Nonlinear Optics Wiki

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Nonlinear opticsFrom Wikipedia, the free encyclopedia

Nonlinear optics(NLO) is the branch ofopticsthat describes the behavior oflightinnonlinearmedia, that is, media inwhich the dielectricpolarizationPresponds nonlinearly to theelectric fieldEof the light. This nonlinearity is typically onlyobserved at very high light intensities (values of the electric field comparable to interatomic electric fields, typically108V/m) such as those provided bylasers.Above theSchwinger limit,the vacuum itself is expected to become nonlinear.n nonlinear optics, thesuperposition principleno longer holds.

Nonlinear optics remained unexplored until the discovery ofSecond harmonic generationshortly after demonstration of

he first laser. (Peter Frankenet al.atUniversity of Michiganin 1961)

Contents

[hide]

1 Nonlinear optical processes

o 1.1 Frequency mixing processes

o 1.2 Other nonlinear processes

o 1.3 Related processes

2 Parametric processes

o 2.1 Theory

2.1.1 Wave-equation in a nonlinear material

2.1.2 Nonlinearities as a wave mixing processo 2.2 Phase matching

3 Higher-order frequency mixing

4 Example uses of nonlinear optics

o 4.1 Frequency doubling

o 4.2 Optical phase conjugation

5 Common SHG materials

6 See also

7 Notes

8 References

9 External links

Nonlinear optical processes[edit]

Nonlinear optics gives rise to a host of optical phenomena:

Frequency mixing processes[edit]

Second harmonic generation(SHG), or frequency doubling, generation of light with a doubled frequency (half thewavelength), two photons are destroyed creating a single photon at two times the frequency.

Third harmonic generation(THG), generation of light with a tripled frequency (one-third the wavelength), threephotons are destroyed creating a single photon at three times the frequency.

High harmonic generation(HHG), generation of light with frequencies much greater than the original (typically 100 to

1000 times greater) Sum frequency generation(SFG), generation of light with a frequency that is the sum of two other frequencies (SHG

is a special case of this)

Difference frequency generation(DFG), generation of light with a frequency that is the difference between two otherfrequencies

Optical parametric amplification(OPA), amplification of a signal input in the presence of a higher-frequency pumpwave, at the same time generating an idlerwave (can be considered as DFG)

Optical parametric oscillation(OPO), generation of a signal and idler wave using a parametric amplifier in a resonator(with no signal input)

Optical parametric generation(OPG), like parametric oscillation but without a resonator, using a very high gaininstead

Spontaneous parametric down conversion(SPDC), the amplification of the vacuum fluctuations in the low gain regime

Optical rectification(OR), generation of quasi-static electric fields. Nonlinear light-matter interaction with free electrons and plasmas[1][2][3][4]

Other nonlinear processes[edit]

