Creating lossless materials

Occasionally, you may wish to create ‘lossless’ versions of materials. For example, while studying a Silicon based photonic crystal cavity, you may want to remove any effects from Silicon material absorption, so you can more easily study the loss due to leakage through the PC structure. The idea is to create a ‘lossless’ version of the material, where the imaginary part of the refractive index (or sometimes the permittivity) is set to zero.

This technique is not recommended because obtaining accurate material fits can be difficult or impossible, and because the simulation results can be quite difficult to interpret. However, for users that do wish to create ‘lossless’ materials, this page provides some information.

Associated files:

usr_materials_lossless.fsp (44.1 KB)
usr_materials_lossless.lsf (1.7 KB)

See also:

Creating sampled data materials
Modifying material fits

Problems with this approach

Broadband fits

Unfortunately, there is a significant problem with this approach. It is often difficult or impossible for the Material Explorer to find an accurate fit to these types of lossless materials over a broad range of wavelength. If you cannot get a good fit, the simulation results will not be accurate. If you cannot get a good fit, but still want to study ‘lossless’ materials, you must run a series of single frequency simulations. This issue only exists when running broadband simulations (ex: source wavelength range is 400-700nm) and it can be avoided by running a series of single frequency simulations, for example using parameter sweeps.

Interpretation of results

The absorption of a material is a fundamental part of its properties, and simply setting the absorption to zero can lead to unexpected effects. Care must be taken when interpreting simulation results when the material absorption has been artificially set to zero.

Example

Step 1: Create a “lossless” material in the database

Creating a lossless material in the Material Database is easy and straightforward. The following lines of script code can be used to generate a text file containing the ‘lossless’ refractive index data. Basically, we get the normal refractive index data, then set the imaginary part of the refractive index to zero. Actually, we set it to some small value like 1e-6, as non-zero numbers cause fewer problems for the material data fitting routines.

f=linspace(c/200e-9,c/1000e-9,100); # specify frequency vector
n=getindex("Si (Silicon) - Palik",f);
data=[f, real(n), imag(n)*0+1e-6];
rm("Si (Silicon) - lossless.txt");
write("Si (Silicon) - lossless.txt",num2str(data));

Note: If you wish to set the imaginary part of the permittivity to zero, rather than the refractive index, simply add this command between lines 2 and 3: “n=n^2;”

Once you have this text file, the data can be imported into the Material Database by following the instructions on the Creating sampled data materials page. The associated example simulation file already has a lossless gold and lossless Silicon material in the Material Database.

Step 2: Check the material fit with the Material Explorer

The Material Explorer is used to check that the material fit (which will be used in the simulation) is a close match to the specified data. When creating ‘lossless’ materials, you will often find that it is not possible to get a good fit. The following screenshots show standard silicon and gold material fits, and the fits for lossless versions of those materials. You can see the fit for lossless silicon is okay (but not perfect), while the fit for lossless gold is poor. It is not possible to get a good fit to this lossless gold data.

Fitting lossless silicon

Standard silicon material fit: the standard fit is good over the range 400-700nm.

Lossless silicon material fit: The fit is quite good, at least when the imaginary index scale is kept constant.

Lossless silicon material fit: If we zoom in on the imaginary part, we can see the fit is not perfect. The imaginary part of the fit oscillates between zero and \(10^{-3}\).

Fitting lossless gold

Standard gold material fit: The standard fit is good over the range 400-700nm.

Lossless gold material fit: The material fit is quite poor for both the real and imaginary refractive index.

Step 3: Run a test simulation

The associated simulation and script file can be used to test the material fits. To reproduce the following results, run the script 4 times. Each time, select a different material from the database.

Standard silicon:

Notice the absorption (red) is quite large.

usr_materials_rt_si

Lossless silicon

Notice the absorption is much smaller. However, it will not be exactly zero, because the imaginary part of the material fit is not zero, as we saw above.

usr_materials_rt_si_lossless

Standard gold

This is the expected reflection and absorption spectrum for a gold slab.

usr_materials_rt_au

Lossless gold

Notice the absorption is very high. This occurs because the material fit still has a large imaginary component. These results are not very meaningful because of the poor material fit.

usr_materials_rt_au_lossless