Four wave mixing

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 

As seen, the term scheme for DFWM is especially simple all four photons induce transitions between real states. This resonance enhancement results in a higher signal strength as compared with, for example, CARS. Momentum conservation determines the direction of fhe resulting signal wave. Since the phase-matching condition is (for the notation see Fig. 6.13)  

DFWM (Fisher 1983) is in fact a real-time variant of optical holography, which has been known since the sixties of the 19 century two laser beams (here, forward pump and object beam) are overlapped coherently imder a small angle 0. They induce in a nonlinear medium with susceptibility an interference pattern (grating), which contains information about the amplitude and phase relations between the contributing waves. This information is recovered via Bragg scattering using a third beam (backward pump) and gen- 

While the break of inversion symmetry at the surface makes nonlinear optical processes of second order intrinsically surface-sensitive in the case of centro-symmetrical solids, this is no longer the case for a nonlinear process of third order. Hence one has to induce surface-sensitivity externally. This 

The nonlinearly optically active medium is an array of spheroidal alkali clusters with index of refraction n, which gives rise to a DFWM signal intensity (Fisher 1983)  

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Pastirk I, Brown E J, Grimberg B I, Lozovoy V V and Dantus M 1999 Sequences for controlling laser excitation with femtosecond three-pulse four-wave mixing Faraday Discuss. 113 401... 

Chen P C, Hamilton J P, Zilian A, Labuda M J and Wright J C 1998 Experimental studies for a new family of infrared four wave mixing spectroscopies Appl. Spectrosc. 52 380-92... 

Albrecht A C, Smith S P, Tan D, Schaertel S A and DeMott D 1995 Ultrasharp spectra and ultrafast timing from noisy coherence in four wave mixing Laser Rhys. 5 667-75... 

Dugan M A and Albrecht A C 1991 Radiation-matter oscillations and spectral line narrowing in field-correlated four-wave mixing I theory Rhys. Rev. A 43 3877-921... 

Ulness D J and Albrecht A C 1996 Four-wave mixing in a Bloch two-level system with incoherent laser light having a Lorentzian spectral density analytic solution and a diagrammatic approach Rhys. Rev. A 53 1081-95... 

Bardeen C J and Shank C V 1994 Ultrafast dynamics of the solvent-solute Interaction measured by femtosecond four-wave mixing LD690 In n-alcohols Chem. Phys. Lett. 226 310-16... 

Joo T and Albrecht A C 1993 Electronic dephasing studies of molecules in solution at room temperature by femtosecond degenerate four wave mixing Chem. Phys. 176 233—47... 

Vaccaro P H 1995 Resonant four-wave mixing spectroscopy a new probe for vibrationally-excited species Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping (Advances in Chemistry Series) vol 7, ed H-L Dai and R W Field (Singapore World Scientific) p 1... 

Deooia P L, Hoohstrasser R M and Trommsdorff H P 1980 Vibrationai reiaxation in moieouiar orystais by four-wave mixing naphthaiene Chem. Phys. Lett. 72 1-4... 

In Equation (9.18) we have treated Vj and V2 differently by involving two photons of Vj and only one of V2. However, four-wave mixing involving one photon of Vj and two of V2 to produce V4, represented by... 

Table 1 Coefficients for 7[ (a ) for third harmonic generation (THG), degenerate four wave mixing (DFWM), electric field induced second harmonic generation (ESHG), and Kerr effect in methane at the experimental geometry rcH = 2.052 a.u. A CCSD wavefunction and the t-aug-cc-pVDZ basis were used. (Results given in atomic units, the number in parentheses indicate powers of ten.)...

For the application of QDs to three-dimensional biological imaging, a large two-photon absorption cross section is required to avoid cell damage by light irradiation. For application to optoelectronics, QDs should have a large nonlinear refractive index as well as fast response. Two-photon absorption and the optical Kerr effect of QDs are third-order nonlinear optical effects, which can be evaluated from the third-order nonlinear susceptibility, or the nonlinear refractive index, y, and the nonlinear absorption coefficient, p. Experimentally, third-order nonlinear optical parameters have been examined by four-wave mixing and Z-scan experiments. 

Ultrafast, time-resolved OKE measurements (which involve another type of four-wave mixing process) may also occasionally be used to determine x(3) and 7 values.5 7 In each of the THG, DFWM, Z-scan, and OKE techniques, 7 is derived from the measured x values by using the solute number density of the solution. In a few cases, x(3) values have also been determined by using Stark spectroscpy. It should be remembered that comparisons of 7 or x values obtained using different techniques with different experimental conditions are generally of little utility. 

Pei-li L, De-xui H, Xin-Liang Z, Guang-xi Z (2006) Ultrahigh-speed all-optical half adder on four-wave mixing in semiconductor optical amplifier. Opt Express 14 11840... 

Optical detection offers the most conventional technique to time-resolve the coherent phonons. It includes four-wave mixing [8], transient reflectivity [9,10] and transmission [7] measurements, as well as second harmonic generation (SHG) [15,32]. Coherent nuclear displacement Q induces a change in the optical properties (e.g., reflectivity R) of the crystal through the refractive index n and the susceptibility y,... 

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