There are so many papers where they select different methods for forming metamaterial. In some papers, they used AC sources in others DNA origami and so on. What interests me most is which exact equations show the result to form metamaterials. Thus I want to know what to select for forming metamaterials.
Fatematuz Zahura are you referring to the physical properties of the metamaterial (e.g., its shape), or the modal properties of the metamaterial (e.g., its dispersion)? While the two are related, generally one of these two is chosen to begin the design with.
Possibly the most simple are transmission-line metamaterials (https://www.waves.utoronto.ca/prof/gelefth/Eleftheriades_Materials_Today_March2009.pdf) -- which can produce very exacting equations -- but are of course simply modelled and are fundamentally just abstractions of physical systems.
On the other hand, complex structures such as your DNA origami can be simulated to a high degree of accuracy, but because they are so complex, it is virtually impossible to find any generalized expression for their behavior.
Somewhere in between is a region where approximate expressions produce reasonably accurate modal results for generalized structures. For example, regular defects made in any material will tend to suppress the propagation of energy when the wavelength of the energy is around one-quarter wavelength in the material.
Selection, I think, should really start with the specifics of your application.
thank you so much Stuart Barth for your answer. for my simulation I need to give some inputs on the comsol file. I have already found a terahertz metamaterial simulation file where they have put an equation which I did not understand why they took it. Also in most of the paper, the exact equation for the input source is not given. thus the struggle. how do I find the input equation or how should I look at it?
Fatematuz Zahura by "input source" do you man an equation to create the physical geometry, or to excite a given structure? Can you let us know which paper you are referring to?
Stuart Barth I found on comsol database one online webinar/workshop where a terahertz metamaterial was modeled and there, input
"(px*py/4/2/Z0_const)*E0^2" this equation is used. I need to know why is this used?
this is used to excite the structure.
https://www.comsol.com/video/simulating-metamaterials-in-the-terahertz-regime-with-comsol-multiphysics
Fatematuz Zahura the "input" you are specifying is detailed in your linked video as being the total input power. I'm not sure why the author has such an expression, but its use ensures that the power is proportional to the input electric field strength (E0) and medium impedance (Z0_const).
The equation for local power density is simply S = E0*H0/2 = (E0^2)/(2*Z0_const). Multiplying this density by the transverse dimensions of the unit cell (px and py) gives the total power incident (P) on the cell (P = S*px*py). The factor of 4 is most likely from the use of a RMS E0 quantity.
Stuart Barth thanks for your answer. I was wondering if I use a light source for exciting the material then would I be using its electric field in the mentioned equation to find total input power? also, the medium impedance was not in the parameter. how it is determined?
Fatematuz Zahura Yes, that's right, using a source with a known field strength would accomplish the same purpose as using a source of known power. In optics the medium impedance is generally assumed to be related to the refractive index (n) as eta/n, in this case it would be the index of the surrounding material (e.g., air).
The factor of 1/4 may be there because only 1/4 of the unit cell is modelled, which may be possible to do using symmetry.
The formula then gives the total power into 1/4 of the unit cell. I think the 1/2 is because E0 is the peak electric field and the RMS electric field squared is E0^2/2, which should be used to calculate the power density.
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