EM waves escaping a metal grating

[hobz]

My understanding so far.

 

Electrons can respond to any EM wave regardless of wavelength.

Ideal conductors have completely free electrons, and thus there electrons can respond to any EM wave.

 

Now if I grate a plate of metal (which is assumed to be an ideal conductor) with holes larger than the wavelength of an incoming EM wave, how can the wave "escape"?

Surely the electrons in the metal surrounding the holes respond to the incoming wave, and if so, I guess they should absorb the energy in the wave?

[Klaynos]

The waves will scatter off of the edges of the grating and diffract through the holes.

 

You might find having a look at waveguide modes interesting, these occur when the wavelength is close to the size of the apertures.

[swansont]

My understanding so far.

 

Electrons can respond to any EM wave regardless of wavelength.

Ideal conductors have completely free electrons, and thus there electrons can respond to any EM wave.

 

Now if I grate a plate of metal (which is assumed to be an ideal conductor) with holes larger than the wavelength of an incoming EM wave, how can the wave "escape"?

Surely the electrons in the metal surrounding the holes respond to the incoming wave, and if so, I guess they should absorb the energy in the wave?

True to a certain extent; you are presenting a classical physics argument. So it fails when QM is important, e.g. high-frequency photons can just ionize the electron or just pass right through without interacting.

 

For the grated sheet, what if you have a wave passing through whose field null occurs where the metal sheet is? Why would the electrons respond? Or if the path of the light was far from the metal?

[hobz]

Thanks for the answers.

 

I will look up some literature on waveguides, Klaynos.

 

swansont: Interesting!

 

From that perspective, there seem to be no answers to your (retorical) questions, but I presume that classical physics would have a way of predicting that microwaves would stay inside the ovens when using a grated piece of metal.

 

What is the QM explanation? Does the photons chance of hitting a free electron vary with its energy (i.e. wavelength)?

[swansont]

Thanks for the answers.

 

I will look up some literature on waveguides, Klaynos.

 

swansont: Interesting!

 

From that perspective, there seem to be no answers to your (retorical) questions, but I presume that classical physics would have a way of predicting that microwaves would stay inside the ovens when using a grated piece of metal.

 

What is the QM explanation? Does the photons chance of hitting a free electron vary with its energy (i.e. wavelength)?

The holes in a microwave are much smaller than the wavelength. 3 GHz EM waves have a wavelength of 10 cm.

 

From a QM standpoint, the photon with a wavelength that large is going to "see" lots of electrons, so it's very likely to interact.

[hobz]

Can you elaborate on how the photon wavelength relates to "seeing" electrons?

[swansont]

The number of electrons it can potentially interact with is large. The cross-section should vary as wavelength^2

[hobz]

This is pretty interesting. Do you have some recommendations of literature dealing with this and perhaps some cue words for google seaches?

Edited August 26, 2012 by hobz