Sinusoidal electric fields, polarization

Figure 4.20 A sinusoidal electric field of angular frequency u> in a second-order nonlinear optical medium creates a polarization with component at 2tn( second-harmonic) and a steady (dc) component...

In impedance spectroscopy [IS also referred to as dielectric spectroscopy (DS)], a sinusoidal electric field is applied across a sample, and the resulting polarization (or electric displacement) is determined as a function of frequency. The frequency sweep typically ranges from about 1 MHz down to about 1 mHz, but measurement may be performed at higher frequencies by using special equipment. 

When a polymer is subject to an intense sinusoidal electric field such as that due to an intense laser pulse, Fourier analysis of the polarization response can be shown to contain not only terms in the original frequency co, but also terms in 2(0 and 3nonlinear response depends on the square of the intensity of the incident beam for 2co, and the third power for 3 . For the second-order effects, the system must have some asymmetry, as discussed previously. For poling, this means both high voltage and a chemical organization that will retain the resulting polarization for extended periods of time. Polymeric systems investigated have been of three basic types ... 

Figure Bl.5.2 Nonlinear dependence of tire polarization P on the electric field E. (a) For small sinusoidal input fields, P depends linearly on hence its hannonic content is mainly tiiat of E. (b) For a stronger driving electric field E, the polarization wavefomi becomes distorted, giving rise to new hannonic components. The second-hamionic and DC components are shown.

Method involves placing a specimen between parallel plate capacitors and applying a sinusoidal voltage (frequencies ranging from 1 mHz to 1 MHz) to one of the plates to establish an electric field in the specimen. In response to this field, a specimen becomes electrically polarized and can conduct a small charge from one plate to the other. Through measurement of the resultant current, the dielectric constant and dielectric loss constant for a specimen can be measured. The sharp increases in both the dielectric constant and the dielectric loss constant during a temperature scan are correlated with the occurrence of Tg... 

Consider a molecule placed in a sinusoidally varying electric field. For simplicity, we will assume that the field is linearly polarized. The Hamiltonian of the molecule is... 

This equation describes a sinusoidal response at frequency, co, to the electric field component at co. This is the basis for the linear optical response. To calculate the optical properties of the Lorenz oscillator the polarization of the medium is obtained as... 

The Lifshitz theory uses only the so-called "local" dielectric and magnetic responses. That is to say, the electric field at a place polarizes that place and that place only. What if the field is from a wave sinusoidally oscillating in space Then the material polarization must oscillate in space to follow the field. What if that oscillation in space is of such a short wavelength that the structure of the material cannot accommodate the spatial variation of the wave We are confronted with what is referred to as a "nonlocal" response a polarization at a particular place is constrained by polarizations and electric fields at other places. 

As already discussed earlier in this book, light consists of a sinusoidally changing electric field normal to, and in phase with, a sinusoidally changing magnetic field. It is the electric vector of the electromagnetic wave that affects matter and thus can be sensed and measured. The plane of the electric vector in normal light takes no particular orientation, but in plane polarized light the electric vector is... 

While in lumped-circuit methods the dielectric response is measured in the frequency domain, following the ajpplication of a sinusoidal alternating electrical field, for frequencies below 10 Hz it is advantageous to cany out the measurements in the time domain because it is less time consuming. The polarization or depolarization current following the application of a step-like electrical field is measured as a function of time. 

The elemental motile unit of an OHC strikingly resembles the flexoelectric domain structure whose calculated period 7rifn(ei ) also depends linearly on the inverse electric field (Fig. 6.9). Such a repetitive arc and pillar nano-architecture, containing sharp points at the confluence of any two adjacent arcs, is inherently polar and enhances the flexoelectric mechanism (e.g., a sinusoidal-shaped membrane will not enhance flexoelectricity while one of the half-waves is reduced the opposite one will be extended and vice versa). This arc motif is repeated a few thousand times along the... 

A great deal of information on the electrical properties of the interface can be obtained if the measurements are performed in alternating fields. In such a case, an effect of the frequency of the sinusoidal external field on the velocity of motion (the dielectrophoretic velocity) can be observed. The relaxations observed can be interpreted in terms of the different contributions to the polarization of the particle and its double layer. 

Fig. 3 illustrates the result of the polarization experiment for two molecules spectrally located in the Oi region around 592.32 nm. Plotted is the angle a between the 6 -axis of the crystal and the electric field vector of the linearly polarized excitation light, before entering the sample, against the fluorescence intensity. Both molecules show a sinusoidally modulated fluorescence intensity, but have different phases and amplitudes. 

Dielectric relaxation means the adjustment of dielectric displacement (D) or polarization ( ) to the time-dependent electrical field (E). Relative permittivity (e) characterizes the capacitance ratio of a condenser filled with an insulating material and with vacuum. If the field is sinusoidal, the permittivity becomes a complex number ... 

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