Electric field propagator

The dominant characteristic of the electrical and magnetic fields that comprise electromagnetic radiation is their periodically oscillating nature, a fact that enables us to describe them by the mathematics of waves. For light scattering, it is the electric field that is of interest. The oscillating nature of an electric field propagating in the positive direction is described by the equation... 

Combining (6.9)-(6.14), an internal transfer coefficient can be derived, reiat-ing the incident plane wave to the internal electric field propagating in the positive x direction in layer j at interface (j — 1 )j ... 

Time-Dependent Uniform Electric Field Propagator. 87... 

Its physical significance is that of an electric field propagator in the sense that it propagates an impressed potential field U 1) at space-time point 2 into the actual, effective field F(l) at space-time point 1 through the (linear) relation... 

Let us set the polarizable element at the origin of the reference system and let ° (z, f) be the incident electric field, propagating in OZ direction, with pulsation cu0. 

Depending on the orientation of the electric field propagation direction, e g. respecting the symmetry directions in the crystal belonging to the 42m point group, with the stereographic projection 19 of Table 2.8, - the crystal under concern, under electric field, will perceive one of the symmetries resulted in Figure 2.57, as based on the application of the relation (2.99). 

Vesicles interact also with electrical fields [54]. Experimentally, it is found that giant liposomes behave differently depending on the frequency of the applied electric field [55] as shown in Figure 13.6. This is due to a change of the water behavior with respect to the electric field frequency v. At frequency smaller than a critical threshold v<, water is a conductive material, whereas at higher fiequency it becomes a dielectric. At v < v., the electric problem is then equivalent to a dielectric thin shell in a conductive media, whereas the electric field propagates through a dielectric bilayer in another dielectric media (water) when v > V .. If is the conductivity of deionized water ( 5 x lO Sm" ) and water... 

The last attribute of tire electromagnetic field we need to discuss is wave polarization. The nature of tire transverse field is such tliat tire oscillating field disturbance (which is perjDendicular to tire propagation direction) has a particular orientation in space. The polarization of light is detennined by tire time evolution of tire direction of tire electric field... 

Plane-polarized electromagnetic radiation showing the electric field, the magnetic field, and the direction of propagation. 

In this discussion we define the x direction to be the direction of propagation of the light waves. This means that the yz plane contains the oscillating electrical and magnetic fields which carry the energy of the radiation. Only the electric field concerns us in scattering. Since the oscillation is periodic in both time t and location x, the electric field can be represented by the equation... 

Materials for Electrooptic Modulation. The fundamental phenomenon of Pockel s effect is a phase change, A( ), of a light beam in response to a low frequency electric field of voltage, V. Relevant relationships for coUinear electrical and optical field propagation are as foUows (1 6) ... 

The poles con espond to excitation energies, and the residues (numerator at the poles) to transition moments between the reference and excited states. In the limit where cj —> 0 (i.e. where the perturbation is time independent), the propagator is identical to the second-order perturbation formula for a constant electric field (eq. (10.57)), i.e. the ((r r))Q propagator determines the static polarizability. 

Choosing a non-zero value for uj corresponds to a time-dependent field with a frequency u, i.e. the ((r r)) propagator determines the frequency-dependent polarizability corresponding to an electric field described by the perturbation operator QW = r cos (cut). Propagator methods are therefore well suited for calculating dynamical properties, and by suitable choices for the P and Q operators, a whole variety of properties may be calculated. " ... 

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