4097:, 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
6281:
6162:
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, phototherapy, biosensing, etc.
31:
4498:
4204:
3614:). There are several schemes of choosing the polarizations for this crystal type. If the signal and idler have the same polarization, it is called "type-I phase matching", and if their polarizations are perpendicular, it is called "type-II phase matching". However, other conventions exist that specify further which frequency has what polarization relative to the crystal axis. These types are listed below, with the convention that the signal wavelength is shorter than the idler wavelength.
3873:
2700:
6131:
974:
1505:
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2620:
3848:. This results in the polarization response of the crystal to be shifted back in phase with the pump beam by reversing the nonlinear susceptibility. This allows net positive energy flow from the pump into the signal and idler frequencies. In this case, the crystal itself provides the additional wavevector
5969:
5303:
Note that the constant of proportionality between the signal and conjugate beams can be greater than 1. This is effectively a mirror with a reflection coefficient greater than 100%, producing an amplified reflection. The power for this comes from the two pump beams, which are depleted by the process.
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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
3819:
axes. In those crystals, type-I and -II phase matching are usually the most suitable schemes. In positive uniaxial crystals, types VII and VIII are more suitable. Types II and III are essentially equivalent, except that the names of signal and idler are swapped when the signal has a longer wavelength
3609:
depends on the polarization and direction of the light that passes through. The polarizations of the fields and the orientation of the crystal are chosen such that the phase-matching condition is fulfilled. This phase-matching technique is called angle tuning. Typically a crystal has three axes, one
6161:
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. The traditional approaches used in the past to enhance nonlinearities include extending
4477:. 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
734:
805:
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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
3828:
that is not parallel to the propagation vector. This would lead to beam walk-off, which limits the nonlinear optical conversion efficiency. Two other methods of phase matching avoid beam walk-off by forcing all frequencies to propagate at a 90° with respect to the optical axis of the crystal.
6149:. This has been observed both in photo-refractive, photonic lattices, as well as photo-reactive systems. In the latter case, optical nonlinearity is afforded by reaction-induced increases in refractive index. Examples of pattern formation are spatial solitons and vortex lattices in framework of
6873:
Bula, C.; McDonald, K. T.; Prebys, E. J.; Bamber, C.; Boege, S.; Kotseroglou, T.; Melissinos, A. C.; Meyerhofer, D. D.; Ragg, W.; Burke, D. L.; Field, R. C.; Horton-Smith, G.; Odian, A. C.; Spencer, J. E.; Walz, D.; Berridge, S. C.; Bugg, W. M.; Shmakov, K.; Weidemann, A. W. (22 April 1996).
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Note: Parametric generation and amplification is a variation of difference-frequency generation, where the lower frequency of one of the two generating fields is much weaker (parametric amplification) or completely absent (parametric generation). In the latter case, the fundamental
1341:
1092:
3950:. 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. Conveniently,
4158:(necessary to obtain phase matching, see below), having a specific crystal symmetry, being transparent for both the impinging laser light and the frequency-doubled wavelength, and having high damage thresholds, which makes them resistant against the high-intensity laser light.
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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.
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The other method is quasi-phase-matching. In this method the frequencies involved are not constantly locked in phase with each other, instead the crystal axis is flipped at a regular interval Λ, typically 15 micrometres in length. Hence, these crystals are called
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of the nonlinear material is not changed by the interaction with the optical field. As a consequence of this, the process is "instantaneous". Energy and momentum are conserved in the optical field, making phase matching important and polarization-dependent.
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8160:
Gu, Bobo; Wu, Wenbo; Xu, Gaixia; Feng, Guangxue; Yin, Feng; Chong, Peter Han Joo; Qu, Junle; Yong, Ken-Tye; Liu, Bin (2017). "Precise Two-Photon
Photodynamic Therapy using an Efficient Photosensitizer with Aggregation-Induced Emission Characteristics".
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6126:{\displaystyle {\begin{aligned}\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{aligned}}}
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One undesirable effect of angle tuning is that the optical frequencies involved do not propagate collinearly with each other. This is due to the fact that the extraordinary wave propagating through a birefringent crystal possesses a
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acts as a driver/source of the electromagnetic waves. One of the consequences of this is a nonlinear interaction that results in energy being mixed or coupled between different frequencies, which is often called a "wave mixing".
969:{\displaystyle \nabla \times \nabla \times \mathbf {E} +{\frac {n^{2}}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}\mathbf {E} =-{\frac {1}{\varepsilon _{0}c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}\mathbf {P} ^{\text{NL}},}
5299:
that is, the generated beam amplitude is the complex conjugate of the signal beam amplitude. Since the imaginary part of the amplitude contains the phase of the beam, this results in the reversal of phase property of the effect.
75:
of the light. The non-linearity is typically observed only at very high light intensities (when the electric field of the light is >10 V/m and thus comparable to the atomic electric field of ~10 V/m) such as those provided by
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1975:
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Yuan, Yufeng; Lin, Yining; Gu, Bobo; Panwar, Nishtha; Tjin, Swee Chuan; Song, Jun; Qu, Junle; Yong, Ken-Tye (2017). "Optical trapping-assisted SERS platform for chemical and biosensing applications: Design perspectives".
6960:
Thaury, C.; Quéré, F.; Geindre, J.-P.; Levy, A.; Ceccotti, T.; Monot, P.; Bougeard, M.; Réau, F.; d’Oliveira, P.; Audebert, P.; Marjoribanks, R.; Martin, Ph (1 June 2007). "Plasma mirrors for ultrahigh-intensity optics".
7736:
Basker, Dinesh K.; Brook, Michael A.; Saravanamuttu, Kalaichelvi (2015-09-03). "Spontaneous
Emergence of Nonlinear Light Waves and Self-Inscribed Waveguide Microstructure during the Cationic Polymerization of Epoxides".
5200:
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means reversal of both polarization state and orbital angular momentum. Reversal of orbital angular momentum of optical vortex is due to the perfect match of helical phase profiles of the incident and reflected beams.
1334:
is true in general, even for an isotropic medium. However, even when this term is not identically 0, it is often negligibly small and thus in practice is usually ignored, giving us the standard nonlinear wave equation:
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or two of which have a different refractive index than the other one(s). Uniaxial crystals, for example, have a single preferred axis, called the extraordinary (e) axis, while the other two are ordinary axes (o) (see
7772:
Biria, Saeid; Malley, Philip P. A.; Kahan, Tara F.; Hosein, Ian D. (2016-03-03). "Tunable
Nonlinear Optical Pattern Formation and Microstructure in Cross-Linking Acrylate Systems during Free-Radical Polymerization".
4109:. 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.
1500:{\displaystyle \nabla ^{2}\mathbf {E} -{\frac {n^{2}}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}\mathbf {E} ={\frac {1}{\varepsilon _{0}c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}\mathbf {P} ^{\text{NL}}.}
6391:
5294:
6363:
1008:
4137:
Practically, frequency doubling is carried out by placing a nonlinear medium in a laser beam. While there are many types of nonlinear media, the most common media are crystals. Commonly used crystals are BBO
3945:
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
3852: = 2π/Λ (and hence momentum) to satisfy the phase-matching condition. Quasi-phase-matching can be expanded to chirped gratings to get more bandwidth and to shape an SHG pulse like it is done in a
3672:
2719:
as a function of wavelength (or increases as a function of frequency). This makes phase matching impossible in most frequency-mixing processes. For example, in SHG, there is no simultaneous solution to
2149:
7693:
Burgess, Ian B.; Shimmell, Whitney E.; Saravanamuttu, Kalaichelvi (2007-04-01). "Spontaneous
Pattern Formation Due to Modulation Instability of Incoherent White Light in a Photopolymerizable Medium".
7808:
Biria, Saeid; Malley, Phillip P. A.; Kahan, Tara F.; Hosein, Ian D. (2016-11-15). "Optical
Autocatalysis Establishes Novel Spatial Dynamics in Phase Separation of Polymer Blends during Photocuring".
3987:
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. In
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Temperature tuning is used when the pump (laser) frequency polarization is orthogonal to the signal and idler frequency polarization. The birefringence in some crystals, in particular
4505:
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.
3087:
2806:
1643:
6284:
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.
7286:
6257:{\displaystyle {\boldsymbol {\mu }}={\boldsymbol {\mu _{0}}}+\alpha \cdot {\boldsymbol {\mathrm {E} }}+{\frac {1}{2}}\beta :{\boldsymbol {\mathrm {E} }}{\boldsymbol {\mathrm {E} }}}
2752:
1132:
6277:
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.
4467:
4396:
4270:
2615:{\displaystyle {\begin{aligned}\mathbf {P} ^{\text{NL}}&=\varepsilon _{0}\chi ^{(2)}\mathbf {E} ^{2}(t)\\&={\frac {\varepsilon _{0}}{4}}\chi ^{(2)}\left,\end{aligned}}}
5950:
4501:
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.
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It is possible, using nonlinear optical processes, to exactly reverse the propagation direction and phase variation of a beam of light. The reversed beam is called a
5895:
3512:
165:(THG), generation of light with a tripled frequency (one-third the wavelength), three photons are destroyed, creating a single photon at three times the frequency.
8014:
Gu, Bobo; Zhao, Chujun; Baev, Alexander; Yong, Ken-Tye; Wen, Shuangchun; Prasad, Paras N. (2016). "Molecular nonlinear optics: recent advances and applications".
5559:
3175:
127:. However, some nonlinear effects were discovered before the development of the laser. The theoretical basis for many nonlinear processes was first described in
6768:
Lewis, Gilbert N.; Lipkin, David; Magel, Theodore T. (November 1941). "Reversible
Photochemical Processes in Rigid Media. A Study of the Phosphorescent State".
5762:
4693:
3049:
6292:, 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
1752:
729:{\displaystyle \mathbf {P} (t)=\varepsilon _{0}\left(\chi ^{(1)}\mathbf {E} (t)+\chi ^{(2)}\mathbf {E} ^{2}(t)+\chi ^{(3)}\mathbf {E} ^{3}(t)+\ldots \right),}
5963:. The photon reflected from phase conjugating-mirror (out) has opposite directions of linear and angular momenta with respect to incident photon (in):
104:
for her PhD in 1931, but it remained an unexplored theoretical curiosity until 1961 and the almost simultaneous observation of two-photon absorption at
6372:. The resulting signal adopts a Lorentzian lineshape with a cross-section proportional to the difference in dipole moments of ground and final states.
6733:
4651:{\displaystyle \Xi _{j}(\mathbf {x} ,t)={\frac {1}{2}}E_{j}(\mathbf {x} )e^{i\left(\omega _{j}t-\mathbf {k} \cdot \mathbf {x} \right)}+{\text{c.c.}},}
1870:
7573:
5556:
which is a linear momentum density of electromagnetic field. In the same way a phase-conjugated wave has an opposite angular momentum density vector
159:, generation of light with a doubled frequency (half the wavelength), two photons are destroyed, creating a single photon at two times the frequency.
6820:
Chen, Szu-yuan; Maksimchuk, Anatoly; Umstadter, Donald (17 December 1998). "Experimental observation of relativistic nonlinear
Thomson scattering".
5008:{\displaystyle P_{\omega }={\frac {1}{2}}\chi ^{(3)}\varepsilon _{0}E_{1}E_{2}E_{3}^{*}e^{i(\omega t-\mathbf {k} \cdot \mathbf {x} )}+{\text{c.c.}}}
7102:
5095:
2800:
The above ignores the position dependence of the electrical fields. In a typical situation, the electrical fields are traveling waves described by
6545:
3405:
2957:
8561:
8331:
6288:
One of the many applications of molecular nonlinear optics is the use in nonlinear bioimaging. These nonlinear materials, like multi-photon
3820:
than the idler. For this reason, they are sometimes called IIA and IIB. The type numbers V–VIII are less common than I and II and variants.
7128:
3853:
1087:{\displaystyle \nabla \times \left(\nabla \times \mathbf {V} \right)=\nabla \left(\nabla \cdot \mathbf {V} \right)-\nabla ^{2}\mathbf {V} }
8139:
4093:
of light in air, in which the light travels without dispersion or divergence in a self-generated waveguide. At even high intensities the
8650:
7352:
Bai, Zhenxu; Wang, Yulei; Lu, Zhiwei; Yuan, Hang; Jiang, Li; Tan, Tan; Liu, Zhaohong; Wang, Hongli; Cui, Can; Hasi, Wuliji (2016-10-01).
5229:
7144:
6295:
4494:
is implemented via stimulated
Brillouin scattering, four-wave mixing, three-wave mixing, static linear holograms and some other tools.
1742: + 1)-wave mixing. As an example, if we consider only a second-order nonlinearity (three-wave mixing), then the polarization
7844:
4687:
If the pump waves and the signal wave are superimposed in a medium with a non-zero χ, this produces a nonlinear polarization field:
3624:
457:
In these processes, the medium has a linear response to the light, but the properties of the medium are affected by other causes:
8529:
5546:{\displaystyle \mathbf {S} (\mathbf {r} ,t)=\epsilon _{0}c^{2}\mathbf {E} (\mathbf {r} ,t)\times \mathbf {B} (\mathbf {r} ,t),}
1627:{\displaystyle \nabla ^{2}\mathbf {E} -{\frac {n^{2}}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}\mathbf {E} =\mathbf {0} ,}
1280:{\displaystyle \nabla ^{2}\mathbf {E} -{\frac {n^{2}}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}\mathbf {E} =\mathbf {0} .}
214:
6566:
4828:
As above, the phase-matching condition determines which of these waves is the dominant. By choosing conditions such that ω = ω
8292:
8252:
7328:
7138:
6678:
6653:
6625:
6589:
6532:
6517:
6170:
Molecular nonlinear optics relate optical properties of bulk matter to their microscopic molecular properties. Just as the
422:
2120:{\displaystyle \mathbf {E} (t)={\frac {1}{2}}E_{1}e^{-i\omega _{1}t}+{\frac {1}{2}}E_{2}e^{-i\omega _{2}t}+{\text{c.c.}},}
3119:
357:(XPM), where one wavelength of light can affect the phase of another wavelength of light through the optical Kerr effect.
