Lorentz-Drude Model

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

 

where

 

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
equation:

 

FDTD - equation 24 and 25

 

Then Equations 24 and 25 are solved numerically together with the modified Equation
26:

 

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.

 

OptiFDTD Manuals

NEW VERSION OptiSystem 13.0

July 17, 2014

OptiSystem 13 includes many important enhancements including several additions to the toolkit for building higher order modulation…

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