OpticalKerr effect,intensity dependent refractive index (a effect)
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tp://en.wikipedia.org/w/index.php?title=Difference_frequency_generation&action=edit&redlink=1http://en.wikipedia.org/wiki/Optical_parametric_amplificationhttp://en.wikipedia.org/wiki/Optical_parametric_amplificationhttp://en.wikipedia.org/wiki/Optical_parametric_oscillationhttp://en.wikipedia.org/wiki/Optical_parametric_oscillationhttp://en.wikipedia.org/wiki/Optical_parametric_generationhttp://en.wikipedia.org/wiki/Optical_parametric_generationhttp://en.wikipedia.org/wiki/Spontaneous_parametric_down_conversionhttp://en.wikipedia.org/wiki/Spontaneous_parametric_down_conversionhttp://en.wikipedia.org/wiki/Optical_rectificationhttp://en.wikipedia.org/wiki/Optical_rectificationhttp://en.wikipedia.org/w/index.php?title=Nonlinear_light-matter_interaction_with_free_electrons_and_plasmas&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Nonlinear_light-matter_interaction_with_free_electrons_and_plasmas&action=edit&redlink=1http://en.wikipedia.org/wiki/Nonlinear_optics#cite_note-2http://en.wikipedia.org/wiki/Nonlinear_optics#cite_note-4http://en.wikipedia.org/wiki/Nonlinear_optics#cite_note-4http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=3http://en.wikipedia.org/wiki/Kerr_effecthttp://en.wikipedia.org/wiki/Kerr_effecthttp://en.wikipedia.org/wiki/Kerr_effecthttp://en.wikipedia.org/wiki/Kerr_effecthttp://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=3http://en.wikipedia.org/wiki/Nonlinear_optics#cite_note-4http://en.wikipedia.org/wiki/Nonlinear_optics#cite_note-2http://en.wikipedia.org/wiki/Nonlinear_optics#cite_note-2http://en.wikipedia.org/w/index.php?title=Nonlinear_light-matter_interaction_with_free_electrons_and_plasmas&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Nonlinear_light-matter_interaction_with_free_electrons_and_plasmas&action=edit&redlink=1http://en.wikipedia.org/wiki/Optical_rectificationhttp://en.wikipedia.org/wiki/Spontaneous_parametric_down_conversionhttp://en.wikipedia.org/wiki/Optical_parametric_generationhttp://en.wikipedia.org/wiki/Optical_parametric_oscillationhttp://en.wikipedia.org/wiki/Optical_parametric_amplificationhttp://en.wikipedia.org/w/index.php?title=Difference_frequency_generation&action=edit&redlink=1http://en.wikipedia.org/wiki/Sum_frequency_generationhttp://en.wikipedia.org/wiki/High_harmonic_generationhttp://en.wikipedia.org/wiki/Third_harmonic_generationhttp://en.wikipedia.org/wiki/Second_harmonic_generationhttp://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=2http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=1http://en.wikipedia.org/wiki/Nonlinear_optics#External_linkshttp://en.wikipedia.org/wiki/Nonlinear_optics#Referenceshttp://en.wikipedia.org/wiki/Nonlinear_optics#Noteshttp://en.wikipedia.org/wiki/Nonlinear_optics#See_alsohttp://en.wikipedia.org/wiki/Nonlinear_optics#Common_SHG_materialshttp://en.wikipedia.org/wiki/Nonlinear_optics#Optical_phase_conjugationhttp://en.wikipedia.org/wiki/Nonlinear_optics#Frequency_doublinghttp://en.wikipedia.org/wiki/Nonlinear_optics#Example_uses_of_nonlinear_opticshttp://en.wikipedia.org/wiki/Nonlinear_optics#Higher-order_frequency_mixinghttp://en.wikipedia.org/wiki/Nonlinear_optics#Phase_matchinghttp://en.wikipedia.org/wiki/Nonlinear_optics#Nonlinearities_as_a_wave_mixing_processhttp://en.wikipedia.org/wiki/Nonlinear_optics#Wave-equation_in_a_nonlinear_materialhttp://en.wikipedia.org/wiki/Nonlinear_optics#Theoryhttp://en.wikipedia.org/wiki/Nonlinear_optics#Parametric_processeshttp://en.wikipedia.org/wiki/Nonlinear_optics#Related_processeshttp://en.wikipedia.org/wiki/Nonlinear_optics#Other_nonlinear_processeshttp://en.wikipedia.org/wiki/Nonlinear_optics#Frequency_mixing_processeshttp://en.wikipedia.org/wiki/Nonlinear_optics#Nonlinear_optical_processeshttp://en.wikipedia.org/wiki/Nonlinear_opticshttp://en.wikipedia.org/wiki/University_of_Michiganhttp://en.wikipedia.org/wiki/Peter_Frankenhttp://en.wikipedia.org/wiki/Second_harmonic_generationhttp://en.wikipedia.org/wiki/Superposition_principlehttp://en.wikipedia.org/wiki/Schwinger_limithttp://en.wikipedia.org/wiki/Laserhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Polarization_(electrostatics)http://en.wikipedia.org/wiki/Nonlinearhttp://en.wikipedia.org/wiki/Lighthttp://en.wikipedia.org/wiki/Optics


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Self-focusing,an effect due to the OpticalKerr effect(and possibly higher order nonlinearities) caused bythespatial variation in the intensitycreating a spatial variation in the refractive index

Kerr-lens modelocking(KLM), the use ofSelf-focusingas a mechanism tomode locklaser.

Self-phase modulation(SPM), an effect due to the OpticalKerr effect(and possibly higher order nonlinearities)caused by thetemporal variation in the intensitycreating a temporal variation in the refractive index

Optical solitons,An equilibrium solution for either anoptical pulse(temporal soliton) orSpatial mode(spatialsoliton) that does not change during propagation due to a balance betweendispersionand theKerreffect(e.g.Self-phase modulationfor temporal andSelf-focusingfor spatial solitons).

