I used optimization codes for ETM. The optimization reduce the PSD of Brownian noise by ~ 3/4 (in units of [m^2/Hz]) from QWL structure.

 Since we have not had all the material parameters for aSi:H at 120K with 1550nm, the optimization here is for room temperature with 1550 nm (for Brownian noise only). 

fig1: optical thickness for ETM with minimized BR noise. The transmission is 5.4 ppm and the reflected phase is ~ 179 degree.

Parameters/configuration used in the optimization:

• T = 300 K   (room temp)
• wavelength = 1550 nm;
• Si substrate, n = 3.5;
• Low index material : fused silica, loss = 0.4e-4, n = 1.444;
• High index material: aSi:H, loss = 1e-6, n = 3.48; 
• The coating has SiO2 cap (air-coating surface) for protection
• Spot radius = 6 cm.
•  This optimization is only for Brownian noise, we can do another optimization once the thermo-optical properties are known (thermal expansion, dn/dT)

It is remarkable that 5ppm transmission can be achieved with just 17 layers of coatings due to the largely different values between nL and nH. This makes the total thickness down to ~ 3 um.

BR noise from the optimized coating is  3.3x 10^-42 [m^2/Hz] at 100 Hz. This is converted to the strain of ~ 5x10^-25 [1/sqrt Hz] for 4 km interferometer. 

Note: for QWL structure, with 14 layers + half wave cap of SiO2 (total of 15 layers), the transmission is ~5.2 ppm and the coating Brownian noise is 4.2x10^-42 [m^2 /Hz]. So the optimization reduced the PSD of BR noise by ~ 25%.