Circular intensity sum

The measurement of optical activity in Raman spectra is most often done by measuring the circular intensity difference (CID) and the circular intensity sum (CIS). Using this technique the linearly polarized la.ser beam used for excitation is modulated with a KD P electrooptical modulator resulting in an excitating beam which changes its state of polarization from left to right circularly polarized at a frequency of about 1/3 Hz. The Raman intensities are then collected separately and the dimensionless Raman CID calculated using ... 

Fig. 6. The depolarized Raman circular intensity sum (I + I ) and difference (Ij — Ij) spectra of (—) menthol in methanol solution...

Fig. 8. The depolarized Raman circular intensity sum and difference spectra of neat (R)—( + ) 3-methylcyclohexanone... 

FIGURE 15. Raman circular intensity spectra for (R)-a-phenylethylamine [(R)-22] in photon counts (A) difference spectrum, (if — if) (B) sum spectrum, (if + if) (C) difference spectrum, (if — if). Reprinted with permission from Reference 160. Copyright (1975) American Chemical Society... 

If the optically active medium is not transparent at the wavelength of the incident radiation, the transmitted intensity may be further reduced by an absorptive contribution to the index of refraction. Because of preferential absorption of either the left or the right circularly polarized component, the emerging beam would no longer be the sum of equal amplitudes and trace out an ellipse with ellipticity tp = (kt — kr). Practical details of the measurement and chemical applications of optical activity are discussed by Charney[34],... 

Fig. 2.8. Left Ratio of doubly to singly charged (7, = 2, , ) and triply to doubly charged (Z = 3, o, ) molecular ions are plotted as a function of effective laser intensity. Circles and squares indicate them by circularly and linearly polarized lights, respectively. Right figure Ratio of the sum of molecular ions of all charge states (JO Mz+) to the total ions (Total). Signals by circularly polarized light are indicated by (o) and for linearly polarized light by ( )...

The most interesting case is photoemission of 4/ electrons in the rare earths as noted in the previous section, because of the collapsed nature of the 4/ orbitals, the photoemission spectrum can be interpreted completely even in the solid by atomic multiplet theory, and this applies also to magnetic circular dichroism. Thole and van der Laan [642] have derived sum rules for magnetic dichroism in rare-earth 4/ photoemission. They have shown that the integrated intensity is simply the sum over each sublevel of its occupation number times the total transition probability from that sublevel to the continuum shell. Polarisation effects in the 4/ photoemission spectra of rare earths are very large, and this tool based on quasiatomic analysis is of considerable significance it provides a new... 

The inverse of this plot represents depletion of DEEP from the polyethylene bulk (circular data points. Figure 22.11), and it is calculated by subtracting the [DEEP-i-H] intensity at each vac point from the maximum summed value. The depletion plot appears as an exponentially decaying function, and in fact is fitted to that... 

FIGURE 22.11 Kinetic plot generated from the DSIMS experiment involving application of DEEP to polyethylene. Square data points are the summed intensity of the [DEEP+H] ions with increasing time in vacuum (t, c)- Circular data points are the inverted values calculated from the summed intensity plots and represent depletion of the DEEP from the polymer. The solid line is plotted from the exponential function that was fitted to the depletion data points. 

The key properties of electromagnetic waves are velocity (V), wavelength (A), frequency (v), amplimde, polarisation, intensity and coherence. These are illustrated in Fig. 1.2. The relationship between the first three is given by V — Av. Polarisation can be either linear, or circular, and hnear polarised light can be represented as the sum of two equal amplitude, circularly polarised waves moving clockwise and anticlockwise in phase. The intensity of the wave is proportional to the square of the amplimde. 

---