Harmonic generation, time dependence

Figure 3. Time dependence of harmonic generation (of polymer/guest induced polar alignment and relaxation) when the laser intensity is overly strong. The poling-field time dependence is depicted at top. (Reproducedfrom Ref. 23. Copyright 1983, American...

Because of the relatively large dispersion from the electrons compared with the almost constant refractivity of the neutrals and the negligible contribution of the ions, it is possible, with simultaneous measurements at two different wavelength, to determine independent values of the density of electrons and of the nonelectronic components in the plasma 274). Alcock and Ramsden 275) used the light from a giant-pulse ruby laser and its second harmonic generated in an ADP-crystal (ammonium dihydrogen phosphate) to probe a pulsed plasma and its time-dependent density in a Mach-Zehnder interferometer. 

Second-harmonic generation of light is a nonlinear phenomenon in which chaotic behavior was discovered in 1983 [83] (for details, see Secction ). In the Kerr effect with an external time-dependent pump, a chaotic output may also occur, which was proved for the first time in 1990 by Milbum [84] (see also Section III). 

T. P. Softley There is little doubt that in most ZEKE experiments using nanosecond lasers the Rydberg level structure is so dense that a coherent superposition of levels is populated initially, and the correct description of the dynamics should be a time-dependent one. It is possible that some control over the dynamics could be achieved using some of the methods described earlier in the conference, for example, simultaneous excitation through three-photon and one-photon transitions, using third-harmonic generation. 

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. 

Basic spectral features of high harmonics can be obtained from the HHG calculation of a single atom. Calculations of the time-dependent Schrodinger equation (TDSE) for a single atom may reveal the characteristic features of high harmonic generation, such as the plateau and cutoff in the high harmonic... 

Solutions to equation (113) with a sinusoidal time dependence are of interest, since they illustrate sound dispersion resulting from finite reaction rates. Suppose one generates sound waves in a gas occupying the region X > 0 by oscillating a piston harmonically about the point x = 0 (see Figure 4.6). The velocity of the piston can be represented by the real part of... 

Finally, forward ISRS excitation can be followed by measurement of time-dependent absorption or Raman spectra, second harmonic generation efficiency, or any other optical property that may be affected by vibrational distortion. Preliminary time-resolved absorption spectroscopy of nonequilibrium, vibrationally distorted species is discussed further in the next section [46]. 

Norman and Jensen27 have implemented a method for obtaining second order response functions within the four component (relativistic) time-dependent Hartree-Fock scheme. Results are presented for the first order hyperpolarizabilities for second harmonic generation, />(—2o o),o ) for CsAg and CsAu. A comparison of the results with those of non-relativistic calculations implies that the nonrelativistic results are over-estimated by 18% and 66% respectively. In this method transitions that are weakly-allowed relativistically can lead to divergences in the frequency-dependent response, which would be removed if the finite lifetimes of the excited states could be taken into account. 

In order to select a particular experimental technique to measure x , it is very important to keep in mind which parameter of the third-order nonlinear response has to be characterized. For example, if one wants to determine the time-response due to molecular reorientation, one cannot choose Third-Harmonic Generation or Electric-Field-Induced Second-Harmonic Generation, since none of these techniques provide time-response information. Depending on the parameter of interest, a specific technique must be chosen. The following physical mechanisms can contribute to the third-order nonlinear response [54] ... 

---