## Photonics

Topics related to Lumerical and more

#### Some questions about structural optimization

• Wini Liao
Subscriber

I want to optimize the thickness and width of the structure including Ge layer, Ti layer and rectangle0 layer (as shown in the figure) to make it have high emissivity in the 5-8 micron segment, and low emissivity in the 3-5 and 8-14 segments. We are designing a metal film, so the emissivity = 1-transmittance - reflectivity. How should I optimize such a structure?Can you outline that or point me in the right direction? Thank you very much！

• Amrita Pati
Ansys Employee

Hi Wini,

The in-built PSO algorithm in FDTD can only optimize a single value. So, by using the in-built tool as it is, you will only be able to optimize the value at a single point (let's say a single wavelength). If you have a broadband simulation, it will result in an error. What is typically done in these situations is find a way to combine the values at multiple wavelengths to create a single objective function. And then optimize this value. One approach is as follow:
Let's say T1 is the transmission in the wavelength range lambda1, T2 is the transmission in wavelength range lambda2 and T3 is the transmission in lambda3. Let's assume you want to maximize transmission in lambda1, and lambda3 ranges and minimize it in lamba2. So, what you can do is create a function like this (the lines below do not represent the actual syntax, just the idea):

FOM1 = integrate(T1^2,lambda1) --> integrating T1^2 over lambda1
FOM2 = integrate((1-T2)^2,lambda2) integrating (1-T2)^2 over lambda2
FOM3 = integrate((T3^2,lambda3) --> integrating T3^2 over lambda3

FOM = FOM1+FOM2+FOM3
Then maximize FOM.

For doing this, you would have to use the user-defined FOM section of the PSO tool:

Let me know if you have any questions.

Regards,
Amrita

• Wini Liao
Subscriber

Hi, Amrita,

Thank you so much for your reply. Could you tell me more about how to formulate these three equations? Like the range of this integral why is it in that range, or is there an example that you can recommend to me?

Regards,

Wini

• Amrita Pati
Ansys Employee

Hi Wini,

You are welcome! I think I might have misunderstood you. When you say "5-8 micron segment, and low emissivity in the 3-5 and 8-14 segments", what exactly do you mean by segments? I thought you were talking about different wavelength ranges. Also, if those are not the wavelength ranges, may I know what wavelength(s), you are looking at?

Regards,
Amrita

• Wini Liao
Subscriber

Hi Amrita,

By 5 to 8, 3 to 5 and 8 to 14 I mean different wavelength ranges, I mean I want my optimized structure to conform to 5 to 8 microns and I want lower reflectivity at 3 to 5 and higher reflectivity at 8 to 14 microns.

Regards,

Wini

• Amrita Pati
Ansys Employee

Hi Wini,

Okay. So, since you want the transmission (or reflection) to be maximum in certain ranges and minimum in others, you would have to incorporate this into the objective funtion of your broadband simulation for wavelengths ranging from 3 um to 14 um. I can share an example code with you that I was working on a while back. I am not sure if the code will work well for your device (also my script was not meant for FDTD but I have made some changes to make it relevant for FDTD). But it can help you getting started on your own optimization.

For this add the transmission (T) and frequency f to the "Figure of merit" section of the Optimization tool.

Then go to the "Advanced" Tab--> "Figure of merit script" tab and check the Use figure of merit option. Then you have to write the script here. The example script is shown below:

lambda = c/f;
df = max(f)-min(f);
filter1 = (lambda >= 3e-06 & lambda <5e-06);
filter2 = (lambda >= 5e-06 & lambda <8e-06);
filter2 = (lambda >= 8e-06 & lambda <14e-06);

FOM1 = integrate(abs(T)^2*filter1,1,f)/df;
FOM2 = integrate(abs(1-T^2)^2*filter2,1,f)/df;
FOM3 = integrate(abs(T)^2*filter3,1,f)/df;

fom = FOM1+FOM2+FOM3;

Here the logic of using filter1, filter2, and filter 3 is that it will be 1 when the wavelength is in that range and 0 when the wavelength is in a different range. So, when you multiply these by T, you can maximize/minimize the different segements of the transmission using separate functions. Since, this function (fom) is being minimized, the transmission (T) is minimized in the first wavelength range (FOM1), which means reflection should be automatically increased.  When term 2 (FOM2) is minimized (1-T^2) will be minimized, which means T^2 will be maximized, reflection minimized. You can play around with the FOM1, FOM2, and FOM3 functions. For, example choose the reflection monitor data instead of transmission. Or, assign weights (multiply by some constant) to FOM1, FOM2, FOM3 to prioritize one over the other. Like I said, the code is just to give you an idea. Let me know if you have any questions.

Regards,

Amrita

• Wini Liao
Subscriber

Hi Amrita,

Thank you so much for your reply, and I'm sorry for not replying you for such a long time. I am using the method you gave to optimize, but there are three errors in the result. As shown below, I am modifying the code, could you please give me some suggestions?

In addition, when I use the method you gave to optimize, the source can set a range instead of a single wavelength, right？