The review is devoted to explanation of SERS in terms of the dipole and quadrupole light-molecule interactions arising in surface fields strongly varying in space in the region of the strongly irregular surface roughness. The main SERS characteristics, the theory of electromagnetic fields near some model kinds of rough surfaces and some other systems, the theory of SERS Raman tensor for arbitrary and symmetrical molecules, selection rules and analysis of the SER spectra, some anomalies in the SER spectra of symmetrical molecules for some specific conditions, electrodynamic forbiddance of the quadrupole scattering mechanism for the methane molecule and molecules with cubic symmetry groups are considered. The huge enhancement and blinking of the SERS signal arising in the phenomenon of Single Molecule detection by the SERS method are explained. The above theory is compared with some another SERS mechanisms, and the phenomena accompanying SERS are accounted for. It is demonstrated that the theory is in a good agreement with the experiment and explains quite a number of characteristics related to the SERS phenomenon.
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