Harmonic generation, nonlinear optics frequency mixing

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). 

We believe that our model can be extended even further to accurately describe other nonlinear optical interactions such as sum and difference frequency mixing, as well as higher-order harmonics generation. 

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... 

Wave mixing of two electric fields can give rise to second-order effects of nonlinear optics [4]. One of these is the harmonic generation that converts the fundamental wavelength of a laser into its half (see Section 12.2.2). But, if electric fields at different frequencies are used, the response of a medium with sufficient second-order dielectric susceptibility can be frequency shifted to the sum and the difference of the two laser frequencies [4]. In particular, sum frequency generation (SFG) is often used to study surfaces and has found applications to examine catalytic combustion [9,36]... 

Applications of second order nonlinear optical materials include the generation of higher (up to sixth) optical harmonics, the mixing of monochromatic waves to generate sum or difference frequencies (frequency conversion), the use of two monochromatic waves to amplify a third wave (parametric amplification) and the addition of feedback to such an amplifier to create an oscillation (parametric oscillation). 

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. 

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