Cross-phase modulation(XPM)

Four-wave mixing(FWM), can also arise from other nonlinearities

Cross-polarized wave generation(XPW), a effect in which a wave with polarization vector perpendicular to theinput one is generated

Modulational instability

Raman amplification

Optical phase conjugation

Stimulated Brillouin scattering,interaction of photons with acoustic phonons

Multi-photon absorption,simultaneous absorption of two or more photons, transferring theenergyto a single electron

Multiplephotoionisation,near-simultaneous removal of many bound electrons by one photon

Chaos in Optical Systems

Related processes[edit]

n these processes, the medium has a linear response to the light, but the properties of the medium are affected by othercauses:

Pockels effect,the refractive index is affected by a static electric field; used inelectro-optic modulators;

Acousto-optics,the refractive index is affected by acoustic waves (ultrasound); used inacousto-optic modulators.

Raman scattering,interaction of photons with opticalphonons;

Parametric processes[edit]

Nonlinear effects fall into two qualitatively different categories,parametricand non-parametric effects. A parametric non-inearity is an interaction in which thequantum stateof the nonlinear material is not changed by the interaction with theoptical field. As a consequence of this, the process is 'instantaneous'; Energy and momentum conserving in the opticalield, making phase matching important; and polarization dependent.[5][6]

Theory[edit]

Parametric and lossy 'instantaneous' (i.e. electronic) nonlinear optical phenomena, in which the optical fields are nottooarge,can be described by aTaylor seriesexpansion of the dielectricPolarization density(dipole moment per unitvolume) P(t) at time tin terms of the electrical field E(t):

Here, the coefficients (n)are the n-th ordersusceptibilitiesof the medium and the presence of such a term isgenerally referred to as an n-th order nonlinearity. In general (n)is an n+1ordertensorrepresenting boththepolarizationdependent nature of the parametric interaction as well as thesymmetries(or lack thereof) of the

nonlinear material.

Wave-equation in a nonlinear material[edit]

Central to the study of electromagnetic waves is thewave equation.Starting withMaxwell's equationsin an isotropicspace containing no free charge, it can be shown that:

where PNLis the nonlinear part of thePolarization densityand n is therefractive indexwhich comes from thelinear term in P.

Note one can normally use the vector identity

andGauss's law,

to obtain the more familiarwave equation
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For nonlinear mediumGauss's lawdoes not imply that the identity

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 nonlinearwave-equation:

Nonlinearities as a wave mixing process[edit]

The nonlinear wave-equation is an inhomogeneous differential equation. The generalsolution comes from the study ofordinary differential equationsand can be solved by the useof aGreen's function.Physically one gets the normalelectromagnetic wavesolutions to thehomogeneous part of the wave equation:

and the inhomogeneous term

acts as a driver/source of the electromagnetic waves. One of the consequences ofthis is a nonlinear interaction that will result in energy being mixed or coupledbetween different frequencies which is often called a 'wave mixing'.

In general an n-th order will lead to n+1-th wave mixing. As an example, if weconsider only a second order nonlinearity (three-wave mixing), then thepolarization, P, takes the form

If we assume that E(t)is made up of two components at frequencies 1and 2,we can write E(t)as

where c.c.stands forcomplex conjugate.Plugging this into the expressionfor Pgives

which has frequency components at 21,22, 1+2, 1-2, and 0.These three-wave mixing processes correspond to the nonlinear effectsknown assecond harmonic generation,sum frequencygeneration,difference frequency generationandopticalrectificationrespectively.

Note: Parametric generation and amplificationis a variation ofdifference frequency generation, where the lower-frequency of one ofthe two generating fields is much weaker (parametric amplification) or

completely absent (parametric generation). In the latter case, thefundamentalquantum-mechanicaluncertainty in the electric fieldinitiates the process.

Phase matching[edit]
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Most transparent materials, like theBK7 glassshown here, havenormal

dispersion:Theindex of refractiondecreasesmonotonicallyas 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 and k'=2kin these

materials.Birefringentmaterials avoid this problem by having two indices of

refraction at once.[7]

The above ignores the position dependence of the electrical fields. In atypical situation, the electrical fields are traveling waves described by

at position , with the wave vector ,

where is the velocity of light in vacuum and is the index

of refraction of the medium at angular frequency . Thus, the

second-order polarization at angular frequency is

At each position within the nonlinear medium, the oscillatingsecond-order polarization radiates at angular frequency and

a corresponding wave vector .Constructive interference, and therefore a highintensity field, will occur only if

The above equation is known as thephase matchingcondition. Typically, three-wave mixing is done in abirefringent crystalline material (I.e., therefractiveindexdepends on the polarization and direction of the lightthat passes through.), where the polarizations of the fieldsand the orientation of the crystal are chosen such that thephase-matching condition is fulfilled. This phase matching

technique is called angle tuning. Typically a crystal hasthree axes, one or two of which have a different refractiveindex 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) (seecrystaloptics). There are several schemes of choosing thepolarizations for this crystal type. If the signal and idler havethe 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 existthat specify further which frequency has what polarizationrelative to the crystal axis. These types are listed below,

with the convention that the signal wavelength is shorterthan the idler wavelength.

