# Light Localization: Exploring the Heisenberg Uncertainty Principle

• ecnyx
In summary, the conversation discusses the concept of light localization and its relation to the Heisenberg uncertainty principle. It also mentions the use of photonic crystals to trap photons and how this relates to the quantization of energy. The speakers also question whether the uncertainty principle allows for the confinement of particles in small spaces.
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!

ecnyx said:
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.

ecnyx said:
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.

## 1. What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle is a fundamental principle in quantum mechanics that states that it is impossible to know both the exact position and momentum of a subatomic particle at the same time. This is due to the wave-particle duality of particles, where they can exhibit characteristics of both waves and particles.

## 2. How does light localization relate to the Heisenberg Uncertainty Principle?

Light localization is a phenomenon that occurs when light is confined to a small space, such as in a cavity or between two mirrors. This confinement leads to an increase in uncertainty in the position of the light particles, in accordance with the Heisenberg Uncertainty Principle.

## 3. What is the significance of studying light localization?

Studying light localization allows us to better understand the behavior of light at a subatomic level and how it interacts with matter. It also has potential applications in fields such as quantum computing and telecommunications.

## 4. How do scientists explore the Heisenberg Uncertainty Principle in relation to light localization?

Scientists use various experimental techniques, such as laser spectroscopy and quantum optics, to study the behavior of light particles in confined spaces and observe how the Heisenberg Uncertainty Principle applies to them.

## 5. Can the Heisenberg Uncertainty Principle be violated?

No, the Heisenberg Uncertainty Principle is a fundamental principle in quantum mechanics and has been extensively tested and proven through experiments. It is a fundamental limitation on our ability to measure the exact position and momentum of a subatomic particle.

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