Nonlinear susceptibility, effect

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. 

For adsorbates on a metal surface, an SFG spectmm is a combination of resonant molecular transitions plus a nonresonant background from the metal. (There may also be a contribution from the water-CaF2 interface that can be factored out by following electrode potential effects see below.) The SFG signal intensities are proportional to the square of the second-order nonlinear susceptibility [Shen, 1984] ... 

These effects Q.2) are all driven by the same third-rank frequency dependent nonlinear susceptibility x2(-u>3 w,, u>2).d is sometimes preferred for second-harmonic generation (SHG). 

In a crystalline medium, the parametric gain (2) T2 is propor-tionnal to d2 Ip n-3 and the oscillation condition r2A2>aA where a is the signal residual absorption (dramatically increased by any crystalline defect), d the efficient phase-matched nonlinear susceptibility, n an average refractive index, Ip the pump intensity (limited by the optical damage threshold) and A the effective interaction length (also limited by any source of crystalline disorientation). 

In order to describe second-order nonlinear optical effects, it is not sufficient to treat (> and x<2) as a scalar quantity. Instead the second-order polarizability and susceptibility must be treated as a third-rank tensors 3p and Xp with 27 components and the dipole moment, polarization, and electric field as vectors. As such, the relations between the dipole moment (polarization) vector and the electric field vector can be defined as ... 

Note 3 A polymer that exhibits a nonlinear optical effect due to anisotropic electric susceptibilities when subjected to electric field together with light irradiation is called an electro-optical polymer. A polymer that exhibits electro-optical behavior combined with photoconductivity is called a photorefractive polymer. 

The same approach can be used to characterize solutions containing colloidal nanoparticles. To do this, we use the effective nonlinear media approach (Stroud and Wood 1989), i.e., express the effective nonlinear susceptibility of solution as... 

This phase shift is akin to the phase shift experienced by a damped harmonic oscillator driven in the vicinity of the oscillator s eigenfreqnency Hence, the presence of a vibrational resonance not only changes the amplitnde of the signal field, bnt also its phase. To incorporate this effect, the resonant nonlinear susceptibility is no longer real as it contains imaginary contributions ... 

Out of the large range of possible nonlinear optical effects, chemists are likely to encounter only a limited number of measurement techniques. These include both second- and third-order NLO characterization methods. A brief listing of the different types of measurements, the nonlinear susceptibility involved and the related molecular nonlinear polarizabilities is given here. 

The discontinuity of the interface leads to two contributions to the second order nonlinear polarizability, the electric dipole effect due to the structural discontinuity and the quadrupole type contribution arising from the large electric field gradient at the surface. Under the electric dipole approximation, the nonlinear susceptibility of the centrosymmetric bulk medium 2 is zero. If the higher order magnetic dipole... 

In this equation, d2u) represents the angle of the radiated SH light with respect to the surface normal, 7(co) is the pump intensity, and e(2co) is the polarization at the SH frequency. The vectors e(co) and e(2co) are related to the unit polarization vectors e(co) and e(2co) in medium 2 by Fresnel coefficients. The effective surface nonlinear susceptibility incorporates the surface nonlinear susceptibility x( and the bulk magnetic dipole contributions to the nonlinearity. The result simplifies since, for isotropic media, there are only three nonzero independent elements of xf These are x%, X% = X%.> and XsfL where 1 =... 

When an adsorbate is present at the surface of a metal, the interfacial region can be viewed as having an effective nonlinear susceptibility, x where... 

FPE become sensitive to a, demonstrating crossovers between different damping-dependent regimes [50,79]. The consequences of this effect for the nonlinear susceptibility were first found in numerical simulations [80] and later confirmed by an analytically calculation in Ref. 81. The results given below are valid for the high-damping regime, that is, a > 1. 

On the route to all-optical signal processing the development of materials with large third-order nonlinear optical effects is of decisive importance. For the material characterization and the assessment of its usefulness for applications the absolute value of the third-order nonlinear optical susceptibility y has to be known. Since most measurements are performed relative to a reference material, the establishment of a well accepted value for a standard material is important. 

---