Raman scattering frequencies, examples

Besides the various types of tunable lasers discussed in the foregoing sections, sources of tunable coherent radiation have been developed that are based on the nonlinear interaction of intense radiation with atoms or molecules in crystals or in liquid and gaseous phases. Second-harmonic generation, sum- or difference-frequency generation, parametric processes, or stimulated Raman scattering are examples of such nonlinear optical mixing techniques. These techniques cover the whole spectral range from the vacuum ultraviolet (VUV)... 

The present study demonstrates that the analytic calculation of hyperpolarizability dispersion coefficients provides an efficient alternative to the pointwise calculation of dispersion curves. The dispersion coefficients provide additional insight into non-linear optical properties and are transferable between the various optical processes, also to processes not investigated here as for example the ac-Kerr effect or coherent anti-Stokes Raman scattering (CARS), which depend on two independent laser frequencies and would be expensive to study with calculations ex-plictly frequency-dependent calculations. 

When a compound is irradiated with monochromatic radiation, most of the radiation is transmitted unchanged, but a small portion is scattered. If the scattered radiation is passed into a spectrometer, we detect a strong Rayleigh line at the unmodified frequency of radiation used to excite the sample. In addition, the scattered radiation also contains frequencies arrayed above and below the frequency of the Rayleigh line. The differences between the Rayleigh line and these weaker Raman line frequencies correspond to the vibrational frequencies present in the molecules of the sample. For example, we may obtain a Raman line at 1640 cm-1 on either side of the Rayleigh line, and the sample thus possesses a vibrational mode of this frequency. The frequencies of molecular vibrations are typically 1012—1014 Hz. A more convenient unit, which is proportional to frequency, is wavenumber (cm-1), since fundamental vibrational modes lie between 4000 and 50 cm-1. 

The first SMS experiments in 1989 utilized either of two powerful doublemodulation FM absorption techniques, laser frequency-modulation with Stark secondary modulation (FM-Stark) or frequency-modulation with ultrasonic strain secondary modulation (FM-US) [3,26]. The secondary modulation was required in order to remove the effects of residual amplitude modulation produced by the imperfect phase modulator. In contrast to fluorescence methods, Rayleigh and Raman scattering were unimportant. Figure 2.3B (specifically trace d) shows examples of the optical absorption spectrum from a single molecule of pentacene in p-terphenyl using the FM-Stark method. 

When many wavelengths are present in the input spectrum, the interfer-ogram is a sum of many sine waves of different frequency and phases. An example is shown in Figure 9.4A, for the Raman scattering from cyclohexane. 

Even a cursory examination of Raman shift values reported in the literature reveals significant variations, often greater than 5 cm . Even small changes in true Raman shift can be scientifically informative, so it is quite unfortunate if such effects are obscured by instrumental or random error. Reported Raman shift values are currently more prone to error than Fourier transform infrared (FTIR) frequencies for two reasons. First, Raman shift involves the difference of two frequencies (laser and Raman scattering), each of which may be subject to measurement error, while FTIR is usually a measurement of one frequency. Second, the higher absolute frequencies involved in Raman must be determined to a higher degree of relative accuracy. For example, measurement of a 1000 cm vibration with FTIR to an accuracy of 1 cm" requires relative frequency error of 0.1 per cent. The same observation with Raman spectroscopy and a 514.5 nm laser requires a frequency measurement accurate to 1 cm" in 18,435 cm (19,435-1000), or 0.005 percent. Such accuracy is readily achievable with modem Raman instmments but does require extra care. 

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