( )
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Phase-matching types

Polarizations

Scheme

Pump Signal Idler

e o o Type I

e o e Type II (or IIA)

e e o Type III (or IIB)

e e e Type IV

o o o Type V (or Type-0[8]or Zero)

o o e Type VI (or IIB or IIIA)

o e o Type VII (or IIA or IIIB)

o e e Type VIII (or I)

Most common nonlinear crystals are negative uniaxial,which means that the eaxis has a smaller refractive indexthan the oaxes. In those crystals, type I and IIphasematching are usually the most suitable schemes. Inpositive uniaxial crystals, types VII and VIII are moresuitable. Types II and III are essentially equivalent, exceptthat the names of signal and idler are swapped when thesignal has a longer wavelength than the idler. For thisreason, they are sometimes called IIA and IIB. The typenumbers VVIII are less common than I and II and variants.

One undesirable effect of angle tuning is that the opticalfrequencies involved do not propagate collinearly with eachother. This is due to the fact that the extraordinary wavepropagating through a birefringent crystal possesses aPoynting vector that is not parallel with the propagationvector. This would lead to beam walk-off which limits thenonlinear optical conversion efficiency. Two other methodsof phase matching avoids beam walk-off by forcing allfrequencies to propagate at a 90 degree angle with respectto the optical axis of the crystal. These methods are calledtemperature tuning andquasi-phase-matching.

Temperature tuning is where the pump (laser) frequency

polarization is orthogonal to the signal and idler frequencypolarization. The birefringence in some crystals, inparticular Lithium Niobate is highly temperature dependent.The crystal is controlled at a certain temperature to achievephase matching conditions.
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The other method is quasi-phase matching. In this methodthe frequencies involved are not constantly locked in phasewith each other, instead the crystal axis is flipped at aregular interval , typically 15 micrometres in length.Hence, these crystals are calledperiodically poled.Thisresults in the polarization response of the crystal to beshifted back in phase with the pump beam by reversing thenonlinear susceptibility. This allows net positive energy flowfrom the pump into the signal and idler frequencies. In thiscase, the crystal itself provides the additional wavevectork=2/ (and hence momentum) to satisfy the phasematching condition. Quasi-phase matching can beexpanded to chirped gratings to get more bandwidth and toshape an SHG pulse like it is done in a dazzler. SHG of apump andSelf-phase modulation(emulated by secondorder processes) of the signal and anoptical parametricamplifiercan be integrated monolithically.

Higher-order frequency mixing[edit]

The above holds for processes. It can be extended for

processes where is nonzero, something that isgenerally true in any medium without any symmetry

restrictions. Third-harmonic generation is a process,although in laser applications, it is usually implemented as atwo-stage process: first the fundamental laser frequency isdoubled and then the doubled and the fundamentalfrequencies are added in a sum-frequency process. The

Kerr effect can be described as a as well.

At high intensities theTaylor series,which led thedomination of the lower orders, does not converge anymoreand instead a time based model is used. When a noble gasatom is hit by an intense laser pulse, which has an electricfield strength comparable to the Coulomb field of the atom,the outermost electron may be ionized from the atom. Oncefreed, the electron can be accelerated by the electric field ofthe light, first moving away from the ion, then back toward itas the field changes direction. The electron may thenrecombine with the ion, releasing its energy in the form of aphoton. The light is emitted at every peak of the laser lightfield which is intense enough, producing a series

ofattosecondlight flashes. The photon energies generatedby this process can extend past the 800th harmonic orderup to a few KeV.This is calledhigh-order harmonicgeneration.The laser must be linearly polarized, so that theelectron returns to the vicinity of the parent ion. High-orderharmonic generation has been observed in noble gas jets,cells, and gas-filled capillary waveguides.
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Example uses of nonlinear optics[edit]Frequency doubling[edit]

One of the most commonly used frequency-mixingprocesses is frequency doublingor second-harmonicgeneration. With this technique, the 1064-nm outputfromNd:YAG lasersor the 800-nm output fromTi:sapphirelaserscan be converted to visible light, with wavelengths of532 nm (green) or 400 nm (violet), respectively.

