Four-wave mixing, third-order effects

For the application of QDs to three-dimensional biological imaging, a large two-photon absorption cross section is required to avoid cell damage by light irradiation. For application to optoelectronics, QDs should have a large nonlinear refractive index as well as fast response. Two-photon absorption and the optical Kerr effect of QDs are third-order nonlinear optical effects, which can be evaluated from the third-order nonlinear susceptibility, or the nonlinear refractive index, y, and the nonlinear absorption coefficient, p. Experimentally, third-order nonlinear optical parameters have been examined by four-wave mixing and Z-scan experiments. 

Where P is the polarisation and the others the linear (1) and non-linear, second (2) and third order (3) terms. Examples of important second order effects are frequency doubling and linear electro-optic effects (Pockles effect), third order effects are third-harmonic generation, four-wave mixing and the quadratic electro-optic effect (Ken-effect). 

Third-order materials which exhibit cubic effects such as third harmonic generation (THG) or four-wave mixing (FWM). These materials have no restrictions on their symmetry. 

For third order effects, it is common to measure y, and some of the problems associated with its determination can be overcome using degenerate four-wave mixing. The "selection rules" for THG are less stringent than for those for SHG, principally in that the requirement for crystals having non-centrosymmetric space groups is irrelevant. 

In most EFISH measurements in solution the intrinsic third-order term is negligible compared with the field-induced jSvec-Another important parametric effect is degenerate four-wave mixing (DFWM), in which all beams have the same frequency but different propagation directions. This is a third-order process written as... 

The limitation of this notation is obvious here, since the description of degenerate four-wave mixing (namely (4.14)) and the optical Kerr effect (OKE) is the same. Two-photon absorption is the loss process in which two photons of equal energy give rise to a dipole-forbidden (i.e. one-photon-forbidden) transition between energy levels of the material. The number of third-order effects is very large, since there are many quantum mechanical matrix elements that can contribute to... 

Several of the third-order nonlinear effects described in section 4.1.3 can be used to characterize bulk materials. Degenerate four-wave mixing (DFWM) is used for measuring third-order properties of films and solutions [43-45], and though this experiment is complex to set up and interpret, it can give valuable information on the magnitude, sign and speed of the nlo process, as well as an indication of the nature of the excitation process. Results from DFWM can be found in section 4.3. Optical Kerr effect (OKE) [46] and electrical Kerr effect (EKE) [47] measurements have also been used to characterize third-order properties of nlo polymers. It is important to note that THG, DFWM, OKE and EKE all measure different parts of the third-order susceptibility, and... 

Tables 1 and 2 and Figure 1 summarize a number of distinct nonlinear optical effects, in particular including those of third order arising from the combined influence of three frequencies, CO2, (Oy These effects are collectively called four-wave mixing, as three incident waves combine coherently to give a fourth resulting one of frequency o)i 0)2 o)y The radiation-induced polarization depends to third order on the electric field strength of the incident radiation, namely, on the triple product E(o)i) 2 ( (O2) E( ( 3). In the particular case where co = a)2 = o)y we may have third-harmonic generation, proportional to E (o)). Correspondingly, the intensity of the third harmonic radiation I(3oo) depends on P((jo),...

Third-order nonlinear optical effects, such as third-harmonic generation or other kinds of four-wave mixing phenomena, occur in all media, irrespective of their symmetry. This follows from the parity-even property of the corresponding tensors. Consequently, third-harmonic generation can be observed both in... 

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