Editing Nonlinear optics (section)

====Principles====
[[Image:wiki_perfect_PCM_photon_recoil.jpg|thumb|right| Vortex photon (blue) with linear momentum <math>\mathbf{P} = \hbar \mathbf{k}</math> and angular momentum <math>L =\pm\hbar\ell</math> is reflected from perfect phase-conjugating mirror. Normal to mirror is <math>\vec{n}</math> , propagation axis is <math>\vec{z}</math>. Reflected photon (magenta) has opposite linear momentum <math>\mathbf{P} = - \hbar \mathbf{k}</math> and angular momentum <math>L = \mp\hbar\ell</math>. Because of conservation laws PC mirror experiences recoil: the vortex phonon (orange) with doubled  linear momentum <math>\mathbf{P} = 2 \hbar \mathbf{k}</math> and angular momentum <math>L = \pm 2 \hbar \ell</math> is excited within mirror.]]

One can interpret optical phase conjugation as being analogous to a [[holography#Dynamic holography|real-time holographic process]].<ref>{{cite journal |first1=David M. |last1=Pepper |first2=Jack |last2=Feinberg |first3=Nicolai V. |last3=Kukhtarev |title=The Photorefractive Effect |journal=Scientific American |volume=263 |issue=4 |pages=62–75 |date=October 1990 |doi=10.1038/scientificamerican1090-62 |jstor=24997062 }}</ref>  In this case, the interacting beams simultaneously interact in a nonlinear optical material to form a dynamic hologram (two of the three input beams), or real-time diffraction pattern, in the material.  The third incident beam diffracts at this dynamic hologram, and, in the process, reads out the ''phase-conjugate'' wave.  In effect, all three incident beams interact (essentially) simultaneously to form several real-time holograms, resulting in a set of diffracted output waves that phase up as the "time-reversed" beam.  In the language of nonlinear optics, the interacting beams result in a nonlinear polarization within the material, which coherently radiates to form the phase-conjugate wave.

Reversal of wavefront means a perfect reversal of photons' linear momentum and angular momentum. The reversal of [[angular momentum]] means reversal of both polarization state and orbital angular momentum.<ref name=Okulov2008/>  Reversal of orbital angular momentum of optical vortex is due to the perfect match of helical phase profiles of the incident and reflected beams.  [[Optical phase conjugation]] is implemented via stimulated Brillouin scattering,<ref name=Okulov2008J/> four-wave mixing, three-wave mixing, static linear holograms and some other tools.

[[Image:PhaseConjugationPrinciple.en.svg|thumb|right|350px|Comparison of a phase-conjugate mirror with a conventional mirror. With the phase-conjugate mirror the image is not deformed when passing through an aberrating element twice.<ref>[http://www.osa-opn.org/home/articles/volume_6/issue_3/features/the_fascinating_behavior_of_light_in_photorefracti/ The Fascinating Behavior of Light in Photorefractive Media | Optics & Photonics News<!-- Bot generated title -->] {{Webarchive|url=https://web.archive.org/web/20150402093011/http://www.osa-opn.org/home/articles/volume_6/issue_3/features/the_fascinating_behavior_of_light_in_photorefracti/ |date=2015-04-02 }}.</ref>]]

The most common way of producing optical phase conjugation is to use a four-wave mixing technique, though it is also possible to use processes such as stimulated Brillouin scattering.