Editing Nonlinear optics (section)

==Molecular nonlinear optics==
The early studies of nonlinear optics and materials focused on the inorganic solids. With the development of nonlinear optics, molecular optical properties  were investigated, forming molecular nonlinear optics.<ref name=":0">{{cite journal |last1=Gu |first1=Bobo |last2=Zhao |first2=Chujun |last3=Baev |first3=Alexander |last4=Yong |first4=Ken-Tye |last5=Wen |first5=Shuangchun |last6=Prasad |first6=Paras N. |title=Molecular nonlinear optics: recent advances and applications |journal=[[Advances in Optics and Photonics]] |date=2016 |volume=8 |issue=2 |page=328 |doi=10.1364/AOP.8.000328 |bibcode=2016AdOP....8..328G }}</ref> The traditional  approaches used in the past to enhance nonlinearities include extending chromophore π-systems, adjusting bond length alternation, inducing intramolecular charge transfer, extending conjugation in 2D, and engineering multipolar charge distributions. Recently, many novel directions were proposed for enhanced nonlinearity and light manipulation, including twisted chromophores, combining rich density of states with bond alternation, microscopic cascading of second-order nonlinearity, etc. Due to the distinguished advantages, molecular nonlinear optics have been widely used in the biophotonics field, including bioimaging,<ref>{{cite journal |last1=Kuzmin |first1=Andrey N. |title=Resonance Raman probes for organelle-specific labeling in live cells |journal=Scientific Reports |date=2016 |volume=6 |page=28483 |doi=10.1038/srep28483 |pmid=27339882 |pmc=4919686 |bibcode=2016NatSR...628483K }}</ref><ref>{{Cite journal |last1=Zhang |first1=Silu |last2=Liu |first2=Liwei |last3=Ren |first3=Sheng |last4=Li |first4=Zilin |last5=Zhao |first5=Yihua |last6=Yang |first6=Zhigang |last7=Hu |first7=Rui |last8=Qu |first8=Junle |date=2020 |title=Recent advances in nonlinear optics for bio-imaging applications |url=http://www.oejournal.org/J/OEA/Article/Details/A201024000006 |journal=Opto-Electronic Advances |language=en |volume=3 |issue=10 |pages=200003 |doi=10.29026/oea.2020.200003 |issn=2096-4579 |doi-access=free |access-date=2023-11-27 |archive-date=2021-01-21 |archive-url=https://web.archive.org/web/20210121085255/http://www.oejournal.org/J/OEA/Article/Details/A201024000006 |url-status=live }}</ref> phototherapy,<ref>{{cite journal |last1=Gu |first1=Bobo |last2=Wu |first2=Wenbo |last3=Xu |first3=Gaixia |last4=Feng |first4=Guangxue |last5=Yin |first5=Feng |last6=Chong |first6=Peter Han Joo |last7=Qu |first7=Junle |last8=Yong |first8=Ken-Tye |last9=Liu |first9=Bin |title=Precise Two-Photon Photodynamic Therapy using an Efficient Photosensitizer with Aggregation-Induced Emission Characteristics |journal=Advanced Materials |date=2017 |volume=29 |issue=28 |page=1701076 |doi=10.1002/adma.201701076 |pmid=28556297 |bibcode=2017AdM....2901076G |s2cid=205279732 }}</ref> biosensing,<ref>{{cite journal |last1=Yuan |first1=Yufeng |last2=Lin |first2=Yining |last3=Gu |first3=Bobo |last4=Panwar |first4=Nishtha |last5=Tjin |first5=Swee Chuan |last6=Song |first6=Jun |last7=Qu |first7=Junle |last8=Yong |first8=Ken-Tye |title=Optical trapping-assisted SERS platform for chemical and biosensing applications: Design perspectives |journal=Coordination Chemistry Reviews |date=2017 |volume=339 |page=138 |doi=10.1016/j.ccr.2017.03.013 }}</ref> etc.

'''Connecting bulk properties to microscopic properties'''

Molecular nonlinear optics relate optical properties of bulk matter to their microscopic molecular properties. Just as the [[polarizability]] can be described as a [[Taylor series|Taylor series expansion]], one can expand the induced dipole moment in powers of the electric field: <math>\boldsymbol{\mu}=\boldsymbol{\mu_0}+\alpha\cdot\boldsymbol{\Epsilon}+\frac{1}{2}\beta:\boldsymbol{\Epsilon}\boldsymbol{\Epsilon}</math>, where μ is the polarizability, α is the first [[hyperpolarizability]], β is the second hyperpolarizability, and so on.<ref name=":1">{{Cite book |last=McHale |first=Jeanne L. |title=Molecular spectroscopy |date=2017 |publisher=CRC Press, Taylor & Francis Group |isbn=978-1-4665-8658-1 |edition=2nd |location=Boca Raton London New York}}</ref>

'''Novel Nonlinear Media'''

Certain molecular materials have the ability to be optimized for their optical nonlinearity at the microscopic and bulk levels. Due to the delocalization of electrons in π bonds electrons are more easily responsive to applied optical fields and tend to produce larger linear and nonlinear optical responses than those in single (𝜎) bonds. In these systems linear response scales with the length of the conjugated pi system, while nonlinear response scales even more rapidly.<ref>{{Citation |last=Boyd |first=Robert W. |author-link=Robert W. Boyd (physicist) |title=Nonlinear Optics of Plasmonic Systems |date=2020 |url=http://dx.doi.org/10.1016/b978-0-12-811002-7.00023-0 |work=Nonlinear Optics |pages=569–582 |access-date=2023-11-27 |publisher=Elsevier|doi=10.1016/b978-0-12-811002-7.00023-0 |isbn=978-0-12-811002-7 }}</ref>
[[File:Example of donor-acceptor chromaphore GFP HBDI.svg|thumb|Green Fluorescent Protein (GFP) chromophore p-hydroxybenzylideneimidazolinone (HBDI) used in nonlinear bioimaging is an example of a pi-conjugated donor-acceptor (D-π-A) chromophore.]]
One of the many applications of molecular nonlinear optics is the use in nonlinear bioimaging. These nonlinear materials, like multi-photon [[chromophore]]s, are used as biomarkers for two-photon spectroscopy, in which  the attenuation of incident light intensity as it passes through the sample is written as <math>{-dI \over dx}= {N\delta I^2 \over \hbar\omega}</math>.<ref name=":1" />

where N is the number of particles per unit volume, I is intensity of light, and δ is the two photon [[absorption cross section]]. The resulting signal adopts a Lorentzian lineshape with a cross-section proportional to the difference in dipole moments of ground and final states.

Similar highly conjugated chromophores with strong donor-acceptor characteristics are used due to their large difference in the dipole moments, and current efforts in extending their pi-conjugated systems to enhance their nonlinear optical properties are being made.<ref name=":0" />