Editing Nonlinear optics (section)

==Higher-order frequency mixing==
[[Image:Supersonic high harmonics.png|thumb|100px]]
The above holds for <math>\chi^{(2)}</math> processes. It can be extended for processes where <math>\chi^{(3)}</math> is nonzero, something that is generally true in any medium without any symmetry restrictions;  in particular resonantly enhanced sum or difference frequency mixing in gasses is frequently used for extreme or [[Ultraviolet#Tunable vacuum ultraviolet (VUV)|"vacuum" ultra-violet light generation]].<ref name=straussfunk />  In common scenarios, such as mixing in dilute gases, the non-linearity is weak and so the light beams are focused which, unlike the plane wave approximation used above, introduces a pi phase shift on each light beam, complicating the phase-matching requirements.<ref name=straussfunk /> Conveniently, [[difference frequency mixing]] with <math>\chi^{(3)}</math>  cancels this focal phase shift and often has a nearly self-canceling overall phase-matching condition, which relatively simplifies broad wavelength tuning compared to   sum frequency generation.<ref name=straussfunk>{{Cite journal
 | last1 = Strauss
 | first1 = CEM
 | last2 = Funk
 | first2 = DJ
 | title = Broadly tunable difference-frequency generation of VUV using two-photon resonances in H2 and Kr
 | journal = Optics Letters
 | volume = 16
 | issue = 15
 | pages = 1192–4
 | date = 1991
 | url = https://www.osapublishing.org/ol/fulltext.cfm?uri=ol-16-15-1192&id=10705
 | doi = 10.1364/ol.16.001192
 | pmid = 19776917
 | bibcode = 1991OptL...16.1192S
 | access-date = 2015-06-23
 | archive-date = 2024-05-29
 | archive-url = https://web.archive.org/web/20240529134804/https://opg.optica.org/captcha/(S(c0bdkdggeh50wqakxbxp1vlf))/?guid=AEC4DC11-0A8D-48DC-8B6E-84817B588FB2
 | url-status = live
 }}</ref> In  <math>\chi^{(3)}</math> all four frequencies are mixing simultaneously, as opposed to sequential mixing via two <math>\chi^{(2)}</math> processes.

The Kerr effect can be described as a <math>\chi^{(3)}</math> as well.  At high peak powers the Kerr effect can cause [[Filament propagation|filamentation]] of light in air, in which the light travels without dispersion or divergence in a self-generated waveguide.<ref name="lanl">{{Cite book|last1=Xhao |first1=X.M. |title=CLEO '97., Summaries of Papers Presented at the Conference on Lasers and Electro-Optics |volume=11 |pages=377–378 |last2=Jones |first2=R.J. |last3=Strauss |first3=C.E.M. |last4=Funk |first4=D.J. |last5=Roberts |first5=J.P. |last6=Taylor |first6=A.J. |author6-link=Antoinette Taylor|year=1997 |publisher=IEEE |doi=10.1109/CLEO.1997.603294 |isbn=978-0-7803-4125-8 |s2cid=120016673 }}{{dead link|date=May 2016|bot=medic}}{{cbignore|bot=medic}}</ref>  At even high intensities the [[Taylor series]], which led the domination of the lower orders, does not converge anymore and instead a time based model is used. When a noble gas atom is hit by an intense laser pulse, which has an electric field strength comparable to the Coulomb field of the atom, the outermost electron may be ionized from the atom. Once freed, the electron can be accelerated by the electric field of the light, first moving away from the ion, then back toward it as the field changes direction. The electron may then recombine with the ion, releasing its energy in the form of a photon. The light is emitted at every peak of the laser light field which is intense enough, producing a series of [[attosecond]] light flashes. The photon energies generated by this process can extend past the 800th harmonic order up to a few K[[Electronvolt|eV]]. This is called [[High harmonic generation|high-order harmonic generation]]. The laser must be linearly polarized, so that the electron returns to the vicinity of the parent ion. High-order harmonic generation has been observed in noble gas jets, cells, and gas-filled capillary waveguides.