6933:
Koga, J.; Esirkepov, T.Z.; Bulanov, S.V. (2005). "Nonlinear Thomson scattering in the strong radiation damping regime".
143:, polarization, phase or path of incident light. These nonlinear interactions give rise to a host of optical phenomena:
6804:
5307:
The frequency of the conjugate wave can be different from that of the signal wave. If the pump waves are of frequency ω
189:(OPA), amplification of a signal input in the presence of a higher-frequency pump wave, at the same time generating an
5839:
4401:
4398:. Because of conservation laws PC mirror experiences recoil: the vortex phonon (orange) with doubled linear momentum
4333:
8324:
5806:
4210:
1515:
The nonlinear wave equation is an inhomogeneous differential equation. The general solution comes from the study of
177:(SFG), generation of light with a frequency that is the sum of two other frequencies (SHG is a special case of this).
6150:
8016:
6557:
4101:
light flashes. The photon energies generated by this process can extend past the 800th harmonic order up to a few K
186:
17:
6996:
Hernández-Acosta, M A; Soto-Ruvalcaba, L; Martínez-González, C L; Trejo-Valdez, M; Torres-Torres, C (2019-09-17).
1140:
4485:
Reversal of wavefront means a perfect reversal of photons' linear momentum and angular momentum. The reversal of
4134:
can be converted to visible light, with wavelengths of 532 nm (green) or 400 nm (violet) respectively.
2919:{\displaystyle E_{j}(\mathbf {x} ,t)=E_{j,0}e^{i(\mathbf {k} _{j}\cdot \mathbf {x} -\omega _{j}t)}+{\text{c.c.}}}
2757:
2676:
1720:{\displaystyle {\frac {1}{\varepsilon _{0}c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}\mathbf {P} ^{\text{NL}}}
1516:
1300:
366:
180:
171:(HHG), generation of light with frequencies much greater than the original (typically 100 to 1000 times greater).
7593:
Soljacic, Marin (2000-01-01). "Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media".
199:(OPO), generation of a signal and idler wave using a parametric amplifier in a resonator (with no signal input).
8477:
7250:
6875:
4143:
3054:
196:
3840:
is highly temperature-dependent. The crystal temperature is controlled to achieve phase-matching conditions.
6487:
1178:
792:
202:
8317:
6744:
3861:
1104:
515:
6145:
owing to the nonlinear medium amplifying spatial and temporal noise. The effect is referred to as optical
3947:
8614:
6471:
4147:
498:
35:
7090:
4437:
8445:
8418:
8268:
8108:
Zhang, Silu; Liu, Liwei; Ren, Sheng; Li, Zilin; Zhao, Yihua; Yang, Zhigang; Hu, Rui; Qu, Junle (2020).
6613:
6385:
4369:
4243:
2723:
2668:
152:
109:
7469:
Pepper, David M.; Feinberg, Jack; Kukhtarev, Nicolai V. (October 1990). "The Photorefractive Effect".
7353:
6542:
8671:
6368:
where N is the number of particles per unit volume, I is intensity of light, and δ is the two photon
5929:
4491:
3375:
within the nonlinear medium, the oscillating second-order polarization radiates at angular frequency
416:
162:
6567:
Robert Boyd plenary presentation: Quantum Nonlinear Optics: Nonlinear Optics Meets the Quantum World
5708:{\displaystyle \mathbf {L} _{\text{out}}(\mathbf {r} ,t)=-\mathbf {L} _{\text{in}}(\mathbf {r} ,t).}
5428:{\displaystyle \mathbf {S} _{\text{out}}(\mathbf {r} ,t)=-\mathbf {S} _{\text{in}}(\mathbf {r} ,t),}
8551:
6369:
6146:
5783:
4106:
2672:
405:
351:
Self-diffraction, splitting of beams in a multi-wave mixing process with potential energy transfer.
208:
174:
168:
5904:
5725:
3356:
2932:
7251:"Broadly tunable difference-frequency generation of VUV using two-photon resonances in H2 and Kr"
6437:
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3990:
3957:
3915:
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465:
372:
246:
183:(DFG), generation of light with a frequency that is the difference between two other frequencies.
85:
7547:
Okulov, A. Yu. (2008). "Optical and Sound Helical structures in a Mandelstam–Brillouin mirror".
7197:"Type-0 second order nonlinear interaction in monolithic waveguides of isotropic semiconductors"
7091:"Non-linear optical channels of the polarizability induction in a pair of interacting molecules"
6390:
4304:
4275:
8635:
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8109:
796:
534:
354:
120:
3591:{\displaystyle {\vec {\mathbf {k} }}_{3}={\vec {\mathbf {k} }}_{1}+{\vec {\mathbf {k} }}_{2}.}
514:
Parametric and "instantaneous" (i.e. material must be lossless and dispersionless through the
211:, the special case of OPO or OPG when the signal and idler degenerate in one single frequency,
8640:
8609:
8472:
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7183:
7168:
7124:
6507:
3857:
2680:
428:
341:
307:
293:
220:
97:
5621:{\displaystyle \mathbf {L} (\mathbf {r} ,t)=\mathbf {r} \times \mathbf {S} (\mathbf {r} ,t)}
3343:{\displaystyle P^{(2)}(\mathbf {x} ,t)\propto E_{1}^{n_{1}}E_{2}^{n_{2}}e^{i}+{\text{c.c.}}}
402:
effect in which a wave with polarization vector perpendicular to the input one is generated.
8599:
8423:
8383:
8170:
8064:
8025:
7977:
7924:
7859:
7649:
7636:
Jablan, Marinko; Buljan, Hrvoje; Manela, Ofer; Bartal, Guy; Segev, Mordechai (2007-04-16).
7602:
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1524:
984:
776:
530:
205:(OPG), like parametric oscillation but without a resonator, using a very high gain instead.
128:
101:
62:
4791:{\displaystyle P_{\text{NL}}=\varepsilon _{0}\chi ^{(3)}(\Xi _{1}+\Xi _{2}+\Xi _{3})^{3},}
4474:
8:
8574:
8433:
8428:
8413:
8388:
8365:
8341:
7891:
7530:
7054:
Zakharov, V. E.; Ostrovsky, L. A. (2009-03-15). "Modulation instability: The beginning".
6265:
3605:. Typically, three-wave mixing is done in a birefringent crystalline material, where the
2712:
1520:
519:
411:
333:
8272:
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7574:
The Fascinating Behavior of Light in Photorefractive Media | Optics & Photonics News
7369:
7266:
7212:
7067:
7013:
6974:
6891:
6843:
6707:
4020:
all four frequencies are mixing simultaneously, as opposed to sequential mixing via two
2667:, and 0. These three-wave mixing processes correspond to the nonlinear effects known as
1824:{\displaystyle \mathbf {P} ^{\text{NL}}=\varepsilon _{0}\chi ^{(2)}\mathbf {E} ^{2}(t).}
8630:
8507:
8502:
8455:
8284:
8194:
8085:
8052:
7993:
7967:
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7516:
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7313:
CLEO '97., Summaries of Papers Presented at the Conference on Lasers and Electro-Optics
7033:
6855:
6829:
5747:
3034:
1981:
501:
and non-parametric effects. A parametric non-linearity is an interaction in which the
7482:
7447:
7412:
7354:"Efficient KDP frequency doubling SBS pulse compressed 532nm hundred picosecond laser"
6453:
6403:
4139:
8645:
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2708:
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2131:
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8247:(2nd ed.). Boca Raton London New York: CRC Press, Taylor & Francis Group.
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7556:
7526:
7478:
7443:
7408:
7373:
7316:
7270:
7216:
7071:
7017:
6978:
6942:
6895:
6847:
6777:
6711:
4486:
4126:, or second-harmonic generation. With this technique, the 1064 nm output from
3606:
992:
780:
481:
360:
332:(spatial soliton) that does not change during propagation due to a balance between
321:
30:
8676:
8604:
8514:
8460:
8360:
7821:
7580:
6573:
6561:
6549:
6536:
6475:
5345:
4482:
within the material, which coherently radiates to form the phase-conjugate wave.
4203:
4151:
3845:
3837:
3825:
439:
124:
81:
7989:
7377:
7194:
7075:
6899:
6529:
1970:{\displaystyle \mathbf {E} (t)=E_{1}\cos(\omega _{1}t)+E_{2}\cos(\omega _{2}t),}
8534:
8489:
8467:
8355:
7614:
7021:
6409:
6171:
4497:
4184:
3611:
1291:
1098:
550:
471:
461:
325:
69:
8226:
7560:
7434:
Pepper, David M. (January 1986). "Applications of Optical Phase Conjugation".
6715:
747:
of the medium, and the presence of such a term is generally referred to as an
84:, the vacuum itself is expected to become nonlinear. In nonlinear optics, the
8665:
8544:
8135:
8126:
7879:
7794:
7786:
7758:
7750:
7714:
7671:
7385:
7320:
7029:
6641:
6175:
5923:
is propagation axis. The angular momentum projection on propagation axis has
5195:{\displaystyle E_{4}={\frac {i\omega l}{2nc}}\chi ^{(3)}E_{1}E_{2}E_{3}^{*},}
4155:
4094:
523:
502:
445:
345:
297:
279:
113:
8309:
7507:
Okulov, A. Yu. (2008). "Angular momentum of photons and phase conjugation".
6694:
Kaiser, W.; Garrett, C. G. B. (1961). "Two-Photon Excitation in CaF2:Eu2+".
6178:, one can expand the induced dipole moment in powers of the electric field:
3872:
217:(SPDC), the amplification of the vacuum fluctuations in the low-gain regime.
8569:
8190:
8182:
8094:
7958:
Okulov, A Yu (2020). "Structured light entities, chaos and nonlocal maps".
7887:
7845:"Self-focusing and self-trapping of optical beams upon photopolymerization"
7829:
7722:
7679:
7622:
7399:
Shkunov, Vladimir; Zel'dovich, Boris (December 1985). "Phase Conjugation".
7282:
7230:
6997:
6907:
4127:
4102:
3811:
Most common nonlinear crystals are negative uniaxial, which means that the
3472:{\displaystyle \|\mathbf {k} _{3}\|=\mathbf {n} (\omega _{3})\omega _{3}/c}
3024:{\displaystyle \|\mathbf {k} _{j}\|=\mathbf {n} (\omega _{j})\omega _{j}/c}
2793:
474:, the refractive index is affected by acoustic waves (ultrasound); used in
329:
301:
287:
140:
58:
5330:
8037:
7871:
7662:
7637:
7274:
7221:
7196:
6289:
6141:
Optical fields transmitted through nonlinear Kerr media can also display
5064:), then the conjugate and signal beams propagate in opposite directions (
2952:
2796:
materials avoid this problem by having two indices of refraction at once.
337:
311:
283:
240:
7490:
7455:
7420:
6834:
6781:
6554:
5089:, the electric field amplitude of the conjugate beam is approximated by
4272:
is reflected from perfect phase-conjugating mirror. Normal to mirror is
8589:
8579:
7936:
6493:
1550 nm: potassium titanyl phosphate (KTP), lithium niobate (LiNbO
4098:
799:
in an isotropic space, containing no free charge, it can be shown that
527:
464:, the refractive index is affected by a static electric field; used in
315:
8076:
8053:"Resonance Raman probes for organelle-specific labeling in live cells"
7915:
Okulov, A Yu (2000). "Spatial soliton laser: geometry and stability".
7706:
7195:
Abolghasem, Payam; Junbo Han; Bhavin J. Bijlani; Amr S. Helmy (2010).
6998:"Optical phase-change in plasmonic nanoparticles by a two-wave mixing"
6946:
8440:
7307:
Xhao, X.M.; Jones, R.J.; Strauss, C.E.M.; Funk, D.J.; Roberts, J.P.;
6982:
2716:
2704:
2699:
105:
6911:
6379:
5959:
the interpretation of phase conjugation is much simpler compared to
4473:
One can interpret optical phase conjugation as being analogous to a
497:
Nonlinear effects fall into two qualitatively different categories,
7972:
7638:"Incoherent modulation instability in a nonlinear photonic lattice"
5289:{\displaystyle E_{4}(\mathbf {x} )\propto E_{3}^{*}(\mathbf {x} ),}
518:) nonlinear optical phenomena, in which the optical fields are not
431:, simultaneous absorption of two or more photons, transferring the
139:
Nonlinear optics explains nonlinear response of properties such as
8110:"Recent advances in nonlinear optics for bio-imaging applications"
7521:
6851:
6358:{\displaystyle {-dI \over dx}={N\delta I^{2} \over \hbar \omega }}
442:, near-simultaneous removal of many bound electrons by one photon.
227:
Nonlinear light-matter interaction with free electrons and plasmas
5081:
Further, it can be shown that for a medium with refractive index
4801:
resulting in generation of waves with frequencies given by ω = ±ω
4154:. These crystals have the necessary properties of being strongly
4513:
For the four-wave mixing technique, we can describe four beams (
767:) are considered as scalar for simplicity. In general, χ is an (
6734:"Schiff base metal complexes for second order nonlinear optics"
5438:("in" means incident field, "out" means reflected field) where
5078:). This results in the retroreflecting property of the effect.
772:
485:
432:
50:
5836:
and angular momentum, whose projection on propagation axis is
4191:
A device producing the phase-conjugation effect is known as a
3667:{\displaystyle \lambda _{p}\leq \lambda _{s}\leq \lambda _{i}}
3089:
is the index of refraction of the medium at angular frequency
7089:
Kouzov, A.P.; Egorova, N.I.; Chrysos, M.; Rachet, F. (2012).
