Frequency mixing, nonlinear optics

The nonlinear optical teclmiques of up- and down-conversion are based on mixing optical beams in a suitable crystal (BBO, LiNbO, KDP, etc) witli tire generation of new optical frequencies tire physical principle is as follows. If two beams having optical frequencies cOp CO2 and wavevectors k, are mixed in a nonlinear optical crystal at tire appropriate angle, a new optical frequency co can be coherently generated witli tire following conditions satisfied ... 

Nonlinear optics. Well, again, why wasn t this already discovered Well, you see, we have particular paths of thought which are very important to us, but they can keep us from considering other paths. In addition, engineering and science had to come together so that ideas such as frequency multiplication and mixing seemed natural. 

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 the degenerate four wave mixing (DFWM) experiment the third-order susceptibility 3)(-tt>,tt>,-CL>,CL>) with degenerate frequencies can be determined [22]. This nonlinear susceptibility is directly proportional to the nonlinear refractive index n2, which is used to describe optically induced refractive index changes. An advantage of this technique is the possibility to record the temporal shape of the third-order nonlinear optical signal. 

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