We should be able to mode match into a cavity with 1.0 m ROC mirrors using only the optics we already have on the table.
Current mirrors: 0.5 m ROC (has -1114 mm FL)
Proposed mirrors: 1 m ROC (has -2227 mm FL)
The various waists for the proposed mode matching are equal to or larger than the waists for the current mode matching, so I don't think we should be any more worried about sensitivity than we already are.
I'm thinking about the spec for AlAs/GaAs coatings. Here is the list of what I have:
==Coating diamter for 0.5m ROC mirror==
About the coatings diameter, Garrett said it depends on the aperture size/ coating diameter. So I made a plot to estimate the loss due to the finite size coating vs Coating diameter for our spot radius of 182 um. The loss is simply calculated by the ratio of the power not falling on the coating = Ploss/Pin = (exp(-2*r0.^2./w0.^2))*1e6*26000/pi
where r0 = coating radius, w0 = spot radius, a factor of 1e6 for showing the result in ppm, 26000/pi is the total loss due to the light bouncing in the cavity.
fig1: Loss vs coating diameter (in meter)
It seems we can go to 2mm coating diameter, and the loss is still much less than 1ppm (the expected loss from absorption and scatter is ~ 10ppm). However, we have to consider about how well they can center the film, how well we can assemble the cavity. So larger coating diameter is always better. If we assume that 1mm error is limiting us, coating diameter of 4-5 mm should be ok for us.
==for mirror with 1m ROC==
If the ROC is 1.0m, the coating diameter can be 8mm. For the cavity with 1.45" long, the spot radius on the mirror will be 215um (182um with 0.5m mirror). This changes the noise budget of the setup a little bit. The total noise level is lower by a factor of ~ 1.2. (see below figure) at 100 Hz.
fig2: Noise budget comparison between setup with 0.5 m and 1.0m RoC mirrors, plotted on top of each other. Noises that change with spotsize are coating brownian, substrate brownian, thermoelastic in substrate, and thermo-optic.
==What do we choose? 0.5m or 1.0m==
For both 0.5 and 1m, the cavity will be stable (see T1200057-v11, fig11). So either choice is fine
if we use 1.0 m,
So at this point, I'm thinking about going with 1.0 m mirror.