Second harmonic generation electric field dependence

As was proven later by Bishop [19], the coefficient A in the expansion (73) is the same for all optical processes. If the expansion (73) is extended to fourth-order [4,19] by adding the term the coefficient B is the same for the dc-Kerr effect and for electric field induced second-harmonic generation, but other fourth powers of the frequencies than are in general needed to represent the frequency-dependence of 7 with process-independent dispersion coefficients [19]. Bishop and De Kee [20] proposed recently for the all-diagonal components yaaaa the expansion... 

The CCSD model gives for static and frequency-dependent hyperpolarizabilities usually results close to the experimental values, provided that the effects of vibrational averaging and the pure vibrational contributions have been accounted for. Zero point vibrational corrections for the static and the electric field induced second harmonic generation (ESHG) hyperpolarizability of methane have recently been calculated by Bishop and Sauer using SCF and MCSCF wavefunctions [51]. 

Two of the most important nonlinear optical (NLO) processess, electro-optic switching and second harmonic generation, are second order effects. As such, they occur in materials consisting of noncentrosymmetrically arranged molecular subunits whose polarizability contains a second order dependence on electric fields. Excluding the special cases of noncentrosymmetric but nonpolar crystals, which would be nearly impossible to design from first principles, the rational fabrication of an optimal material would result from the simultaneous maximization of the molecular second order coefficients (first hyperpolarizabilities, p) and the polar order parameters of the assembly of subunits. (1)... 

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. 

We have obtained SERS and second harmonic generation (SHG) from the doublehole structures with different hole distances. The dependence of the SHG efficiency on the spacing between the holes in the basis is shown in Fig. 11 for two polarizations of the fundamental beam. It can be seen that, as expected from the calculations shown in Fig. lOd, the SHG signal maximizes when the two holes overlap [63,64]. This optimum distance has also been observed in SERS experiments using the double-hole basis [65]. The double-hole structure offers two degrees of freedom, shape and periodicity, for electric field optimization and enhanced spectroscopy. 

Effective second harmonic generation is attained in materials which have both high second-order molecular hyperpolarizability, p, and high second-order bulk susceptability, x - Molecular polarization is described by the field dependent molecular dipole moment, p (eq 1), expanded as a function of the applied field strength, E, which may be electric or optical (that is, electromagnetic) in nature. The field strength E is a vector, and Pq is the intrinsic dipole... 

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] ... 

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... 

The phenomenon of frequency doubling or second-harmonic generation can be visualized as follows. If the applied electric field is of frequency m, it can be represented as sinort. and the quadratic terms are seen to have a 2o) dependence. 

The Hartree-Fock method for periodic systems nowadays represents a routine approach coded in several ab initio computer packages. We may analyze the total energy, its dependence on molecular conformation, the density of states, the atomic charges, etc. Also, calculations of first-order responses to the electric field (poljmiers are of interest for optoelectronics) have been successful in the past. However, nonlinear problems (like the second harmonic generation see Chapter 12) stiU represent a challenge. 

The second harmonic generation in a uniform electric field depends on the following molecular property... 

Furthermore, they examined the performance of different density functionals, including a local-density approximation and a generalized-gradient approximation as well as the functional of van Leeuwen and Baerends that has been constructed to have the correct asymptotic behaviour. Moreover, they considered different frequency-dependent processes, including third-harmonic generation [THG, corresponding to y( 3electric-field-induced second harmonic generation (EFISH, y( 2electro-optic Kerr effect [EOKO, y(—ft> optical rectification [OR, /S(0 [Pg.161]

This article introduces the field of nonlinear optics and the electronic nonlinear optical (NLO) response of polymers and pol5mier composites. Both second- and third-order NLO phenomena are included, with primary emphasis on harmonic generation, the intensity-dependent refractive index, and nonlinear (multiphoton) absorption effects. The beginning sections introduce the phenomena and explain how the order of the nonlinearity can be understood from a series expansion of the polarization in powers of the electric-field. In addition to listing the variety of nonlinear optical phenomena and some applications, some of the advantages of polymeric materials for NLO applications are also surveyed. 

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