I used GWINC code to calculate TO noise in AlGaAs coatings, with some modifications to the code I can get the result that is comparable to Cole etal's result. However, there seems to be some minor details that I have to check. The half wave cap solutions for TO cancellation is not verified by the current calculation yet.
What I modified and checked in the code:
- The variable called thermaldiffusivity in the code is actually treated as thermal conductivity in the calculation, so all calculations in the past are still correct.
- The layer structure in the code was originally for Ta2O5/SiO2. The first layer started with SiO2 (low index material,nL), and ended with Ta2O5(high index material,nH) at the substrate surface. However, the AlGaAs coatings start with nH and ends with nH. I changed the calculation for effective thermal expansion accordingly. With the correct layer structure and materials parameters from Matt, the TO nosie is closer to JILA's result. However, the shape is still not the same, what reported in JILA is almost flat across 1-100 Hz. The calculated transmission from the layers is 1.8 ppm, but the paper says 4ppm. I'm looking into this.
Above figures: top plot is the result from GWINC. Its title should be Al0.92Ga0.08As coatings, not SiO2/Ta2O5, bottom picture is taken from Cole, etal. TO noise crosses coating brownian noise around 3 Hz for both plots, however the slope is very different. NOTE: the y axes are in Hz^2 / Hz.
As a quick check for the proposed half wavelength cap solution to reduce TO noise, I modified the layer structure and computed TO noise. Since they did not mention what kind of material for the cap I tried:
- 81 layers, starts with nH, ends with nH, the first layer is 0.5 lambda thick. This is not working.
- 82 layers, starts wit half wave nL, followed by the original 81 layers. This also does not work. Both cases have comparable TO noise, but transmissions are different.
I'll check their formula and GWINC to see where the differences are.
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[matt, tara] Got AlxGa1-xAs material parameters from Matt Abernathy. I plug the numbers (all in SI) in GWINC, but the result is still not quite similar to that in Cole etal paper.
ioffe has materials parameters for TO noise calculation.
Specific heat: 0.33+0.12x J/gK
Mass density rho = 5.3165-1.5875x g/cm^3
Thermal conductivity,kappa: 0.55-2.12x+2.48x^2 W/cmK (There is also thermal diffusivity = kapp/(rho*specific heat) [m^2/s]. The results are the same)
Thermal Expansion: (5.73-0.53x)·10-6/K
dn/dT: 3.66-2.03x *10^-4/K
This is from a paper, "Thermal dependence of the refractive index of GaAs and AlAs measured using semiconductor multilayer optical cavities", by Talghader and Smith. Keep in mind that this paper has an important Erratum if you want use values from it.
Unfortunately, this paper measures dn/dT at a max wavelength of 1030nm, so it's not quite accurate, but probably good enough.
Note:
One of the variables in GWINC code is ThermalDiffusivity. But the numbers used in previous TO plot is thermal conductivity of materials. I'll check the TO calculation codes and see if it is just a naming error, or the calculation is actually wrong.
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