Four-wave mixing components

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... 

Under the influence of an optical pump, the molecular angular distribution described by Equation 12.4 can be considerably modified. In turn, this results in modification of the X ijkl tensor components. Further, we discuss the influence of a polarized pump beam on third-order nonlinear phenomena such as third harmonic generation (THG) [(described by (-3a),ft>,w,a>) coefficient], electric field induced second harmonic generation (EFISH) [x / kl -2(0, (o, o), 0)] and degenerate four-wave mixing (DFWM) X kl ... 

Two standard wave-mixing techniques are commonly used to characterize PR polymers the four-wave mixing and the two-beam coupling technique (43), The samples consist of the polymer sandwiched between two transparent ITO (Indium-Tin-Oxide) electrodes. The external field is applied to the electrodes and is therefore perpendicular to the polymer film. To have a component of the electric field along the grating vector, the sample is tilted as shown in Figure 2. 

There are several four-wave mixing techniques that can be used to evaluate Xotl components of a material [3]. It should be noted that there are numerous third-order processes that are described by different ) ukl terms. Hence, a comparison of derived from one technique with evaluated with another technique should be made cautiously. 

A typical time-resolved degenerate four-wave mixing signal consists of at least two components a fast component limited by the laser pulse duration and a longer decay due to the medium response. When all three beams are polarized parallel to each other (xxxx geometry), three gratings are formed one grating is from the two... 

To see how interferometry can detect the difference between resonant and nonresonant processes, consider the experimental set-up shown in Figure 2 (a) and the shape of the anti-Stokes pulses produced by the long pump and short Stokes pulses previously mentioned. This combination of pulses is illustrated in Figure 2 (b). en the pump and Stokes pulses overlap, the molecule will be excited by SRS. This excitation will remain after the Stokes pulse passes. At the moment of the overlap, nonresonant four-wave-mixing processes can also be excited. However, because there is no persistent state associated with nonresonant processes, the nonresonant emission will end quickly after the Stokes pulse passes. With a Raman-active resonance, however, the pump can produce anti-Stokes radiation via SRS even after the Stokes has passed, because the resonance persists. Therefore, the nonresonant component can be discarded by rejecting any anti-Stokes radiation that occurs coincident with the Stokes pulse. 

Note that to detect the difference between resonant and nonresonant processes did not require that the pump be lengthened to the lifetime of the resonance of the acetone. This is because the nonresonant component stops abruptly at the end of the Stokes pulse. Unlike the incoherent detection case, one can actually reject the nonresonant component based on its time of arrival, and not Just depend on minimizing the amount of nonresonant four-wave-mixing that is generated. 

The integration in Equation [4] considers the existence of several frequency combinations matching the condition = Ey cOy, within the bandwidth of the applied field. A single laser whose bandwidth is large enough to include frequency components that match 0) -0) = O) can drive the nonlinear response. However, more frequently the laser bandwidth is smaller than o) and different beams with distinct centre frequencies at needed to match the Raman resonance. Let us now consider a field composed of a superposition of quasi-monochromatic beams, i.e. the amplitude at a carrier frequency is modulated by a complex envelope that defines its spectral shape. The central frequencies are chosen to match the Raman resonant four-wave mixing scheme (see Table 1), which can be later adapted to other colour choices. Three laser beams are present of frequencies o)q, cOp, cOg, with 0) -0) = 0) as the only resonant frequency combination. 

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