Tunneling of light through thin metal films

[Dale]

Metal is normally opaque in the visible range of the spectrum, so that makes it a good "barrier" to photons in that range. But if a film of metal is made thin enough then it is semi-transparent.

Is this an example of tunneling or is it based on some other principle? Does the attenuation as a function of thickness follow the expected amount for tunneling?

 

[PeterDonis]

I think the basic idea here is optical depth: any material has a finite depth that is required to absorb a given amount of incoming light. "Opaque" really just means "thicker than the optical depth required to absorb all incoming light, at least to the sensitivity we can measure".

I'm not sure tunneling is involved here; I think it's just the basics of absorption. That still requires QM to explain how the light is absorbed and what internal degrees of freedom in the material take up the absorbed energy, but I don't think any of that requires tunneling.

 

[tech99]

Maybe it is just the skin effect?

 

[Vanadium 50]

I think this is classical.

Imagine an EM wave impinging on a conductor. At the conductor, E is forced to zero, but B keeps right on going, and it generates an E field on the other side. (Both sides, actually - a transmitted and a reflected wave). No tunneling, or even quantum.

This model also sets the scale for the thickness limit - maybe 100 nm, but not thousands.

 

[Dale]

Thanks!

 

[Dale]

I think the basic idea here is optical depth: any material has a finite depth that is required to absorb a given amount of incoming light. "Opaque" really just means "thicker than the optical depth required to absorb all incoming light, at least to the sensitivity we can measure".

Ok, my understanding is that tunneling is exponential in the thickness. So as the barrier gets thinner the number that make it through increases exponentially.

If a material is thinner than the optical depth, do we get some other behavior classically?

At the conductor, E is forced to zero, but B keeps right on going, and it generates an E field on the other side. (Both sides, actually - a transmitted and a reflected wave). No tunneling, or even quantum.

This sounds like there shouldn’t be much dependence on the thickness for small thicknesses. In other words, it should be more or less a fixed attenuation for at least a couple of wavelengths.

 

[PeterDonis]

If a material is thinner than the optical depth, do we get some other behavior classically?

I believe attenuation is generally linear in the thickness of the medium for gases, such as analyzing absorption of light in the atmosphere.

I have not been able to find an analysis specific to metals. However, I think your response to @Vanadium 50 is reasonable given that the thickness he gave is smaller than EM wavelengths in the optical range. For the case of gases like the atmosphere, the thickness is of course a huge number of wavelengths.

 

[Vanadium 50]

it should be more or less a fixed attenuation for at least a couple of wavelengths.

I think the argument says its not much larger than a wavelength. Make the conductor too thick and the B field also loses support because the E field is zero for a long distance.

the atmosphere

...is not a good conductor.

 

[Dale]

Ok, either linear or constant at small distances precludes tunneling as a possible explanation.

 

[Vanadium 50]

I'm not sure where you are getting that from.

To me, "tunneling" means the particle traverses a classically forbidden region. For a thin metal film, it's attenuated, sure, but not classically forbidden. So I would not use this as an example.

 

[Dale]

I'm not sure where you are getting that from.

My understanding is that the probability of tunneling is exponential in the thickness of the barrier. As the thickness goes up the probability goes down exponentially.

 

[PeterDonis]

...is not a good conductor.

Yes, good point. I assume the large difference in density between a gas and a metal would also be a factor.

 

[anuttarasammyak]

School exercises of tunneling effect deal with particle with mass. The particles go through or back but do not be absorbed or annihilate. Apparently basic tunneling effect formula does not cover photons.