# A Radiation from a dielectric body

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1. Jun 2, 2016

### Karthiksrao

Dear all,

I needed help in finding a source where the derivation of radiation emitted by a dielectric body is laid out.

The derivation of spectral density of radiation emitted from a blackbody at a temperature $T$ is given in many books by populating the energy states using Bose-Einstein statistics. However, try as I might, I have not been able to find any source where the derivation of the spectral density of radiation emitted by a semi-infinite body with a dielectric function $\varepsilon (\omega)$ and at a temperature $T$ is derived from first-principles (populating the quantum states).

I'd assume it should be straightforward since the dielectric function can be approximated by Lorentzian harmonic oscillators. Is it not so ?

Do you know any book/paper which discusses this in detail ?

Many thanks!

2. Jun 2, 2016

I think it takes more than a dielectric function and/or oscillators. It is necessary to have anharmonic terms (essentially non-linear in the restoring force or non-quadratic in the energy) in the Hamiltonian, which may give you a complex dielectric function (with imaginary components) and a complex index of refraction. A completely harmonic Hamiltonian would give you a completely transparent dielectric and thereby the emissivity would likely be near zero. I think the solid state physics book by Ashcroft and Mermin discusses the anharmonic Hamiltonian. I don't have any handy references that have the precise derivation you are looking for, but hopefully this is helpful.

3. Jun 3, 2016

### Karthiksrao

I'm surprised why this topic of radiated energy density by a dielectric body is not commonly dealt with from first principles. I'd assume it to be of primary academic interest.

4. Jun 3, 2016

### Karthiksrao

Regarding what you mentioned, won't damped harmonic oscillators account for absorption in the dielectric ?

5. Jun 3, 2016