Nonlinear sampling

The phase matching condition is Afc L ir, which means that for the generation of CARS the coherence length defined by 7r/ Afc has to exceed the effective interaction length L. The latter is determined by the axial dimension of the nonlinear sample. Thus, the actual extent of Afc acts as a size filter for the scatterer of dimensions for which an efficient CARS signal is generated. When the slab thickness is smaller than the pump wavelength, i.e., L 0, the... 

For broad distributions this equation predicts that at least several hundred linearly-spaced channels are required. Nonlinear sample time spacing is superior. Both the fixed-angle instrument and the correlator used in this work operate with up to the equivalent of several thousand linearly-spaced data channels. 

In the Third-Harmonic Generation (THG) experiment an input beam at frequency w is incident into the nonlinear sample and an optical signal oscillating at frequency 3w is generated through the nonlinear interaction inside of the material. This is described by w, w, w) ... 

L focusing lens S nonlinear sample A optical aperture D detector... 

Figure 11. Schematic diagram representing the Power Limiting at high input intensities. L focusing lens S nonlinear sample A optical aperture D detector...

The preceding discussion and Eqs. (2-l)-(2-5) assume that the sample distribution coefficient K is constant throughout separation. Quite frequently K varies with sample concentration, however. Separations in which K is independent of sample concentration are referred to as linear isotherm separations, from the definition of an isotherm as a plot of X versus (20 in an equilibrium system at a given temperature. Linearity, of the plot is equivalent to constant K. A nonlinear sample isotherm... 

Jaravine VA, Zhuravleva AV, Permi P, Ibraghimov I, Orekhov VY (2008) Hyperdimenslonal NMR spectroscopy with nonlinear sampling. J Am Chem Soc 130 3927-3936... 

Schmieder P, Stem AS, Wagner G, Hoch JC (1993) Application of nonlinear sampling schemes to COSY-type spectra. J Biomol NMR 3 569-576... 

Hyberts SG, Heffron GJ, Tarragona NG, Solanky K, Edmonds KA, Luithardt H, Fejzo J, Chorev M, Aktas H, Colson K et al (2007) Ultrahigh-resolution (1)H-(13)C HSQC spectra of metabolite mixtures using nonlinear sampling and forward maximum entropy reconstruction. J Am Chem Soc 129 5108-5116... 

Note that this expression has the nonlinear sample thickness L and electric field dependences characteristic of dispersive transport. 

Optical Kerr Effect. Another important method used to characterize polymers is the optical Kerr effect (OKE). The optical Kerr effect differs from the quadratic electrooptic effect in that the birefringence effects are induced solely by an optical field (37). In this measurement, an intense linearly polarized pump pulse induces birefringence in the nonlinear sample through an intensity-dependent refractive index change. The sample is placed between crossed polarizers and a weak, typically tunable, continuous wave (cw) probe laser (usually at a different wavelength and polarized at 45° to the pump pulse) overlaps the pumped region. The increased transmission of the probe beam when the pump pulse arrives is proportional to (Xeff), a combination of elements of the tensor. Many... 

Optical Kerr Eftect. Another important method used to characterize polymers is the optical Kerr effect (OKE). The optical Kerr effect differs from the quadratic electrooptic effect in that the birefringence effects are induced solely by an optical field (37). In this measurement, an intense linearly polarized pump pulse induces birefringence in the nonlinear sample through an... 

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