Optical processability

The second-order nonlinear optical processes of SHG and SFG are described correspondingly by second-order perturbation theory. In this case, two photons at the drivmg frequency or frequencies are destroyed and a photon at the SH or SF is created. This is accomplished tlnough a succession of tlnee real or virtual transitions, as shown in figure Bl.5.4. These transitions start from an occupied initial energy eigenstate g), pass tlnough intennediate states n ) and n) and return to the initial state g). A fiill calculation of the second-order response for the case of SFG yields [37]... 

Pankove J I 1971 Optical Processes in Semiconductors (New York Dover)... 

Besides W, there are two other definitions of FOM for all-optical processing ... 

Phototypesetting represented an easier way to compose type. Eady phototypesetters used an optical process, whereby a disk of characters, ia different sizes and typefaces, was spun under computer control. Each character was projected ia turn onto photosensitive film or paper. This was followed by systems where characters drawn on a cathode ray tube (CRT) exposed the photosensitive material. In each case, the operator iateracted with the system at a video screen that only showed the characters of the text (the iaformation content) and codes that iadicated how the characters were to look on paper. An experienced operator was required to obtain high quaUty results. 

E. M. Rabinovich, in L. C. Klein, eds., Sol-Gel Optics Processing andMpplications, Kluwer Academic Pubhshers, Boston, Mass., 1994, p. 1. 

Frequency-dependent polarizability a and second hyperpolarizability y corresponding to various third-order nonlinear optical processes have been... 

Laser-optical process used to measure the potential of zero charge (Fredlein and Bockris), 34... 

An alternative compact expansion with coefficients which are independent of the optical process can be derived for the isotropic parallel average of the second hyperpolarizability 7 defined as [13]... 

As was proven later by Bishop [19], the coefficient A in the expansion (73) is the same for all optical processes. If the expansion (73) is extended to fourth-order [4,19] by adding the term the coefficient B is the same for the dc-Kerr effect and for electric field induced second-harmonic generation, but other fourth powers of the frequencies than are in general needed to represent the frequency-dependence of 7 with process-independent dispersion coefficients [19]. Bishop and De Kee [20] proposed recently for the all-diagonal components yaaaa the expansion... 

These effective frequencies are chosen such that contributes only for optical processes with at least three non-zero frequency arguments, while u 4 is only non-zero if all four frequency arguments are non-zero. During the implementation it was also found that this choice for the effective frequencies leads to the most compact expressions for the coefficients Ak,i,m in terms of D n,m,l). Using a similar notation as in Eq. (73), 7 (o o Wi,o 2i 3) can up to sixth order in the frequencies be expanded... 

The present study demonstrates that the analytic calculation of hyperpolarizability dispersion coefficients provides an efficient alternative to the pointwise calculation of dispersion curves. The dispersion coefficients provide additional insight into non-linear optical properties and are transferable between the various optical processes, also to processes not investigated here as for example the ac-Kerr effect or coherent anti-Stokes Raman scattering (CARS), which depend on two independent laser frequencies and would be expensive to study with calculations ex-plictly frequency-dependent calculations. 

An important specific feature of the present experiment is worth noting. The X-ray photons have energies that are several orders of magnitude larger than those of optical photons. The pump and probe processes thus evolve on different time scales and can be treated separately. It is convenient to start with the X-ray probing processes, and treat them by Maxwellian electrodynamics. The pumping processes are studied next using statistical mechanics of nonlinear optical processes. The electron number density n(r,t), supposed to be known in the first step, is actually calculated in this second step. 

In the previous Maxwelhan description of X-ray diffraction, the electron number density n(r, t) was considered to be a known function of r,t. In reality, this density is modulated by the laser excitation and is not known a priori. However, it can be determined using methods of statistical mechanics of nonlinear optical processes, similar to those used in time-resolved optical spectroscopy [4]. The laser-generated electric field can be expressed as E(r, t) = Eoo(0 exp(/(qQr ot)), where flo is the optical frequency and q the corresponding wavevector. The calculation can be sketched as follows. 

Liquid interfaces are widely found in nature as a substrate for chemical reactions. This is rather obvious in biology, but even in the diluted stratospheric conditions, many reactions occur at interfaces like the surface of ice crystallites. The number of techniques available to carry out these studies is, however, limited and this is particularly true in optics, since linear optical methods do not possess the ultimate molecular resolution. This resolution is inherent to nonlinear optical processes of even order. For liquid-liquid systems, optics turns out to be rather powerful owing to the possibility of nondestructive y investigating buried interfaces. Furthermore, it appears that planar interfaces are not the only config-... 

G. Pankove, Optical Processes in Semiconductors, Englewood Cliffs (USA) Prentice-Hall, 1971. 

Frequency degenerate 2PA is a third order, y° nonlinear optical process whereby two photons of equal energy are simultaneously absorbed to raise a system into an excited state of energy equal to that of the sum of the two photons. The propagation... 

In conclusion, we stress that the complementary NLO characterization techniques of pump-probe, Z-scan, and 2PF allow for the unambiguous determination of nonlinear optical processes in organic materials. The important molecular parameters of 2PA cross section, fluorescence efficiency, reorientation lifetimes, excited state cross sections, etc. can be determined. 

Klein L.C. (ed.), Sol-Gel Optics, Processing and Applications, Kluwer Academic Publishers, Boston, 1994. 

We consider a model for the pump-probe stimulated emission measurement in which a pumping laser pulse excites molecules in a ground vibronic manifold g to an excited vibronic manifold 11 and a probing pulse applied to the system after the excitation. The probing laser induces stimulated emission in which transitions from the manifold 11 to the ground-state manifold m take place. We assume that there is no overlap between the two optical processes and that they are separated by a time interval x. On the basis of the perturbative density operator method, we can derive an expression for the time-resolved profiles, which are associated with the imaginary part of the transient linear susceptibility, that is,... 

X in most strong Kerr, nonlinear refraction, etc. media. For use in extremely high bandwidth applications, such as totally optical processing, predominantly electronic responding media are needed (M). 

The unique properties of liquid crystals have also provided opportunity for study of novel nonlinear optical processes. An example involves the ability to modify the pitch of cholesteric liquid crystals. Because a pseudo-wave vector may be associated with the period of pitch, a number of interesting Umklapp type phasematching processes (processes in which wave vector conservation is relaxed to allow the vector addition to equal some combination of the material pseudo-wave vectors rather than zero) are possible in these pseudo-one-dimensional media. Shen and coworkers have investigated these employing optical third harmonic generation (5.) and four-wavemixing (6). 

The third order nonlinear susceptibility is an important optical property of materials because of its contributions to numerous nonlinear optical processes. (1)(2) With the growing interest in all-op ical signal processing it has been proposed (3) recently that x ( 1, 2 3) and especially the degenerate third order nonlinear susceptibility x 3 (-w, to, 00) [defined as x (< >)], be utilized through its contributions to the changes in dielectric constant e with optical field strength E ... 

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