Nonlinear frequency response significance

In order to illustrate some of the basic aspects of the nonlinear optical response of materials, we first discuss the anliannonic oscillator model. This treatment may be viewed as the extension of the classical Lorentz model of the response of an atom or molecule to include nonlinear effects. In such models, the medium is treated as a collection of electrons bound about ion cores. Under the influence of the electric field associated with an optical wave, the ion cores move in the direction of the applied field, while the electrons are displaced in the opposite direction. These motions induce an oscillating dipole moment, which then couples back to the radiation fields. Since the ions are significantly more massive than the electrons, their motion is of secondary importance for optical frequencies and is neglected. 

The frequency dependence of SHG at simple metal surface has been the focus of a recent theoretical study of Liebsch [100]. Time-dependent density functional theory was used in these calculations. The results suggest that the perpendicular surface contribution to the second harmonic current is found to be significantly larger than had been assumed previously. He also concludes that for 2 a> close to the threshold for electron emission, the self-consistently screened nonlinear electronic response becomes resonantly enhanced, analogous to local field enhancement in the linear response near the bulk plasma frequency. 

The complex quantity, y6br = e (y(3)r) + i Im (x r), represents the nuclear response of the molecules. The induced polarization is resonantly enhanced when the Raman shift wp — ws matches the frequency Qr of a Raman-active molecular vibration (Fig. 6.1A). Therefore, y(3)r provides the intrinsic vibrational contrast mechanism in CRS-based microscopies. The nonresonant term y6bnr represents the electronic response of both the one-photon and the two-photon electronic transitions [30]. Typically, near-infrared laser pulses are used to prevent the effect of two-photon electronic resonances. With input laser pulse frequencies away from electronic resonances, y(3)nr is independent of frequency and is a real quantity. It is important to realize that the nonresonant contribution to the total nonlinear polarization is simply a source for an unspecific background signal, which provides no chemical contrast in some of the CRS microscopies. While CARS detection can be significantly effected by the nonresonant contribution y6bnr [30], SRS detection is inherently insensitive to it [27, 29]. As will be discussed in detail in Sects. 6.3 and 6.4, this has major consequences for the image contrast mechanism of CARS and SRS microscopy, respectively. 

Positioner Application Positioners are widely used on pneumatic valve actuators. Often they provide improved process loop control because they reduce valve-related nonlinearity. Dynamically, positioners maintain their ability to improve control valve performance for sinusoidal input frequencies up to about one-hall of the positioner bandwidth. At input frequencies greater than this, the attenuation in the positioner amplifier network gets large, and valve nonlinearity begins to affect final control element performance more significantly. Because of this, the most successful use of the positioner occurs when the positioner response bandwidth is greater than twice that of the most dominant time lag in the process loop. 

Discrepancies between numerical values of the estimated damping coefficients is shown in Table I. The frequency domain approach invariably produced an indication of strong cross-coupling terms which was not confirmed either by the time-domain results or by direct observation of the damper ring response. The authors believe that the squeeze-film was probably over-excited during the frequency domain tests and consequently driven out of the linear regime. The presence of significant nonlinear stiffness effects in the squeeze-film could account for the discrepancies which have been observed. 

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