Practically, frequency-doubling is carried out by placing anonlinear medium in a laser beam. While there are manytypes of nonlinear media, the most common media arecrystals. Commonly used crystals are BBO (-bariumborate), KDP (potassium dihydrogen phosphate), KTP(potassium titanyl phosphate), andlithium niobate.Thesecrystals have the necessary properties of beingstronglybirefringent(necessary to obtain phase matching,see below), having a specific crystal symmetry and ofcourse being transparent for both the impinging laser lightand the frequency doubled wavelength, and have highdamage thresholds which make them resistant against thehigh-intensity laser light. However,organic

polymericmaterials are set to take over from crystals asthey are cheaper to make, have lower drive voltages andsuperior performance.[citation needed]

Optical phase conjugation[edit]

It is possible, using nonlinear optical processes, to exactlyreverse the propagation direction and phase variation of abeam of light. The reversed beam is calleda conjugatebeam, and thus the technique is knownas optical phase conjugation[9][10](also called timereversal, wavefront reversalandretroreflection).

One can interpret this nonlinear optical interaction as beinganalogous to areal-time holographic process.[11]In thiscase, the interacting beams simultaneously interact in anonlinear optical material to form a dynamic hologram (twoof the three input beams), or real-time diffraction pattern, inthe material. The third incident beam diffracts off thisdynamic hologram, and, in the process, reads outthephase-conjugatewave. In effect, all three incidentbeams interact (essentially) simultaneously to form severalreal-time holograms, resulting in a set of diffracted outputwaves that phase up as the "time-reversed" beam. In thelanguage of nonlinear optics, the interacting beams result ina nonlinear polarization within the material, which

coherently radiates to form the phase-conjugate wave.
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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.

The most common way of producing optical phaseconjugation is to use a four-wave mixing technique, thoughit is also possible to use processes such as stimulatedBrillouin scattering. A device producing the phaseconjugation effect is known as a phase conjugatemirror(PCM).

For the four-wave mixing technique, we can describe fourbeams (j= 1,2,3,4) with electric fields:

where Ejare the electric field amplitudes. 1and 2areknown as the two pump waves, with 3being the signalwave, and 4being the generated conjugate wave.

If the pump waves and the signal wave aresuperimposed in a medium with a non-zero (3), thisproduces a nonlinear polarization field:

resulting in generation of waves with frequencies

given by = 123in addition to thirdharmonic generation waves with = 31, 32, 33.

As above, the phase-matching conditiondetermines which of these waves is the dominant.By choosing conditions such that = 1+ 2-3and k= k1+ k2- k3, this gives a polarizationfield:

This is the generating field for the phase

conjugate beam, 4. Its direction is givenby k4= k1+ k2- k3, and so if the two pumpbeams are counterpropagating (k1= -k2), thenthe conjugate and signal beams propagate inopposite directions (k4= -k3). This results in theretroreflecting property of the effect.
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Further, it can be shown for a medium withrefractive index nand a beam interactionlength l, the electric field amplitude of theconjugate beam is approximated by

(where cis the speed of light). If the pumpbeams E1and E2are plane(counterpropagating) waves, then:

that is, the generated beam amplitudeis the complex conjugate of the signalbeam amplitude. Since the imaginarypart of the amplitude contains thephase of the beam, this results in thereversal of phase property of theeffect.

Note that the constant ofproportionality between the signal andconjugate beams can be greater than1. This is effectively a mirror with areflection coefficient greater than100%, producing an amplifiedreflection. The power for this comesfrom the two pump beams, which aredepleted by the process.

The frequency of the conjugate wavecan be different from that of the signalwave. If the pump waves are offrequency 1= 2= , and the signalwave higher in frequency such that

3= + , then the conjugate waveis of frequency 4= . This isknown as frequency flipping.

Common SHGmaterials[edit]

(Second Harmonic Generation)

Dark-Red Gallium Selenide in its bulk

form.

800 nm light :BBO

806 nm light :lithium iodate(LiIO3)

860 nm light :potassiumniobate(KNbO3)

980 nm light : KNbO3 1064 nm light :monopotassium

phosphate(KH2PO4, KDP),lithiumtriborate(LBO) and-bariumborate(BBO).