77:
54:
7692:
5018:
This is the generating field for the phase-conjugate beam, Ξ
4122:
One of the most commonly used frequency-mixing processes is
3479:. Constructive interference, and therefore a high-intensity
751:-th-order nonlinearity. Note that the polarization density
123:, both shortly after the construction of the first laser by
5315:= ω, and the signal wave is higher in frequency such that ω
3116:. Thus, the second-order polarization at angular frequency
7088:
4813:
in addition to third-harmonic generation waves with ω = 3ω
4330:. Reflected photon (magenta) has opposite linear momentum
3860:(emulated by second-order processes) of the signal and an
1510:
2691:
uncertainty in the electric field initiates the process.
314:(and possibly higher-order nonlinearities) caused by the
286:(and possibly higher-order nonlinearities) caused by the
38:, viewed down b axis, used in second harmonic generation.
7735:
7635:
6876:"Observation of Nonlinear Effects in Compton Scattering"
6872:
6539:, with content on nonlinear optics, by Rüdiger Paschotta
4089:
as well. At high peak powers the Kerr effect can cause
1527:
solutions to the homogeneous part of the wave equation:
786:
779:-dependent nature of the parametric interaction and the
7468:
6819:
5331:
Angular and linear momenta in optical phase conjugation
5050:, and so if the two pump beams are counterpropagating (
96:
The first nonlinear optical effect to be predicted was
7807:
7771:
6959:
6136:
318:
creating a temporal variation in the refractive index.
7398:
6298:
6184:
5972:
5932:
5907:
5883:
5842:
5809:
5786:
5750:
5728:
5637:
5562:
5447:
5357:
5232:
5098:
4874:
4696:
4526:
4440:
4404:
4372:
4336:
4307:
4278:
4246:
4213:
4062:
4026:
3993:
3960:
3918:
3885:
3627:
3515:
3485:
3408:
3381:
3359:
3178:
3122:
3095:
3057:
3037:
2960:
2935:
2809:
2760:
2726:
2147:
1993:
1873:
1755:
1646:
1536:
1344:
1303:
1189:
1143:
1107:
1011:
808:
791:
Central to the study of electromagnetic waves is the
569:
375:
290:
creating a spatial variation in the refractive index.
249:
7306:
6932:
6166:
Connecting bulk properties to microscopic properties
5344:
a phase-conjugating mirror performs reversal of the
7049:
7047:
5319:= ω + Δω, then the conjugate wave is of frequency ω
3162:{\displaystyle \omega _{3}=\omega _{1}+\omega _{2}}
1002:Note that one can normally use the vector identity
6357:
6268:, β is the second hyperpolarizability, and so on.
6256:
6125:
5944:
5915:
5889:
5869:
5828:
5795:
5756:
5736:
5707:
5620:
5545:
5427:
5288:
5194:
5007:
4790:
4650:
4461:
4426:
4390:
4358:
4322:
4293:
4264:
4232:
4081:
4045:
4012:
3979:
3937:
3912:processes. It can be extended for processes where
3904:
3666:
3590:
3498:
3471:
3394:
3367:
3342:
3161:
3108:
3081:
3043:
3023:
2943:
2918:
2784:
2746:
2614:
2119:
1969:
1823:
1719:
1626:
1499:
1323:
1279:
1166:
1126:
1086:
968:
728:
394:
268:
7951:
7908:
7843:Kewitsch, Anthony S.; Yariv, Amnon (1996-01-01).
7053:
6380:Common second-harmonic-generating (SHG) materials
223:(OR), generation of quasi-static electric fields.
8663:
7169:1.2.10 Parametric versus Nonparametric Processes
7044:
6767:
6264:, where μ is the polarizability, α is the first
5870:{\displaystyle L_{\mathbf {z} }=\pm \hbar \ell }
4427:{\displaystyle \mathbf {P} =2\hbar \mathbf {k} }
4359:{\displaystyle \mathbf {P} =-\hbar \mathbf {k} }
3867:
3829:These methods are called temperature tuning and
363:(FWM), can also arise from other nonlinearities.
8211:
6727:
6725:
5829:{\displaystyle \mathbf {P} =\hbar \mathbf {k} }
4233:{\displaystyle \mathbf {P} =\hbar \mathbf {k} }
8013:
7542:
7540:
7244:
7242:
7240:
1842:) is made up of two components at frequencies
425:, interaction of photons with acoustic phonons
134:
8339:
8325:
8107:
7842:
7502:
7500:
7351:
6693:
6543:An Intuitive Explanation of Phase Conjugation
6156:
4508:
3815:axis has a smaller refractive index than the
146:
7130:Encyclopedia of Laser Physics and Technology
7095:Nanosystems: Physics, Chemistry, Mathematics
6722:
6530:Encyclopedia of laser physics and technology
4161:
3424:
3409:
2976:
2961:
1167:{\displaystyle \nabla \cdot \mathbf {D} =0,}
233:
7537:
7248:
7237:
6794:
5223:are plane (counterpropagating) waves, then
2785:{\displaystyle \mathbf {k} '=2\mathbf {k} }
1324:{\displaystyle \nabla \cdot \mathbf {E} =0}
8332:
8318:
8159:
7497:
6394:Dark-red gallium selenide in its bulk form
4207:Vortex photon (blue) with linear momentum
243:, intensity-dependent refractive index (a
8125:
8084:
7971:
7661:
7520:
7220:
7122:
6833:
6731:
5209:is the speed of light. If the pump beams
4170:beam, and thus the technique is known as
3082:{\displaystyle \mathbf {n} (\omega _{j})}
2134:. Plugging this into the expression for
7695:Journal of the American Chemical Society
7592:
7315:. Vol. 11. IEEE. pp. 377–378.
7158:
6770:Journal of the American Chemical Society
6389:
6279:
4496:
4202:
3871:
3051:is the velocity of light in vacuum, and
2698:
324:, an equilibrium solution for either an
29:
8273:"Nonlinear Optics of Plasmonic Systems"
6668:
6662:
6634:
6606:
6555:SNLO - Nonlinear Optics Design Software
6195:
6186:
4676:are known as the two pump waves, with Ξ
1511:Nonlinearities as a wave-mixing process
492:
14:
8664:
8530:Atomic, molecular, and optical physics
8242:
8050:
7957:
7914:
7546:
7506:
7433:
4056:The Kerr effect can be described as a
3948:"vacuum" ultra-violet light generation
995:, which comes from the linear term in
484:, interaction of photons with optical
215:Spontaneous parametric down-conversion
8313:
8238:
8236:
8009:
8007:
4117:
2703:Most transparent materials, like the
1738:-th order nonlinearity will lead to (
1127:{\displaystyle \rho _{\text{free}}=0}
787:Wave equation in a nonlinear material
783:(or lack) of the nonlinear material.
8267:
7300:
7179:
7164:
6640:
6612:
6579:
6518:Category:Nonlinear optical materials
5335:
4684:being the generated conjugate wave.
4668:are the electric field amplitudes. Ξ
4517:= 1, 2, 3, 4) with electric fields:
4182:and is significantly different from
1519:and can be obtained by the use of a
452:
310:(SPM), an effect due to the optical
7775:The Journal of Physical Chemistry C
7739:The Journal of Physical Chemistry C
6137:Nonlinear optical pattern formation
4865:, this gives a polarization field:
3601:The above equation is known as the
2625:which has frequency components at 2
316:temporal variation in the intensity
61:media, that is, media in which the
24:
8285:10.1016/b978-0-12-811002-7.00023-0
8233:
8004:
6646:The Principles of Nonlinear Optics
6523:
5771:
4766:
4753:
4740:
4528:
4462:{\displaystyle L=\pm 2\hbar \ell }
3864:can be integrated monolithically.
1689:
1679:
1592:
1582:
1538:
1523:. Physically one gets the normal
1466:
1456:
1400:
1390:
1346:
1304:
1245:
1235:
1191:
1144:
1070:
1050:
1042:
1023:
1012:
935:
925:
866:
856:
815:
809:
288:spatial variation in the intensity
25:
8688:
7483:10.1038/scientificamerican1090-62
7448:10.1038/scientificamerican0186-74
7413:10.1038/scientificamerican1285-54
6110:
6074:
6028:
5999:
5936:
5861:
5818:
5342:classical Maxwell electrodynamics
4453:
4416:
4391:{\displaystyle L=\mp \hbar \ell }
4382:
4348:
4265:{\displaystyle L=\pm \hbar \ell }
4256:
4222:
2747:{\displaystyle \omega '=2\omega }
2694:
1294:does not imply that the identity
739:where the coefficients χ are the
131:'s monograph "Nonlinear Optics".
8017:Advances in Optics and Photonics
6673:(4th ed.). Academic Press.
6620:(3rd ed.). Academic Press.
6249:
6242:
6216:
6199:
6094:
6051:
6032:
6015:
6003:
5979:
5909:
5849:
5822:
5811:
5730:
5689:
5675:
5654:
5640:
5628:with respect to incident field:
5605:
5597:
5589:
5572:
5564:
5527:
5519:
5502:
5494:
5457:
5449:
5409:
5395:
5374:
5360:
5323:= ω − Δω. This is known as
5276:
5247:
4988:
4980:
4626:
4618:
4581:
4541:
4420:
4406:
4352:
4338:
4226:
4215:
3569:
3545:
3521:
3431:
3414:
3402:and a corresponding wave vector
3361:
3307:
3290:
3275:
3199:
3059:
2983:
2966:
2937:
2883:
2869:
2824:
2778:
2763:
2199:
2154:
1995:
1875:
1799:
1758:
1707:
1617:
1609:
1548:
1484:
1417:
1356:
1311:
1270:
1262:
1201:
1151:
1080:
1057:
1030:
953:
883:
822:
693:
653:
619:
571:
193:wave (can be considered as DFG).
187:Optical parametric amplification
53:that describes the behaviour of
8651:Timeline of physics discoveries
8261:
8205:
8153:
8142:from the original on 2021-01-21
8101:
8044:
7836:
7801:
7765:
7729:
7686:
7629:
7586:
7567:
7462:
7427:
7392:
7345:
7289:from the original on 2024-05-29
7249:Strauss, CEM; Funk, DJ (1991).
7188:
7173:
7147:from the original on 2011-08-22
7116:
7105:from the original on 2017-06-13
7082:
6989:
6953:
6926:
5945:{\displaystyle \pm \hbar \ell }
5803:also possesses linear momentum
5718:The above identities are valid
4130:or the 800 nm output from
4112:
2677:difference-frequency generation
1517:ordinary differential equations
423:Stimulated Brillouin scattering
367:Cross-polarized wave generation
282:, an effect due to the optical
181:Difference-frequency generation
8279:, Elsevier, pp. 569–582,
8215:Coordination Chemistry Reviews
7960:Chaos, Solitons & Fractals
7531:10.1088/0953-4075/41/10/101001
7509:J. Phys. B: At. Mol. Opt. Phys
7056:Physica D: Nonlinear Phenomena
6866:
6813:
6795:Bloembergen, Nicolaas (1965).
6788:
6761:
6732:Rigamonti, Luca (April 2010).
6687:
6151:nonlinear Schrödinger equation
5901:of photon, or winding number,
5766:ideal phase-conjugating mirror
5699:
5685:
5664:
5650:
5615:
5601:
5582:
5568:
5537:
5523:
5512:
5498:
5467:
5453:
5419:
5405:
5384:
5370:
5280:
5272:
5251:
5243:
5149:
5143:
5085:and a beam interaction length
4992:
4967:
4909:
4903:
4776:
4736:
4731:
4725:
4585:
4577:
4551:
4537:
4314:
4285:
4144:potassium dihydrogen phosphate
4107:high-order harmonic generation
4074:
4068:
4038:
4032:
4005:
3999:
3972:
3966:
3930:
3924:
3897:
3891:
3763:Type V (or type 0, or "zero")
3573:
3549:
3525:
3448:
3435:
3327:
3300:
3270:
3267:
3209:
3195:
3190:
3184:
3076:
3063:
3000:
2987:
2903:
2864:
2834:
2820:
2508:
2482:
2428:
2402:
2256:
2250:
2215:
2209:
2192:
2186:
2005:
1999:
1961:
1945:
1923:
1907:
1885:
1879:
1815:
1809:
1792:
1786:
709:
703:
686:
680:
669:
663:
646:
640:
629:
623:
613:
607:
581:
575:
387:
381:
261:
255:
197:Optical parametric oscillation
13:
1:
6599:
6488:ammonium dihydrogen phosphate
5796:{\displaystyle \hbar \omega }
4475:real-time holographic process
4198:
3868:Higher-order frequency mixing
983:is the nonlinear part of the
203:Optical parametric generation
68:responds non-linearly to the
7822:10.1021/acsmacrolett.6b00659
6743:(3): 118–122. Archived from
6741:La Chimica & l'Industria
6398:Ordered by pump wavelength:
5916:{\displaystyle \mathbf {z} }
5737:{\displaystyle \mathbf {r} }
5022:. Its direction is given by
4680:being the signal wave, and Ξ
3862:optical parametric amplifier
3368:{\displaystyle \mathbf {x} }
2944:{\displaystyle \mathbf {x} }
1984:to convert to exponentials,
1177:to obtain the more familiar
7:
8615:Quantum information science
7990:10.1016/j.chaos.2020.109638
7378:10.1016/j.ijleo.2016.07.021
7125:"Parametric Nonlinearities"
7123:Paschotta, Rüdiger (2008).
7076:10.1016/j.physd.2008.12.002
6900:10.1103/PhysRevLett.76.3116
6501:
6472:potassium titanyl phosphate
5722:, i.e. in each space point
4148:potassium titanyl phosphate
4082:{\displaystyle \chi ^{(3)}}
4046:{\displaystyle \chi ^{(2)}}
4013:{\displaystyle \chi ^{(3)}}
3980:{\displaystyle \chi ^{(3)}}
3952:difference frequency mixing
3938:{\displaystyle \chi ^{(3)}}
3905:{\displaystyle \chi ^{(2)}}
3499:{\displaystyle \omega _{3}}
3395:{\displaystyle \omega _{3}}
3109:{\displaystyle \omega _{j}}
1637:and the inhomogeneous term
1101:(assuming no free charges,
395:{\displaystyle \chi ^{(3)}}
269:{\displaystyle \chi ^{(3)}}
135:Nonlinear optical processes
10:
8693:
8446:Classical electromagnetism
8243:McHale, Jeanne L. (2017).
