Can Relative Permittivity of Aluminum Be Calculated from Its Plasma Frequency?

[minerva]

Consider a metal such as Al.
How do we look up or determine the relative permittivity of the metal?

Suppose we have some known incident frequency, say about c/500nm for visible light.
We can look up the bulk plasma frequency (3.7 PHz for Al), can it be calculated from that?

For context, what I want to calculate is the desired hole diameter and geometry as a function of the desired filter centre wavelength, in a nanoscale plasmonic hole-grid structure like this.

https://www.intechopen.com/books/pl...ce-plasmon-polaritons-in-cmos-digital-imaging

We know the metal thickness, want to design the appropriate hole spacing and diameter, know the metal chosen, and know the permittivity of the substrate (glass etc) material.

 

[Useful nucleus]

Consider a metal such as Al.
How do we look up or determine the relative permittivity of the metal?

Suppose we have some known incident frequency, say about c/500nm for visible light.
We can look up the bulk plasma frequency (3.7 PHz for Al), can it be calculated from that?

For context, what I want to calculate is the desired hole diameter and geometry as a function of the desired filter centre wavelength, in a nanoscale plasmonic hole-grid structure like this.

https://www.intechopen.com/books/pl...ce-plasmon-polaritons-in-cmos-digital-imaging

We know the metal thickness, want to design the appropriate hole spacing and diameter, know the metal chosen, and know the permittivity of the substrate (glass etc) material.

It has been a while since I touched the topic of dielectrics. But as far as I recall, the relative permittivity of a metal is essentially infinite. It is finite, however, for an insulator/semiconductor.

 

[Lord Jestocost]

I think there are some papers reporting measurements on the dielectric response of aluminum as a function of frequency.

 

[DrDu]

It has been a while since I touched the topic of dielectrics. But as far as I recall, the relative permittivity of a metal is essentially infinite.

Not in the optical region.

 

[Henryk]

It has been a while since I touched the topic of dielectrics. But as far as I recall, the relative permittivity of a metal is essentially infinite

That's true only at DC. At non-zero frequency, the permittivity is finite, see for example http://muri.lci.kent.edu/References/NIM_Papers/Permittivity/1983_Ordal_optical.pdf

How do we look up or determine the relative permittivity of the metal?

If I remember correctly (it has been many years ago) you can get permittivity numbers from ellipsometry measurements.