Electric field induced second harmonic generation , nonlinear optical

Electric Field Induced Second-Harmonic Generation. An essential aspect of the development of materials for second-order nonlinear optics is the determination of the p tensor components. The technique that has been developed to accomplish this is called electric field induced second harmonic generation (EFISH) (13,14). 

Poly(3-alkyl-a-thiophene) systems show significant third-order nonlinear susceptibilities ( ) Though, oligothiophenes have been studied for their third-order susceptibilities, accurate third-order optical nonlinearity data obtained by degenerate four-wave mixing or electric-field-induced second harmonic generation (EFISH) are difficult to attain reliably on samples with poor solubility characteristics (92MM1901). 

TDDFT methods have also been applied successfully to the description of the linear and nonlinear optical properties of heteroleptic sandwich complexes. The optical spectrum and the hyperpolarizability of Zr(OEP)(OEPz,) for which large first hyperpolarizabilities, /JSHG (SHG=second-harmonic generation) were measured in an electric field induced second-harmonic generation (EFISH) experiment [182], have been investigated by TDDFT methods [134]. The excitation energies and oscillator strengths calculated... 

The most widely employed material characterization techniques in third-order nonlinear optics are third-harmonic generation (THG) [21], degenerate four wave-mixing (DFWM) [22], Z-scan [6], and optical limiting by direct two-photon absorption (TPA) and fluorescence spectroscopy induced by TPA [23]. All of them will be discussed in the following. Further measurement techniques such as electric-field induced second-harmonic generation (EFISH) [24], optical Kerr... 

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 ijkl tensor components. Further, we discuss the influence of a polarized pump beam on third-order nonlinear phenomena such as third harmonic generation (THG) [(described by (-3a),ft>,w,a>) coefficient], electric field induced second harmonic generation (EFISH) [x / kl -2(0, (o, o), 0)] and degenerate four-wave mixing (DFWM) X kl ... 

The first common method for molecular first hyperpolarizability determination is the electric field-induced second harmonic generation (EFISH) technique in solution [6-10]. This technique can be applied only to dipolar molecules. Under an applied external electric field, molecules in solution orient approximately in the direction of the field giving rise to second harmonic generation. The measured third-order nonlinear optical susceptibility is given by the following expression ... 

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. 

A method utilizing differential scanning calorimetry has been developed for quick and reproducible estimation of the thermal stability of nonlmear optical chromophores under consideration for incorporation into polymers for use in second-order nonlinear optical devices. The mediod which uses sealed glass ampoules has been used to compare a large number of chromophores and has been compared to electric field-induced second harmonic generation methods. 

P -Values can be measured by several techniques, including electric field induced second harmonic generation and solvatochromic measurements of absorption and fluorescence Moreover, quantum mechanical calculations can be used to estimate these nonlinearities For a more detailed description of the physical backgrounds of nonlinear optics we like to refer to excellent reviews and books< ° >. 

First, let us turn our attention to the issue of optimizing chromophore hyperpolarizability. An obviously important and necessary aspect of the process is the characterization of hyperpolarizabilities. The two most popular methods for characterizing chromophore second-order molecular optical nonlinearity are electric field-induced second harmonic generation (EFISH) [3,10,21-24] and hyper-... 

Combination with Static Fieids. A common technique, useful for optoelectronic devices, is to combine a monochromatic optical field with a DC or quasistatic field. This combination can lead to refractive index and absorption changes (linear or quadratic electrooptic effects and electroabsorption), or to electric-field induced second-harmonic generation (EFISH or DC-SHG, 2o) = co + co + 0) in a quasi-third-order process. In EFISH, the DC field orients the molecular dipole moments to enable or enhance the second-harmonic response of the material to the applied laser frequency. The combination of a DC field component with a single optical field is referred to as the linear electrooptic (Pockels) effect (co = co -I- 0), or the quadratic electrooptic (Kerr) effect ( = -I- 0 -I- 0). EFISH is discussed in this article, however, for the important role that it has played in the characterization of nonlinear optical materials for other applications. 

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. 

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

On the assumption of total symmetry of the tensor of third-order nonlinear polarizability c(— co coi, cog, cog), its non-zero and independent elements are the same as those of Table 12. Direct theoretical calculations of c = c(0 0,0,0) have been performed for the atoms of inert gases and some simple molecules. Values of the tensor elements = c(— cu cu, 0,0) have been determined for numerous molecules from static Kerr effect studies and values of c = c(— cd ot>,coi — col) from measurements of optical birefringence induced by laser li t. Measurements of second-harmonic generation by gases in the presence of a static electric field yield the tensor elements c " = c( — 2co co, to, 0), which can also be obtained from second-harmonic scattering in centro-symmetric liquids. The elements of the tensor c = c(— 3co co, co, co)... 

The summation runs over repeated indices, /r, is the i-th component of the induced electric dipole moment and , are components of the applied electro-magnetic field. The coefficients aij, Pijic and Yijki are components of the linear polarizability, the first hyperpolarizability, and the second hyperpolarizability tensor, respectively. The first term on the right hand side of eq. (12) describes the linear response of the incident electric field, whereas the other terms describe the nonhnear response. The ft tensor is responsible for second order nonlinear optical effects such as second harmonic generation (SHG, frequency AotAAin, frequency mixing, optical rectification and the electro-optic effect. The ft tensor vanishes in a centrosymmetric envirorunent, so that most second-order nonlinear optical materials that have been studied so far consists of non-centrosyrmnetric, one-dimensional charge-transfer molecules. At the macroscopic level, observation of the nonlinear optical susceptibility requires that the molecular non-symmetry is preserved over the physical dimensions of the bulk stmcture. 

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