By Lorentz dispersion materials, we mean materials for which the frequency
dependence of the dielectric permittivity can be described by a sum of multiple
resonance Lorentzian functions:
|ω0m||are the resonant frequencies|
|Gm||is related to the oscillator strengths|
|Γm||is the damping coefficient|
|ε∞||is the permittivity at infinite frequency|
|X0||is the permittivity at ω = 0 .|
In the lossless case Equation 20 is directly related to the Sellmeier equation which in
the three resonances can be presented as:
In the lossy case, the Sellmeier equation can be written in a generalized form,
accounting for a non-zero damping coefficient Γm as well as for anisotropy in the
There are different ways to implement Equation 20 into the FDTD formalism. Here we
consider the so-called polarization equation approach in the single resonance case.
It uses the dielectric susceptibility function:
and the relation between the polarization and the electric field Py = ε0x (ω) Ey .
Taking the Fourier transform of the last equation leads to the following differential
Then Equations 24 and 25 are solved numerically together with the modified Equation
The FDTD approach can also account for a large variety of materials such as Drude
dispersion materials, perfect metal, second-order, and third-order materials.
Lorentz model only supports 2D simulation. Lorentz_Drude material that covers
Lorentz model supports both 2D and 3D simulation.
Drude material in OptiFDTD is marked as
Where εr∞ is the permittivity for infinity frequency, ωp is the plasma frequency, and Γ
is the collision frequency or damping factor.
Drude model only supports 2D simulation, Lorentz_Drude model that covers Drude
model supports both 2D and 3D simulation.