Nonlinear resonances

Resonance, nonlinear, 354 Resonance, subharmonic, 372,376 Rhombus rules, 85 Risk matrix, 315 Risk rule, 315... 

The proper phase shift introduced to the signal wave allows direct measurements of the imaginary part of the resonant nonlinear optical susceptibility, i.e ... 

This phase shift is akin to the phase shift experienced by a damped harmonic oscillator driven in the vicinity of the oscillator s eigenfreqnency Hence, the presence of a vibrational resonance not only changes the amplitnde of the signal field, bnt also its phase. To incorporate this effect, the resonant nonlinear susceptibility is no longer real as it contains imaginary contributions ... 

A formal expression for the resonant nonlinear susceptibility can be obtained by describing the light-matter interactions in a density matrix formalism (Boyd 2003 Mukamel 1995), which is beyond the scope of this chapter. A third-order perturbative expansion of the system s density matrix yields the following form for the nonlinear susceptibility ... 

Thus if p(u), or at high temperature S(t), is known, then all linear and third-order resonant nonlinear spectroscopies can be calculated. In practice this can be quite a laborious task when finite laser pulses are included in the calculation [37]. In the following section we explore the reverse procedure, that is, attempts to obtain S(t) and p(w) from experiment. 

Another class of conducting polymer that has been examined for resonant nonlinear response are the poly(thiophene) polymers. DFWM has been reported for poly(alkyIthiophene) and for several model... 

Third-Order Near-Resonance Nonlinearities in Dithiolenes and Rare Earth Metallocenes... 

Two classes of material will be described here - the metal dithiolenes and rare earth metallocenes. In the metal dithiolenes a strong, low energy pi-pi transistion occurs in the near IR (9.10). This can be tuned from about 700 nm to 1400 nm by altering the metal ion, substituents or charge state of the dithiolene. The dithiolenes are particularly attractive because of their optical stability which has been exploited in their use as laser Q-switch materials. In the rare earth complexes the near IR band is provided by/-/transistions of the rare earth ion rather than the cyclopentadienyl ring structure various nonlinear optical phenomena have been observed in glasses incorporating similar ions. Previous studies have shown that dicyclopentadienyl complexes such as ferrocene have off-resonant nonlinearities similar to nitrobenzene or carbon disulphide (11-13)... 

A clear-cut distinction between the two processes is the time response, which is ultrafast in the former (essentially instantaneous), and finite (associated with the lifetime of real excitations) in the latter. Here we limit our discussion to resonant nonlinearities, which are crucial for describing the fundamental working mechanisms of organic photovoltaic cells. Examples will be reported concerning isolated molecules and the condensed phase. 

Del Fatti N, Vallde F, Hamanaka Y, Nakamura A. Electron dynamics and surface plasmon resonance nonlinearities in metal nanoparticles. Chem Phys 2000 251 215-26. 

The connection between the non-resonant nonlinear optical (NLO) response to optical pumping well below the absorption edge and the resonant NLO response following absorption and photo-excitation has been discussed in terms of contributions from virtual soliton pairs enabled by nonlinear zero-point fluctuations in the ground state [82,221,222]. Because of the nonlinear zero-point fluctuations, there are finite matrix elements connecting the ground state with the relaxed state following the creation of a soliton-antisoliton (S-AS ) pair. This... 

P. N. Prasad and G. S. He, Multiphoton Resonant Nonlinear Optical Processes in Organic Molecules. In Nonlinear Optical Materials. Theory and Modeling, Vol. 628, S. P. Kama and A. T. Yeates, Eds., American Chemical Society, Washington, DC, 1995, p. 225. 

Trehak, S., Chernyak, V. Resonant nonlinear polarizabilities in the time-dependent density lunctional theory. J. Chem. Phys. 119, 8809-8823 (2003)... 

Grund, A., Kaltbeitzel, A., Mathy. A.. Schwarz, R., Bubeck, C., Vermehren, P., Hanack, M. Resonant nonlinear optical properties of spin-cast films of soluble oligomeric bridged (phthalo-cyaninato)ruthenium(II) complexes. J. Phys. Chem. 96, 7450-7454 (1992)... 

In the above discussion, we have only considered the effects due to the CTE-CTE repulsion, which contribute to the resonant nonlinear absorption (as well as to other resonant nonlinearities) by the CTE themselves. Here, however, we want to mention a more general mechanism by which the nonlinear optical properties of media containing CTEs in the excited state can be enhanced. This influence is due to the strong static electric field arising in the vicinity of an excited CTE, If, for example, the CTE (or CT complex) static electric dipole moment is 20 Debye, at a distance of 0.5 nm it creates a field Ecte of order 107 V/cm. Such strong electric fields have to be taken into account in the calculation of the nonlinear susceptibilities, because they change the hyperpolarizabilities a, / , 7, etc. of all molecules close to the CTE. For instance, in the presence of these CTE induced static fields, the microscopic molecular hyperpolarizabilities are modified as follows... 

One subject that attracted much attention is the nonlinear optical properties of these semiconductor nanoclusters [17], The primary objective is to find materials with exceptional nonlinear optical response for possible applications such as optical switching and frequency conversion elements. When semiconductors such as GaAs are confined in two dimensions as ultrathin films (commonly referred to as multiple quantum well structures), their optical nonlinearities are enhanced and novel prototype devices can be built [18], The enhancement is attributed mostly to the presence of a sharp exciton absorption band at room temperature due to the quantum confinement effect. Naturally, this raises the expectation on three-dimensionally confined semiconductor nanoclusters. The nonlinearity of interest here is the resonant nonlinearity, which means that light is absorbed by the sample and the magnitude of the nonlinearity is determined by the excited state... 

Different parameters are required to characterize the resonant and the nonresonant optical nonlinearity. This has often been a source of confusion in the literature, even today. For nonresonant processes, the magnitude of the nonlinearity is measured by either x(3) or n2. However, for resonant processes, x(3)> a2> or ni alone cannot measure the magnitude of the nonlinearity. For example, a different x(3) value can result from the same material when lasers with different pulse widths are used for the measurement. A complete characterization of the nonlinearity requires a set of parameters, including % 3), the ground state absorption coefficient, the laser pulse width, and the excited state relaxation time. In a simple two- or three-level system, once all these factors are properly taken into account, the best parameter for measuring the resonant nonlinearity is simply the ground state absorption cross section of the material. In the following section I focus on the resonant nonlinearity only as this is closely related to the photophysical properties. The discussion of nonresonant nonlinearity of semiconductor nanoclusters can be found elsewhere [17, 84-86],... 

For bulk semiconductors at room temperature, the mechanism for the resonant nonlinearity can be described by the band-filling model [82,87]. This is shown schematically in Figure 16b for a direct gap semiconductor such as CdS. Absorption of photons across the band gap, g, generates electrons and holes which fill up the conduction and valence band, respectively, due to the Pauli exclusion principle. If one takes a snap shot of the absorption spectrum before the electrons and holes can relax, one finds that the effective band gap, , increases (Figure 166), since transitions to the filled states are forbidden. The bleaching efficiency per photon absorbed can be derived as... 

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