Response harmonic

The optical properties of liquid crystals determine their response to high frequency electromagnetic radiation, and encompass the properties of reflection, refraction, optical absorption, optical activity, nonlinear response (harmonic generation), optical waveguiding, and light scattering [1], Most applications of thermotropic liquid crystals rely on their optical properties and how they respond to changes of the electric field, temperature or pressure. The optical properties can be described in terms of refractive indices, and anisotropic materials have up to three independent principal refractive indices defined by a refractive index ellipsoid. 

SHG Optical second-harmonic generation [95, 96] A high-powered pulsed laser generates frequency-doubled response due to the asymmetry of the interface Adsorption and surface coverage rapid surface changes... 

Keller G 1986 Random-phase-approximation study of the response function describing optical second-harmonic generation from a metal selvedge Rhys. Rev. B 33 990-1009... 

While cost will probably decrease with increased usage, this is a factor to be evaluated before a decision to use the variable frequency is made. Because of the harmonics, the output torque contains some unsteady torsional components. These can be handled by evaluating the compressor train torsional response. This will be further covered in a later chapter. 

Unlike linear optical effects such as absorption, reflection, and scattering, second order non-linear optical effects are inherently specific for surfaces and interfaces. These effects, namely second harmonic generation (SHG) and sum frequency generation (SFG), are dipole-forbidden in the bulk of centrosymmetric media. In the investigation of isotropic phases such as liquids, gases, and amorphous solids, in particular, signals arise exclusively from the surface or interface region, where the symmetry is disrupted. Non-linear optics are applicable in-situ without the need for a vacuum, and the time response is rapid. 

Fig. 6.2 Harmonic response diagram. Substituting equation (6.6) into (6.3)...

For a given value of lu, equation (6.9) represents a point in complex space P(lu). When LU is varied from zero to infinity, a locus will be generated in the complex space. This locus, shown in Figure 6.2, is in effect a polar plot, and is sometimes called a harmonic response diagram. An important feature of such a diagram is that its shape is uniquely related to the dynamic characteristics of the system. 

Hence equation (6.14) can be plotted in the complex space (Argand Diagram) to produce a harmonic response diagram as shown in Figure 6.3. 

The TEOM sampler draws air through a hollow tapered tube, the wide end of the tube being fixed, while the narrow end oscillates in response to an applied electric field. The narrow end of the tube contains the filter cartridge. The sampled air flows from the sampling inlet, through the filter and tube, to a flow controller. The tube-filter unit acts as a simple harmonic oscillator with ... 

We now want to study the consequences of such a model with respect to the optical properties of a composite medium. For such a purpose, we will consider the phenomenological Lorentz-Drude model, based on the classical dispersion theory, in order to describe qualitatively the various components [20]. Therefore, a Drude term defined by the plasma frequency and scattering rate, will describe the optical response of the bulk metal or will define the intrinsic metallic properties (i.e., Zm((a) in Eq.(6)) of the small particles, while a harmonic Lorentz oscillator, defined by the resonance frequency, the damping and the mode strength parameters, will describe the insulating host (i.e., /((0) in Eq.(6)). 

Harmonic Analysis of Random Processes.—The response Y(t) of a linear, time-invariant electrical filter to an input X(t) can be expressed in the familiar form 66... 

Friedly (F4) expanded the theoretical analysis of Hart and McClure and included second-order perturbation terms. His analysis shows that the linear response of the combustion zone (i.e., the acoustic admittance) is not sign-ficantly altered by the incorporation of second-order perturbation terms. However, the second-order perturbation terms predict changes in the propellant burning rate (i.e., transition from the linear to nonlinear behavior) consistent with experimental observation. The analysis including second-order terms also shows that second-harmonic frequency oscillations of the combustion chamber can become important. 

At sufficiently low strain, most polymer materials exhibit a linear viscoelastic response and, once the appropriate strain amplitude has been determined through a preliminary strain sweep test, valid frequency sweep tests can be performed. Filled mbber compounds however hardly exhibit a linear viscoelastic response when submitted to harmonic strains and the current practice consists in testing such materials at the lowest permitted strain for satisfactory reproducibility an approach that obviously provides apparent material properties, at best. From a fundamental point of view, for instance in terms of material sciences, such measurements have a limited meaning because theoretical relationships that relate material structure to properties have so far been established only in the linear viscoelastic domain. Nevertheless, experience proves that apparent test results can be well reproducible and related to a number of other viscoelastic effects, including certain processing phenomena. 

FT is essentially a mathematical treatment of harmonic signals that resolved the information gathered in the time domain into a representation of the measured material property in the frequency domain, as a spectrum of harmonic components. If the response of the material was strictly linear, then the torque signal would be a simple sinusoid and the torque spectrum reduced to a single peak at the applied frequency, for instance 1 Hz, in the case of the experiments displayed in the figure. A nonlinear response is thus characterized by a number of additional peaks at odd multiples of the... 

The overall sound pressure level reaches 91 dB. The pressure spectrum in Figure 5.2.8b is quite similar to that associated with the flame-plate interaction in Figure 5.2.8a. The presence of harmonics of the fundamental frequency indicates that the pressure signal is also periodic with an oscillation frequency corresponding to the flame oscillation frequency, but that the flame response is nonlinear with a rich harmonic content. These energetic harmonics indicate that the... 

T. Lieuwen. Nonlinear kinematic response of premixed flames to harmonic velocity disturbances. Proc. Combust. Inst., 30 1725-1732, 2005. 

Visco-elastic fluids like pectin gels, behave like elastic solids and viscous liquids, and can only be clearly characterized by means of an oscillation test. In these tests the substance of interest is subjected to a harmonically oscillating shear deformation. This deformation y is given by a sine function, [ y = Yo sin ( t) ] by yo the deformation amplitude, and the angular velocity. The response of the system is an oscillating shear stress x with the same angular velocity . 

The polarizability expresses the capacity of a system to be deformed under the action of electric field it is the first-order response. The hyperpolarizabilities govern the non linear processes which appear with the strong fields. These properties of materials perturb the propagation of the light crossing them thus some new phenomenons (like second harmonic and sum frequency generation) appear, which present a growing interest in instrumentation with the lasers development. The necessity of prediction of these observables requires our attention. 

Because the second harmonic response is sensitive to the polarizability of the interface, it is sensitive to the adsorption and desorption of surface species and is capable of quantifying surface species concentrations. Furthermore, SHG can be used to quantify surface order and determine surface symmetry by measuring the anisotropic polarization dependence of the second harmonic response. SHG can also be used to determine important molecular-level and electrochemical quantities such as molecular orientation and surface charge density. 

Raman excitation. and I2s are the high-frequency and low-frequency components of the pump light pulse. A probe pulse of frequency 12 interacts with the coherence to present the optical response of the fundamental frequency 12 + C0fsl2. (c) Fourth-order coherent Raman scattering, the optical response of the second harmonic frequency 212 + co 2I2 is modulated by the vibrational coherence. 

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