Transmitted vector plane wave

In terms of the x-component of the local wave vector of Eq. (35-27) and the WKB solutions of Eq. (35-29), the solutions of the scalar wave equation for the incident, reflected and transmitted local plane waves, respectively, are expressible as... 

For the incident vector plane wave given by (2.193), the transmitted (or the refracted) vector plane wave is... 

Figure 4.4.18. General set-up of a scattering experiment ki, k, - wave vectors of the incident and the scattered plane waves, q - scattering (or wave) vector, D- detector, S - sample, 0 - scattering angle from the transmitted beam, h - incident intensity of unpolaiized light, r - the distance between sample and detector.

For normal incidence, we have that 0, = 0 = 0 = 0. In this case the parallel or perpendicular orientations coincide and the plane-wave transmitted in the second medium is uniform. Considering the power (i.e. from the Po3mting vector) instead of the amplitude coefficients, we obtain the reflectance (R) and the transmittance (T)... 

The vectorial nature of the electromagnetic fields representing light implies polarization, a fundamental property of light. The particular orientation of the e-vector of a plane wave incident on an interface has a profound effect on the detailed interaction that takes place and influences, for example, the amount of light that is reflected or transmitted. If the electric field vector is confined to oscillate in a plane (e.g. the X- z plane in Figure 1), the wave is said to be linearly polarized. If the tip of the electric field vector traverses an elliptical path around the direction of... 

It is instructive to pursue the interpretation of the calcite rhomb experiment beyond the simple Huyghenian construction to learn something about the polarization of the transmitted light. The electromagnetic theory of light requires that the electric vector shall be contained in the plane of the wave front. The ordinary disturbances vibrate perpendicular to a principal section. Also the extraordinary disturbance must vibrate in the principal section plane. 

Figure 2.4. The effect on the transmitted plane by refraction of circularly polarized light beams relative to the incident plane of polarized light (dashed line), (a) When = n, the vector sum (solid arrows) of the two circularly polarized beams (dashed arrows) remains in the same plane as the incident beam, (b) When n , the vector sum of the two waves is rotated a° away from the plane of the incident light.

First, consider the interference of the reflected and the refracted (or transmitted) waves. We treat only the case <(>=0 and the electrical vector perpendicular to the plane of incidence. In the diagram of Fig. 4.1, 1 and 3... 

We also mention the following interesting effect, which curs, e.g., in planar-homeotropic (hybrid) oriented LC s and is not directly related to nonlinear optical effects, ccording to (10), in the adiabatic approximation with 0, the polarization vector of the light wave transmitted f the cell will be rotated by 90 relative to the incident wave Dlarization. A wave with polarization e = incident in le ZvF plane will be an ordinary wave (o-wave) if it is inci- nt from the homeotropic wall (z = 0) and an e-wave if it is cident from the planar wall (z = ). 

Aiming to analyze the direction of this vector in relation with the dispersion described by the Eq. (5.196), a tangential plane to DS is considered, so that the modified wave vector of transmitted direction... 

If a polarizer which rotates the polarisation plane of the incident wave is placed between two crossed linear polarizers (Fig. 2.13) the electric vector of the input beam will be turned and the crossed polarizer transmits only a fraction of the input intensity which depends on the turning angle 9 of the rotating polarizer. The Jones formahsm yields the output electric vector as... 

Some crystals polarize radiation electromagnetic waves transmitted through the crystal have electric field vectors that aU he in the same plane. What property of these crystals permits this ... 

The second solution is the use of Fabry-Perot cavities, where the laser spots from aU reflections coincide. A Fabry-Perot cavity consists of two plane mirrors at distance L. The power transmitted by the cavity is maximum at the resonance, when kL = nit, where is the wave vector. In this case, the power trapping in the cavity replaces the many round-trips of the laser beam. The phase of the light leaving from the cavity depends on the cavity length. If the cavity is working at resonance, the passage of a gravitational wave produces a phase shift near the resonance. The resonance characteristics of the Fabry-Perot cavity are described by the finesse F, which is related to the reflectivities ri, ri of the mirrors ... 

Assume a stack of layers, as shown in Fig. 5.6.1. In each layer there exists a downward and an upward propagating field, indicated by the arrows A and R, respectively. The amplitude, phase, polarization, and direction of the arriving wave in the top layer, m, is assumed to be known as well as the material properties, jurci and r + i i, of the substances forming the stack of plane parallel layers. We are interested in the amplitudes and phases of the reflected, Rm, and transmitted wave, Aq. In the lowest medium, 0, only a transmitted wave is postulated. All waves are assumed to be plane with the Poynting vectors in the x-y plane, that is, = 0. To apply the boundary conditions to each interface the downward and the upward waves need to be calculated for each layer (y = 1,2,..., m). For layer j they are, respectively,... 

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