# Optical material models in DGTD and FEEM

This section describes the basic permittivity (or refractive index) material models supported by the Material Database. Model parameters can be edited in the Material property panel of the Material Database window. Models can also be created using addemmaterialproperty script command and all properties may be edited in script. For more information about handling optical materials using scripts, visit Scripting The Optical Materials

## Conductive

The Conductive model is used to create a material with the the following relative permittivity.

$$\varepsilon_{\text {total}}(f)=\varepsilon+i \frac{\sigma}{2 \pi f \varepsilon_{o}}$$

- \(\varepsilon\): permittivity
- \(\sigma\): conductivity in units of \({(\Omega m)}^{-1}\)

Note: Comparison with PEC As the conductivity becomes very large, the performance of this model approaches the ideal PEC (Perfect Electrical Conductor). |

## Dielectric

The Dielectric model is used to create a material with a constant real index. This material will have the specified index at all frequencies (non-dispersive).

- REFRACTIVE INDEX: The refractive index of the material. Must be \(\geq 1\).

## (n,k) Material

The (n,k) material model is used to create a material with a specific value of n and k at a single frequency. The refractive index modeled is \(n+ik\).

- REFRACTIVE INDEX: Real part of the index, n, at the center frequency of the simulation. Must be > 0.
- IMAGINARY REFRACTIVE INDEX: Imaginary part of the index, k, at the center frequency of the simulation. Positive values correspond to loss, negative values will produce gain.

NOTE: Single frequency simulations only! This type of material model should only be used for single frequency simulations. The implementation of the (n,k) material model is such that the material properties will only be correct at the center frequency of the simulation. |

## Debye

The Debye model is used to create a material with the the following relative permittivity.

$$\varepsilon_{total}(f)=\varepsilon+\frac{\varepsilon_{debye} v_{C}}{\left(v_{C}-i 2 \pi f\right)}$$

- \(\varepsilon\): permittivity
- \(\varepsilon_{debye}\): Debye permittivity
- \(v_C\): Debye collision in units of rad/s

## Plasma (Drude)

The Plasma model is used to create a material with the the following relative permittivity.

$$\varepsilon_{total}(f)=\varepsilon-\frac{\omega_{P}^{2}}{2 \pi f\left(i v_{C}+2 \pi f\right)}$$

- \(\varepsilon\): permittivity
- \(\omega_{P}\): plasma resonance in units of rad/s
- \(v_C\): plasma collision in units of rad/s

## Lorentz

The Lorentz model is used to create a material with the the following relative permittivity.

$$\varepsilon_{\text {total}}(f)=\varepsilon+\frac{\varepsilon_{\text {lorent} z} \omega_{0}^{2}}{\left(\omega_{0}^{2}-2 i \delta_{o} \cdot 2 \pi f-(2 \pi f)^{2}\right)}$$

- \(\varepsilon\): permittivity
- \(\varepsilon_{lorentz}\): Lorentz permittivity
- \(\omega_0\): Lorentz resonance in units of rad/s
- \(\delta_0\): Lorentz linewidth in units of rad/s

NOTE: Lorentz model reference Kurt Oughstun and Natalie Cartwright, "On the Lorentz-Lorenz formula and the Lorentz model of dielectric dispersion," Opt. Express 11, 1541-1546 (2003) |

## Sampled Data 3D

The Sampled data model is used to import experimental refractive index or permittivity data.

### Data tab

The experimental data can be imported from a text file with the IMPORT DATA button.

The imported data is displayed in a table after data has been imported.

### Fitting Configuration tab

The Sampled Data material definition uses an automatic fitting routine to generate a multi-coefficient material model of the experimental data over the frequency range specified by the source. The fits can be checked and adjusted in the Material Explorer by clicking on the GO TO MATERIAL EXPLORER button.

- TOLERANCE: The desired RMS error between the permittivity of the experimental data and the material fit. The fitting routine will use the least number of coefficients that produce a fit with an RMS error less than the tolerance.
- MAX COEFFICIENTS: The maximum number of coefficients allowed to be used in the material fit. More coefficients can produce a more accurate fit, but will make the simulation slower.

The following advanced settings are shown if the SHOW ADVANCED SETTINGS option at the bottom of the Fitting Configuration tab is selected:

- MAKE FIT PASSIVE: Set to be true to prevent the fit from having gain at any frequency. By default this is true in order to prevent diverging simulations.
- IMPROVE STABILITY: If this setting is true, the fitting routine restricts the range of coefficients in the fit in order to reduce numerical instabilities which cause simulations to diverge.
- IMAGINARY WEIGHT: Increasing the weight increases the importance of the imaginary part of the permittivity when calculating a fit. A weight of 1 gives equal weight to the imaginary and real parts of the permittivity.
- SPECIFY FIT RANGE: Set to true to decouple the bandwidth used to generate the material fit and the source bandwidth. This option is used in parameter sweeps where the source frequency is changed, and where it is important to keep the material parameters constant over the whole parameter sweep. The fit range should cover the simulation bandwidth.
- WAVELENGTH MIN/MAX and FREQUENCY MIN/MAX: Bandwidth to be used for the fit when Specify Fit Range is true.