Depolarised scattering

Thus the value of p depends on the degree of asymmetry in the tensor. For pure symmetric scattering, as in the normal Raman effect for instance, Opp = pp and Pi = 3/4 (depolarised scattering). For pure antisymmetric scatteringOpp = - pp and therefore G = 0, giving Pi = (inverse polarisation). For an asymmetric tensor lappi Iflppl and < Pi < ° , which is called anomalous polarisation. 

DLS instruments typically employ vertically polarised light (Lvl Xu 2000, p. 230). Depolarised scattered light (Lh) results from anisometry or multiple scattering—signals are usually very weak. 

For depolarised scattering, where E defines the z direction and we observe 1, the first term does not contribute and... 

In the usual experimental set up, the scattered radiation is collected in some small solid angle around an observation direction at 90° to that of the incident radiation. A schematic diagram of a typical laser Raman set-up involving 90° collection optics is shown in Fig. I, together with the definition of the depolarisation ratio... 

Fig. 1. Experimental set up (90° collection optics) for the measurement of laser Raman scattering, illustrating the definition of the depolarisation ratio. ly and Ij are the intensities of light scattered, respectively, parallel and perpendicular to the polarisation of the incident exciting beam...

Pi Ii/I for linearly polarised incident radiation. In this case, Eq. (1) must be multiplied by the factor (3/8 rr) (1 + pj)/(l + 2pi). (5a). If only the parallel component of scattered radiation is measured the factor is (3/8 tt) (1 + 2 px) . (I = Pi I ). For naturally polarised (unpolarised) or circularly polarised incident light the relevant factors are given in terms of the depolarisation ratio, p , for natural polarisation, where... 

An interesting consequence of the long lifetimes for discrete resonance is that the molecule may perform numerous rotations before re-emission. This causes depolarisation of the resonance-scattered radiation. For totally-symmetric vibrational modes in the normal Raman effect the scattering is polarised since the lifetime of the intermediate state is very short compared with a rotational period ( 10 s). 

In the normal vibrational Raman effect it has been traditionally assumed that the scattering tensor is symmetric ( p = ffap). However, even in 92 Placzek (5) considered the consequences of antisymmetric contributions, which he termed magnetic-dipole scattering because of the agreement between the selection rules for an antisymmetric Raman process and for a magnetic-dipole transition. Placzek gave the expected value of the depolarisation ratio, p i = Ij /I = > for purely antisymmetric scat-... 

So, in this case a y = Uy owing only to the difference in the energy denominators. The tensor is therefore asymmetric. In resonance with the 0-0 transition, scattering is dominated by the element tty and, for the 0-1 resonance, by the element a y. The behaviour of the depolarisation ratio in this case (anomalous polarisation) is discussed in Section 2.11.2. 

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... 

The symmetries of the modes active in coupling the two states are ig - 2g ig 2g> however, theAjg modes are known to be ineffective. The Bjg (but apparently not the 52g) modes are effective, and yield depolarised bands. The A2g modes are also effective but, owing to the fact (Section 2.9.2) that their scattering tensors are antisymmetric, the resulting bands are not observed off resonance they appear only on resonance and are then inversely polarised (pi =°°). 

Fig. 21. Resonance Raman spectra of oxyhaemoglobin (bottom pair of curves) and ferrocyto-chrome c (top pair). The scattering geometry is shown schematically in the diagram at the top. Both the direction and the polarisation vector of the incident laser radiation are perpendicular to the scattering direction. The scattered radiation is analysed into components perpendicular (Ij ) and parallel (I ) to the incident polarisation vector. The exciting wavelength was 568.2 nm for oxyhaemoglobin and 514.5 nm for cytochrome c. The slit width was about 10 cm". The concentrations were about 0.5 mM for each. The anomalously polarised, polarised and depolarised bands, are indicated by ip, p, and dp respectively. [From Spiro and Strekas, Ref. (42) ...

In the usual Raman experiment, the observations are made perpendicular to the direction of the incident beam, which is plane polarised. The depolarisation ratio is defined as the intensity ratio of the two polarised components of the scattered light which are parallel and perpendicular to the direction of the propagation of the (polarised) incident light. The polarisation of the incident beam is perpendicular to the plane of propagation and observation. For this geometry, the depolarisation ratio is defined as the intensity ratio ... 

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. 

One characteristic of the scattered light from hqttid crystals is that it is highly depolarised. That is, if linearly polarised light is incident on the sample, the scattered light has polarisation components perpendicular to the indderrt polarisation direction. The reason for this becomes obvious if we return to orrr discussion on arrisotropy in Chapter 2. If the amplitude of the electric field in the incident light has componerrts... 

With increasing sensitivity of detectors, the detection of unenhanced surface Raman scattering becomes a possibility, and if this is achieved a wide range of effects can be investigated. In particular the determination of adsorbate orientation from depolarisation ratios and the angular dependence of the Raman signal will be possible. Currently, such measurements only serve as a means of investigating the enhancement mechanism. 

Bartoli and Litovitz [6] found values of C of about 0.2% for some typical polarised (A) bands - by making measurements on the 459 cm" band of CCl which has a well-known [18] depolarisation ratio. Calculation of I ((1d) is then straightforward. Polarisation scrambling behind the main entrance slit ensures that the monochromator is equally sensitive to transmission of and lyy scattered light. There have been reports of local heating effects caused by a relatively high powered laser beam. However, we have never found this to be a problem although, of course, it is not possible to physically monitor the microscopic temperature. Stokes/Antistokes intensity ratios which measure the Boltzman population factors (and hence the microscopic temperature) have always corresponded well to the laboratory (bath) temperature even for input powers up to 2w. 

Fig.3 The intensity of the depolarised Kaiyleigh scattering from argon as a function of density at room temperature (ref 34). l/density is plotted the dashed line shows the 2-body intensity.

A26. Molecular Orientation in Liquid Diphenyl Ether as Probed by Depolarised Light Scattering. 

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