How is momentum conserved in phase mismatch?

  • #1
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.
 

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  • #2
Dale
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The momentum of the field plus the matter is conserved. The momentum of the field alone or the matter alone need not be conserved.
 
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  • #3
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?
 
  • #5
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.
 

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