8051:Kuzmin, Andrey N. (2016).
7615:10.1103/PhysRevLett.84.467
6386:Second-harmonic generation
6383:
6157:Molecular nonlinear optics
4509:Four-wave mixing technique
4323:{\displaystyle {\vec {z}}}
4294:{\displaystyle {\vec {n}}}
3791:Type VII (or IIA or IIIB)
3506:field, will occur only if
2669:second-harmonic generation
153:Second-harmonic generation
147:Frequency-mixing processes
110:second-harmonic generation
91:
8623:
8560:
8488:
8404:
8376:
8348:
8227:10.1016/j.ccr.2017.03.013
7561:10.1134/S0021364008200046
6716:10.1103/PhysRevLett.7.229
6584:(4th ed.). Academi.
5961:classical electrodynamics
4492:Optical phase conjugation
4469:is excited within mirror.
4172:optical phase conjugation
4162:Optical phase conjugation
3777:Type VI (or IIB or IIIA)
3681:
3678:
509:
417:Optical phase conjugation
234:Other nonlinear processes
163:Third-harmonic generation
8552:Condensed matter physics
8127:10.29026/oea.2020.200003
8114:Opto-Electronic Advances
7787:10.1021/acs.jpcc.5b11377
7751:10.1021/acs.jpcc.5b07117
7321:10.1109/CLEO.1997.603294
7022:10.1088/1402-4896/ab3ae9
6882:(Submitted manuscript).
6669:Agrawal, Govind (2006).
6370:absorption cross section
3603:phase-matching condition
2673:sum-frequency generation
2130:where "c.c." stands for
1290:For a nonlinear medium,
771: + 1)-th-rank
522:, can be described by a
516:Kramers–Kronig relations
476:acousto-optic modulators
466:electro-optic modulators
446:Chaos in optical systems
406:Modulational instability
209:Half-harmonic generation
175:Sum-frequency generation
169:High-harmonic generation
108:and the discovery of
7917:Optics and Spectroscopy
7595:Physical Review Letters
6696:Physical Review Letters
6438:monopotassium phosphate
6176:Taylor series expansion
5957:quantum electrodynamics
5780:the photon with energy
5778:quantum electrodynamics
759:) and electrical field
429:Multi-photon absorption
86:superposition principle
8636:Nobel Prize in Physics
8498:Relativistic mechanics
8245:Molecular spectroscopy
8183:10.1002/adma.201701076
6671:Nonlinear Fiber Optics
6648:. Wiley-Interscience.
6395:
6359:
6285:
6258:
6174:can be described as a
6147:modulation instability
6127:
5946:
5917:
5891:
5871:
5830:
5797:
5758:
5738:
5709:
5622:
5547:
5429:
5290:
5196:
5009:
4792:
4652:
4502:
4470:
4463:
4428:
4392:
4360:
4324:
4301:, propagation axis is
4295:
4266:
4234:
4193:phase-conjugate mirror
4083:
4047:
4014:
3981:
3939:
3906:
3876:
3668:
3592:
3500:
3473:
3396:
3369:
3344:
3163:
3110:
3083:
3045:
3025:
2945:
2920:
2797:
2786:
2748:
2616:
2121:
1971:
1825:
1721:
1628:
1501:
1325:
1281:
1168:
1128:
1088:
970:
775:representing both the
730:
535:electric dipole moment
396:
355:Cross-phase modulation
348:for spatial solitons).
328:(temporal soliton) or
270:
121:University of Michigan
39:
8641:Philosophy of physics
6393:
6360:
6283:
6272:Novel Nonlinear Media
6259:
6128:
5947:
5918:
5892:
5890:{\displaystyle \ell }
5872:
5831:
5798:
5759:
5739:
5710:
5623:
5548:
5430:
5291:
5197:
5010:
4793:
4653:
4500:
4464:
4434:and angular momentum
4429:
4393:
4366:and angular momentum
4361:
4325:
4296:
4267:
4240:and angular momentum
4235:
4206:
4084:
4048:
4015:
3982:
3940:
3907:
3875:
3858:self-phase modulation
3669:
3618:Phase-matching types
3593:
3501:
3474:
3397:
3370:
3345:
3164:
3111:
3084:
3046:
3026:
2946:
2921:
2787:
2749:
2702:
2681:optical rectification
2617:
2122:
1972:
1826:
1722:
1629:
1502:
1326:
1282:
1169:
1129:
1089:
971:
731:
435:to a single electron.
397:
342:self-phase modulation
308:Self-phase modulation
294:Kerr-lens modelocking
271:
221:Optical rectification
98:two-photon absorption
33:
8600:Mathematical physics
8038:10.1364/AOP.8.000328
7872:10.1364/OL.21.000024
7663:10.1364/OE.15.004623
7275:10.1364/ol.16.001192
7222:10.1364/OE.18.012681
6799:. World Scientific.
6513:Filament propagation
6296:
6182:
5970:
5930:
5905:
5881:
5840:
5807:
5784:
5748:
5726:
5635:
5560:
5445:
5355:
5230:
5096:
4872:
4694:
4524:
4438:
4402:
4370:
4334:
4305:
4276:
4244:
4211:
4060:
4024:
3991:
3958:
3916:
3883:
3879:The above holds for
3856:. SHG of a pump and
3831:quasi-phase-matching
3625:
3513:
3483:
3406:
3379:
3357:
3176:
3120:
3093:
3055:
3035:
2958:
2933:
2807:
2792:in these materials.
2758:
2724:
2145:
1991:
1871:
1753:
1644:
1534:
1525:electromagnetic wave
1342:
1301:
1187:
1141:
1105:
1009:
985:polarization density
806:
567:
531:polarization density
493:Parametric processes
373:
247:
102:Maria Goeppert Mayer
63:polarization density
8575:Atmospheric physics
8414:Classical mechanics
8342:branches of physics
8175:2017AdM....2901076G
8069:2016NatSR...628483K
8030:2016AdOP....8..328G
7982:2020CSF...13309638O
7929:2000OptSp..89..131O
7864:1996OptL...21...24K
7745:(35): 20606–20617.
7654:2007OExpr..15.4623J
7607:2000PhRvL..84..467S
7471:Scientific American
7436:Scientific American
7401:Scientific American
7370:2016Optik.127.9201B
7267:1991OptL...16.1192S
7213:2010OExpr..1812681A
7207:(12): 12681–12689.
7184:2.3. Phase Matching
7068:2009PhyD..238..540Z
7014:2019PhyS...94l5802H
6975:2007NatPh...3..424T
6892:1996PhRvL..76.3116B
6844:1998Natur.396..653C
6782:10.1021/ja01856a043
6708:1961PhRvL...7..229K
6580:Boyd, R.W. (2020).
6266:hyperpolarizability
5271:
5188:
4958:
3675:
3619:
3258:
3236:
2713:index of refraction
797:Maxwell's equations
412:Raman amplification
49:) is the branch of
8631:History of physics
8163:Advanced Materials
8057:Scientific Reports
7937:10.1134/BF03356001
7579:2015-04-02 at the
6935:Physics of Plasmas
6572:2016-03-17 at the
6560:2011-07-07 at the
6548:2007-11-08 at the
6535:2009-06-03 at the
6466:1319 nm: KNbO
6396:
6355:
6286:
6254:
6123:
6121:
5942:
5913:
5899:topological charge
5887:
5867:
5826:
5793:
5754:
5744:in a given moment
5734:
5705:
5618:
5543:
5425:
5325:frequency flipping
5286:
5257:
5192:
5174:
5005:
4944:
4788:
4648:
4503:
4471:
4459:
4424:
4388:
4356:
4320:
4291:
4262:
4230:
4180:wavefront reversal
4132:Ti:sapphire lasers
4124:frequency doubling
4118:Frequency doubling
4079:
4043:
4010:
3977:
3935:
3902:
3877:
3846:periodically poled
3735:Type III (or IIB)
3664:
3620:
3617:
3588:
3496:
3469:
3392:
3365:
3340:
3237:
3215:
3159:
3106:
3079:
3041:
3021:
2941:
2916:
2798:
2782:
2744:
2689:quantum-mechanical
2612:
2610:
2117:
1967:
1834:If we assume that
1821:
1717:
1624:
1497:
1321:
1277:
1164:
1124:
1084:
966:
726:
392:
300:as a mechanism to
296:(KLM), the use of
266:
157:frequency doubling
40:
8659:
8658:
8646:Physics education
8595:Materials science
8562:Interdisciplinary
8520:Quantum mechanics
8294:978-0-12-811002-7
8254:978-1-4665-8658-1
8077:10.1038/srep28483
7816:(11): 1237–1241.
7810:ACS Macro Letters
7707:10.1021/ja068967b
7701:(15): 4738–4746.
7364:(20): 9201–9205.
7330:978-0-7803-4125-8
7167:, pp. 13–15
7140:978-3-527-40828-3
6947:10.1063/1.2013067
6886:(17): 3116–3119.
6828:(6712): 653–655.
6776:(11): 3005–3018.
6680:978-0-12-369516-1
6655:978-0-471-43080-3
6627:978-0-12-369470-6
6591:978-0-12-811003-4
6508:Born–Infeld model
6450:lithium triborate
6430:980 nm: KNbO
6421:potassium niobate
6353:
6320:
6232:
6143:pattern formation
6104:
6061:
6022:
5986:
5757:{\displaystyle t}
5682:
5647:
5402:
5367:
5336:Classical picture
5136:
5003:
4896:
4704:
4643:
4565:
4317:
4288:
4105:. This is called
3809:
3808:
3805:Type VIII (or I)
3721:Type II (or IIA)
3576:
3552:
3528:
3353:At each position
3338:
3044:{\displaystyle c}
2914:
2709:normal dispersion
2707:shown here, have
2598:
2243:
2161:
2132:complex conjugate
2112:
2068:
2019:
1765:
1714:
1703:
1674:
1606:
1577:
1491:
1480:
1451:
1414:
1385:
1259:
1230:
1115:
960:
949:
920:
880:
851:
795:. Starting with
537:per unit volume)
526:expansion of the
453:Related processes
344:for temporal and
88:no longer holds.
27:Branch of physics
16:(Redirected from
8684:
8672:Nonlinear optics
8585:Chemical physics
8525:Particle physics
8451:Classical optics
8334:
8327:
8320:
8311:
8310:
8304:
8303:
8302:
8301:
8277:Nonlinear Optics
8265:
8259:
8258:
8240:
8231:
8230:
8209:
8203:
8202:
8157:
8151:
8150:
8148:
8147:
8129:
8105:
8099:
8098:
8088:
8048:
8042:
8041:
8011:
8002:
8001:
7975:
7955:
7949:
7948:
7912:
7906:
7905:
7903:
7902:
7896:
7890:. Archived from
7849:
7840:
7834:
7833:
7805:
7799:
7798:
7781:(8): 4517–4528.
7769:
7763:
7762:
7733:
7727:
7726:
7690:
7684:
7683:
7665:
7633:
7627:
7626:
7590:
7584:
7571:
7565:
7564:
7544:
7535:
7534:
7524:
7504:
7495:
7494:
7466:
7460:
7459:
7431:
7425:
7424:
7396:
7390:
7389:
7349:
7343:
7342:
7304:
7298:
7297:
7295:
7294:
7246:
7235:
7234:
7224:
7192:
7186:
7177:
7171:
7162:
7156:
7155:
7153:
7152:
7120:
7114:
7113:
7111:
7110:
7086:
7080:
7079:
7051:
7042:
7041:
6993:
6987:
6986:
6983:10.1038/nphys595
6957:
6951:
6950:
6930:
6924:
6923:
6921:
6919:
6910:. Archived from
6880:Phys. Rev. Lett.
