Coherency vector incident field

As mentioned above, the XSW field arises from the interference between the coherently related incident and Bragg-diffracted beams from the surface of a perfect crystal. In the vicinity of a Bragg reflection (Fig. 24A-B), an incident plane wave (with wave vector fco) and a reflected wave (with wave vector kfi) interfere to generate a standing wave with a periodicity equivalent to that of the (h, k, 1) diffracting planes. The ratio of the electric field amplitudes of the reflected and incident waves is given by... 

The polarization characteristics of the incident field can also be described by the coherency and Stokes vectors. Although the ellipsometric parameters completely specify the polarization state of a monochromatic wave, they are difEcult to measure directly (with the exception of the intensity Eq). In contrast, the Stokes parameters are measurable quantities and are of greater usefulness in scattering problems. The coherency vector is defined as... 

As mentioned before, a scattering particle can change the state of polarization of the incident beam after it passes the particle. This phenomenon is called dichroism and is a consequence of the different values of attenuation rates for different polarization components of the incident light. A complete description of the extinction process requires the introduction of the so-called extinction matrix. In order to derive the expression of the extinction matrix we consider the case of the forward-scattering direction, = 6fc, and define the coherency vector of the total field E = Eg + E. by... 

If we specifically consider the mixing of two single-mode, amplitude-stabilized, first-order coherent waves, both of which are well collimated, parallel, plane polarized along a common unit vector, and normally incident onto a photosensitive material, we may write the positive portion of the electric field operator as the superposition of two scalar fields... 

We consider interference of mutually coherent polarized light in uniaxial anisotropic media. As illustrated in Fig. 1, the xz -plane is the incident plane and the z -axis is taken normal to the film plane. Assuming that the two recording beams are plane waves and that the amplitude of their incident angles is small, the electric field of interference light is described using the Jones vector as... 

A = amplitude, d = thickness of crystalline material, D = degeneracy factors, E, Ej, = energy levels. Eg = cohesive electric field intensity, E = laser field amplitude, /j = intensity of the fundamental, = vector sum of the wave vectors, = coherence length, L = interaction length, P = polarization induced by an incident electric field, T = carrier period, = group velocity, a = linear absorption coefficient, = dipolar susceptibility of order ,A = grating period, ft) =fre-quency, tOj = scattered wave frequency, h = Planck s constant/2jt. 

Two major experimental techniques exist to probe the molecular first hyperpolarizability of solutions the EFISHG [41, 42] and the HRS [43]. The EFISHG technique consists in measuring the coherent light intensity at a frequency equal to twice the fundamental frequency of an incident laser pulse, generated by a solution submitted to a static electric field. This method is applicable only to polar and neutral molecules, and gives information on the projection of the vector part of on the dipole moment vector, so that only a combination of tensorial components of P can be obtained ... 

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