# Conservation Laws in Photon Parametric Down-Conversion

As Wikipedia explains, one photon passing through a crystal sometimes down-converts to two photons. Wikipedia says total energy and momentum are conserved by just considering the three photon states; is Wikipedia wrong here?

It seems a phonon (or something else) is needed too. If Wikipedia is right, can you provide 3 example (non-parallel) momenta vectors so that I can see my logic mistake?

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 The crystal itself breaks translation symmetry and absorbs a tiny amount of momentum as a whole during a seeming momentum violating process. This is because the phenomenon is coherent along all the crystal atoms, it's not paradoxical. – Ron Maimon Sep 7 '12 at 15:28

That doesn't solve the problem, because the parametric downconversion happens in a material, and materials always have dispersion (different refractive index at different wavelengths). The nature of dispersion makes it difficult in normal circumstances to simultaneously have $\omega = \omega_1 + \omega_2$ and $k = k_1 + k_2$, even when the wavevectors are parallel. But with a bit of cleverness and effort it is possible.