1300 nm light :galliumselenide(GaSe)
http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=14http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=14http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=14http://en.wikipedia.org/wiki/Second-harmonic_generationhttp://en.wikipedia.org/wiki/Second-harmonic_generationhttp://en.wikipedia.org/wiki/Second-harmonic_generationhttp://en.wikipedia.org/wiki/%CE%92-barium_boratehttp://en.wikipedia.org/wiki/%CE%92-barium_boratehttp://en.wikipedia.org/wiki/%CE%92-barium_boratehttp://en.wikipedia.org/wiki/Lithium_iodatehttp://en.wikipedia.org/wiki/Lithium_iodatehttp://en.wikipedia.org/wiki/Lithium_iodatehttp://en.wikipedia.org/wiki/Potassium_niobatehttp://en.wikipedia.org/wiki/Potassium_niobatehttp://en.wikipedia.org/wiki/Potassium_niobatehttp://en.wikipedia.org/wiki/Potassium_niobatehttp://en.wikipedia.org/wiki/Monopotassium_phosphatehttp://en.wikipedia.org/wiki/Monopotassium_phosphatehttp://en.wikipedia.org/wiki/Monopotassium_phosphatehttp://en.wikipedia.org/wiki/Monopotassium_phosphatehttp://en.wikipedia.org/wiki/Lithium_triboratehttp://en.wikipedia.org/wiki/Lithium_triboratehttp://en.wikipedia.org/wiki/Lithium_triboratehttp://en.wikipedia.org/wiki/Lithium_triboratehttp://en.wikipedia.org/wiki/%CE%92-barium_boratehttp://en.wikipedia.org/wiki/%CE%92-barium_boratehttp://en.wikipedia.org/wiki/%CE%92-barium_boratehttp://en.wikipedia.org/wiki/%CE%92-barium_boratehttp://en.wikipedia.org/wiki/%CE%92-barium_boratehttp://en.wikipedia.org/wiki/Gallium(II)_selenidehttp://en.wikipedia.org/wiki/Gallium(II)_selenidehttp://en.wikipedia.org/wiki/Gallium(II)_selenidehttp://en.wikipedia.org/wiki/Gallium(II)_selenidehttp://en.wikipedia.org/wiki/File:GaSeBulk.jpghttp://en.wikipedia.org/wiki/File:GaSeBulk.jpghttp://en.wikipedia.org/wiki/File:GaSeBulk.jpghttp://en.wikipedia.org/wiki/Gallium(II)_selenidehttp://en.wikipedia.org/wiki/Gallium(II)_selenidehttp://en.wikipedia.org/wiki/%CE%92-barium_boratehttp://en.wikipedia.org/wiki/%CE%92-barium_boratehttp://en.wikipedia.org/wiki/Lithium_triboratehttp://en.wikipedia.org/wiki/Lithium_triboratehttp://en.wikipedia.org/wiki/Monopotassium_phosphatehttp://en.wikipedia.org/wiki/Monopotassium_phosphatehttp://en.wikipedia.org/wiki/Potassium_niobatehttp://en.wikipedia.org/wiki/Potassium_niobatehttp://en.wikipedia.org/wiki/Lithium_iodatehttp://en.wikipedia.org/wiki/%CE%92-barium_boratehttp://en.wikipedia.org/wiki/Second-harmonic_generationhttp://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=14


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1319 nm light : KNbO3, BBO,KDP,potassium titanylphosphate(KTP),lithiumniobate(LiNbO3), LiIO3,andammonium dihydrogenphosphate(ADP)

1550 nm light :potassium titanylphosphate(KTP),lithiumniobate(LiNbO3)

See also[edit] Born-Infeld action

Filament propagation

Category:Nonlinear opticalmaterials

Parametric process (optics)

Notes[edit]

1. Jump

up^http://www.nature.com/nature/journal/v396/n6712/abs/396653a0.html

2. Jumpup^http://prl.aps.org/abstract/PRL/v76/i17/p3116_1

3. Jumpup^http://pop.aip.org/phpaen/v12/i9/p093106_s1

4. Jumpup^http://www.nature.com/nphys/journal/v3/n6/full/nphys595.html

5. Jump up^Paschotta, Rdiger."ParametricNonlinearities".[[Encyclopediaof Laser Physics andTechnology]]Wikilink embeddedin URL title (help)

6. Jump up^SeeSection Parametric versusNonparametricProcesses,NonlinearOpticsbyRobert W. Boyd(3rded.), pp. 13-15.

7. Jump up^Robert W. Boyd,Nonlinear optics, Third edition,Chapter 2.3.

8. Jump up^Abolghasem,Payam; Junbo Han; Bhavin J.Bijlani; Amr S. Helmy (2010)."Type-0 second order nonlinearinteraction in monolithicwaveguides of isotropicsemiconductors". OpticsExpress18(12): 1268112689.doi:10.1364/OE.18.012681.PMID20588396.

