風行電磁模擬 FonSinEM - Electric & Magnetic Models

Electric & Magnetic Models

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Electric Dispersion Models

Magnetic Dispersion Models

There are five electric dispersion models and five magnetic dispersion models in FonSinEM,. This means we could use both five models in the same simulation.

Debye, Drude, Lorentz, Modified Lorentz these dispersion models are often use in FDTD.

Debye: usually use to fit the Skin, Blood, Bone, Brain(white matter), Brain(grey matter), Mussle, Heart, liver, etc, can refer to this paper

Mohammed Eleiwa and Atef Z. Elsherbeni, “Debye Constants for Biological Tissues from 30 Hz to 20 GHz,” Applied Computational Electromagnetics Society (ACES), vol. 16, no. 3, pp. 202-213, November 2001.

Drude, Lorentz : these two dispersion models are usually use together, often use to fit the metal, FonSinEM have built-in parameters for Ag, Au, Cu, Al, Be, Cr, Ni, Pd, Pt, Ti, W, etc. The detail can refer to this paper

Aleksandar D. Rakić, Aleksandra B. Djurišić, Jovan M. Elazar, and Marian L. Majewski, "Optical properties of metallic films for vertical-cavity optoelectronic devices," Appl. Opt. 37, 5271-5283 (1998)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-22-5271

This is the Matlab file for the paper.

Drude-Lorentz and Debye-Lorentz models for the dielectric constant of metals and water

http://www.mathworks.com/matlabcentral/fileexchange/18040-drude-lorentz-and-debye-lorentz-models-for-the-dielectric-constant-of-metals-and-water/content/LD.m

The following is the Matlab script exmple that transfer the parameter into FonSinEM using

clear ; clc;

lambda=[100:5:1000]*1e-9;

twopic = 1.883651567308853e+09; % twopic=2*pi*c where c is speed of light

omega = twopic.*(lambda.^(-1)); % angular frequency of light (rad/s)

invsqrt2 = 0.707106781186547;  % 1/sqrt(2)

ehbar = 1.51926751447914e+015; % e/hbar where hbar=h/(2*pi) and e=1.6e-19

 '================Ag===============================';

        Name='Ag';

        epsinf=1;

        % Plasma frequency

        omegad = 9.01*ehbar;

        % Oscillators' strenght

        f0 = 0.845;

        f = [ 0.065 0.124 0.011 0.840 5.646];

        % Damping frequency of each oscillator

        Gamma0=0.048*ehbar;

        Gamma = [ 3.886 0.452 0.065 0.916 2.419]*ehbar;

        % Resonant frequency of each oscillator

        omegap = [0.816 4.481 8.185 9.083 20.29]*ehbar;

 '================Ag===============================';

轉成風行

'========(FonSinEM)========'

epsinf

Wd=sqrt(f0)*omegad

gamad=Gamma0

eps_p=sqrt(f).*omegad

Wp=omegap

gamap=Gamma

'========(FonSinEM)========'

%drude

epsilon=epsinf-Wd^2./(omega.^2+1j*omega*gamad);

%lorentz

for i=1:length(eps_p)

    epsilon=epsilon-eps_p(i)^2./(omega.^2+1j.*omega*gamap(i)-Wp(i)^2);

end

figure(1);hold on;

plot(lambda*1e9,real(epsilon),'r','linewidth',3);

plot(lambda*1e9,imag(epsilon),'b','linewidth',3);

legend('real part','imaginary part')

hold off;

title('Ag');

xlabel('\lambda (nm)');

ylabel('\epsilon');

執行結果 : 對照風行的材料輸入方塊

epsinf =

Wd =

    1.258309273122320e+016

gamad =

    7.292484069499872e+013

eps_p =

  1.0e+016 *

  Columns 1 through 4

   0.348992200356488   0.482025357341264   0.143567251194280   1.254580941155052

  Column 5

   3.252591176906756

Wp =

  1.0e+016 *

  Columns 1 through 4

   0.123972229181498   0.680783773238103   1.243520460601176   1.379950683401403

  Column 5

   3.082593786878175

gamap =

  1.0e+015 *

  Columns 1 through 4

   5.903873561265938   0.686708916544571   0.098752388441144   1.391649043262892

  Column 5

   3.675108117525039

Modified Lorentz : reference

A. Deinega and S. John, “Effective optical response of silicon to sunlight in the finite-difference time-domain method,” Opt. Lett. 37, 112-114 (2012)

http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-37-1-112

The dispersion models (Debye, Drude, Lorentz, Modified Lorentz) fitting tools by EMTL, also in FonSinEM, has built-in fitting tool for Drude-Lorentz model.

Electromagnetic Template Library (EMTL)

http://fdtd.kintechlab.com/en/fitting

As you read the paper, you might fund the other dispersion model use in FDTD

Complex-Conjugate Pole-Residue Pairs Model

M. Han , R. W. Dutton and S. Fan  "Model dispersive media in finite-difference time-domainmethod with complex-conjugate pole-residue pairs",  IEEEMicrow. Wireless Comp. Lett.,  vol. 16,  no. 3,  pp.119 -121 2006

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1603585&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D1603585

D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” Journal of Nanophotonics, vol. 8, no. 1,  083097, 2014

http://nanophotonics.spiedigitallibrary.org/article.aspx?articleid=1812806

Brendeland Bormann Model

Aleksandar D. Rakić, Aleksandra B. Djurišić, Jovan M. Elazar, and Marian L. Majewski, "Optical properties of metallic films for vertical-cavity optoelectronic devices," Appl. Opt. 37, 5271-5283 (1998)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-22-5271

Critical Points Models

Dominique Barchiesi ; Thomas Grosges, "Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth",J. Nanophoton. 8(1), 083097 (Jan 06, 2014)

http://nanophotonics.spiedigitallibrary.org/article.aspx?articleid=1812806

These are good dispersion models for simulation too, but the FonSinEM four built-in dispersion models is enough to use.

if we'd like to simulate the metal material, we can use the Debye model to fit in some wavelength region (not use Drude + Lorentz), can refer to this paper.

Hongfeng Gai, Jia Wang, and Qian Tian, "Modified Debye model parameters of metals applicable for broadband calculations," Appl. Opt. 46, 2229-2233 (2007)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-12-2229

Also, the Drude, Lorentz, Modified Lorentz models can use to fitting the Graphene. The conductivity depends on the temperature and wavelength can separate to Interband and intraband of Graphene.

refer to this paper

Adam Mock, "Padé approximant spectral fit for FDTD simulation of graphene in the near infrared," Opt. Mater. Express 2, 771-781 (2012)

http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-2-6-771

we can bring the s(l) into ε_r(l)=1-s(l)/(iwε₀) (relative permittivity）, and then obtain the ε_r(l) and use the Drude + Modified Lorentz model to fit it.

The following paper shows how to use Complex-Conjugate Pole-Residue Pairs to simulate Graphene, you can try using Drude + Modified Lorentz to fit it.

H. Lin , M. F. Pantoja , L. D. Angulo , J. Alvarez , R. G. Martin and S. G. Garcia  "FDTD modeling of graphene devicesusing complex conjugate dispersion material model",  IEEEMicrow. Wireless Compon. Lett.,  vol. 22,  no. 12,  pp.612 -614 2012

http://ieeexplore.ieee.org/xpl/abstractReferences.jsp?arnumber=6845375&navigation=1

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