sidebands

 
  The usual explanation of the Raman Effect relies on inelastic particle (photon) scattering, not wave interference.
  Photons are quanta of energy located somewhere within wave packets with average emission times of 10^-8s. 
  Their positions within the wave packets are considered indeterminate.
  Wave packets are not infinite in length and this limits the sharpness of their wavelength.
  A good reference in this case is Fundamentals of Optics by Jenkins and White.
  
  There is probably a corresponding wave theory explanation of the Raman Effect. 
  The closest example I can find is the Raman effect in gas-phase matter.
  A "double sideband supressed carrier" spectrum resulting from FM/PM modulation in radio communications
  seems to be treated mathematically the same way as the rotational Raman spectrum of gas phase media
  (yielding "branches" instead of "bands") and justifies the Δj = ± 2 selection rule
  in the case of anisotropic polarizability? 

  The Science of Radio, Paul Nahin
  Rotational Spectroscopy