SEHRS. (a) Schematic of the two-photon inelastic scattering process HRS: two near-IR photons hνL interact with a molecule. The results are scattering signals shifted relative to twice of the excitation energy by an amount equal to the vibrational energies of the molecule hνM. Depending on whether the two photons interact with a molecule in its vibrational ground or first excited vibrational state, the scattering signals appear at the low-energy (Stokes, hνS, left pair of arrows) or high-energy (anti-Stokes, hνaS, right pair of arrows) side of the doubled excitation energy. (b) SEHRS Stokes and anti-Stokes spectra of 10−7 M of the dye molecule crystal violet attached to silver nanoaggregates in aqueous solution. The spectra were measured by using 1,064-nm mode-locked picosecond pulses at an average power of 40 mW (peak intensity 2 × 1025 photons cm−2·s−1) and collection times of 10 and 60 s, respectively. Anti-Stokes scattering appears at much lower signal level than Stokes scattering, because the number of molecules in the excited vibrational state is much smaller than those in the vibrational ground state, but here anti-Stokes HRS can be observed because of the extremely high effective cross-section of SEHRS. In most practical bioanalytical applications and in the spectra shown in this article, the more intense, Stokes-shifted hyper-Raman light is used for label detection and molecular probing. (c) The square-law dependence of the HRS signal on the excitation intensity verifies the two-photon process. A logarithmic plot of the dependence of the SEHRS signal on excitation intensity shows a slope of 1.93 (plot not displayed here).