6870:
6864:
6863:
6837:
6817:
6811:
6810:
6797:Nonlinear Optics
6792:
6786:
6785:
6765:
6759:
6758:
6756:
6755:
6749:
6738:
6729:
6720:
6719:
6691:
6685:
6684:
6666:
6660:
6659:
6638:
6632:
6631:
6618:Nonlinear Optics
6610:
6595:
6582:Nonlinear optics
6461:gallium selenide
6364:
6362:
6361:
6356:
6354:
6352:
6344:
6343:
6342:
6326:
6321:
6319:
6311:
6300:
6263:
6261:
6260:
6255:
6253:
6252:
6246:
6245:
6233:
6225:
6220:
6219:
6204:
6203:
6202:
6189:
6132:
6130:
6129:
6124:
6122:
6106:
6105:
6102:
6100:
6099:
6098:
6097:
6063:
6062:
6059:
6057:
6056:
6055:
6054:
6035:
6024:
6023:
6020:
6018:
6006:
5988:
5987:
5984:
5982:
5951:
5949:
5948:
5943:
5922:
5920:
5919:
5914:
5912:
5896:
5894:
5893:
5888:
5876:
5874:
5873:
5868:
5854:
5853:
5852:
5835:
5833:
5832:
5827:
5825:
5814:
5802:
5800:
5799:
5794:
5763:
5761:
5760:
5755:
5743:
5741:
5740:
5735:
5733:
5714:
5712:
5711:
5706:
5692:
5684:
5683:
5680:
5678:
5657:
5649:
5648:
5645:
5643:
5627:
5625:
5624:
5619:
5608:
5600:
5592:
5575:
5567:
5552:
5550:
5549:
5544:
5530:
5522:
5505:
5497:
5492:
5491:
5482:
5481:
5460:
5452:
5434:
5432:
5431:
5426:
5412:
5404:
5403:
5400:
5398:
5377:
5369:
5368:
5365:
5363:
5295:
5293:
5292:
5287:
5279:
5270:
5265:
5250:
5242:
5241:
5201:
5199:
5198:
5193:
5187:
5182:
5173:
5172:
5163:
5162:
5153:
5152:
5137:
5135:
5124:
5113:
5108:
5107:
5014:
5012:
5011:
5006:
5004:
5001:
4996:
4995:
4991:
4983:
4957:
4952:
4943:
4942:
4933:
4932:
4923:
4922:
4913:
4912:
4897:
4889:
4884:
4883:
4797:
4795:
4794:
4789:
4784:
4783:
4774:
4773:
4761:
4760:
4748:
4747:
4735:
4734:
4719:
4718:
4706:
4705:
4702:
4657:
4655:
4654:
4649:
4644:
4641:
4636:
4635:
4634:
4630:
4629:
4621:
4610:
4609:
4584:
4576:
4575:
4566:
4558:
4544:
4536:
4535:
4487:angular momentum
4468:
4466:
4465:
4460:
4433:
4431:
4430:
4425:
4423:
4409:
4397:
4395:
4394:
4389:
4365:
4363:
4362:
4357:
4355:
4341:
4329:
4327:
4326:
4321:
4319:
4318:
4310:
4300:
4298:
4297:
4292:
4290:
4289:
4281:
4271:
4269:
4268:
4263:
4239:
4237:
4236:
4231:
4229:
4218:
4088:
4086:
4085:
4080:
4078:
4077:
4052:
4050:
4049:
4044:
4042:
4041:
4019:
4017:
4016:
4011:
4009:
4008:
3986:
3984:
3983:
3978:
3976:
3975:
3944:
3942:
3941:
3936:
3934:
3933:
3911:
3909:
3908:
3903:
3901:
3900:
3676:
3673:
3671:
3670:
3665:
3663:
3662:
3650:
3649:
3637:
3636:
3616:
3607:refractive index
3597:
3595:
3594:
3589:
3584:
3583:
3578:
3577:
3572:
3567:
3560:
3559:
3554:
3553:
3548:
3543:
3536:
3535:
3530:
3529:
3524:
3519:
3505:
3503:
3502:
3497:
3495:
3494:
3478:
3476:
3475:
3470:
3465:
3460:
3459:
3447:
3446:
3434:
3423:
3422:
3417:
3401:
3399:
3398:
3393:
3391:
3390:
3374:
3372:
3371:
3366:
3364:
3349:
3347:
3346:
3341:
3339:
3336:
3331:
3330:
3323:
3322:
3310:
3299:
3298:
3293:
3284:
3283:
3278:
3257:
3256:
3255:
3245:
3235:
3234:
3233:
3223:
3202:
3194:
3193:
3168:
3166:
3165:
3160:
3158:
3157:
3145:
3144:
3132:
3131:
3115:
3113:
3112:
3107:
3105:
3104:
3088:
3086:
3085:
3080:
3075:
3074:
3062:
3050:
3048:
3047:
3042:
3030:
3028:
3027:
3022:
3017:
3012:
3011:
2999:
2998:
2986:
2975:
2974:
2969:
2950:
2948:
2947:
2942:
2940:
2925:
2923:
2922:
2917:
2915:
2912:
2907:
2906:
2899:
2898:
2886:
2878:
2877:
2872:
2855:
2854:
2827:
2819:
2818:
2791:
2789:
2788:
2783:
2781:
2770:
2766:
2753:
2751:
2750:
2745:
2734:
2621:
2619:
2618:
2613:
2611:
2604:
2600:
2599:
2596:
2591:
2590:
2581:
2577:
2576:
2575:
2570:
2566:
2565:
2548:
2547:
2542:
2538:
2537:
2515:
2514:
2507:
2506:
2494:
2493:
2470:
2469:
2464:
2463:
2462:
2451:
2450:
2435:
2434:
2427:
2426:
2414:
2413:
2390:
2389:
2380:
2379:
2364:
2363:
2359:
2358:
2335:
2334:
2329:
2328:
2327:
2313:
2312:
2308:
2307:
2284:
2283:
2278:
2277:
2276:
2260:
2259:
2244:
2239:
2238:
2229:
2221:
2208:
2207:
2202:
2196:
2195:
2180:
2179:
2163:
2162:
2159:
2157:
2126:
2124:
2123:
2118:
2113:
2110:
2105:
2104:
2100:
2099:
2079:
2078:
2069:
2061:
2056:
2055:
2051:
2050:
2030:
2029:
2020:
2012:
1998:
1976:
1974:
1973:
1968:
1957:
1956:
1938:
1937:
1919:
1918:
1900:
1899:
1878:
1830:
1828:
1827:
1822:
1808:
1807:
1802:
1796:
1795:
1780:
1779:
1767:
1766:
1763:
1761:
1726:
1724:
1723:
1718:
1716:
1715:
1712:
1710:
1704:
1702:
1701:
1700:
1687:
1686:
1677:
1675:
1673:
1672:
1671:
1662:
1661:
1648:
1633:
1631:
1630:
1625:
1620:
1612:
1607:
1605:
1604:
1603:
1590:
1589:
1580:
1578:
1576:
1575:
1566:
1565:
1556:
1551:
1546:
1545:
1521:Green's function
1506:
1504:
1503:
1498:
1493:
1492:
1489:
1487:
1481:
1479:
1478:
1477:
1464:
1463:
1454:
1452:
1450:
1449:
1448:
1439:
1438:
1425:
1420:
1415:
1413:
1412:
1411:
1398:
1397:
1388:
1386:
1384:
1383:
1374:
1373:
1364:
1359:
1354:
1353:
1330:
1328:
1327:
1322:
1314:
1286:
1284:
1283:
1278:
1273:
1265:
1260:
1258:
1257:
1256:
1243:
1242:
1233:
1231:
1229:
1228:
1219:
1218:
1209:
1204:
1199:
1198:
1173:
1171:
1170:
1165:
1154:
1133:
1131:
1130:
1125:
1117:
1116:
1113:
1093:
1091:
1090:
1085:
1083:
1078:
1077:
1065:
1061:
1060:
1038:
1034:
1033:
993:refractive index
975:
973:
972:
967:
962:
961:
958:
956:
950:
948:
947:
946:
933:
932:
923:
921:
919:
918:
917:
908:
907:
894:
886:
881:
879:
878:
877:
864:
863:
854:
852:
850:
849:
840:
839:
830:
825:
745:susceptibilities
735:
733:
732:
727:
722:
718:
702:
701:
696:
690:
689:
662:
661:
656:
650:
649:
622:
617:
616:
596:
595:
574:
549:in terms of the
482:Raman scattering
401:
399:
398:
393:
391:
390:
361:Four-wave mixing
322:Optical solitons
275:
273:
272:
267:
265:
264:
43:Nonlinear optics
21:
18:Nonlinear Optics
8692:
8691:
8687:
8686:
8685:
8683:
8682:
8681:
8662:
8661:
8660:
8655:
8619:
8605:Medical physics
8556:
8515:Nuclear physics
8484:
8478:Non-equilibrium
8400:
8372:
8344:
8338:
8308:
8307:
8299:
8297:
8295:
8269:Boyd, Robert W.
8266:
8262:
8255:
8241:
8234:
8210:
8206:
8169:(28): 1701076.
8158:
8154:
8145:
8143:
8106:
8102:
8049:
8045:
8012:
8005:
7956:
7952:
7913:
7909:
7900:
7898:
7894:
7847:
7841:
7837:
7806:
7802:
7770:
7766:
7734:
7730:
7691:
7687:
7634:
7630:
7591:
7587:
7581:Wayback Machine
7572:
7568:
7545:
7538:
7505:
7498:
7467:
7463:
7432:
7428:
7397:
7393:
7350:
7346:
7331:
7305:
7301:
7292:
7290:
7247:
7238:
7193:
7189:
7178:
7174:
7163:
7159:
7150:
7148:
7141:
7121:
7117:
7108:
7106:
7087:
7083:
7052:
7045:
7002:Physica Scripta
6994:
6990:
6958:
6954:
6931:
6927:
6917:
6915:
6914:on 21 June 2019
6871:
6867:
6835:physics/9810036
6818:
6814:
6807:
6793:
6789:
6766:
6762:
6753:
6751:
6747:
6736:
6730:
6723:
6692:
6688:
6681:
6667:
6663:
6656:
6639:
6635:
6628:
6611:
6607:
6602:
6592:
6574:Wayback Machine
6562:Wayback Machine
6550:Wayback Machine
6537:Wayback Machine
6526:
6524:Further reading
6504:
6496:
6485:
6481:
6476:lithium niobate
6469:
6454:β-barium borate
6447:
6443:
6433:
6426:
6415:
6388:
6382:
6345:
6338:
6334:
6327:
6325:
6312:
6301:
6299:
6297:
6294:
6293:
6248:
6247:
6241:
6240:
6224:
6215:
6214:
6198:
6194:
6193:
6185:
6183:
6180:
6179:
6159:
6139:
6120:
6119:
6101:
6093:
6092:
6088:
6087:
6086:
6064:
6058:
6050:
6049:
6045:
6044:
6043:
6040:
6039:
6031:
6019:
6014:
6013:
6002:
5989:
5983:
5978:
5977:
5973:
5971:
5968:
5967:
5931:
5928:
5927:
5925:discrete values
5908:
5906:
5903:
5902:
5882:
5879:
5878:
5848:
5847:
5843:
5841:
5838:
5837:
5821:
5810:
5808:
5805:
5804:
5785:
5782:
5781:
5774:
5772:Quantum picture
5749:
5746:
5745:
5729:
5727:
5724:
5723:
5688:
5679:
5674:
5673:
5653:
5644:
5639:
5638:
5636:
5633:
5632:
5604:
5596:
5588:
5571:
5563:
5561:
5558:
5557:
5526:
5518:
5501:
5493:
5487:
5483:
5477:
5473:
5456:
5448:
5446:
5443:
5442:
5408:
5399:
5394:
5393:
5373:
5364:
5359:
5358:
5356:
5353:
5352:
5346:Poynting vector
5338:
5333:
5322:
5318:
5314:
5310:
5275:
5266:
5261:
5246:
5237:
5233:
5231:
5228:
5227:
5222:
5215:
5183:
5178:
5168:
5164:
5158:
5154:
5142:
5138:
5125:
5114:
5112:
5103:
5099:
5097:
5094:
5093:
5077:
5070:
5063:
5056:
5049:
5042:
5035:
5028:
5021:
5000:
4987:
4979:
4963:
4959:
4953:
4948:
4938:
4934:
4928:
4924:
4918:
4914:
4902:
4898:
4888:
4879:
4875:
4873:
4870:
4869:
4864:
4857:
4850:
4839:
4835:
4831:
4824:
4820:
4816:
4812:
4808:
4804:
4779:
4775:
4769:
4765:
4756:
4752:
4743:
4739:
4724:
4720:
4714:
4710:
4701:
4697:
4695:
4692:
4691:
4683:
4679:
4675:
4671:
4666:
4640:
4625:
4617:
4605:
4601:
4600:
4596:
4592:
4588:
4580:
4571:
4567:
4557:
4540:
4531:
4527:
4525:
4522:
4521:
4511:
4479:phase-conjugate
4439:
4436:
4435:
4419:
4405:
4403:
4400:
4399:
4371:
4368:
4367:
4351:
4337:
4335:
4332:
4331:
4309:
4308:
4306:
4303:
4302:
4280:
4279:
4277:
4274:
4273:
4245:
4242:
4241:
4225:
4214:
4212:
4209:
4208:
4201:
4185:retroreflection
4164:
4152:lithium niobate
4140:β-barium borate
4120:
4115:
4067:
4063:
4061:
4058:
4057:
4031:
4027:
4025:
4022:
4021:
3998:
3994:
3992:
3989:
3988:
3965:
3961:
3959:
3956:
3955:
3923:
3919:
3917:
3914:
3913:
3890:
3886:
3884:
3881:
3880:
3870:
3838:lithium niobate
3826:Poynting vector
3658:
3654:
3645:
3641:
3632:
3628:
3626:
3623:
3622:
3579:
3568:
3566:
3565:
3564:
3555:
3544:
3542:
3541:
3540:
3531:
3520:
3518:
3517:
3516:
3514:
3511:
3510:
3490:
3486:
3484:
3481:
3480:
3461:
3455:
3451:
3442:
3438:
3430:
3418:
3413:
3412:
3407:
3404:
3403:
3386:
3382:
3380:
3377:
3376:
3360:
3358:
3355:
3354:
3335:
3318:
3314:
3306:
3294:
3289:
3288:
3279:
3274:
3273:
3263:
3259:
3251:
3247:
3246:
3241:
3229:
3225:
3224:
3219:
3198:
3183:
3179:
3177:
3174:
3173:
3153:
3149:
3140:
3136:
3127:
3123:
3121:
3118:
3117:
3100:
3096:
3094:
3091:
3090:
3070:
3066:
3058:
3056:
3053:
3052:
3036:
3033:
3032:
3013:
3007:
3003:
2994:
2990:
2982:
2970:
2965:
2964:
2959:
2956:
2955:
2936:
2934:
2931:
2930:
2911:
2894:
2890:
2882:
2873:
2868:
2867:
2860:
2856:
2844:
2840:
2823:
2814:
2810:
2808:
2805:
2804:
2777:
2762:
2761:
2759:
2756:
2755:
2727:
2725:
2722:
2721:
2697:
2666:
2659:
2652:
2645:
2638:
2631:
2609:
2608:
2595:
2586:
2582:
2571:
2561:
2557:
2553:
2552:
2543:
2533:
2529:
2525:
2524:
2523:
2519:
2502:
2498:
2489:
2485:
2475:
2471:
2465:
2458:
2454:
2453:
2452:
2446:
2442:
2422:
2418:
2409:
2405:
2395:
2391:
2385:
2381:
2375:
2371:
2354:
2350:
2340:
2336:
2330:
2323:
2319:
2318:
2317:
2303:
2299:
2289:
2285:
2279:
2272:
2268:
2267:
2266:
2265:
2261:
2249:
2245:
2234:
2230:
2228:
2219:
2218:
2203:
2198:
2197:
2185:
2181:
2175:
2171:
2164:
2158:
2153:
2152:
2148:
2146:
2143:
2142:
2109:
2095:
2091:
2084:
2080:
2074:
2070:
2060:
2046:
2042:
2035:
2031:
2025:
2021:
2011:
1994:
1992:
1989:
1988:
1982:Euler's formula
1952:
1948:
1933:
1929:
1914:
1910:
1895:
1891:
1874:
1872:
1869:
1868:
1856:, we can write
1855:
1848:
1803:
1798:
1797:
1785:
1781:
1775:
1771:
1762:
1757:
1756:
1754:
1751:
1750:
1746:takes the form
1734:In general, an
1711:
1706:
1705:
1696:
1692:
1688:
1682:
1678:
1676:
1667:
1663:
1657:
1653:
1652:
1647:
1645:
1642:
1641:
1616:
1608:
1599:
1595:
1591:
1585:
1581:
1579:
1571:
1567:
1561:
1557:
1555:
1547:
1541:
1537:
1535:
1532:
1531:
1513:
1488:
1483:
1482:
1473:
1469:
1465:
1459:
1455:
1453:
1444:
1440:
1434:
1430:
1429:
1424:
1416:
1407:
1403:
1399:
1393:
1389:
1387:
1379:
1375:
1369:
1365:
1363:
1355:
1349:
1345:
1343:
1340:
1339:
1310:
1302:
1299:
1298:
1269:
1261:
1252:
1248:
1244:
1238:
1234:
1232:
1224:
1220:
1214:
1210:
1208:
1200:
1194:
1190:
1188:
1185:
1184:
1150:
1142:
1139:
1138:
1112:
1108:
1106:
1103:
1102:
1079:
1073:
1069:
1056:
1049:
1045:
1029:
1022:
1018:
1010:
1007:
1006:
957:
952:
951:
942:
938:
934:
928:
924:
922:
913:
909:
903:
899:
898:
893:
882:
873:
869:
865:
859:
855:
853:
845:
841:
835:
831:
829:
821:
807:
804:
803:
789:
697:
692:
691:
679:
675:
657:
652:
651:
639:
635:
618:
606:
602:
601:
597:
591:
587:
570:
568:
565:
564:
512:
495:
455:
440:photoionisation
380:
376:
374:
371:
370:
254:
250:
248:
245:
244:
236:
149:
137:
125:Theodore Maiman
94:
82:Schwinger limit
28:
23:
22:
15:
12:
11:
5:
8690:
8680:
8679:
8674:
8657:
8656:
8654:
8653:
8648:
8643:
8638:
8633:
8627:
8625:
8621:
8620:
8618:
8617:
8612:
8607:
8602:
8597:
8592:
8587:
8582:
8577:
8572:
8566:
8564:
8558:
8557:
8555:
8554:
8549:
8548:
8547:
8542:
8537:
8527:
8522:
8517:
8512:
8511:
8510:
8505:
8494:
8492:
8486:
8485:
8483:
8482:
8481:
8480:
8475:
8468:Thermodynamics
8465:
8464:
8463:
8458:
8448:
8443:
8438:
8437:
8436:
8431:
8426:
8421:
8410:
8408:
8402:
8401:
8399:
8398:
8397:
8396:
8386:
8380:
8378:
8374:
8373:
8371:
8370:
8369:
8368:
8358:
8352:
8350:
8346:
8345:
8337:
8336:
8329:
8322:
8314:
8306:
8305:
8293:
8260:
8253:
8232:
8204:
8152:
8120:(10): 200003.
