Polarisability symmetry dependence

Consequently, the Raman scattered light emanating from even a random sample is polarised to a greater or lesser extent. For randomly oriented systems, the polarisation properties are determined by the two tensor invariants of the polarisation tensor, i.e., the trace and the anisotropy. The depolarisation ratio is always less than or equal to 3/4. For a specific scattering geometry, this polarisation is dependent upon the symmetry of the molecular vibration giving rise to the line. 

Figure 3 Polarisation dependence of the n resonance intensity at the 0 1s edge for Ni 100 (/2x/2)R45°-C0. Degree of photoionisation, P, of the incident radiation is taken to be 0.85 for the calculated curve. 6 is the angle of tilt of the C-0 axis relative to the surface normal. The analysis assumes no reduction in symmetry from Ca>v.

The pump induced transient polarisation of the medium modifies the polarisation state of a time delayed probe pulse. Phenomenologically, this process can be regarded as a transient pump induced linear or circular birefringence, also called the Specular Optical Kerr Effect (SOKE) and the Specular Inverse Faraday Effect (SIFE) [18], These are cubic non-linear effects and are predicted to exist from symmetry arguments. Both effects consist of coherent and incoherent parts. For the coherent part, the pump drives the coherent electron-hole pair that affects the probe polarisation. The effect depends upon the probe phase relative to that of the electron-hole pair, and hence, that of the pump. For the incoherent part of the SIFE and the SOKE, the relative pump-probe phase is not important, since the probe pulse polarisation is modified by the pump induced sample polarisation that survives after the decoherence of the electron-hole pair. 

One of the most basic properties of the optical gain in nitride-based structures is its polarisation dependence. In contrast to other bulk III-V materials, where the optical gain is isotropic, nitride structures exhibit almost exclusively TE-mode gain [14]. This is due to the symmetry-induced splitting of the valence bands in the wurtzite structure. 

The usefulness of Frohhch s formula (2.53) is mainly restricted by our ignorance of the correlation factor g, which necessarily depends on the shapes of molecules and the disposition of the permanent dipoles within them, the anisotropy of pOlarisability and the presence of charge distributions of higher orders of symmetry. The theory gives us a good general understanding of the behaviour of polar materials, but deviations from the simple Debye equation (2.44) can often only be discussed in qualitative terms. 

The above description of the excited states in terms of excitation amplitudes is frame and basis set dependent. A more convenient description is in terms of state multipoles. It can be generalised to excited states of different orbital angular momentum and provides more physical insight into the dynamics of the excitation process and the subsequent nature of the excited ensemble. The angular distribution and polarisation of the emitted photons are closely related to the multipole parameters (Blum, 1981). The representation in terms of state multipoles exploits the inherent symmetry of the excited state, leads to simple transformations under coordinate rotations, and allows for easy separation of the dynamical and geometric factors associated with the radiation decay. 

The definition of the depolarisation ratio, pi, is illustrated in Fig. 1 for linearly-polarised incident radiation and a 90° scattering geometry. In the normal Raman effect it is well known that the measurement of p may identify the symmetry of the vibrational mode responsible for a given Raman band pi < 3/4 (pi = 0 in cubic or higher symmetries) for totally symmetric modes and Pi= 3/4 for non-totally symmetric modes. In the resonance Raman effect, the value of P, and its dependence on the exciting frequency, may be more informative. This is because the symmetries of... 

For an elastic wave in a medium that is both isotropic and continuous the acoustic phonons have three different wave-polarisations, one longitudinal, with the atomic displacements in the direction of the wave propagation and two with transverse polarisation, the atomic displacements perpendicular to the propagation vector. In a crystal, the transverse modes are not necessarily degenerate except in specific symmetry directions and, because the atoms are located in discrete positions, the velocity of propagation will depend on its direction. 

Another useful method, especially when only a single wavelength is available, is the different dependence of Y and surface electric field on the polarisation and angle of incidence.72 From the Fresnel equations and the known optical constants of metals the electric field experienced by the adsorbate and the absorbance of the substrate can be calculated. 72.73 por substrate excitation Y should follow (1-R). For adsorbate excitation some knowledge (or model) of the symmetry of the adsorbate layer (orientation of transition dipole) is required to relate the electric field to the excitation probability. The angle of incidence dependence of Y for different input polarisations have been calculated for some typical cases.72.74 Cavanagh s group have... 

According to the SERS selection rules, the spectral profile of the adsorbate is strongly dependent on the orientation of the main molecular axes with respect to the surface . Thus, SERS intensities would also provide valuable information about the molecular orientation that the adsorbate adopts once adsorbed on the metal surface. For this reason, symmetry assignments are central to the discussion of molecular orientation of adsorbed species on the surface of island or colloidal metal particles. If the molecules, i.e. N4 macrocycles, are oriented face-on the metal surface, with the N atoms face to the metal atoms, the C4 axis of the molecule and the normal to the surface are parallel thus, the most symmetric vibrational modes, that derive their intensity from the zz-component of the polarisability derivative tensor a z will be the most intense at the surface plasmon resonance frequency and to the red of that frequency. 

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