Dispersive Material Property

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General Usage
CSX = AddLorentzMaterial(CSX, name, varargin)

with the following parameters:
 * CSX: The original CSX structure
 * name: name of the property
 * varargin: a list of variable arguments

To define the material properties use: CSX = SetMaterialProperty(CSX, name, varargin)

with the following parameters:
 * CSX: The original CSX structure
 * name: name of this property (same as above!)
 * varargin: a list of variable arguments to define the properties:

Conventional material parameters:

 * Epsilon: relative electric permittivity for $$f \to \infty$$ (must be >=1)
 * Mue: relative magnetic permeability for $$f \to \infty$$ (must be >=1)
 * Kappa: electric conductivity (must be >=0)
 * Sigma: magnetic conductivity (non-physical property, must be >=0)

See also: Material Property

Drude material parameters:

 * EpsilonPlasmaFrequency: electric plasma frequency ($$f_{plasma,1}$$, see below)
 * MuePlasmaFrequency: magnetic plasma frequency
 * EpsilonRelaxTime: electric plasma relaxation time ($$\tau_p$$, losses, see below)
 * MueRelaxTime: magnetic plasma relaxation time (losses)

Drude higher order parameter (p>1):

 * EpsilonPlasmaFrequency_p: p-th order electric plasma frequency ($$f_{plasma,p}$$, see below)
 * MuePlasmaFrequency_p:     p-th order magnetic plasma frequency
 * EpsilonRelaxTime_p:       p-th order electric plasma relaxation time (losses)
 * MueRelaxTime_p:           p-th order magnetic plasma relaxation time (losses)

Lorentz material parameters:
Note: Available only for openEMS >= v0.0.31!!

In addition to the drude parameter, the Lorentz-pole frequency can be defined:
 * EpsilonLorPoleFrequency: first electric Lorentz pole frequency ($$f_{Lor,1}$$, see below)
 * EpsilonLorPoleFrequency_p: p-th electric Lorentz pole frequency ($$f_{Lor,p}$$, see below)
 * MueLorPoleFrequency: first magnetic Lorentz pole frequency
 * MueLorPoleFrequency_p: p-th magnetic Lorentz pole frequency

Physical Model & Parameter
$$ \varepsilon(f) = \varepsilon_0\varepsilon_\infty \left( 1 - \sum_{p=1}^N \frac{f_{plasma,p}^2}{f^2-j f/(2\pi\tau_p)}\right) - j\frac{\kappa}{2\pi f} $$

with the parameter:
 * $$\varepsilon_\infty$$ the relative permittivity for $$f \to \infty$$
 * $$\kappa$$ the electric conductivity
 * $$f_{plasma,p}$$ the p-th "plasma" frequency
 * $$\tau_p$$ the p-th relaxation time (damping)

Example
CSX = AddLorentzMaterial(CSX,'drude'); CSX = SetMaterialProperty(CSX,'drude','Epsilon',eps_r,'Kappa',kappa); CSX = SetMaterialProperty(CSX,'drude','EpsilonPlasmaFrequency', 5e9, 'EpsilonRelaxTime', 5e-9);

Physical Model & Parameter
$$ \varepsilon(f) = \varepsilon_0\varepsilon_\infty \left( 1 - \sum_{p=1}^N \frac{f_{plasma,p}^2}{f^2-f_{Lor,p}^2-jf/(2\pi\tau_p)}\right) - j\frac{\kappa}{2\pi f} $$

with the parameter:
 * $$\varepsilon_\infty$$ the relative permittivity for $$f \to \infty$$
 * $$\kappa$$ the electric conductivity
 * $$f_{plasma,p}$$ the p-th drude "plasma" frequency
 * $$f_{Lor,p}$$ the p-th Lorentz pole frequency
 * $$\tau_p$$ the p-th relaxation time (damping)

Example
CSX = AddLorentzMaterial(CSX,'lorentz'); CSX = SetMaterialProperty(CSX,'lorentz','Epsilon',eps_r,'Kappa',kappa); CSX = SetMaterialProperty(CSX,'lorentz','EpsilonPlasmaFrequency', 5e9, 'EpsilonLorPoleFrequency', 10e9, 'EpsilonRelaxTime', 5e-9);

Relation to other formulations
\varepsilon(\omega) = \varepsilon_0\varepsilon_\infty + \varepsilon_0 \sum_{p=1}^N \frac{(\varepsilon_{dc,p}-\varepsilon_\infty)\omega^2_{p}}{\omega_{p}^2+2j\omega\delta_p-\omega^2} $$ Conversion: $$f_{Lor,p} = \frac{\omega_{p}}{2\pi}$$ $$f_{plasma,p} = \omega_{p}\frac{\sqrt{(\varepsilon_{dc,p}-\varepsilon_\infty)}}{2\pi}$$ $$\tau_p = \frac{1}{2\delta_p}$$ $$\kappa=0$$ Researchers in Physics often adopt a different sign convention, in which they use $$e^{-i\omega t}$$ for time-harmonic quantities rather than $$e^{i\omega t}$$ in engineering. Therefor in some textbook the Lorentz model is: $$ \epsilon(\omega) = \epsilon_0\epsilon_{\infty} (1+ \frac{\omega_p^2}{\omega_0^2 - \omega^2 - i\gamma \omega}) $$ And the Drude model is: $$ \epsilon(\omega) = \epsilon_0\epsilon_{\infty} (1- \frac{\omega_p^2}{\omega^2 + i\gamma \omega}) $$ Where $$\omega_p$$ is the plasma frequency and $$\omega_0$$ is the plasmonic resonant frequency and $$\gamma$$ represents the damping effect in material.