Frequency-mixing processes

In general, x<3> is several orders of magnitude smaller than x(2) [78]. However, this contribution can be comparable to the second-order response when the dc field is large (i.e. 104 — 105 V/cm) as is the case for a metal electrode in solution held at a bias on either side of the PZC. The SH fields can be viewed as arising from a sum frequency mixing process where two incident ac fields at frequency co are mixed with a dc field at frequency co = 0 to produce a reflected and transmitted wave at frequency 2co. 

ABSTRACT. Tunable coherent radiation in the ultraviolet and vacuum ultraviolet has been generated by stimulated Raman scattering, by anti-Stokes Raman lasers, and by frequency mixing processes in nonlinear media. The theory and experimental progress in the development of these laser-driven sources is reviewed, and examples of available systems and their characteristics are discussed. Various applications in spectroscopy of radiation tunable in the wavelength region 200-90 nm are presented. 

Similar expressions can be obtained for the other second-order processes with minor changes. For second-harmonic generation, co =co2, while for difference-frequency mixing processes of the form co =co — C02, 0 2 appears with a minus sign and the complex conjugate... 

Anti-Stokes Raman scattering involves the generation of radiation at shorter wavelengths than those of the pump wave. Anti-Stokes scattering can occur in one of two ways. The more common method involves a four-wave difference frequency mixing process of the form... 

Two-dimensional spectroscopy has two broad classes of experiments (a) 2D /-resolved spectra (Mtlller et ai, 1975 Aue et ai, 1976), in which no coherence transfer or mixing process normally occurs, and chemical shift and coupling constant frequencies are spread along two different axes. 

Five different types of peaks can occur in 3D spectra. These are illustrated in an ABC spin system, in which the Larmor frequencies of the three nuclei are v,, Vg, and v, -, and the coherence transfers are associated with two different mixing processes, M, and Mj ... 

Non-linear optical interactions occur in materials with high optical intensities and have been used to produce coherent light over a wide range of frequencies from the far infra-red to the ultra-violet. The three wave mixing process is of particular interest as it can be used for optical parametric amplification and optical second harmonic generation (SHG) and occurs in non-centrosymmetric materials. 

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). 

An interesting method of detecting infrared signals with sensitive and fast visible photomultipliers has been demonstrated by Boyd et al. The authors used the frequency mixing of infrared signals with visible light (10.6 yt COj laser with 0.6328 y He-Ne laser) in nonlinear crystals to produce the difference frequency wave ( at X = 0.6729 y) which can be detected by an S 20 photomultiplier. No additional source of noise due to the mixing process was observed. 

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. 

X lT + E r Xij ki, which refer in their order of appearance to the Cartesian polarization components of the CRS, pump, probe, and Stokes fields in the four-wave mixing process [31]. In transparent and optically inactive media, where the input frequencies are away from any electronic transition frequencies, and only the molecular ground state is populated, the selection rules of both resonant coherent and spontaneous Raman scattering are identical... 

Analysis. We can divide analysis algorithms into time and frequency domain processes. Certainly, the division between these categories is arbitrary since we can mix them together to solve an audio problem. However, it suffices for our purposes. 

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