# Radiation from a dielectric body

• A
• Karthiksrao
In summary, the author is looking for a source where the spectral density of radiation emitted by a dielectric body is derived from first principles. He is surprised why this topic is not commonly dealt with from the outset. He thinks it would be of primary academic interest. However, he is unsure if damped harmonic oscillators will account for absorption in the dielectric. He thinks another factor to consider is a Kirckhoff's law type equation where the emissivity and reflectivity are equal for an opaque material and for a dielectric, respectively.

#### 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!

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.

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.

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

Karthiksrao said:
Regarding what you mentioned, won't damped harmonic oscillators account for absorption in the dielectric ?
I think the two are mathematically quite similar, but you might find it written up in the solid state textbooks as an anharmonic term. Meanwhile, one other thing to consider would be a Kirckhoff's law type equation where for an opaque material the emissivity plus the reflectivity is equal to unity. For a dielectric, I think you have a similar relation with a transmission term included. I don't know of a good source that discusses this concept in depth, but hopefully you might find one.

## 1. What is radiation from a dielectric body?

Radiation from a dielectric body refers to the process of electromagnetic waves being emitted from a non-conducting material, such as glass or plastic. This occurs when the molecules in the material are excited and release energy in the form of electromagnetic radiation.

## 2. How is radiation from a dielectric body different from radiation from a conductor?

Radiation from a dielectric body differs from radiation from a conductor in that it is not caused by the movement of free electrons. In a conductor, the free electrons move in response to an electric field and emit radiation. In a dielectric, the molecules themselves are excited and emit radiation without the need for free electrons.

## 3. What factors affect the amount of radiation emitted from a dielectric body?

The amount of radiation emitted from a dielectric body is affected by several factors, including the material's dielectric constant, temperature, and the strength of the electric field applied to it. The size and shape of the body can also influence the amount of radiation emitted.

## 4. How is the radiation from a dielectric body measured?

The radiation emitted from a dielectric body is measured using a device called a spectrometer, which can detect and measure the intensity and wavelength of the electromagnetic waves. This data can then be used to calculate the total amount of radiation emitted by the body.

## 5. What are some practical applications of radiation from a dielectric body?

Radiation from dielectric bodies has various practical applications, including in communication technologies such as antennas and satellite dishes. It is also used in medical imaging techniques such as MRI and in the manufacturing of electronic devices such as computer chips and solar cells.