This page discusses different ways of creating linear gain materials.
With Lorentz Model
To create a material with gain, we need a material with a negative imaginary index. This can be achieved with a Lorentz model when the Lorentz permittivity is negative. A screenshot of the material database, with Gain_material selected, is shown below.
In this case, the permittivity can be calculated with the following formula.
$$ \varepsilon(f)=\varepsilon+\frac{\varepsilon_{\text{LORENTZ}} \cdot \omega_{O}^{2}}{\left(\omega_{O}^{2}-2 i \delta_{O} 2 \pi \cdot f-(2 \pi \cdot f)^{2}\right)} $$
Roughly speaking, the gain center frequency is set with ω (Lorentz Resonance) while the width is set with δ (Lorentz Linewidth). The gain amplitude is set by the magnitude of the Lorentz permittivity, while the sign controls if the material has loss or gain.
The material properties can be checked graphically in the Material Explorer, shown in the following figure. As expected, for a material with gain, the imaginary part of the index is negative over the frequency range of interest.
With Experimental Data
One can also create a material with gain by importing customized data and allow the fitting routine to automatically generate the index profile.
If the imported material data will lead to gain, the following warning will appear.
|
Note : At least one value of the imaginary permittivity is negative. This will lead to optical gain and can cause FDTD simulations to diverge, but may be desired in certain cases such as calculations with MODE. If you would like to force the imaginary permittivity to be positive which will make the material have optical loss (recommended), you can click the following checkbox. |
The following figure shows that the fitting routine will generate a model with a negative imaginary index.In this case since we actually desire a material with optical gain, we can ignore the warning and complete the data import.
Tips
Gain materials: Auto shut-off maximum
The FDTD solver has an automatic shutoff feature that stops the simulation when the energy in the simulation goes below (auto shutoff min) or above (auto shutoff max) a predefined threshold. For simulations with gain, it may be necessary to adjust or disable the auto shutoff max feature to prevent the simulation from stopping earlier than desired. The Auto shut-off feature settings can be accessed in the Advanced tab of the simulation region properties.
See also
PC with gain material, Material Database, Creating sampled material data