal lens added as phase front error

scatter = 1- OL

The resulting plot shows the fractional scatter versus the absorbed power.

For reference, we'd really like to keep the round-trip scatter to 0.1% or less. The next step should be reviewing a detailed SIS model to try to refine these numbers. 

Conclusion: we should consider a more appropriate CO2 heating beam shape for O2B.