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Resonantly enhanced Raman scattering in dielectric nanostructures has beenrecently proven to be an effcient tool for developing nanothermometry andexperimental determination of their mode- composition. In this paper, wedevelop a rigorous analytical theory based on the Green's function approach tocalculate the Raman emission from crystalline high-index dielectricnanoparticles. As an example, we consider silicon nanoparticles which have astrong Raman response due to active optical phonon modes. We relate enhancementof Raman signal emission to Purcell effect due to the excitation of Mie modesinside the nanoparticles. We also employ the numerical approach to thecalculation of inelastic Raman emission in more sophisticated geometries, whichdo not allow a straightforward analytical form of the Green's functiondescription. The Raman response from a silicon nanodisk has been analyzedwithin the proposed method, and the contribution of the various Mie modes hasbeen revealed.

Enhancement of inherent Raman scattering in dielectric nanostructures with electric and magnetic Mie resonances