I tried to replicate the S-parameter retrieval from the paper from Smith. I got the following responses. I got exactly the same plot for magnitude plot. And even phase plot using cang_rad(), but it was inverted. What I mean is, when I created a output variable with
-cang_rad(). I got exactly the same phase plot that is given in the paper. And I attached the images.
Is there any reason for taking negative of the phase plot or am I missing anything?
You may be interested in downloading the notes and listening to Lecture 15 at the link below. In this lecture, I give an overview and references for a bunch of methods for doing parameter retrieval.
http://emlab.utep.edu/ee5390em21.htm
Hope this helps!
The reference you need to read is: D. R. Smith et al., "Electromagnetic parameter retrieval from inhomogeneous metamaterials", Phys Rev E 71, 036617 (2005)
Link: http://pre.aps.org/pdf/PRE/v71/i3/e036617
Best,
Thorsten
Certain softwares, as HFSS for example, provide results with negative phase for S parameters.
In order to perform retrieval procedure you need to invert the phase sign. Taking a positive sign for the phase is consistent with the general definition of phase index in optics.
Another important point, is to choose the right branch of arcosine function.
For more details:
C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
A. Lupu, N. Dubrovina, R. Ghasemi, A. Degiron, and A. de Lustrac, “Metal−dielectric metamaterials for guided wave silicon photonics,” Opt. Express 19, 24746−24761 (2011).
In physics people use i=sqrt(-1). In engineering, people use j=-sqrt(-1).
Smith has written the retrieval derivation with i (as most physicist do). You need to check whether your program uses i or j.
The reflection (as a complex quantity) is of the form =|R|*exp(i*phase) or =|R|*esp(-j*phase). I'm assuming that your code is using j, which means you need to correct the phase with a minus, before you apply the Smith retrieval method.
Most commercial softwares addressed to engineers use j, and not i.
As a rule, metamaterial has no local parameters at all. Wave number is a good parameter but impedance is a mesoscopic one. Sometime consideration of transition layer (Drude theory) helps. See Constantin R. Simovski, Mikhail Popov, and Sailing He Phys Rev B 62, 13 718 (2000) and related papers by Simovski..
You may be interested in downloading the notes and listening to Lecture 15 at the link below. In this lecture, I give an overview and references for a bunch of methods for doing parameter retrieval.
http://emlab.utep.edu/ee5390em21.htm
Hope this helps!
Two interesting papers for you :
"Robust method to retrieve the constitutive effective parameters of metamaterials", PHYSICAL REVIEW E 70, 016608 (2004) http://journals.aps.org/pre/abstract/10.1103/PhysRevE.70.016608
IEEE Xplore : "A Unique Extraction of Metamaterial Parameters Based on Kramers–Kronig Relationship". The authors provide their matlab tool online.
This paper gives a detail explanation about your question with source code.:"A Unique Extraction of Metamaterial Parameters Based on Kramers–Kronig Relationship"
Several answers were given, which are all correct. Another one is to say that the "+/-jwt" conventions are different in the paper and for the simulation code. If one is +jwt and the other one is -jwt, then you have to change all the signs in front of all the "j", thus leading to opposite sign of the phase.
Can you kindly clarify? What does the usage of |R|exp(-j*theta) or |R|exp(+j*theta) depend on? Does it depend on the time harmonic assumption (exp(-jwt) or exp(jwt))?
The retrieval procedure can be used to extract parameters from experimental S-parameters as well, right? Which convention should one use in that case?
Kindly reply.
Yes the sign before the 'j' depends on the convention. The convention you must use is the one that is used by the computer code used to calculate S parameters.
Hi all, Has anyone tried to replicate the results of the paper referred by Thorstein, D.R. Smith, using COMSOL Multiphysics? I am having trouble getting those results, i am not sure whether it is my model which is not correct or it is something else, if anyone has tried it with using COMSOL, please let me know.
Link: http://pre.aps.org/pdf/PRE/v71/i3/e036617
CST uses time engineering convention (harmonic variation) exp (i wt),
instead of physics and optics communities, which uses exp(-i wt).
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