Electric third harmonic generation

Table 1 Coefficients for 7[ (a ) for third harmonic generation (THG), degenerate four wave mixing (DFWM), electric field induced second harmonic generation (ESHG), and Kerr effect in methane at the experimental geometry rcH = 2.052 a.u. A CCSD wavefunction and the t-aug-cc-pVDZ basis were used. (Results given in atomic units, the number in parentheses indicate powers of ten.)...

Third-Order NLO Techniques. There is a wider range of third-order techniques commonly used to characterize materials, including electric field induced second harmonic generation (EFISH) (15, 16), third harmonic generation (THG) (17) and degenerate four wave mixing (DFWM) (18). EFISH and DFWM will be discussed briefly then... 

From TEEs unsubstituted, mono-, di-, tri-, and tetrasubstituted compounds were synthesized and investigated with third-harmonic generation [56] as well as electric field induced second-harmonic generation [67]. We here concentrate on the discussion of monomers of the most intriguing tetrasubstituted molecules and the symmetry dependence of their third-order nonlinearities [72]. Taking two donors and two acceptors three possible geometries can be realized (Fig. 23). The DDAA(cross)-TEE molecule has a mirror plane perpendicular to the y-axis, DDAA(ds)-TEE a mirror plane perpendicular to the x-axis, and DDAA(fra s)-TEE a two-fold rotation axis along z. 

While the above discussion clearly highlights the importance of including solvent effects in the calculations, the calculated properties cannot be compared directly with experimental results. This is mainly caused by the many different conventions used for representing hyperpolarizabilities and susceptibilities. However, the calculated properties can be combined with appropriate, calculated Lorentz/Onsager local field factors to obtain macroscopic susceptibilities that can be compared with experimental results. For water, we used this to calculate the refractive index and the third harmonic generation (THG) and the electric field-induced second harmonic (EFISH) non-linear susceptibilities. The results are collected in Table 3-11. 

Here Xo (2w), x (wiiw2) and Xo (O) are the non-resonant values of the hyperpolarisabilities. Thus second harmonic generation is resonantly enhanced at both the fundamental and the harmonic of the optical transition, sum and difference frequency generation at the fundamentals and the sum and difference frequencies, and the rarely observed optical rectification only at the fundamental frequency. The term 3 in the expansion gives rise to effects such as third harmonic generation, x(3) -3oj oj, oj,u>), electric field induced second harmonic generation, x(3) (- 2w 0,w, oj), the optical Kerr effect, x(3) (-oj oj, oj, -cj), etc. that will display resonances at oj, 2oj and 3u>. 

Electric field-induced second harmonic generation, f Third-harmonic generation. 

In order to select a particular experimental technique to measure x , it is very important to keep in mind which parameter of the third-order nonlinear response has to be characterized. For example, if one wants to determine the time-response due to molecular reorientation, one cannot choose Third-Harmonic Generation or Electric-Field-Induced Second-Harmonic Generation, since none of these techniques provide time-response information. Depending on the parameter of interest, a specific technique must be chosen. The following physical mechanisms can contribute to the third-order nonlinear response [54] ... 

Puccetti, G. Electric field induced second harmonic generation/third harmonic generation measurements on molecules with extended charge transfer Absorption domain and strong resonance effects, J. Chem. Phys. 102, 6463-6475 (1995)... 

The first contribution to the polarization induces a modification of the wave propagation in the material, for both its amplitude and phase, but without any frequency change. This phenomenon is known as the optical Kerr effect, by analogy with the magneto-optic and electro-optic Kerr effects where the medium refractive index varies proportionally with the square of the applied magnetic or electric static field. The second contribution corresponds to the third harmonics generation (THG). 

Another approach has been proposed to enhance the optical nonlinearity of semiconductor nanoclusters based on surface plasmon resonance [99,100], In the proposed method, the semiconductor nanocluster is coated with metals such as silver. The local electric field inside the cluster can be enhanced because of the surface plasmon resonance of the metal particles. The local field enhancement effect on nonresonant xl3) of CdS clusters has already been demonstrated using the third harmonic generation technique [17, 84, 85]. In this case enhancement in the local field originates from the difference in dielectric properties between the clusters and the host. The proposed enhancement of x 3) of metal-coated semiconductor nanoclusters owing to surface plasmon resonance has not been demonstrated experimentally. 

Under the influence of an optical pump, the molecular angular distribution described by Equation 12.4 can be considerably modified. In turn, this results in modification of the X/ kl tensor components. Further, we discuss the influence of a polarized pump beam on third-order nonlinear phenomena such as third harmonic generation (TFIG) [(described by XyfCL (-3a ,o ,w, u) coefficient], electric field induced second harmonic generation (EFISH) i 2co, (o, (o, 0)] and degenerate four-wave mixing (DFWM) X/yx/ -... 

The tensors and 7 constitute the molecular origin of the second-and third-order nonlinear optical phenomena such as electro-optic Pock-els effect (EOPE), optical rectification (OR), third harmonic generation (THG), electric field induced second harmonic generation (EFI-SHG), intensity dependent refractive index (IDRI), optical Kerr effect (OKE), electric field induced optical rectification (EFI-OR). To save space we do not indicate the full expressions for and 7 related to the different second and third order processes but we introduce the notations —(Ajy,ui,cj2) and 7(—a , o i,W2,W3), where the frequency relations to be used for the various non-linear optical processes which can be obtained in the case of both static and oscillating monochromatic fields are reported in Table 1.7. 

P( P(-o> w,0) P(0 -fa>,w) Y( - Y(-2(i) (i>,tD,0) Y(-o) (i>,0,0) Second harmonic generation (SHG) Electrooptic Pockels effect Optical rectification Third harmonic generation DC electric-field-induced SHG Intensity-dependent refractive index Optical Kerr effect Coherent anti-Stokes Raman pSHG pEOPE pOR. yTHG. EFISH oj DC-SHG. JlDRI or. yOKE. yCARS... 

In Eqs. 1 and 2. the indices i, j. k. and I refer to the coordinate system of the bulk material and molecule, respectively. Illustrated in Fig. 1 are the linear and nonlinear polarizations with respect to electric field. The Fourier decomposition of this nonlinear polarization comprising components of zero frequency, the fundamental frequency, the second-harmonic frequency, the third-harmonic frequency, etc., is shown in Fig. 2. The effects up to the second order, which are easily observed experimentally, are called the optical rectification. P(0) linear electro-optic effect P((u) second-harmonic generation P(2a>), and third-harmonic generation P(3co). 

Third Harmonic Generation A frequency tripling of light in materials with nonlinear electric properties. 

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