Whispering-gallery mode resonators: Surface enhanced Raman scattering without plasmons

Calculations based on the Mie theory are performed to determine the locally enhanced electric fields due to whispering-gallery mode resonances for dielectric microspheres, with emphasis on electromagnetic "hot spots" that are located along the wavevector direction on the surface of the sphere. The local electric field enhancement associated with these hot spots is used to determine the surface enhanced Raman scattering enhancement factors for a molecule, here treated as a classical dipole, located near the surface of the sphere. Both incident and Raman emission enhancements are calculated accurately using an extension of the Mie theory that includes interaction of the Raman dipole field with the sphere. The enhancement factors are calculated for dielectric spheres in vacuum with a refractive index of 1.9 and radii of 5, 10, and 20 μm and for wavelengths that span the visible spectrum. Maximum Raman scattering enhancement factors on the order of 103 - 104 are found at locations slightly off the propagation axis when the incident excitation but not the Stokes-shifted radiation is coincident with a whispering-gallery mode resonance. The enhancement factors are found to vary inversely with the resonance width, and this determines the influence of the mode number and order on the results. Additional calculations are performed for the case where the Stokes-shifted radiation is also on-resonance and Raman enhancement factors as large as 108 are found. These enhancement factors are typically a factor of 102 smaller than would be obtained from ∫E∫4 enhancement estimates, as enhancement of the Raman dipole emission is significantly reduced compared to the local field enhancement for micron size particles or larger. Conditions under which single-molecule or few-molecule measurements are feasible are identified.