Lorentz-Drude Model

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Finite-Difference Time-Domain Simulation Design

Lorentz-Drude Model (FDTD)

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:


FDTD - equation 20




ω0mare the resonant frequencies
Gmis related to the oscillator strengths
Γmis the damping coefficient
εis the permittivity at infinite frequency
X0is 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:


FDTD - equation 21


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
dispersion properties:


FDTD - equation 22


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:


FDTD - equation 23


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


FDTD - equation 24 and 25


Then Equations 24 and 25 are solved numerically together with the modified Equation


FDTD - equation 26


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 Model


Drude material in OptiFDTD is marked as


FDTD - equation 27


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.


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