How Does Light Localization Relate to the Heisenberg Uncertainty Principle?

[ecnyx]

Hi! I am a first timer, and I have a question regarding light localization (hope I'm in the right section). I was wondering about light localization and how it relates to the Heisenberg uncertainty principle, if at all. I am currently studying photonic crystals, and this question deals exclusively to photonic crystals, but perhaps could be extended to other structures.
Suppose I have a photonic crystal with no defects which consist of a square lattice of air holes in dielectric material, and suppose it has a photonic band gap at 1.3um. Suppose I impose a defect somewhere in the crystal (a defect being that choose an air hole, and fill it up with the dielectric material of the crystal, so there no longer is a hole at that point), light at 1.3um will be able to exist in this defect, but must decay away into the crystal by definition of the photonic band gap. However, the uncertainty principle states that dx*dp >= h, so doesn't this imply that you cannot confine a small particle into a small "box"? In this case, I am trying to trap photons in a resonant cavity, so how does that work? In addition, how about electron in a box? In the case of electron in a box, energy becomes quantized because only certain values satisfy the eigenvalue equation, so is this analogous to photons in a box? I don't think this violates the principle, but I can't figure out why it doesn... Can someone explain this? Am I not thinking on the right track? Am I confused?
Thanks!

 

[DrClaude]

However, the uncertainty principle states that dx*dp >= h, so doesn't this imply that you cannot confine a small particle into a small "box"?

No, it doesn't imply that. Simply, the smaller the box, the more uncertain the momentum of the particle trapped in it.

In the case of electron in a box, energy becomes quantized because only certain values satisfy the eigenvalue equation, so is this analogous to photons in a box?

Yes. Not all modes of the electromagnetic field exist in a cavity. The possible value of the frequency (or wavelength) of the photons in the cavity is quantized.