How is momentum conserved in phase mismatch?

[Korak Biswas]

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.

 

[Dale]

The momentum of the field plus the matter is conserved. The momentum of the field alone or the matter alone need not be conserved.

 

[Korak Biswas]

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?

 

[Dale]

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

 

[Korak Biswas]

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.