What Are the Connections Between Tunneling and Wave Phenomena?

[AronH]

Hi!

I always thought that tunneling was a quantum phenomenum. So another day I found a problem which is about the part of the light that can be transmitted (refracted) even if you send I light beam in an angle greater then the limit angle of two material boundary. By the way looking at a physics book I found that tunnelling can also happen with mechanical waves.
I just want to find where I can get a good explanation to this, tunneling.
Thank you,


Aron

 

[Tide]

This phenomenon has been known for a very long time. It's sometimes called the "skin effect" in electromagnetism and was first studied by Lord Kelvin and Nicola Tesla.

You easily verify the theory behind the effect by simply considering the wave equation for a light wave normally incident onto a conductor with a given number density for unbound electrons. While you will find an oscillatory solution for, say, the electric field outside the conductor, the solution is exponentially decaying inside the conductor (the evanescent wave).

Physically, it is due to the fact that given a finite number density for electrons in the conductor it takes a finite amount of time for the electrons to accelerate and reradiate in a way to destructively interfere with the incident wave. Of course the further into the conductor the cumulative effect of electrons exposed to the fields becomes more effective at excluding the incident field.

Also, if the electron number density is not above a critical density for the incident wave then some portion of the wave will propagate in the usual fashion through the material.

 

[somy]

Well, let's say it in mathematical words:
It is because of the existence of a complex answer in the domain that we have a potential grater than our energy. That answer decreases in a logaritmic way.
That makes the tunneling effect.

 

[AronH]

Thank you guys.

I got the point about the reflection and skin effect.
So let me ask more about this. Where I can find some information about the quantitative necessities to this phenomenum happens. Like the espesure of the material and dependence of it is electron density and how to measure it.
Thank you again, in advance.



Aron

 

[Tide]

Any competent textbook on electricity and magnetism will discuss the skin effect. You can also get additional information with a web search (e.g. Google).