9. Jump up^Scientific American,December 1985, "PhaseConjugation," by VladimirShkunov and Boris Zel'dovich.

10.Jump up^Scientific American,January 1986, "Applications of
http://en.wikipedia.org/wiki/Potassium_titanyl_phosphatehttp://en.wikipedia.org/wiki/Potassium_titanyl_phosphatehttp://en.wikipedia.org/wiki/Potassium_titanyl_phosphatehttp://en.wikipedia.org/wiki/Potassium_titanyl_phosphatehttp://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/wiki/Ammonium_dihydrogen_phosphatehttp://en.wikipedia.org/wiki/Ammonium_dihydrogen_phosphatehttp://en.wikipedia.org/wiki/Ammonium_dihydrogen_phosphatehttp://en.wikipedia.org/wiki/Ammonium_dihydrogen_phosphatehttp://en.wikipedia.org/wiki/Potassium_titanyl_phosphatehttp://en.wikipedia.org/wiki/Potassium_titanyl_phosphatehttp://en.wikipedia.org/wiki/Potassium_titanyl_phosphatehttp://en.wikipedia.org/wiki/Potassium_titanyl_phosphatehttp://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=15http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=15http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=15http://en.wikipedia.org/wiki/Born-Infeld_actionhttp://en.wikipedia.org/wiki/Born-Infeld_actionhttp://en.wikipedia.org/wiki/Filament_propagationhttp://en.wikipedia.org/wiki/Filament_propagationhttp://en.wikipedia.org/wiki/Category:Nonlinear_optical_materialshttp://en.wikipedia.org/wiki/Category:Nonlinear_optical_materialshttp://en.wikipedia.org/wiki/Category:Nonlinear_optical_materialshttp://en.wikipedia.org/wiki/Category:Nonlinear_optical_materialshttp://en.wikipedia.org/wiki/Category:Nonlinear_optical_materialshttp://en.wikipedia.org/wiki/Parametric_process_(optics)http://en.wikipedia.org/wiki/Parametric_process_(optics)http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=16http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=16http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=16http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-1http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-1http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-1http://www.nature.com/nature/journal/v396/n6712/abs/396653a0.htmlhttp://www.nature.com/nature/journal/v396/n6712/abs/396653a0.htmlhttp://www.nature.com/nature/journal/v396/n6712/abs/396653a0.htmlhttp://www.nature.com/nature/journal/v396/n6712/abs/396653a0.htmlhttp://www.nature.com/nature/journal/v396/n6712/abs/396653a0.htmlhttp://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-2http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-2http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-2http://prl.aps.org/abstract/PRL/v76/i17/p3116_1http://prl.aps.org/abstract/PRL/v76/i17/p3116_1http://prl.aps.org/abstract/PRL/v76/i17/p3116_1http://prl.aps.org/abstract/PRL/v76/i17/p3116_1http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-3http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-3http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-3http://pop.aip.org/phpaen/v12/i9/p093106_s1http://pop.aip.org/phpaen/v12/i9/p093106_s1http://pop.aip.org/phpaen/v12/i9/p093106_s1http://pop.aip.org/phpaen/v12/i9/p093106_s1http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-4http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-4http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-4http://www.nature.com/nphys/journal/v3/n6/full/nphys595.htmlhttp://www.nature.com/nphys/journal/v3/n6/full/nphys595.htmlhttp://www.nature.com/nphys/journal/v3/n6/full/nphys595.htmlhttp://www.nature.com/nphys/journal/v3/n6/full/nphys595.htmlhttp://www.nature.com/nphys/journal/v3/n6/full/nphys595.htmlhttp://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-5http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-5http://www.rp-photonics.com/parametric_nonlinearities.htmlhttp://www.rp-photonics.com/parametric_nonlinearities.htmlhttp://www.rp-photonics.com/parametric_nonlinearities.htmlhttp://www.rp-photonics.com/parametric_nonlinearities.htmlhttp://www.rp-photonics.com/parametric_nonlinearities.htmlhttp://en.wikipedia.org/wiki/Help:CS1_errors#wikilink_in_urlhttp://en.wikipedia.org/wiki/Help:CS1_errors#wikilink_in_urlhttp://en.wikipedia.org/wiki/Help:CS1_errors#wikilink_in_urlhttp://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-Boyd_NLO_6-0http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-Boyd_NLO_6-0http://en.wikipedia.org/wiki/Robert_W._Boyd_(physicist)http://en.wikipedia.org/wiki/Robert_W._Boyd_(physicist)http://en.wikipedia.org/wiki/Robert_W._Boyd_(physicist)http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-7http