Editing Nonlinear optics (section)

====Quantum picture ====
<!-- Deleted image removed: [[Image:Pointing Oam wiki okulov.jpg|thumb|right|350px|Reversal of Linear Momentum '''''<math>\vec \mathbf{P} </math>''''' and Angular Momentum '''<math>\vec \mathbf{L} </math>''' in Phase Conjugating Mirror.]]
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In ''quantum electrodynamics'' the photon with energy <math>\hbar \omega</math> also possesses linear momentum <math>\mathbf{P} = \hbar \mathbf{k}</math> and angular momentum, whose projection on propagation axis is <math>L_\mathbf{z} = \pm \hbar \ell</math>, where <math>\ell</math> is ''topological charge'' of photon, or winding number, <math>\mathbf{z}</math> is propagation axis. The angular momentum projection on propagation axis has ''discrete values'' <math>\pm \hbar \ell</math>.

In ''quantum electrodynamics'' the interpretation of phase conjugation is much simpler compared to ''classical electrodynamics''.  The photon reflected from phase conjugating-mirror (out) has opposite directions of linear and angular momenta with respect to incident photon (in):

:<math>\begin{align}
  \mathbf{P}_\text{out} &= -\hbar \mathbf{k} = -\mathbf{P}_\text{in} = \hbar\mathbf{k}, \\
       {L_\mathbf{z}}_\text{out} &= -\hbar \ell = -{L_\mathbf{z}}_\text{in} = \hbar \ell.
\end{align}</math>