Raman Scattering and Four Wave Mixing

            When two photons strike an atom of Sodium at almost the same time, the Na atom may be excited to a high-energy state.  The energy of this state is the sum of the energies of the two incident photons.  This high-energy state may be a real energy state for the atom, or a “virtual state” of energy close to that of a real state.

            The atom must release this energy somehow.  Two possible avenues for this release of energy are Raman scattering and Four Wave Mixing.

            In Raman scattering, the excited electron drops down to a real energy state between the virtual and ground states, and then down to ground.  A shift in the energy of the virtual state will affect the first emitted photon, but the second will have a constant wavelength.

~ The law of conservation of momentum necessitates this phase matching.  The relationship governing this phase match, in terms of the k of the photons, is: 2k_i = k_g1 + k_g2.  A rare occurrence is axial phase matching.  That is, when the two generated photons have zero angles with respect to the incident photons.  The momenta are related by 2|k_i| - |k_g1| = |k_g2|.  In this case, the atom drops from the high-energy state to a virtual state between the two real intermediary states (or the virtual states corresponding to those states in the off-resonance shifted spectrum). ~  For the example studied, this looks like so:

Here is a complete energy level diagram of the element Sodium, which Phil Stewart and I studied together and I continued to study independently.

    The first stimulation that we observed was up to the E1 virtual state, near the real 5s state.  To determine what energy virtual state to use, we scanned quickly through stimulation wavelengths to find an emission peak.  We found this peak for stimulation to an energy level with the energy of 32865.0 cm^-1.  Through normal Raman scattering, this virtual state could decay to the 4p or 3p states.  Decay to the 4p states produces infrared light, and decay to the 3p results in a reddish light.  

    The second stimulation that we observed was up to the 3d state (see table).  This state will decay only to the 3p states, which will then decay to ground.  We looked for the transitions to ground here, and the color associated with these transitions is the sodium streetlamp color.  To produce stimulation to virtual states above and below the 3d state, we varied the wavelength of the stimulation photons above and below the 3d energy.  This allowed us to look for evidence of Four Wave Mixing in the form of shifts in the wavelengths of the sodium light.

I later stimulated the sample to the 4d state in order to search for the following transitions.