Retrieve the effective parameters of metamaterial

Read some of those papers? The fourth from the top, the Robust one by Chen et al, is one of the best. Begin with that and actually read the references listed in it. This is pretty well-understood and straightforward.

hi
now i have read this paper---- "Robust method to retrieve the constitutive effective parameters of metamaterials", but i can't understand part B. why should we determine the effective boundary and thickness? and why isn't the effective thickness identical to the cell thickness?

Hello everyone!
I am trying to implement the equations from the article "Robust method to retrieve the constitutive effective parameters of metamaterials",in MATLAB and I have done the first part. I am confused though on how to proceed with the second part for the determination of m for the correct branch (equation 7 in the paper). I have already finished the code that gives me the correct e and mu, but I would like to improve the results using the method from Chen's paper.Could anyone give me a hint?
Thank you all!

Can you upload your code?

Is it correct to say the imaginary part of permittivity and permeability should be positive? (mentioned in this paper)

plz upload ur code

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA456941

By this paper, http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA456941
How to load the S-parameters data from CST to the matlab code it gives?

Does anyone have the same question?

If you are simulating the metamaterial, use field averaging.

If you are retrieving from measured S parameters, use Chen.

% RUN SMITH EXAMPLE ON CST

directory = pwd;
% START CST STUDIO
cst = actxserver('CSTStudio.application');

% OPEN MWS MODEL
mws = invoke(cst, 'OpenFile', [directory '\Smith_Parameter_Extraction_Working.cst']);

% START SOLVER
fdsolver = invoke(mws, 'FDSolver');
invoke(fdsolver, 'Start');
invoke(mws, 'Save');

% RETRIEVE RESULT
absS11 = invoke(mws, 'Result1D','a1(1)1(1)');
angS11 = invoke(mws, 'Result1D','p1(1)1(1)');
absS21 = invoke(mws, 'Result1D','a2(1)1(1)');
angS21 = invoke(mws, 'Result1D','p2(1)1(1)');

% STORE RESULT IN .TXT FILE
invoke(absS11, 'Save', [directory '\absS11.txt']);
invoke(angS11, 'Save', [directory '\angS11.txt']);
invoke(absS21, 'Save', [directory '\absS21.txt']);
invoke(angS21, 'Save', [directory '\angS21.txt']);
invoke(mws, 'Save');
invoke(mws, 'Quit');

release(absS11);
release(angS11);
release(fdsolver);
release(mws);
release(cst);

It's important to note that there is a branching ambiguity due to the arc cosine function. This issue causes some regions in the calculated spectrum, for the real part of the refractive index, to have the wrong sign or amplitude. As a result, these regions require correction by hand. The "Robust method to retrieve the constitutive effective parameters of metamaterials" outlines an approach to determing the correct branching parameter m. There is another approach that I like more, which implements the Kramers Kronig relationships. This can be found in "A Unique Extraction of Metamaterial Parameters Based on Kramers–Kronig Relationship."

This is a great list, but don't forget about the field averaging method!

Rrumpf, please post your code and references. Also, does anyone have any nonlinear or anistropic metamaterial effective parameter extraction codes?

I wrote this code
Is that right?

clc
% extracted values of frequency %

f=[30.0 , 30.625, 31.25, 31.875,32.500,33.125,33.750,34.375,35.000,35.625,36.2500,36.8750,37.5000,38.1250,38.750,39.3750,40.0000,40.6250,41.2500,41.8750,42.5000,43.12500,43.75000,44.37500,45.00000,45.6250,46.2500,46.8750,47.5000,48.1250,48.7500,49.3750,50.0000]

% s11 parameter %

s11=[-1.56 ,-1.80 ,-2.05,-2.33,-2.6504,-3.0252,-3.4710,-4.0084,-4.6659,-5.4769,-6.4890,-7.7728,-9.434,-11.6765,-14.7990,-19.919,-33.7676,-24.888,-17.720,-14.089,-11.767,-10.1313,-8.92165,-8.00691,-7.3044,-6.766008,-6.3570,-6.05145,-5.83227,-5.6948,-5.6225,-5.6197,-5.6727]

%extracted s21 parameter from simulation%

s21=[-5.19,-4.70,-4.25,-3.82,-3.411,-3.003,-2.601,-2.207,-1.822,-1.454,-1.110,-0.8003,-0.5318,-0.3126,-0.1526,-0.0508,-0.0078,-0.0208,-0.08314,-0.17887,-0.30498,-0.44897,-0.60147,-0.75405,-0.8998,-1.0334,-1.1489,-1.2454,-1.3220,-1.3707,-1.3972,-1.3981,-1.3782]
    
% formula from IEEE paper %

n=(acos((1./(2.*s21)).*(1-(s11).^2-(s21).^2)))./1.6; % Index %

z=sqrt(((1+s11).^2)-(s21).^2)./(((1-s11).^2)-(s21).^2); % Impedence %



plot(f, real(n), 'blue', f, imag(n), 'r');
title('index');

I think It's wrong.
S11 and S21 in these formulae must be complex number while you used the value of S11 and S21 in dB.

Right?

Thank you for your Guidance
How can I extract them In that form from HFSS?

I upload an thesis only talking about Retrieval Method of Parameters here. It's very detailed in Simulation and Others.
They used method from paper of Xudong Chen. They also provided Matlab code in Appendixad. It's very useful.
Hope that it will help you

thank you but where is the thesis?Where did you upload?

Sorry, may be there is some problem.
You type "extracting material constitutive parameters from scattering parameters" on Google, and Find the Master Thesis about it.
Best