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-7http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-8http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-8http://en.wikipedia.org/wiki/Digital_object_identifierhttp://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.1364%2FOE.18.012681http://dx.doi.org/10.1364%2FOE.18.012681http://dx.doi.org/10.1364%2FOE.18.012681http://dx.doi.org/10.1364%2FOE.18.012681http://en.wikipedia.org/wiki/PubMed_Identifierhttp://en.wikipedia.org/wiki/PubMed_Identifierhttp://www.ncbi.nlm.nih.gov/pubmed/20588396http://www.ncbi.nlm.nih.gov/pubmed/20588396http://www.ncbi.nlm.nih.gov/pubmed/20588396http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-9http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-9http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-10http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-10http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-10http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-10http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-9http://www.ncbi.nlm.nih.gov/pubmed/20588396http://en.wikipedia.org/wiki/PubMed_Identifierhttp://dx.doi.org/10.1364%2FOE.18.012681http://dx.doi.org/10.1364%2FOE.18.012681http://en.wikipedia.org/wiki/Digital_object_identifierhttp://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-8http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-7http://en.wikipedia.org/wiki/Robert_W._Boyd_(physicist)http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-Boyd_NLO_6-0http://en.wikipedia.org/wiki/Help:CS1_errors#wikilink_in_urlhttp://www.rp-photonics.com/parametric_nonlinearities.htmlhttp://www.rp-photonics.com/parametric_nonlinearities.htmlhttp://www.rp-photonics.com/parametric_nonlinearities.htmlhttp://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-5http://www.nature.com/nphys/journal/v3/n6/full/nphys595.htmlhttp://www.nature.com/nphys/journal/v3/n6/full/nphys595.htmlhttp://www.nature.com/nphys/journal/v3/n6/full/nphys595.htmlhttp://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-4http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-4http://pop.aip.org/phpaen/v12/i9/p093106_s1http://pop.aip.org/phpaen/v12/i9/p093106_s1http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-3http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-3http://prl.aps.org/abstract/PRL/v76/i17/p3116_1http://prl.aps.org/abstract/PRL/v76/i17/p3116_1http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-2http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-2http://www.nature.com/nature/journal/v396/n6712/abs/396653a0.htmlhttp://www.nature.com/nature/journal/v396/n6712/abs/396653a0.htmlhttp://www.nature.com/nature/journal/v396/n6712/abs/396653a0.htmlhttp://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-1http://en.wikipedia.org/wiki/Nonlinear_optics#cite_ref-1http://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=16http://en.wikipedia.org/wiki/Parametric_process_(optics)http://en.wikipedia.org/wiki/Category:Nonlinear_optical_materialshttp://en.wikipedia.org/wiki/Category:Nonlinear_optical_materialshttp://en.wikipedia.org/wiki/Filament_propagationhttp://en.wikipedia.org/wiki/Born-Infeld_actionhttp://en.wikipedia.org/w/index.php?title=Nonlinear_optics&action=edit&section=15http://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/wiki/Potassium_titanyl_phosphatehttp://en.wikipedia.org/wiki/Potassium_titanyl_phosphatehttp://en.wikipedia.org/wiki/Ammonium_dihydrogen_phosphatehttp://en.wikipedia.org/wiki/Ammonium_dihydrogen_phosphatehttp://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/wiki/Lithium_niobatehttp://en.wikipedia.org/wiki/Potassium_titanyl_phosphatehttp://en.wikipedia.org/wiki/Potassium_titanyl_phosphate


11/12

Optical Phase Conjugation," byDavid M. Pepper.

11.Jump up^Scientific American,October 1990, "ThePhotorefractive Effect," by DavidM. Pepper, Jack Feinberg, andNicolai V. Kukhtarev.

References[edit]

Boyd, Robert(2008).NonlinearOptics(3rd ed.). AcademicPress.ISBN978-0-12-369470-6.

Shen, Yuen-Ron(2002).ThePrinciples of Nonlinear Optics.Wiley-Interscience.ISBN978-0-471-43080-3.

Agrawal, Govind (2006).NonlinearFiber Optics(4th ed.). AcademicPress.ISBN978-0-12-369516-1.

External links[edit]

Encyclopedia of laser physics andtechnology,with content onnonlinear optics, by RdigerPaschotta

An Intuitive Explanation of PhaseConjugation

AdvR - NLO FrequencyConversion in KTP Waveguides

SNLO - Nonlinear Optics DesignSoftware

Topics on photo-physics andnonlinear optics

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