We present a method for deriving limits on Raman scattering in structured media and exploit it to constrain the maximum Raman signal resulting from a plane wave incident on either a single Raman molecule in the vicinity of a structured medium or a designable Raman medium. Results pertaining to metallic and dielectric structures illustrate the importance of accounting for the nonlinear interplay between pump and signal fields, showing that treating the pump-focusing and signal-extraction processes separately, as in prior work, leads to unrealistic enhancements. The formulation could readily find applications in further enhancing surface-enhanced Raman scattering (SERS) spectroscopy and Raman-assisted lasing.

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• Nanophotonics
• Nonlinear optics
• Photonics
• Numerical techniques
• Raman spectroscopy
• Surface-enhanced Raman spectroscopy