Quasi-static electric field

Before going into details of optical reorientation we survey the effects caused by static electric fields in nematic layers. (More precisely we consider quasi-static electric fields for which the complications arising from space-charges and fiexo-electricity can be neglected.) The interaction between the field and the nematic can be described by including an interaction term in the free-energy density of the liquid crystal. In the electric-dipole approximation this term is... 

The aim of this paragraph is to recall the basic principles of electrostatics and their application to electrolytes and interfaces. After presenting the quasi static electric fields, we discuss some dielectric properties. We emphasize then the Poisson-Boltzmann equation and its solutions for different symmetries, giving the Gouy-Chapman, the Debye-Hiickel and the Lifson-Katchalsky approximations. 

The Pittsburgh experiments differ from the Stony Brook experiments by the presence of a small static electric field which produces and stabilizes the extremal quasi-one-dimensional Stark states used in the Pittsburgh apparatus. The quasi-one-dimensional character of the Rydberg states used in the Pittsburgh experiments malces a direct comparision with inexpensive one-dimensional calculations possible. 

When a metallic particle is small compared with the illuminating wavelength, the variation of the electric field can be ignored, and the scattering behaviors can be described under the quasi-static approximation. Consider a smaller metallic sphere with radius a and a A placed in a uniform static electric field E — EqZ. The field potentials inside and outside the sphere, < ). and, are written by... 

Magnetic field-flow fractionation (FFF) employs static or quasi-static magnetic fields and excludes electromagnetic fields. Electromagnetic fields having frequencies in the kilohertz to megahertz range are used in dielectrophoretic FFF. Static electric fields are used in electrical FFF (see the entry Field-Flow Fractionation Fundamentals). 

There are several methods for solving either numerically or analytically for the electric field and static or quasi-static electric current. We solve Poisson s equation inside and outside of the electrodes under the constraint that the potential on the surface of the electrodes is constant. This is a type of boundary-value problem. The application of anal3dical methods is limited to the case when the arrangement of the electrodes is simple. Instead, we use a numerical solution method which is applicable to multiple electrodes. 

The theoretical approach is based on the solution to the mixed type linear/nonlinear generalized Schrodinger equation for spatiotemporal envelope of electrical field with account of transverse spatial derivatives and the transverse profile of refractive index. In the quasi-static approximation, this equation is reduced to the linear/nonlinear Schrodinger equation for spatiotemporal pulse envelope with temporal coordinate given as a parameter. Then the excitation problem can be formulated for a set of stationary light beams with initial amplitude distribution corresponding to temporal envelope of the initial pulse. 

The difference between the quasi-static coupling for ammonia in the solid state — 3.47 MHz - and that measured in the gas by microwave spectroscopy — 4.08 MHz — cannot be explained by the contribution of the crystalline electric field gradient alone, but must be attributed to a redistribution of the bonding electrons in the molecule under the influence of the crystalline electric field or of the intermolecular hydrogen bonds. 

Metal nanostructures (such as particles and apertures) can permit local resonances in the optical properties. These local resonances are referred to as localized surface plasmons (LSPs). The simplest version of the LSP resonance comes for a spherical nanoparticle, where the electromagnetic phase-retardation can be neglected in the quasi-static approximation, so that the electric field inside the particle is uniform and given by the usual electrostatic solution [3] ... 

We will restrict ourselves with consideration of small-amplitude waves and, therefore, use only the second-order moduli. Besides, we will discuss the phenomena in the zero electric and magnetic fields. It makes it possible to omit the superscripts and subscripts DB. In this case and will represent adiabatic and isothermal moduli, respectively. The first one does characterize very fast processes, while the second is a quasi-static modulus. Regardless of the definite form of the moduli (isothermal, adiabatic or another one) the equation of motion (1) at fi = 0 may be written in the form... 

When the plasma is not in local thermal equilibrium (LTE), the electron number densities cannot be determined on the basis of the Saha equation. Irrespective of the plasma being in local thermal equilibrium or not, the electron number density can be derived directly from the Stark broadening of the Hg line or of a suitable argon line. This contribution to broadening is a result of the electrical field of the quasi-static ions on one side and the mobile electrons on the other side. As described in Ref. [17] it can be written as ... 

Following the method of Stroud aird Hui [81], Stroud and Wood [82], and later Ma et al. [83], have derived from Maxwell s equations the general expression of the effective in the quasi-static approximation. For this, they have considered that the magnimde of the nonlinear coefficients remains sufficiently small to neglect the nonlinearity in the electric field evaluation, x // then writes... 

The electric field inside the sample is usually evaluated from the quasi-static approximation... 

The velocity of propagation of the electrical field is much higher than the one occurring in the chemo-electrical field, (19). Hence, the quasi-static form of the Poisson equation is adequate. Equation (20) results from the second and fourth Maxwell equations ... 

Interaction of Static and Time-dependent Electric Fields with Quasi ID Polymers... 

Now, by virtue of the quasi-static conditions, the electric field may be derived from a scalar potential d)... 

Electroconvection in nematics is certainly a prominent paradigm for nonequilibrium pattern-forming instabilities in anisotropic systems. As mentioned in the introduction, the viscous torques induced by a flow field are decisive. The flow field is caused by an induced charge density p i when the director varies in space. The electric properties of nematics with their quite low electric conductivity 10 (fl m) ] are well described within the electric quasi-static approximation, i.e. by charge conservation and Pois-... 

When the film thickness is small compared to the wavelength of light, the maaoscopic electric field can be assumed to be constant across the film, and the solution can be found in the quasi-static regime [24, 25]. Formally, the quasistatic regime is reached by setting the velocity of light to be infinite (c -> oo). As a result, instead of the Maxwell equations, the electrostatic laws... 

In the quasi-static approximation, the electric field inside a nanoparticle is changed compared with the field outside by a local-field factor /, given by... 

Combination with Static Fieids. A common technique, useful for optoelectronic devices, is to combine a monochromatic optical field with a DC or quasistatic field. This combination can lead to refractive index and absorption changes (linear or quadratic electrooptic effects and electroabsorption), or to electric-field induced second-harmonic generation (EFISH or DC-SHG, 2 > = > - - third-order process. In EFISH, the DC field orients the molecular dipole moments to enable or enhance the second-harmonic response of the material to the applied laser frequency. The combination of a DC field component with a single optical field is referred to as the linear electrooptic (Pockels) effect co = co + 0), or the quadratic electrooptic (Kerr) effect ( > = > - - 0 -I- 0). These electrooptic effects are discussed extensively in the article Electrooptical Applications (qv). EFISH is... 

Quasi-static direct methods are both versatile and well suited to investigating fully the piezoelectric response of polymers. Direct methods of this type are especially appropriate for amorphous polymers. TSC measurements (68) are used to measure the remanent polarization imparted to a polymer, and direct strain or charge measurements are used to investigate the piezoelectric coefficients with respect to the electric field, frequency, and stress. 

---