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I'm just curious if given $\epsilon(\omega), \mu(\omega)$ for a fixed frequency $\omega$,could for example a material scientist be able to determine what the material is?

In a follow up question, does anyone know better material parameters such that if I was to give them to a material scientist they would be able to fabricate a material with these material properties?

Thank you.

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  • $\begingroup$ In principle, for a single frequency $\omega_0$ it might be possible to make a dielectric with a certain refractive index, by amorphous mixing of two materials with very different bandgaps, for example $\text{SiO}_2$ and $\text{TiO}_2$. You need to be using them of course within reason, i.e. way below bandgap photon energies. But a certain dispersion curve would be impossible. $\endgroup$
    – José Andrade
    Jun 22, 2020 at 9:53

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Probably not. Most materials are non-magnetic, meaning $\mu\approx\mu_0$. Among non-magnetic materials, you can surely find a pair that have equal $\epsilon$ at some frequency. At this frequency, it wouldn't be possible to tell the materials apart based on $\epsilon$ and $\mu$ alone.

I'm confused by your second question. If you ask for a material that is $1\ \text{mm}$ thick, there are tons of different materials that you could grow/deposit $1\ \text{mm}$ of. If you ask for a material with a certain electrical conductivity that is not too high, you could achieve it with lots of different semiconductors with the appropriate doping. Certainly there are other properties possible.

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  • $\begingroup$ Hi Puk, thanks for answering. I guess just a follow up question: I've posed a math problem where I'm applying an electromagnetic wave at a fixed frequency, and the goal is to figure out what is the permittivity and permeability of a material is that meets a goal I have (its an optimal control problem if you are into math). So really the essence of my question is what other constraints would I have to enforce so that when I solve the math problem I can look at a material scientist and they tell me they would be able to build a material with those properties. Thanks a lot. $\endgroup$
    – Vogtster
    Jun 22, 2020 at 7:59
  • $\begingroup$ It sounds like pretty much any material property you can think of would fit the bill, too many of them might exhaust the available material options though. I'm still not sure why you would make the material scientist's job harder by imposing additional constraints, unless they are necessary. $\endgroup$
    – Puk
    Jun 22, 2020 at 8:08

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