8100:
8043:
8003:
7950:
7923:(1): 145–147.
7907:
7852:Optics Letters
7835:
7800:
7764:
7728:
7685:
7648:(8): 4623–33.
7642:Optics Express
7628:
7601:(3): 467–470.
7585:
7566:
7555:(8): 561–566.
7536:
7515:(10): 101001.
7496:
7461:
7426:
7391:
7344:
7329:
7299:
7261:(15): 1192–4.
7255:Optics Letters
7236:
7201:Optics Express
7187:
7172:
7157:
7139:
7115:
7081:
7062:(5): 540–548.
7043:
7008:(12): 125802.
6988:
6969:(6): 424–429.
6952:
6925:
6865:
6812:
6806:978-9810225995
6805:
6787:
6760:
6721:
6686:
6679:
6661:
6654:
6642:Shen, Yuen-Ron
6633:
6626:
6604:
6603:
6601:
6598:
6597:
6596:
6590:
6577:
6564:
6552:
6540:
6525:
6522:
6521:
6520:
6515:
6510:
6503:
6500:
6499:
6498:
6494:
6491:
6483:
6479:
6467:
6464:
6459:1300 nm:
6457:
6445:
6441:
6436:1064 nm:
6434:
6431:
6428:
6424:
6417:
6413:
6410:lithium iodate
6406:
6381:
6378:
6351:
6348:
6341:
6337:
6333:
6330:
6324:
6318:
6315:
6310:
6307:
6304:
6251:
6244:
6239:
6236:
6231:
6228:
6223:
6218:
6213:
6210:
6207:
6201:
6197:
6192:
6188:
6172:polarizability
6158:
6155:
6138:
6135:
6134:
6133:
6118:
6115:
6112:
6109:
6096:
6091:
6085:
6082:
6079:
6076:
6073:
6070:
6067:
6065:
6053:
6048:
6042:
6041:
6038:
6034:
6030:
6027:
6017:
6012:
6009:
6005:
6001:
5998:
5995:
5992:
5990:
5981:
5976:
5975:
5941:
5938:
5935:
5911:
5886:
5866:
5863:
5860:
5857:
5851:
5846:
5824:
5820:
5817:
5813:
5792:
5789:
5773:
5770:
5753:
5732:
5716:
5715:
5704:
5701:
5698:
5695:
5691:
5687:
5677:
5672:
5669:
5666:
5663:
5660:
5656:
5652:
5642:
5617:
5614:
5611:
5607:
5603:
5599:
5595:
5591:
5587:
5584:
5581:
5578:
5574:
5570:
5566:
5554:
5553:
5542:
5539:
5536:
5533:
5529:
5525:
5521:
5517:
5514:
5511:
5508:
5504:
5500:
5496:
5490:
5486:
5480:
5476:
5472:
5469:
5466:
5463:
5459:
5455:
5451:
5436:
5435:
5424:
5421:
5418:
5415:
5411:
5407:
5397:
5392:
5389:
5386:
5383:
5380:
5376:
5372:
5362:
5337:
5334:
5332:
5329:
5320:
5316:
5312:
5308:
5297:
5296:
5285:
5282:
5278:
5274:
5269:
5264:
5260:
5256:
5253:
5249:
5245:
5240:
5236:
5220:
5213:
5203:
5202:
5191:
5186:
5181:
5177:
5171:
5167:
5161:
5157:
5151:
5148:
5145:
5141:
5134:
5131:
5128:
5123:
5120:
5117:
5111:
5106:
5102:
5075:
5068:
5061:
5054:
5047:
5040:
5033:
5026:
5019:
5016:
5015:
4999:
4994:
4990:
4986:
4982:
4978:
4975:
4972:
4969:
4966:
4962:
4956:
4951:
4947:
4941:
4937:
4931:
4927:
4921:
4917:
4911:
4908:
4905:
4901:
4895:
4892:
4887:
4882:
4878:
4862:
4855:
4848:
4837:
4833:
4829:
4822:
4818:
4814:
4810:
4806:
4802:
4799:
4798:
4787:
4782:
4778:
4772:
4768:
4764:
4759:
4755:
4751:
4746:
4742:
4738:
4733:
4730:
4727:
4723:
4717:
4713:
4709:
4700:
4681:
4677:
4673:
4669:
4664:
4659:
4658:
4647:
4639:
4633:
4628:
4624:
4620:
4616:
4613:
4608:
4604:
4599:
4595:
4591:
4587:
4583:
4579:
4574:
4570:
4564:
4561:
4556:
4553:
4550:
4547:
4543:
4539:
4534:
4530:
4510:
4507:
4458:
4455:
4452:
4449:
4446:
4443:
4422:
4418:
4415:
4412:
4408:
4387:
4384:
4381:
4378:
4375:
4354:
4350:
4347:
4344:
4340:
4316:
4313:
4287:
4284:
4261:
4258:
4255:
4252:
4249:
4228:
4224:
4221:
4217:
4200:
4197:
4163:
4160:
4119:
4116:
4114:
4111:
4076:
4073:
4070:
4066:
4040:
4037:
4034:
4030:
4007:
4004:
4001:
3997:
3974:
3971:
3968:
3964:
3932:
3929:
3926:
3922:
3899:
3896:
3893:
3889:
3869:
3866:
3807:
3806:
3803:
3800:
3797:
3793:
3792:
3789:
3786:
3783:
3779:
3778:
3775:
3772:
3769:
3765:
3764:
3761:
3758:
3755:
3751:
3750:
3747:
3744:
3741:
3737:
3736:
3733:
3730:
3727:
3723:
3722:
3719:
3716:
3713:
3709:
3708:
3705:
3702:
3699:
3695:
3694:
3691:
3688:
3684:
3683:
3680:
3679:Polarizations
3661:
3657:
3653:
3648:
3644:
3640:
3635:
3631:
3612:crystal optics
3599:
3598:
3587:
3582:
3575:
3571:
3563:
3558:
3551:
3547:
3539:
3534:
3527:
3523:
3493:
3489:
3468:
3464:
3458:
3454:
3450:
3445:
3441:
3437:
3433:
3429:
3426:
3421:
3416:
3411:
3389:
3385:
3363:
3351:
3350:
3334:
3329:
3326:
3321:
3317:
3313:
3309:
3305:
3302:
3297:
3292:
3287:
3282:
3277:
3272:
3269:
3266:
3262:
3254:
3250:
3244:
3240:
3232:
3228:
3222:
3218:
3214:
3211:
3208:
3205:
3201:
3197:
3192:
3189:
3186:
3182:
3156:
3152:
3148:
3143:
3139:
3135:
3130:
3126:
3103:
3099:
3078:
3073:
3069:
3065:
3061:
3040:
3020:
3016:
3010:
3006:
3002:
2997:
2993:
2989:
2985:
2981:
2978:
2973:
2968:
2963:
2939:
2927:
2926:
2910:
2905:
2902:
2897:
2893:
2889:
2885:
2881:
2876:
2871:
2866:
2863:
2859:
2853:
2850:
2847:
2843:
2839:
2836:
2833:
2830:
2826:
2822:
2817:
2813:
2780:
2776:
2773:
2769:
2765:
2743:
2740:
2737:
2733:
2730:
2696:
2695:Phase matching
2693:
2683:respectively.
