Raman scattering basic theory

The most often used detection method for the optical sensors are based on absorption, luminescence, reflectance, and Raman scattering measurements. The basic theory and instrumentation of most of these... 

As mentioned above, the basic theory of the Raman effect was developed before its discovery. However, at this time numerical calculations of the intensity of Raman lines were impossible, because these require information on all eigenstates of a scattering system. Placzek (1934) introduced a semi-classical approach in the form of his polarizability theory. This provided a basis for many other theoretical and experimental studies. Physicists and chemists worldwide realized the importance of the Raman effect as a tool for qualitative and quantitative analysis and for the detennination of structure. 

D. A. Long, Raman Spectroscopy , McGraw-Hill, New York, 1977. The most comprehensive, unified and fully illustrated treatment of the basic theory and physical principles of Raman, resonance Raman and nonlinear Raman scattering. Readers will be inspired by the elegance and information content of the technique to delve further into the book. 

This chapter covers the electromagnetic radiation scattering behavior of semiconductor nanowires as it impacts their Raman scattering properties, as well as how the basic theory of Raman scattering in semiconductor crystals may be applied to the corresponding nanowire forms, with specific examples from the recent literature. The discussion then turns to more specific ways in which Raman spectroscopy can be used to precisely determine crystal structure, crystal size (or quality), composition, impurity concentration, strain, and temperature with submicron resolution, as demonstrated in recent literature examples. 

This article reviews all the published work concerned with the study of vibrational optical activity in chiral molecules from measurements of a small difference in the intensity of Raman scattering in right and left circularly polarized incident light. The history and basic theory are described briefly, followed by an account of the instrumentation and the precautions that must be observed in order to suppress spurious signals. The various theories that have been proposed in order to relate stereochemical features to the observations are then outlined, this being followed by a survey of all reported Raman optical activity spectra. 

This chapter briefly reviews recent progress in the investigation of fluorescent and phosphorescent properties of stilbenes as well as such phenomena as triplet-triplet and singlet-singlet energy transfer and Raman scattering. The trends in this area include the use of a wide arsenal of stilbenes, employment of elaborated experimental methods such as nano and picosecond time-resolved absorption and fluorescent spectroscopy, and the use of modern theoretical calculations, for example, density function theory. The importance of these research endeavors for further basic and applied applications of stilbenes cannot be overestimated. 

In this section we review the basic theory of Raman scattering and list or derive the formulas necessary for the calculation of scattering cross sections... 

In this chapter, we will provide a very basic, unified treatment of the theory of Raman scattering and ROA. More extensive descriptions of theory of Raman and ROA scattering can be found elsewhere [6-10,12,14,15]. 

As was shown in Chapter 8, the experimental gas phase differential Raman scattering cross sections are directly related to the molecular polarizability derivatives wifli respect to normal coordinates forming the supeitensor intensity analysis die dot/dQj derivatives are usually further transformed into different types of parameters. The eventual goal is to transfonn the experimental observables into molecular quantities reflecting electro-optical properties of simple molecular sub-units. Several formulations for parametric interpretation of Raman intensities have been put forward. In this chapter the basic principles and characteristics of the theories developed will be discussed. The mathematical formalism inherent of each theoretical approach will be illustrated with examples. 

These results apply specifically to Rayleigh, or elastic, scattering. For Raman, or inelastic, scattering the same basic CID expressions apply but with the molecular property tensors replaced by corresponding vibrational Raman transition tensors between the initial and final vibrational states nv and rn . In this way a s are replaced by (mv aap(Q) nv), where aQ/3(<3) s are effective polarizability and optical activity operators that depend parametrically on the normal vibrational coordinates Q such that, within the Placzek polarizability theory of the Raman effect [23], ROA intensity depends on products such as (daaf3 / dQ)0 dG af3 / dQ) and (daaf3 / dQ)0 eajS dAlSf / dQ)0. 

Many theories have been published which relate the third-order susceptibility to molecular properties. These theories range from full quantum electrodynamics treatments to simple classical models. The simple semi-classical treatment given below is sufficient for our purposes since it will expose the basic physics of the coherent scattering process and will also give us an expression in terms of the conventional spontaneous Raman transition polarizabilities. 

---