Degenerate four-wave mixing methods

In a separate study, the cross section of diphenylbutadiene in chloroform has been measured at 532 nm by two different methods and reported to be 40 8GM by degenerate four-wave mixing, and 34 12GM by nonlinear transmission [66]. It should be pointed out that both results were obtained using ns excitation pulses, but that the cross sections obtained by the two methods are comparable one to the other and on the same order of the cross sections listed earher (although those were obtained in a different wavelength range). 

The third-harmonic generation method has the advantage that it probes purely electronic nonlinearity. Therefore, orientational and thermal effects as well as other dynamic nonlinearities derived from excitations under resonance condition are eliminated (7). The THG method, however, does not provide any information on the time-response of optical nonlinearity. Another disadvantage of the method is that one has to consider resonances at oj, 2w and 3o> as opposed to degenerate four wave mixing discussed below which utilizes the intensity dependence of refractive index and where only resonances at a) and 2a) manifest. 

Banerjee and Harbola [69] have worked out a variation perturbation method within the hydrodynamic approach to the time-dependent density functional theory (TDDFT) in order to evaluate the linear and nonlinear responses of alkali metal clusters. They employed the spherical jellium background model to determine the static and degenerate four-wave mixing (DFWM) y and showed that y evolves almost linearly with the number of atoms in the cluster. 

Tlie usual experimental techniques developed to study the optical Kerr effect in materials have already been described in a preceding chapter of this book. We only mention here the methods which have especially been used for nanocomposite materials as colloidal solutions or thin films Degenerate four-wave mixing (DFWM) and optical phase conjugation, which provide the modulus of x only and may be completed by Interferometry techniques to get its phase as well, optical limiting, optical Kerr shutter, and z-scan, which is probably the most common technique used in recent years due to its ability to provide simultaneously the nonlinear refraction and absorption coefficients of the same sample point [118],... 

To review some of the applicative problems related to the use of coherent methods for the detection of chemical species, we concentrate on two specific examples belonging to the realm of third-order dielectric nonlinearities. One is the so-called CARS and the other is the degenerate four-wave mixing (DFWM). This choice is also suggested by the thermometric uses of these two techniques (see the corresponding section below). 

Very new methods, such as biosensors using immobilized apoenzymes [56] or degenerate four-waves mixing using low-power off-resonant laser excitation [57], are currently developed but their applicability to serum, plasma, and other biological fluids has not yet been demonstrated. 

Bulk and molecular nonlinear optical properties have been measured by laser optical techniques such as second and third harmonic generation (SHG, THG), electric field-induced second harmonic generation (EFISH), and degenerate four-wave mixing (DFWM). Molecular NLO responses can also be calculated by quantum-mechanical (ab initio and semiempirical) methods, and suitable computing programs are being developed. 

Before going into the details of various materials and their third-order NLO properties, it would serve well to have an idea of the characterization techniques used for their study. To study the effect of the real part of third-order susceptibility, Z-scan measurements, degenerate four-wave mixing (DFWM), optical heterodyne detection of optical Kerr effect (OHD-OKE), and differential optical Kerr effect (DOKE) detection are employed. For the study of TPA, techniques such as nonlinear transmission (NLT) method, two-photon excited fluorescence (TPEF) method, and Z-scan measurements are used. The observables from the above-mentioned techniques vary depending on the inherent limitations of the technique. The nature of the light source employed like the central wavelength of the laser. 

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