Propagation field

Simons J 1972 Energy-shift theory of low-lying excited electronic states of molecules J. Chem. Phys. 57 3787-92 A more recent overview of much of the EOM, Greens function, and propagator field is given in ... 

Starting from Maxwell s equations with the ansatz of monochromatic, z-propagating fields, E, H Qx i k- co t)), transversal and longitudinal components get decoupled if the refractive index distribution is z-independent. Two physically equivalently meaningful equations for the transversal electric and the transversal magnetic field. 

The Bii] component [which is nonzero only on the 0(3) level] is a solution of the Beltrami equation (885) with k = 0. Therefore, in Beltrami electrodynamics, Bii] is a solenoidal, irrotational, complex lamellar and Beltrami field in the vacuum, and is also a propagating field. The B 1 component in Beltrami... 

This is an exact system of equations that describes the evolution of modal amplitudes along the z-axis for the forward propagating field. A similar equation holds for the backward propagating component, of course. 

In other words, to obtain a closed system to solve numerically, we must require that the nonlinear polarization is well approximated by the nonlinear polarization calculated only from the forward propagating field. This means that the equation is only applicable when the back-reflected portion of the field is so small that its contribution to the nonlinearity can be neglected. 

The complete description of the individual components of the propagating field amplitudes with their appropriate projection onto the interface of the two media is given by the Fresnel equations. 

We will show below in this chapter that the back-propagated field corresponds to a migration transformation of seismic data. Thus we see that Born imaging can be treated as an algorithm from a family of migration transformations. 

Therefore, the auxiliary field (r,f ) is the back-propagated field, and the adjoint Kirchhoff operator K for a residual field can be calculated by back propagation of the residual field. We will show in the next sections that this procedure is similar to Stolt s Fourier-based migration transformation. Thus, this result demonstrates that migration is similar to applying an adjoint Kirchhoff operator to observed scattered wavefield data. 

Therefore, the scattered field (r,f ) is the back-propagated field. We can also write the result of an application of the adjoint Frechet operator to the scattered field as the correlation of this back-propagated scattered field and the incident field U (r, t) acted on by the relevant differeirtial operators ... 

These practical aspects are governed by the interaction of electromagnetic radiation with matter at the molecular level this interaction polarizes the charge distribution and alters the propagated field. The linear response is described by the polarizability (a) and the non-linear response (the subject of this article) is described by the hyperpolarizabilities (P, y, etc.). The word hyperpolarizability was first used by Coulson, Macoll and Sutton [1] some 40 years ago. 

Furthermore, we recall that the propagating field E R) for a single array is given by [63]... 

FIGURE 13 Amplitudes of the propagating fields in an integrated optic S-bend waveguide. 

Similarly, the average energy allocated in diffraction through the quantum dynamic transfer is obtained for the propagated fields associated with the beta branch of DS in the dispersive medium (Biagini, 1990 Birau Putz, 2000) ... 

When the propagation constant p is positive, the fields of the waveguide propagate in the positive z-direction in Fig. 11-1 (a). Under the transformation p- —p, the backward-propagating fields are simply related to the forward-propagating fields. If we denote forward and backward by -I- and — superscripts, then we deduce from Eq, (30-5) that there are two possibilities. Either... 

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