Dear all, how I can determine the negative refractive index of the metamaterials by CST studio suite or by using S-Parameters?
Hi Abuzar,
To my knowledge if you want to predict RI (refrective Index) for non magnetic material it can be calculated from its dielectric permittivity. as RI= Squre root of Epsilon.
I recorded an entire lecture on this subject. See Lecture 15 here...
http://emlab.utep.edu/ee5390em21.htm
I suggest that you also read these papers:
http://journals.aps.org/pre/abstract/10.1103/PhysRevE.71.036617
http://journals.aps.org/pre/abstract/10.1103/PhysRevE.70.016608
http://journals.aps.org/pre/abstract/10.1103/PhysRevE.71.046610
The ones below might be a bit informative as well, depending on what structure you are simulating:
http://www.opticsinfobase.org/josab/abstract.cfm?uri=josab-23-3-391
http://journals.aps.org/pre/abstract/10.1103/PhysRevE.68.065602
If you simulated/ measured the transmission and reflection coefficients for your metamaterial, then you can use parameter retrieval to obtain the complex permittivity and permeability. Consider the metamaterial as a single object and proceed further.
If you work with (A,B,C,D) matrix (M) the negative refraction index results in det(M)
And a related question - is it possible to tell if a material is a NIM based on its dispersion relation, since that's what many 3D codes compute... something like negative slope for example.
At first I thought a negative slope (negative group velocity) was an indicator of negative index, but after doing some calculations, I'm not convinced that it is.
The sign of the imaginary part depends on the sign convention. If you define a wave travelling in the +z direction as exp(+jkz) then a positive sign on the imaginary component indicates loss. If instead you define a wave travelling in the +z direction as exp(-jkz), then a negative sign on the imaginary component indicates loss. So either can be correct depending on the sign convention you have chosen.
Yes. In my experience, the real and imaginary parts change sign at just about the same time. I suggest finding a good journal article where the authors perform a parameter retrieval for some metamaterial. Try to duplicate those results. It will also give you a feel of what you should be seeing in your simulations.
If you want to solely go by the S-parameters, follow this:
a) If there is a full (or very high) reflectivity, it may be due to single negative nature or due to the very high impedance contrast. If so, cheque for the phase, if the phase reverses, then this is due to the single negative material.
b) If there is absorption (ie. Both reflection and transmission are very low) and if the material is non-lossy, then you can expect double negative nature.
Alternatively, you can follow the extraction of parameters using the formulae provided in one of my papers (The European Physical Journal Applied Physics, 72, 20402, 2015) and find out the nature
Dear fellows, let me know the physical meaning of negative permittivity. Why after resonance (plasma frequency), metals have negative permittivity. How should I interpret it?
I'm working with the method mentioned in the lecture of Raymond Rumpf
When I'm calculating the S-Parameters theoretically(with known refractive index n and using Fabry Perot coefficients(like the formulas in the lecture)), I'm getting the correct result and can painless invert the parameters to get back my n. But when I simulate the s-Parameters of the same material, I need to multiplate my S21 by a factor e^(i*k0*d) to get my theoretical value and to invert for n. Sometimes even my S11 has to be multiplated by this factor. Where does this e^(i*k0*d) comes from??
Richard J Williams Thank you for your answer!
I have no idea what it is...
What does the insertion phase delay depend on?
I'm not understanding why sometimes only my S21 and sometimes S11 and S21depend on this phase....
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