Plane polarized modes

Unfortunately, Maxwell s equations can be solved analytically for only a few simple canonical resonator structures, such as spheres (Stratton, 1997) and infinitely long cylinders of circular cross-sections (Jones, 1964). For arbitrary-shape microresonators, numerical solution is required, even in the 2-D formulation. Most 2-D methods and algorithms for the simulation of microresonator properties rely on the Effective Index (El) method to account for the planar microresonator finite thickness (Chin, 1994). The El method enables reducing the original 3-D problem to a pair of 2-D problems for transverse-electric and transverse-magnetic polarized modes and perform numerical calculations in the plane of the resonator. Here, the effective... 

Fig. 11.4. Velocities of bulk and surface waves in an (001) plane the angle of propagation in the plane is relative to a [100] direction, (a) Zirconia, anisotropy factor Aan = 0.36 (b) gallium arsenide, anisotropy factor Aan = 1.83 material constants taken from Table 11.3. Bulk polarizations L, longitudinal SV, shear vertical, polarized normal to the (001) plane SH, shear horizontal, polarized in the (001) plane. Surface modes R, Rayleigh, slower than any bulk wave in that propagation direction PS, pseudo-surface wave, faster than one polarization of bulk shear wave propagating in...

However, in the normal mode Qx, each nucleus has the same angle of rotation about the molecular axis t = [Pg.141]

Schippers and Dekkers reported on the CD and circularly polarized fluorescence of 4,4-dideuterio-adamantan-2-one (85)193. The CD of 85 originates in transitions to a totally symmetric n -+ n excited state with double minimum potential in the C=0 out-of-plane bending mode. 

If the incident radiation is plane-polarized, such as that produced by lasers in Raman spectroscopy, scattering theory predicts that totally symmetric modes... 

There are materials, for example in the form of certain specially prepared polymer films, which, for light incident normal to the film, absorb to an extent dependent on the inclination of the plane of polarization to a unique axis in the plane of the film. Devices made from such films are termed polarizers approximately 60% of the incident unpolarized light is absorbed, and that part transmitted is plane polarized. The E vectors for the transmitted light are perpendicular to the high-absorbance direction. If the incident light is plane polarized, the intensity transmitted depends on the orientation of the polarizer axis with respect to the plane of polarization of the light. A device used in this mode is usually referred to as an analyser . 

A frequently discussed phenomenon of IR vibrational spectroscopy is the electron - molecular vibration coupling of totally symmetric in-plane molecular modes. As a consequence of coupling to the free carriers, these modes become visible in the IR absorption if the light is polarized parallel to the stacking direction. This effect was first observed in TEA(TCNQ)z (triethylammonium (TCNQ)2), as shown in Fig. 4.8-17a, b. 

Raman spectra as a function of temperature are shown in Fig. 21.6b for the C2B4S2 SL. Other superlattices exhibit similar temperature evolution of Raman spectra. These data were used to determine Tc using the same approach as described in the previous section, based on the fact that cubic centrosymmetric perovskite-type crystals have no first-order Raman active modes in the paraelectric phase. The temperature evolution of Raman spectra has indicated that all SLs remain in the tetragonal ferroelectric phase with out-of-plane polarization in the entire temperature range below T. The Tc determination is illustrated in Fig. 21.7 for three of the SLs studied SIBICI, S2B4C2, and S1B3C1. Again, the normalized intensities of the TO2 and TO4 phonon peaks (marked by arrows in Fig. 21.6b) were used. In the three-component SLs studied, a structural asymmetry is introduced by the presence of the three different layers, BaTiOs, SrTiOs, and CaTiOs, in each period. Therefore, the phonon peaks should not disappear from the spectra completely upon transition to the paraelectric phase at T. Raman intensity should rather drop to some small but non-zero value. However, this inversion symmetry breakdown appears to have a small effect in terms of atomic displacement patterns associated with phonons, and this residual above-Tc Raman intensity appears too small to be detected. Therefore, the observed temperature evolution of Raman intensities shows a behavior similar to that of symmetric two-component superlattices. 

The plane-polarized light pulses characteristic of mode-locked lasers also provide an ideal excitation source for time-dependent fluorescence depolarization studies although conventional excitation sources can be used. If the rotational relaxation time of the excited molecule is comparable to its fluorescence decay time, then the vertical (I ) and horizontal (Ix) components of the fluorescence decay observed through suitable polarizers following excitation by polarized li t pulses, may be analysed to provide information concerning the size and motion of die molecule and Sect. 5. However, if only the true fluorescence decay characteristics are of interest it is necessary to compensate for these emission anisotropy effects Perhaps the simplest technique is to analyse only that component of fluorescence emitted at 54.7° to the direction of pdarization of the excitation source, the so-called magic-angle ... 

Figure 8.21. Schematic illustration of hierarchical structures involved in photogenerated SRG of a block copolymer after Irradiation with (p- p-) and (s- s-) mode Interference laser beam. Note that the In-plane direction of the cylinder is clearly controlled by the polarization mode. The out-of-plane change is because of the thickness variation. See color insert.

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... 

Furthermore, polarization dependences of the SRRS intensity observed for the single platelet crystal of TPCOs [7] have predicted the existence of a cooperative interaction due to phonon-coupled molecular vibrations. In the case of the TPCOs with the C2v symmetry, two SRRS emission lines from the symmetric and asymmetric in-plane stretching modes were observed. The former emission was polarized parallel to the crystal face whereas the latter was perpendicular. This polarization difference is not consistent with the molecular symmetry of the Raman-active modes in the single crystal. Therefore, we assume coherent phonons built up from the Raman-active molecular vibrations to explain the observed SRRS polarizations. 

FIGURE 8 Linear dichroism FTIR spectra of a self-supporting clay film of DNOC sorbed to K-SWy-2 montmorillonite. The clay film was tilted at an angle of 45° about its vertical axis with respect to the incident IR beam in the sample compartment. The spectrum represented by the dashed line was obtained with an IR polarizer along the vertical axis. The solid line spectrum was obtained with the IR polarizer at 90° (along the horizontal axis). In this configuration (sohd hne), the intensities of the out-of-plane vibrational modes will have maximum intensity. (From Ref. 82.)... 

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