I'm trying to find another optimization that is less sensitive to change in nH and nL. Here is a few thought and a few examples.
==problem==
We have seen that uncertainties (withing +/- 1%)in nH and nL result in higher TO noise (up to 10 time as much) in the coating. So we are trying to see if there is another possible optimized structure that is less sensitive to the values of n. We estimate the value of nH to be 3.51 +/- 0.03, and nL to be 3.0 +/-0.03. (The numbers we have used so far are nH/nL = 3.51/3.0, while G.Cole etal use nH/nL = 3.48/2.977.
==Optimization method==
The algorithm is similar to what I did before[PSL]. But this time the cost function is taken from different values of refractive indices. The values of nH and nL used in this optimization are
- nH = 3.48, 3.51, 3.54
- nL = 2.97, 3.00, 3.03.
The cost function is the sum of the TO noise level at 100Hz, Transmission, and reflected phase, calculated from 9 possible pairs of nH and nL values. The weight number from each parameters (which parameter is more important) are chosen to be 1, as a test run. I have not had time to try other values yet, but the prelim result seems to be ok.
[Details about the codes, attached codes]
Note about the calculation,
The calculation follows these facts:
- The nominal values of nH/nL are 3.51/3.00
- The optical thickness is designed based on the above nH and nL
- The optimized design is reported in optical thickness which is converted to physical thickness with the nominal values of nH/nL
- The procurement of coatings control the physical thickness (with error in thickness discussed before PSL:)
- If the values of nH/nL changes from the nominal values, this will affect in the coatings properties because of the change in optical thickness.
==results from QWL (55layers) and 4 other optimized coatings.==
- Left plot shows TO noise at 100Hz in m^2/Hz unit,
- Middle plot:Transmission [ppm]
- Right plot: reflection phase away from 180 degree.
Each plot has three traces (blue, black, red) for different values of nH (3.48, 3.51, 3.54). nL is varied on x-axis from 2.97 to 3.03. The first result is from QWL coating, with 55 layers. This serves as a reference, to see how much each property changes with the uncertainty in nH and nL.
I tried to change the cost function in the optimization code and numbers of layer to see if better optimized structure can be done. The optimized structure (V3,4,5) seems to be less sensitive to the values of n, see below.
Above: from QWL coatings, 55 layers. nominal transmission = 100ppm. We can see that the transmission of QWL coatings is still quite sensitive to uncertainties in nH and nL.
Above: First optimization reported before, TO noise is larger by a factor of 10 in certain case, and transmission can be up to 500 ppm. This coating is very sensitive to the change in refractive indices.
Above: opt3, obtained from the code using the new cost function discussed above. 55 layers, nominal transmission = 150ppm. The TO noise is less dependent on nH and nL, but the transmission is still quite high.
Above: opt4, the weight parameter for transmission is changed to 3, 57 layers.
above opt5,the weight parameter for transmission is changed to 50, Lower/Upper thickness bound = 0.1/0.5 lambda, 59 layers
Above: Opt6, the weight parameter for transmission is changed to 500, Lower/Upper thickness bound = 0.1/1.2 lambda, 59 layers
From the results, optimized structure # 3,4,5 seem to be good candidates. So I ran another monte carlo error analysis on opt1 (as a reference), opt3, opt4, and opt5, assuming errors in both material properties and coating thickness. Each one has 5e4 runs. Surprisingly, the results from all designs are very similar (see the plot below). It is possible that, by making the coatings less sensitive to changes in nH/nL, it is more sensitive to other parameters (which I have to check like I did before). Or the properties are more dependent on coating thickness, not material parameters (this is not likely, see psl:1345). Or perhaps, there might be a mistake in the monte carlo run. I'll check this too.
I'll update the coating structure and forward it in google doc soon. |