Third order harmonic generation

In a third order harmonic generation process the system absorbs three photons of energy Hlo and emits one photon of energy 3fiw, as shown schematically in Fig. 8.6. The susceptibility for this process is defined as 

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All applications quoted so far were for the linear response. Very few investigations have dealt with the higher-order response described in Sect. 5.2. The frequency-dependent third-order hyperpolarizabilities of rare-gas atoms were calculated by Senatore and Subbaswamy [86] within the ALDA the calculated values turned out to bee too large by a factor of two, further indicating the need for self-interaction corrected functionals in the calculation of response properties. The effect of adsorbates on second-harmonic generation at simple metal surfaces was invested by Kuchler and Rebentrost [205, 206]. Most recently, the second-order harmonic generation in bulk insulators was calculated within the ALDA [207]. 

The index ms indicates that j s transforms according to the mixed symmetry representation of the symmetric Group 54 [33]. 7 5 is an irreducible tensor component which describes a deviation from Kleinman symmetry [34]. It vanishs in the static limit and for third harmonic generation (wi = u>2 = W3). Up to sixth order in the frequency arguments it can be expanded as [33] ... 

A similar convergence is found for the third harmonic generation process at the lower of the two frequencies, 671.5 nm. At the higher frequency, 476.5 nm, the Taylor approximations for the third harmonic generation hyperpolarizability converge only very slowly, even with a tenth-order Taylor approximation a one-percent accuracy is not obtained. This accuracy, however, is still achieved with a [1,2] Fade approximant calculated from the dispersion coefficients up to sixth order. 

Fig. 8. Examples of some of the donor-acceptor substituted TEEs prepared for the exploration of structure-property relationships in the second- and third-order nonlinear optical effects of fully two-dimensionally-conjugated chromophores. For all compounds, the second hyperpolarizability y [10 esu], measured by third harmonic generation experiments in CHCI3 solution at a laser frequency of either A = 1.9 or 2.1 (second value if shown) pm is given in parentheses. n.o. not obtained...

The first and third order terms in odd powers of the applied electric field are present for all materials. In the second order term, a polarization is induced proportional to the square of the applied electric field, and the. nonlinear second order optical susceptibility must, therefore, vanish in crystals that possess a center of symmetry. In addition to the noncentrosymmetric structure, efficient second harmonic generation requires crystals to possess propagation directions where the crystal birefringence cancels the natural dispersion leading to phase matching. 

Third-order susceptibilities of the PAV cast films were evaluated with the third-harmonic generation (THG) measurement [31,32]. The THG measurement was carried out at fundamental wavelength of 1064 nm and between 1500 nm and 2100 nm using difference-frequency generation combined with a Q-switched Nd YAG laser and a tunable dye laser. From the ratio of third-harmonic intensities I3m from the PAV films and a fused quartz plate ( 1 thick) as a standard, the value of x(3) was estimated according to the following equation derived by Kajzar et al. [33] ... 

These effects of second and third order optical non-linearity are just exploited in the generation of the second and third harmonics, respectively. In this connection, Figure 40 schematizes an experiment in which the incidence of a laser light working in the near infrared at X 1060 nm on a crystal of KU02(P04) emits a light of X = 532 nm.70... 

We have listed the hrst three of the six experiments (a-c) below. Arrange them in order of complexity (and, hence, the order in which they will be performed), identifying the correct ordinal language (hrst, second, third) where indicated. (SHG = second harmonic generation SAM = self-assembled monolayer.)... 

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). 

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