2664:
2657:
2650:
2643:
2636:
2629:
2623:
2622:
2607:
2603:
2594:
2589:
2585:
2580:
2574:
2569:
2564:
2560:
2556:
2551:
2546:
2541:
2536:
2532:
2528:
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2518:
2513:
2510:
2505:
2501:
2497:
2492:
2488:
2484:
2481:
2478:
2474:
2468:
2461:
2457:
2449:
2445:
2441:
2438:
2433:
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2421:
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2408:
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2401:
2398:
2394:
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2374:
2370:
2367:
2362:
2357:
2353:
2349:
2346:
2343:
2339:
2333:
2326:
2322:
2316:
2311:
2306:
2302:
2298:
2295:
2292:
2288:
2282:
2275:
2271:
2264:
2258:
2255:
2252:
2248:
2242:
2237:
2233:
2227:
2224:
2222:
2220:
2217:
2214:
2211:
2206:
2201:
2194:
2191:
2188:
2184:
2178:
2174:
2170:
2167:
2165:
2156:
2151:
2150:
2128:
2127:
2116:
2108:
2103:
2098:
2094:
2090:
2087:
2083:
2077:
2073:
2067:
2064:
2059:
2054:
2049:
2045:
2041:
2038:
2034:
2028:
2024:
2018:
2015:
2010:
2007:
2004:
2001:
1997:
1978:
1977:
1966:
1963:
1960:
1955:
1951:
1947:
1944:
1941:
1936:
1932:
1928:
1925:
1922:
1917:
1913:
1909:
1906:
1903:
1898:
1894:
1890:
1887:
1884:
1881:
1877:
1853:
1846:
1832:
1831:
1820:
1817:
1814:
1811:
1806:
1801:
1794:
1791:
1788:
1784:
1778:
1774:
1770:
1760:
1728:
1727:
1709:
1699:
1695:
1691:
1685:
1681:
1670:
1666:
1660:
1656:
1651:
1635:
1634:
1623:
1619:
1615:
1611:
1602:
1598:
1594:
1588:
1584:
1574:
1570:
1564:
1560:
1554:
1550:
1544:
1540:
1512:
1509:
1508:
1507:
1496:
1486:
1476:
1472:
1468:
1462:
1458:
1447:
1443:
1437:
1433:
1428:
1423:
1419:
1410:
1406:
1402:
1396:
1392:
1382:
1378:
1372:
1368:
1362:
1358:
1352:
1348:
1332:
1331:
1320:
1317:
1313:
1309:
1306:
1288:
1287:
1276:
1272:
1268:
1264:
1255:
1251:
1247:
1241:
1237:
1227:
1223:
1217:
1213:
1207:
1203:
1197:
1193:
1175:
1174:
1163:
1160:
1157:
1153:
1149:
1146:
1123:
1120:
1111:
1095:
1094:
1082:
1076:
1072:
1068:
1064:
1059:
1055:
1052:
1048:
1044:
1041:
1037:
1032:
1028:
1025:
1021:
1017:
1014:
977:
976:
965:
955:
945:
941:
937:
931:
927:
916:
912:
906:
902:
897:
892:
889:
885:
876:
872:
868:
862:
858:
848:
844:
838:
834:
828:
824:
820:
817:
814:
811:
788:
785:
737:
736:
725:
721:
717:
714:
711:
708:
705:
700:
695:
688:
685:
682:
678:
674:
671:
668:
665:
660:
655:
648:
645:
642:
638:
634:
631:
628:
625:
621:
615:
612:
609:
605:
600:
594:
590:
586:
583:
580:
577:
573:
551:electric field
511:
508:
494:
491:
490:
489:
479:
472:Acousto-optics
469:
462:Pockels effect
454:
451:
450:
449:
443:
436:
426:
420:
414:
409:
403:
389:
386:
383:
379:
364:
358:
352:
349:
319:
305:
291:
277:
263:
260:
257:
253:
235:
232:
231:
230:
224:
218:
212:
206:
200:
194:
184:
178:
172:
166:
160:
148:
145:
136:
133:
93:
90:
70:electric field
26:
9:
6:
4:
3:
2:
8689:
8678:
8675:
8673:
8670:
8669:
8667:
8652:
8649:
8647:
8644:
8642:
8639:
8637:
8634:
8632:
8629:
8628:
8626:
8622:
8616:
8613:
8611:
8610:Ocean physics
8608:
8606:
8603:
8601:
8598:
8596:
8593:
8591:
8588:
8586:
8583:
8581:
8578:
8576:
8573:
8571:
8568:
8567:
8565:
8563:
8559:
8553:
8550:
8546:
8545:Modern optics
8543:
8541:
8538:
8536:
8533:
8532:
8531:
8528:
8526:
8523:
8521:
8518:
8516:
8513:
8509:
8506:
8504:
8501:
8500:
8499:
8496:
8495:
8493:
8491:
8487:
8479:
8476:
8474:
8471:
8470:
8469:
8466:
8462:
8459:
8457:
8454:
8453:
8452:
8449:
8447:
8444:
8442:
8439:
8435:
8432:
8430:
8427:
8425:
8422:
8420:
8417:
8416:
8415:
8412:
8411:
8409:
8407:
8403:
8395:
8394:Computational
8392:
8391:
8390:
8387:
8385:
8382:
8381:
8379:
8375:
8367:
8364:
8363:
8362:
8359:
8357:
8354:
8353:
8351:
8347:
8343:
8335:
8330:
8328:
8323:
8321:
8316:
8315:
8312:
8296:
8290:
8286:
8282:
8278:
8274:
8270:
8264:
8256:
8250:
8246:
8239:
8237:
8228:
8224:
8220:
8216:
8208:
8200:
8196:
8192:
8188:
8184:
8180:
8176:
8172:
8168:
8164:
8156:
8141:
8137:
8133:
8128:
8123:
8119:
8115:
8111:
8104:
8096:
8092:
8087:
8082:
8078:
8074:
8070:
8066:
8062:
8058:
8054:
8047:
8039:
8035:
8031:
8027:
8023:
8019:
8018:
8010:
8008:
7999:
7995:
7991:
7987:
7983:
7979:
7974:
7969:
7966:(4): 109638.
7965:
7961:
7954:
7946:
7942:
7938:
7934:
7930:
7926:
7922:
7918:
7911:
7897:on 2020-04-20
7893:
7889:
7885:
7881:
7877:
7873:
7869:
7865:
7861:
7857:
7853:
7846:
7839:
7831:
7827:
7823:
7819:
7815:
7811:
7804:
7796:
7792:
7788:
7784:
7780:
7776:
7768:
7760:
7756:
7752:
7748:
7744:
7740:
7732:
7724:
7720:
7716:
7712:
7708:
7704:
7700:
7696:
7689:
7681:
7677:
7673:
7669:
7664:
7659:
7655:
7651:
7647:
7643:
7639:
7632:
7624:
7620:
7616:
7612:
7608:
7604:
7600:
7596:
7589:
7582:
7578:
7575:
7570:
7562:
7558:
7554:
7550:
7543:
7541:
7532:
7528:
7523:
7518:
7514:
7510:
7503:
7501:
7492:
7488:
7484:
7480:
7476:
7472:
7465:
7457:
7453:
7449:
7445:
7441:
7437:
7430:
7422:
7418:
7414:
7410:
7406:
7402:
7395:
7387:
7383:
7379:
7375:
7371:
7367:
7363:
7359:
7355:
7348:
7340:
7336:
7332:
7326:
7322:
7318:
7314:
7310:
7303:
7288:
7284:
7280:
7276:
7272:
7268:
7264:
7260:
7256:
7252:
7245:
7243:
7241:
7232:
7228:
7223:
7218:
7214:
7210:
7206:
7202:
7198:
7191:
7185:
7181:
7176:
7170:
7166:
7161:
7146:
7142:
7136:
7132:
7131:
7126:
7119:
7104:
7100:
7096:
7092:
7085:
7077:
7073:
7069:
7065:
7061:
7057:
7050:
7048:
7039:
7035:
7031:
7027:
7023:
7019:
7015:
7011:
7007:
7003:
6999:
6992:
6984:
6980:
6976:
6972:
6968:
6964:
6956:
6948:
6944:
6940:
6936:
6929:
6913:
6909:
6905:
6901:
6897:
6893:
6889:
6885:
6881:
6877:
6869:
6861:
6857:
6853:
6852:10.1038/25303
6849:
6845:
6841:
6836:
6831:
6827:
6823:
6816:
6808:
6802:
6798:
6791:
6783:
6779:
6775:
6771:
6764:
6750:on 2016-01-01
6746:
6742:
6735:
6728:
6726:
6717:
6713:
6709:
6705:
6701:
6697:
6690:
6682:
6676:
6672:
6665:
6657:
6651:
6647:
6643:
6637:
6629:
6623:
6619:
6615:
6609:
6605:
6593:
6587:
6583:
6578:
6576:SPIE Newsroom
6575:
6571:
6568:
6565:
6563:
6559:
6556:
6553:
6551:
6547:
6544:
6541:
6538:
6534:
6531:
6528:
6527:
6519:
6516:
6514:
6511:
6509:
6506:
6505:
6492:
6489:
6477:
6473:
6465:
6462:
6458:
6455:
6451:
6439:
6435:
6429:
6422:
6419:860 nm:
6418:
6411:
6408:806 nm:
6407:
6405:
6402:800 nm:
6401:
6400:
6399:
6392:
6387:
6377:
6373:
6371:
6366:
6349:
6346:
6339:
6335:
6331:
6328:
6322:
6316:
6313:
6308:
6305:
6302:
6291:
6282:
6278:
6274:
6273:
6269:
6267:
6237:
6234:
6229:
6226:
6221:
6211:
6208:
6205:
6190:
6177:
6173:
6168:
6167:
6163:
6154:
6152:
6148:
6144:
6116:
6113:
6107:
6089:
6083:
6080:
6077:
6071:
6068:
6066:
6046:
6036:
6025:
6010:
6007:
5996:
5993:
5991:
5966:
5965:
5964:
5962:
5958:
5953:
5939:
5933:
5926:
5900:
5884:
5864:
5858:
5855:
5844:
5815:
5790:
5787:
5779:
5769:
5767:
5751:
5721:
5702:
5696:
5693:
5670:
5667:
5661:
5658:
5631:
5630:
5629:
5612:
5609:
5593:
5585:
5579:
5576:
5540:
5534:
5531:
5515:
5509:
5506:
5488:
5484:
5478:
5474:
5470:
5464:
5461:
5441:
5440:
5439:
5422:
5416:
5413:
5390:
5387:
5381:
5378:
5351:
5350:
5349:
5347:
5343:
5328:
5326:
5305:
5301:
5283:
5267:
5262:
5258:
5254:
5238:
5234:
5226:
5225:
5224:
5219:
5212:
5208:
5189:
5184:
5179:
5175:
5169:
5165:
5159:
5155:
5146:
5139:
5132:
5129:
5126:
5121:
5118:
5115:
5109:
5104:
5100:
5092:
5091:
5090:
5088:
5084:
5079:
5074:
5067:
5060:
5053:
5046:
5039:
5032:
5025:
4997:
4984:
4976:
4973:
4970:
4964:
4960:
4954:
4949:
4945:
4939:
4935:
4929:
4925:
4919:
4915:
4906:
4899:
4893:
4890:
4885:
4880:
4876:
4868:
4867:
4866:
4861:
4854:
4847:
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4826:
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4770:
4762:
4757:
4749:
4744:
4728:
4721:
4715:
4711:
4707:
4698:
4690:
4689:
4688:
4685:
4667:
4645:
4637:
4631:
4622:
4614:
4611:
4606:
4602:
4597:
4593:
4589:
4572:
4568:
4562:
4559:
4554:
4548:
4545:
4532:
4520:
4519:
4518:
4516:
4506:
4499:
4495:
4493:
4488:
4483:
4480:
4476:
4456:
4450:
4447:
4444:
4441:
4413:
4410:
4385:
4379:
4376:
4373:
4345:
4342:
4311:
4282:
4259:
4253:
4250:
4247:
4219:
4205:
4196:
4194:
4189:
4187:
4186:
4181:
4177:
4176:time reversal
4174:(also called
4173:
4169:
4159:
4157:
4153:
4149:
4145:
4141:
4135:
4133:
4129:
4128:Nd:YAG lasers
4125:
4110:
4108:
4104:
4100:
4096:
4095:Taylor series
4092:
4091:filamentation
4071:
4064:
4054:
4035:
4028:
4002:
3995:
3969:
3962:
3953:
3949:
3927:
3920:
3894:
3887:
3874:
3865:
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3855:
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3834:
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3804:
3801:
3798:
3795:
3794:
3790:
3787:
3784:
3781:
3780:
3776:
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3767:
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3728:
3725:
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3700:
3697:
3696:
3692:
3689:
3686:
3685:
3677:
3659:
3655:
3651:
3646:
3642:
3638:
3633:
3629:
3615:
3613:
3608:
3604:
3585:
3580:
3561:
3556:
3537:
3532:
3509:
3508:
3507:
3491:
3487:
3466:
3462:
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3427:
3419:
3387:
3383:
3332:
3324:
3319:
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3311:
3303:
3295:
3285:
3280:
3264:
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3252:
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3206:
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3141:
3137:
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3128:
3124:
3101:
3097:
3071:
3067:
3038:
3018:
3014:
3008:
3004:
2995:
2991:
2979:
2971:
2954:
2908:
2900:
2895:
2891:
2887:
2879:
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2845:
2841:
2837:
2831:
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2803:
2802:
2801:
2795:
2774:
2771:
2767:
2741:
2738:
2735:
2731:
2728:
2718:
2717:monotonically
2714:
2710:
2706:
2701:
2692:
2690:
2684:
2682:
2678:
2674:
2670:
2663:
2660: −
2656:
2649:
2646: +
2642:
2635:
2628:
2605:
2601:
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2587:
2583:
2578:
2572:
2567:
2562:
2558:
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2549:
2544:
2539:
2534:
2530:
2526:
2520:
2516:
2511:
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2495:
2490:
2486:
2479:
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2472:
2466:
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2455:
2447:
2443:
2439:
2436:
2431:
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2396:
2392:
2386:
2382:
2376:
2372:
2368:
2365:
2360:
2355:
2351:
2347:
2344:
2341:
2337:
2331:
2324:
2320:
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2293:
2290:
2286:
2280:
2273:
2269:
2262:
2253:
2246:
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2225:
2223:
2212:
2204:
2189:
2182:
2176:
2172:
2168:
2166:
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2140:
2139:
2137:
2133:
2114:
2106:
2101:
2096:
2092:
2088:
2085:
2081:
2075:
2071:
2065:
2062:
2057:
2052:
2047:
2043:
2039:
2036:
2032:
2026:
2022:
2016:
2013:
2008:
2002:
1987:
1986:
1985:
1983:
1964:
1958:
1953:
1949:
1942:
1939:
1934:
1930:
1926:
1920:
1915:
1911:
1904:
1901:
1896:
1892:
1888:
1882:
1867:
1866:
1865:
1863:
1859:
1852:
1845:
1841:
1837:
1818:
1812:
1804:
1789:
1782:
1776:
1772:
1768:
1749:
1748:
1747:
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1741:
1737:
1732:
1697:
1693:
1683:
1668:
1664:
1658:
1654:
1649:
1640:
1639:
1638:
1621:
1613:
1600:
1596:
1586:
1572:
1568:
1562:
1558:
1552:
1542:
1530:
1529:
1528:
1526:
1522:
1518:
1494:
1474:
1470:
1460:
1445:
1441:
1435:
1431:
1426:
1421:
1408:
1404:
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1380:
1376:
1370:
1366:
1360:
1350:
1338:
1337:
1336:
1318:
1315:
1307:
1297:
1296:
1295:
1293:
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1253:
1249:
1239:
1225:
1221:
1215:
1211:
1205:
1195:
1183:
1182:
1181:
1180:
1179:wave equation
1161:
1158:
1155:
1147:
1137:
1136:
1135:
1121:
1118:
1109:
1100:
1074:
1066:
1062:
1053:
1046:
1039:
1035:
1026:
1019:
1015:
1005:
1004:
1003:
1000:
998:
994:
990:
986:
982:
963:
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939:
929:
914:
910:
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900:
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890:
887:
874:
870:
860:
846:
842:
836:
832:
826:
818:
812:
802:
801:
800:
798:
794:
793:wave equation
784:
782:
778:
774:
770:
766:
762:
758:
754:
750:
746:
742:
723:
719:
715:
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698:
683:
676:
672:
666:
658:
643:
636:
632:
626:
610:
603:
598:
592:
588:
584:
578:
563:
562:
561:
559:
555:
552:
548:
544:
540:
536:
532:
529:
525:
524:Taylor series
521:
517:
507:
504:
503:quantum state
500:
487:
483:
480:
477:
473:
470:
467:
463:
460:
459:
458:
447:
444:
441:
437:
434:
430:
427:
424:
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418:
415:
413:
410:
407:
404:
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377:
368:
365:
362:
359:
356:
353:
350:
347:
346:self-focusing
343:
339:
335:
331:
327:
326:optical pulse
323:
320:
317:
313:
309:
306:
303:
299:
298:self-focusing
295:
292:
289:
285:
281:
280:Self-focusing
278:
258:
251:
242:
238:
237:
228:
225:
222:
219:
216:
213:
210:
207:
204:
201:
198:
195:
192:
188:
185:
182:
179:
176:
173:
170:
167:
164:
161:
158:
154:
151:
150:
144:
142:
132:
130:
126:
122:
118:
115:
114:Peter Franken
111:
107:
103:
99:
89:
87:
83:
79:
74:
71:
67:
64:
60:
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52:
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44:
37:
34:Structure of
32:
19:
8570:Astrophysics
8384:Experimental
8298:, retrieved
8276:
8263:
8244:
8218:
8214:
8207:
8166:
8162:
8155:
8144:. Retrieved
8117:
8113:
8103:
8060:
8056:
8046:
8021:
8015:
7963:
7959:
7953:
7920:
7916:
7910:
7899:. Retrieved
7892:the original
7855:
7851:
7838:
7813:
7809:
7803:
7778:
7774:
7767:
7742:
7738:
7731:
7698:
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7645:
7641:
7631:
7598:
7594:
7588:
7569:
7552:
7548:
7512:
7508:
7477:(4): 62–75.
