Second-harmonic generation , nonlinear frequency mixing

In recent years there has been a growing interest in the search for materials with large macroscopic second-order nonlinearities [20-22] because of their practical utility as frequency doublers, frequency converters and electro-optic modulators [23] by means of second-harmonic generation, parametric frequency conversion (or mixing) and the electro-optic (EO) effect. They are described by X (2w w, u)), 0, w), respectively. In order to optimize... 

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. 

Figure 9.3 Schematic illustration of second-order nonlinear optical effects, (a) Second-harmonic generation. Two light fields at frequency go are incident on medium with nonvanishing / 2. Nonlinear interaction with medium creates new field at frequency 2 go. (b) Frequency mixing. One light field at frequency GO and one at frequency go2 is incident on nonlinear medium. Nonlinear interaction with medium creates new field at frequency goi + go2. (c) electro-optic effect. Static electric field E (0) applied over nonlinear medium changes phase of an incoming light field.

The proportionality constants a and (> are the linear polarizability and the second-order polarizability (or first hyperpolarizability), and x(1) and x<2) are the first- and second-order susceptibility. The quadratic terms (> and x<2) are related by x(2) = (V/(P) and are responsible for second-order nonlinear optical (NLO) effects such as frequency doubling (or second-harmonic generation), frequency mixing, and the electro-optic effect (or Pockels effect). These effects are schematically illustrated in Figure 9.3. In the remainder of this chapter, we will primarily focus on the process of second-harmonic generation (SHG). 

Second harmonic generation (SHG) involves the mixing of two photons at frequency co, and producing one photon at frequency 2co. This is frequently referred to as a three-wave mixing process. Third order nonlinearities are four-wave mixing processes. 

Sum-fretiuencv generation (SI Ci) is a nonlinear optical technique basoil on the interaction of two plu tons at a surface. The result of the wave-mixing interaction is the production of a single photon whose frequency is the sum of the incident frequencies. If the two incident photons are of Ihe same frequency, the technique is called second-harmonic generation because the exiting photon has a frequency Iwice iha of the incident photons. Because this is a weak second-order process, intense lasers must be used. 

Polymeric materials are playing an increasingly important role in electronic and photonic applications ". This includes application in active devices utilizing optical effects attributable to the nonlinear polarization of the medium, A number of applications such as frequency mixing, second harmonic generation, optical bistability, optical parametric amplification and oscillation, electrooptic and all optical switching and modulation etc. have been proposed. 

Besides the various types of tunable lasers discussed in the foregoing sections, sources of tunable coherent radiation have been developed that are based on the nonlinear interaction of intense radiation with atoms or molecules in crystals or in liquid and gaseous phases. Second-harmonic generation, sum- or difference-frequency generation, parametric processes, or stimulated Raman scattering are examples of such nonlinear optical mixing techniques. These techniques cover the whole spectral range from the vacuum ultraviolet (VUV)... 

Optical second harmonic and sum frequency generation are three-wave mixing processes, which are intrinsically surface sensitive. The nonlinear polarization, which is necessary for the generation of the third photon, can be described by the second term in Eq. 6.1. If one takes additional photons into account, multi-wave mixing processes and especially four-wave mixing takes... 

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