# Propagation of EM waves in non-conducting medium

Let's say I produce a thin electromagnetic wave beam that is directed towards a non-conductive large plastic block (let's say 30cm x 30cm x 30cm). Let's say that the EM beam enters into the solid plastic from point A and goes out from the other side of the block at point B. I want to heat (without melting) the plastic particles that is located closest to the line AB. But I want the rest of the plastic cube to stay relatively cold. In fact, I couldn't find solid answers to the following questions:

1. What would be the best frequency range of the EM wave for this purpose?

2. What is the name of the phenomenon when the EM beam heats the non-conductive plastic material as it propagates from point A to B?

3. As the EM beam propagates from point A to B, would the em beam disperse, or would it propagate in a linear way just like a standard laser pointer?

4. what would be the decay rate of the energy of the EM beam as it travels from A to B in plastic.

Could you help me find answers to these questions and could you provide sources that can help me find answers? Also, it would help a lot if you could give the names of the phenomena that happen in this situation.

## 1 Answer

I don't have a comprehensive (or coherent, sadly) answer, but I tried to explain as much as I could.

1. Absorption (see here and here). Basically, when light goes thorough matter, some photons interact with the matter (which are Compton scattering, absorption and re-emission by atoms, and pair production) that changes the photon count and direction in a way that effectively decreases the number of photons going in the initial direction.

For example, in Compton scattering, the wavelength (and thus, energy) of a photon changes as it interacts with a (free) electron while changing its direction. This effect means that the photon beam will both lose energy and disperse progressively as it moves further in the medium. For different frequency (energy) ranges of the light, the type of interaction that dominates this relationship changes as well.

2. Yes, since the media in general are not ideal nor really isotropic. Any and all nonlinear effects cause dispersion. For example, Compton scattering always makes the beam spread out.

However, I think photon absorption from bound electrons and chemical bounds are the dominating phenomena in the usual energies that are used in these applications, so I will leave here this link to a previous post here. Using this, we can deduce the following:

1. Usually, a resonant frequency is chosen to maximize the photon absorption probability while propagating in the medium (e.g. water and the frequency of microwave ovens). However I am not sure which specific frequencies are used to heat plastics.

Regarding your last question, all I could find was this Wikipedia page on how "Attenuation coefficients" are defined for different kind of waves and media.