7474:
7470:
7464:
7442:(1): 74–83.
7439:
7435:
7429:
7407:(6): 54–59.
7404:
7400:
7394:
7361:
7357:
7347:
7312:
7309:Taylor, A.J.
7302:
7291:. Retrieved
7258:
7254:
7204:
7200:
7190:
7175:
7160:
7149:. Retrieved
7129:
7118:
7107:. Retrieved
7098:
7094:
7084:
7059:
7055:
7005:
7001:
6991:
6966:
6962:
6955:
6938:
6934:
6928:
6916:. Retrieved
6912:the original
6883:
6879:
6868:
6825:
6821:
6815:
6796:
6790:
6773:
6769:
6763:
6752:. Retrieved
6745:the original
6740:
6699:
6695:
6689:
6670:
6664:
6645:
6636:
6617:
6614:Boyd, Robert
6608:
6581:
6470:, BBO, KDP,
6397:
6374:
6367:
6290:chromophores
6287:
6275:
6271:
6270:
6169:
6165:
6164:
6160:
6140:
5960:
5956:
5954:
5924:
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5339:
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4662:
4660:
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4484:
4478:
4472:
4192:
4190:
4183:
4179:
4175:
4171:
4167:
4165:
4156:birefringent
4136:
4123:
4121:
4113:Example uses
4055:
3878:
3849:
3842:
3835:
3822:
3816:
3812:
3810:
3602:
3600:
3352:
2929:at position
2928:
2799:
2794:Birefringent
2685:
2661:
2654:
2647:
2640:
2633:
2626:
2624:
2135:
2129:
1979:
1861:
1857:
1850:
1843:
1839:
1835:
1833:
1743:
1739:
1735:
1733:
1729:
1636:
1514:
1333:
1289:
1176:
1096:
1001:
996:
988:
980:
978:
790:
777:polarization
768:
764:
760:
756:
752:
748:
740:
738:
557:
553:
546:
542:
538:
513:
496:
456:
330:spatial mode
190:
156:
138:
116:
95:
80:. Above the
72:
65:
46:
42:
41:
8473:Statistical
8389:Theoretical
8366:Engineering
7858:(1): 24–6.
6918:6 September
4053:processes.
2953:wave vector
2951:, with the
1292:Gauss's law
1099:Gauss's law
338:Kerr effect
312:Kerr effect
284:Kerr effect
241:Kerr effect
129:Bloembergen
36:KTP crystal
8666:Categories
8590:Geophysics
8580:Biophysics
8424:Analytical
8377:Approaches
8300:2023-11-27
8146:2023-11-27
8024:(2): 328.
7973:1901.09274
7901:2019-08-26
7293:2015-06-23
7151:2011-08-16
7109:2015-10-31
6754:2015-10-21
6702:(6): 229.
6600:References
6452:(LBO) and
6384:See also:
4199:Principles
4099:attosecond
2715:decreases
1980:and using
781:symmetries
743:-th-order
545:) at time
528:dielectric
499:parametric
334:dispersion
155:(SHG), or
8540:Molecular
8441:Acoustics
8434:Continuum
8429:Celestial
8419:Newtonian
8406:Classical
8349:Divisions
8199:205279732
8136:2096-4579
8063:: 28483.
7998:118828500
7945:122790937
7880:1539-4794
7795:1932-7447
7759:1932-7447
7715:0002-7863
7672:1094-4087
7549:JETP Lett
7522:0801.2675
7386:0030-4026
7339:120016673
7180:Boyd 2008
7165:Boyd 2008
7133:. Wiley.
7101:(2): 55.
7038:202145209
7030:0031-8949
6350:ω
6347:ℏ
6332:δ
6303:−
6235:β
6212:⋅
6209:α
6196:μ
6187:μ
6114:ℓ
6111:ℏ
6084:−
6078:ℓ
6075:ℏ
6072:−
6029:ℏ
6011:−
6000:ℏ
5997:−
5940:ℓ
5937:ℏ
5934:±
5885:ℓ
5865:ℓ
5862:ℏ
5859:±
5819:ℏ
5791:ω
5788:ℏ
5671:−
5594:×
5516:×
5475:ϵ
5391:−
5268:∗
5255:∝
5185:∗
5140:χ
5119:ω
4985:⋅
4977:−
4971:ω
4955:∗
4916:ε
4900:χ
4881:ω
4767:Ξ
4754:Ξ
4741:Ξ
4722:χ
4712:ε
4623:⋅
4615:−
4603:ω
4529:Ξ
4457:ℓ
4454:ℏ
4448:±
4417:ℏ
4386:ℓ
4383:ℏ
4380:∓
4349:ℏ
4346:−
4315:→
4286:→
4260:ℓ
4257:ℏ
4254:±
4223:ℏ
4168:conjugate
4065:χ
4029:χ
3996:χ
3963:χ
3921:χ
3888:χ
3656:λ
3652:≤
3643:λ
3639:≤
3630:λ
3574:→
3550:→
3526:→
3488:ω
3453:ω
3440:ω
3425:‖
3410:‖
3384:ω
3316:ω
3312:−
3304:⋅
3213:∝
3151:ω
3138:ω
3125:ω
3098:ω
3068:ω
3005:ω
2992:ω
2977:‖
2962:‖
2892:ω
2888:−
2880:⋅
2742:ω
2729:ω
2705:BK7 glass
2500:ω
2496:−
2487:ω
2477:−
2467:∗
2420:ω
2407:ω
2397:−
2352:ω
2342:−
2301:ω
2291:−
2247:χ
2232:ε
2183:χ
2173:ε
2093:ω
2086:−
2044:ω
2037:−
1950:ω
1943:
1912:ω
1905:
1783:χ
1773:ε
1690:∂
1680:∂
1655:ε
1593:∂
1583:∂
1553:−
1539:∇
1467:∂
1457:∂
1432:ε
1401:∂
1391:∂
1361:−
1347:∇
1308:⋅
1305:∇
1246:∂
1236:∂
1206:−
1192:∇
1148:⋅
1145:∇
1110:ρ
1071:∇
1067:−
1054:⋅
1051:∇
1043:∇
1027:×
1024:∇
1016:×
1013:∇
936:∂
926:∂
901:ε
891:−
867:∂
857:∂
819:×
816:∇
813:×
810:∇
716:…
677:χ
637:χ
604:χ
589:ε
520:too large
438:Multiple
378:χ
369:(XPW), a
302:mode-lock
252:χ
141:frequency
106:Bell Labs
59:nonlinear
8271:(2020),
8191:28556297
8140:Archived
8095:27339882
7888:19865292
7830:35614732
7723:17378567
7680:19532708
7623:11015940
7577:Archived
7491:24997062
7456:24975872
7421:24967871
7311:(1997).
7287:Archived
7283:19776917
7231:20588396
7145:Archived
7103:Archived
6963:Nat Phys
6908:10060879
6860:16080209
6644:(2002).
6616:(2008).
6570:Archived
6558:Archived
6546:Archived
6533:Archived
6502:See also
6448:, KDP),
5877:, where
4146:), KTP (
4142:), KDP (
3749:Type IV
3031:, where
2768:′
2732:′
336:and the
276:effect).
239:Optical
8624:Related
8508:General
8503:Special
8361:Applied
8221:: 138.
8171:Bibcode
8086:4919686
8065:Bibcode
8026:Bibcode
7978:Bibcode
7925:Bibcode
7860:Bibcode
7650:Bibcode
7603:Bibcode
7366:Bibcode
7263:Bibcode
7209:Bibcode
7064:Bibcode
7010:Bibcode
6971:Bibcode
6888:Bibcode
6840:Bibcode
6704:Bibcode
6482:), LiIO
6474:(KTP),
5764:for an
5720:locally
4195:(PCM).
4150:), and
3854:dazzler
3707:Type I
3690:Signal
3682:Scheme
991:is the
486:phonons
92:History
8677:Optics
8535:Atomic
8490:Modern
8340:Major
8291:
8251:
8197:
8189:
8134:
8093:
8083:
7996:
7943:
7886:
7878:
7828:
7793:
7757:
7721:
7713:
7678:
7670:
7621:
7489:
7454:
7419:
7384:
7337:
7327:
7281:
7229:
7137:
7036:
7028:
6906:
6858:
6822:Nature
6803:
6677:
6652:
6624:
6588:
6486:, and
6478:(LiNbO
6463:(GaSe)
5205:where
4661:where
3693:Idler
2711:: the
2138:gives
987:, and
979:where
773:tensor
510:Theory
433:energy
340:(e.g.
304:laser.
117:et al.
78:lasers
51:optics
8195:S2CID
7994:S2CID
7968:arXiv
7941:S2CID
7895:(PDF)
7848:(PDF)
7517:arXiv
7487:JSTOR
7452:JSTOR
7417:JSTOR
7358:Optik
7335:S2CID
7034:S2CID
6941:(9).
6856:S2CID
6830:arXiv
6748:(PDF)
6737:(PDF)
6490:(ADP)
6456:(BBO)
6423:(KNbO
6412:(LiIO
4672:and Ξ
3954:with
3687:Pump
2754:and
1864:) as
1849:and
191:idler
100:, by
55:light
8461:Wave
8356:Pure
8289:ISBN
8249:ISBN
8187:PMID
8132:ISSN
8091:PMID
7884:PMID
7876:ISSN
7826:PMID
7791:ISSN
7755:ISSN
7719:PMID
7711:ISSN
7676:PMID
7668:ISSN
7619:PMID
7382:ISSN
7325:ISBN
7279:PMID
7227:PMID
7135:ISBN
7026:ISSN
6920:2018
6904:PMID
6801:ISBN
6675:ISBN
6650:ISBN
6622:ISBN
6586:ISBN
5216:and
5002:c.c.
4840:and
4821:, 3ω
4817:, 3ω
4642:c.c.
3337:c.c.
2913:c.c.
2679:and
2597:c.c.
2111:c.c.
1114:free
1097:and
8456:Ray
8281:doi
8223:doi
8219:339
8179:doi
8122:doi
8081:PMC
8073:doi
8034:doi
7986:doi
7964:133
7933:doi
7868:doi
7818:doi
7783:doi
7779:120
7747:doi
7743:119
7703:doi
7699:129
7658:doi
7611:doi
7557:doi
7527:doi
7479:doi
7475:263
7444:doi
7440:254
7409:doi
7405:253
7374:doi
7362:127
7317:doi
7271:doi
7217:doi
7072:doi
7060:238
7018:doi
6979:doi
6943:doi
6896:doi
6848:doi
6826:396
6778:doi
6712:doi
6440:(KH
6404:BBO
6060:out
5985:out
5955:In
5897:is
5776:In
5646:out
5366:out
5340:In
5311:= ω
5071:= −
5057:= −
4836:− ω
4832:+ ω
4809:± ω
4805:± ω
4188:).
3169:is
2632:, 2
1940:cos
1902:cos
1134:),
560:):
119:at
112:by
57:in
47:NLO
8668::
8287:,
8275:,
8235:^
8217:.
8193:.
8185:.
8177:.
8167:29
8165:.
8138:.
8130:.
8116:.
8112:.
8089:.
8079:.
8071:.
8059:.
8055:.
8032:.
8020:.
8006:^
7992:.
7984:.
7976:.
7962:.
7939:.
7931:.
7921:89
7919:.
7882:.
7874:.
7866:.
7856:21
7854:.
7850:.
7824:.
7812:.
7789:.
7777:.
7753:.
7741:.
7717:.
7709:.
7697:.
7674:.
7666:.
7656:.
7646:15
7644:.
7640:.
7617:.
7609:.
7599:84
7597:.
7553:88
7551:.
7539:^
7525:.
7513:41
7511:.
7499:^
7485:.
7473:.
7450:.
7438:.
7415:.
7403:.
7380:.
7372:.
7360:.
7356:.
7333:.
7323:.
7285:.
7277:.
7269:.
7259:16
7257:.
7253:.
7239:^
7225:.
7215:.
7205:18
7203:.
7199:.
7182:,
7143:.
7127:.
7097:.
7093:.
7070:.
7058:.
7046:^
7032:.
7024:.
7016:.
7006:94
7004:.
7000:.
6977:.
6965:.
6939:12
6937:.
6902:.
6894:.
6884:76
6878:.
6854:.
6846:.
6838:.
6824:.
6774:63
6772:.
6739:.
6724:^
6710:.
6698:.
6444:PO
6365:.
6153:.
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