How is momentum conserved in phase mismatch?

  • Context: Graduate 
  • Thread starter Thread starter Korak Biswas
  • Start date Start date
  • Tags Tags
    Momentum Phase
Click For Summary

Discussion Overview

The discussion centers around the conservation of momentum in the context of light interacting with a second order non-linear medium, specifically addressing the phenomenon of frequency doubling and the implications of phase mismatch on momentum conservation. Participants explore theoretical aspects and seek clarification on the underlying principles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that shining light of frequency ω on a non-linear medium results in radiation of frequency 2ω, raising questions about the source of momentum mismatch despite the principle of momentum conservation.
  • Another participant asserts that the conservation of momentum applies to the combined system of the field and matter, suggesting that the individual conservation of momentum for the field or matter alone is not necessary.
  • A participant expresses a desire for further elaboration on how momentum is transferred from the fields to matter, indicating a gap in understanding related to Maxwell's equations.
  • References to a longstanding debate in the literature are made, with a participant sharing a paper they believe addresses the issue comprehensively.

Areas of Agreement / Disagreement

Participants generally agree that momentum conservation applies to the combined system of field and matter, but there is no consensus on the specifics of how momentum mismatch arises or is resolved in this context. The discussion remains unresolved with multiple viewpoints presented.

Contextual Notes

The discussion highlights limitations in understanding the transfer of momentum and the role of Maxwell's equations, as well as the ongoing debate in the literature regarding these concepts.

Korak Biswas
Messages
28
Reaction score
8
From classical EM theory, we know that if we shine light of frequency ω on a second order non-linear medium, a radiation of frequency 2ω is created. The amplitude of the radiation of frequency 2ω is dependent on the momentum difference between the incident field and the created field. But I can't understand where this momentum mismatch comes from. The momentum should be conserved always.
 
Physics news on Phys.org
The momentum of the field plus the matter is conserved. The momentum of the field alone or the matter alone need not be conserved.
 
  • Like
Likes   Reactions: Korak Biswas
Dale said:
The momentum of the field plus the matter is conserved. The momentum of the field alone or the matter alone need not be conserved.
Thanks for your reply. I guessed it. The fields somehow transfer some amount of momentum to matter. But I couldn't explain this using Maxwell's equations. Will you please elaborate?
 
Korak Biswas said:
Will you please elaborate?
This is a longstanding debate in the literature, but my favorite paper on the topic is this one (which I think completely resolves the debate)

https://arxiv.org/abs/0710.0461
 
Dale said:
This is a longstanding debate in the literature, but my favorite paper on the topic is this one (which I think completely resolves the debate)

https://arxiv.org/abs/0710.0461
Thanks once again. I will go through this and come back to you if necessary.
 
  • Like
Likes   Reactions: Dale

Similar threads

Undergrad Conservation of angular momentum during collisions
  • · Replies 3 ·
Replies
3
Views
3K
High School Why is KE not conserved when momentum is?
  • · Replies 53 ·
2
Replies
53
Views
5K
Graduate Conceptual questions about Angular Momentum Conservation and torque
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Conservation of Momentum in Classical Field Theory
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Do electromagnetic fields have momentum?
  • · Replies 15 ·
Replies
15
Views
2K
Graduate Momentum not conserved for Contracting Concentric Shells
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Speed of light after exiting a transparent medium
  • · Replies 17 ·
Replies
17
Views
2K
Graduate Independence of Energy and Momentum Conservation
  • · Replies 30 ·
2
Replies
30
Views
5K
Graduate Can conservation of angular momentum cause rotational phase shift?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate How Does Retracting Robot Arms Affect Angular and Linear Momentum?
  • · Replies 3 ·
Replies
3
Views
2K