Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New features!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

123 submissions , 104 unreviewed
3,547 questions , 1,198 unanswered
4,549 answers , 19,356 comments
1,470 users with positive rep
410 active unimported users
More ...

Quantum barrier for photons

+ 5 like - 0 dislike
15 views

In quantum mechanics, a particle may tunnel through a barrier it would not be able to surmount in a classical sense.

My question is this:

What are all the factors that may prevent a photon from propagating (thus it would need quantum tunneling to do so), and can they be described in a general way for any given material?

This post imported from StackExchange Physics at 2014-03-21 17:03 (UCT), posted by SE-user Yuval Weissler
asked Dec 14, 2013 in Theoretical Physics by Yuval Weissler (25 points) [ no revision ]
Do photons have a wave function associated with them? I believe last I heard those developed violate some necessary properties of a Schrodinger wave equation. If it doesn't fill that definition, one would not expect them to behave like a particle in the sense of tunneling.

This post imported from StackExchange Physics at 2014-03-21 17:03 (UCT), posted by SE-user sakanojo

2 Answers

+ 3 like - 0 dislike

Photons have some conditions to have an evanescent wave, e.g. total internal reflection.

Suppose we have some material with index of refraction $n_1$ and a layer of another material, with smaller $n_2<n_1$. At some angle we'll see total internal reflection, i.e. when the light totally reflects, but leaves some exponentially decaying trails in layer with $n_2$. If this layer is continued with original bulk material with $n_1$, we'll intercept these evanescent waves and get normal propagating waves.

Qualitatively, this would look something like this (light goes from bottom-left side, reflected wave is not displayed):

enter image description here

If you necessarily want one-dimensional picture (i.e. not needing the light falling at some angle to surface), then one can use a reflecting surface, having it sufficiently thin - e.g. a thin metal foil.

In fact, any perfect reflector can be used for this (by perfect I mean 100% reflection if reflector is infinitely thick). A special case is a photonic crystal. If wavelength of the light you shine at it is in band gap of the photonic crystal, the light will totally reflect from such crystal because it'll have imaginary wave vector inside, which also means evanescent wave. If the photonic crystal is thin enough, you can have the light tunneled through it and it'll partially go to the other side and then propagate as usual.

This post imported from StackExchange Physics at 2014-03-21 17:03 (UCT), posted by SE-user Ruslan
answered Dec 15, 2013 by Ruslan (85 points) [ no revision ]
+ 1 like - 0 dislike

The potential barrier problem and solution in quantum mechanics is discussed within the solutions of Schrodineger's equation in which there exist potentials, and the solutions of the equations with the boundary conditions give the wave function of a particle, i.e an entity with a mass. In addition it is a non relativistic equation.Thus in this framework:

tunneling

relativistic velocities are not allowed as a particle cannot be described by a wave function that is a solution of the Schrodinger equation.

The photon enters as an interpretation of the energy conservation between transitions of bound state energy levels, a hypothesis that has been amply experimentally observed and validated the use of the Schrodinger equation in first quantization.

The answers to the question What equation describes the wavefunction of a single photon?, asked here a while ago, cover the way the photon is described in first (Dirac equation) and second quantization.

In this preprint a view is suggested of using Maxwell's equations for the wave function of the photon. One could use these and define a barrier and solve for it to get the behavior of the photon's probability to pass the barrier, but it is not a simple problem I could tackle. Generally when one calculates behaviors of photons on reaching a barrier it is wise to use classical solutions of Maxwell's equations. Transmission, reflectance etc describe the behavior of light at barrier. Going down to the individual photon is complicated mathematically and not worth the effort since it can be shown that the classical and the quantum description for photons merges naturally.

This post imported from StackExchange Physics at 2014-03-21 17:03 (UCT), posted by SE-user anna v
answered Dec 15, 2013 by anna v (1,710 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
$\varnothing\hbar$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...