Threshold intensity and coefficient of raman scattering amplification in a high-$Q$ bilayer microresonator during the formation of internal and external submicron photonic jets: A photonic nanojet in the near field

Using quantum and semiclassical approaches, the energy excitation threshold for induced Raman scattering is estimated and a relationship between the excitation threshold and the concentration of optically active molecules in a bilayer microresonator is established. Estimates are made during the formation of specially configured optical fields: internal and external photonic nanojets. Based on the amount of stored energy per mode and the value of the threshold intensity, an additional generalized selection rule for whispering gallery modes is suggested. It is shown that the bilayer microresonator can focus incident radiation (laser pumping) into a submicron focal volume at a low threshold intensity.