Editing Nonlinear optics (section)

== Nonlinear optical pattern formation ==
Optical fields transmitted through nonlinear Kerr media can also display [[pattern formation]] owing to the nonlinear medium amplifying spatial and temporal noise. The effect is referred to as optical [[Modulational instability|modulation instability]].<ref name="Zakharov 540–548"/> This has been observed both in photo-refractive,<ref>{{Cite journal|last=Soljacic|first=Marin|date=2000-01-01|title=Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media|journal=Physical Review Letters|volume=84|issue=3|pages=467–470|doi=10.1103/PhysRevLett.84.467|pmid=11015940|bibcode=2000PhRvL..84..467S}}</ref> photonic lattices,<ref>{{Cite journal|last1=Jablan|first1=Marinko|last2=Buljan|first2=Hrvoje|last3=Manela|first3=Ofer|last4=Bartal|first4=Guy|last5=Segev|first5=Mordechai|date=2007-04-16|title=Incoherent modulation instability in a nonlinear photonic lattice|journal=Optics Express|language=EN|volume=15|issue=8|pages=4623–33|doi=10.1364/OE.15.004623|pmid=19532708|issn=1094-4087|bibcode=2007OExpr..15.4623J|doi-access=free}}</ref> as well as photo-reactive systems.<ref>{{Cite journal|last1=Burgess|first1=Ian B.|last2=Shimmell|first2=Whitney E.|last3=Saravanamuttu|first3=Kalaichelvi|date=2007-04-01|title=Spontaneous Pattern Formation Due to Modulation Instability of Incoherent White Light in a Photopolymerizable Medium|journal=Journal of the American Chemical Society|volume=129|issue=15|pages=4738–4746|doi=10.1021/ja068967b|pmid=17378567|issn=0002-7863}}</ref><ref>{{Cite journal|last1=Basker|first1=Dinesh K.|last2=Brook|first2=Michael A.|last3=Saravanamuttu|first3=Kalaichelvi|date=2015-09-03|title=Spontaneous Emergence of Nonlinear Light Waves and Self-Inscribed Waveguide Microstructure during the Cationic Polymerization of Epoxides|journal=The Journal of Physical Chemistry C|volume=119|issue=35|pages=20606–20617|doi=10.1021/acs.jpcc.5b07117|issn=1932-7447}}</ref><ref>{{Cite journal|last1=Biria|first1=Saeid|last2=Malley|first2=Philip P. A.|last3=Kahan|first3=Tara F.|last4=Hosein|first4=Ian D.|date=2016-03-03|title=Tunable Nonlinear Optical Pattern Formation and Microstructure in Cross-Linking Acrylate Systems during Free-Radical Polymerization|journal=The Journal of Physical Chemistry C|volume=120|issue=8|pages=4517–4528|doi=10.1021/acs.jpcc.5b11377|issn=1932-7447}}</ref><ref>{{Cite journal|last1=Biria|first1=Saeid|last2=Malley|first2=Phillip P. A.|last3=Kahan|first3=Tara F.|last4=Hosein|first4=Ian D.|date=2016-11-15|title=Optical Autocatalysis Establishes Novel Spatial Dynamics in Phase Separation of Polymer Blends during Photocuring|journal=ACS Macro Letters|volume=5|issue=11|pages=1237–1241|doi=10.1021/acsmacrolett.6b00659|pmid=35614732 }}</ref> In the latter case, optical nonlinearity is afforded by reaction-induced increases in refractive index.<ref>{{Cite journal|last1=Kewitsch|first1=Anthony S.|last2=Yariv|first2=Amnon|date=1996-01-01|title=Self-focusing and self-trapping of optical beams upon photopolymerization|journal=Optics Letters|language=EN|volume=21|issue=1|pages=24–6|doi=10.1364/OL.21.000024|pmid=19865292|issn=1539-4794|bibcode=1996OptL...21...24K|url=https://authors.library.caltech.edu/2845/1/KEWol96.pdf|access-date=2019-08-26|archive-url=https://web.archive.org/web/20200420092429/https://authors.library.caltech.edu/2845/1/KEWol96.pdf|archive-date=2020-04-20|url-status=dead}}</ref> Examples of pattern formation are spatial solitons and vortex lattices in framework of [[nonlinear Schrödinger equation]].<ref name="Okulov, A Yu 2000">{{cite journal |title=Spatial soliton laser: geometry and stability
|journal=Optics and Spectroscopy|volume=89 |issue=1 |pages=145–147 |year=2000 |last1= Okulov |first1=A Yu|s2cid=122790937|doi=10.1134/BF03356001  |bibcode=2000OptSp..89..131O}}</ref><ref name="Okulov, A Yu 2020">{{cite journal |title=Structured light entities, chaos and nonlocal maps
|journal=Chaos, Solitons & Fractals|volume=133 |issue=4|page=109638 |year=2020|last1=  Okulov |first1=A Yu|doi=10.1016/j.chaos.2020.109638|arxiv=1901.09274|bibcode=2020CSF...13309638O|s2cid=118828500}}</ref>