Raman Spectroscopy and Four-Wave Mixing in Sodium Atoms

Raman Scattering:

In the 1920’s, an Indian physicist named C.V. Raman noticed that light incident on a variety of surfaces is sometimes scattered with different wavelengths (Milonni 682). With the invention of the laser this phenomenon known as the Raman effect could be studied extensively. Such a non-linear process occurs when a photon of energy E₁ excites an atom to a "virtual state" and then quickly relaxes to an eigenstate E₃ , releasing a photon E₂ = E₁ –E₃. Unlike a fluorescence process, Raman scattering involves no transfer of electron population to the intermediate state.  It is an effect of superpositioning of waves. The electron simply begins in state E₁ and ends in state E₃.   If the electron ends up in a higher state than its initial state, this is called "Stokes scattering;" if it ends up in a lower state, the effect is called "Anti-Stokes scattering." 

A very useful and popular spectroscopic technique known as Coherent Anti-Stokes Raman Spectroscopy (C.A.R.S.) employs these phenomena.  Raman scattering may also take place in molecules: transitions to a vibrational virtual state and then to various vibrational and rotational levels yield Stokes and Anti-Stokes line.

We believe we have observed this effect in our data for two-photon absorption of Cesium: one photon at 6548 angstroms excited the atoms to a virtual state which quickly decayed to the 5d state, absorbed another atom to the 12p state and then ionized.

Four Wave Mixing

Four-wave mixing refers to the general phenomenon by which four photons of light, some of which are incident on an atom, constructively interfere leaving the atom in its original state. This may be in the form of third-harmonic generation in which an atom absorbs three photons simultaneously and transitions to an eigenstate before relaxing back to the original state with the release of a photon with energy equal to the sum of the three incident photon energies. In the particular case of Sodium which we studied, an atom absorbs two photons of light simultaneously and transitions to a virtual state just below the 3d_3/2 and 3d_5/2 eigenstates.  In this kind of "parametric four-wave mixing," there is no transfer of population to this virtual state, only an induced polarization of the atom and a superposition of waves (Moore 3, 20).  The two photons are Raman scattered, generating two more photons and bringing the atom to another virtual state (very close to the 3p_1/2 and 3p_3/2 lines) before returning to the initial state (1s² 2s² 2p⁶ 3s). In the end, we have put in two identical photons but find two different photons scattered; the polarization of the atom induced by an incident electric field is non-linear.

As in all photon excitation processes, four-wave mixing must conserve energy and momentum. To obtain the constructive interference required for four-wave mixing, there must also be a phase correspondence between incident and scattered photons.  The electric fields of the photons are:

where k_i are the phase vectors of the fields.

The phase vectors ki of the incident photons must match head to tail with the vectors of the two emitted photon. When the two incident photons bring the atom to an eigenstate, the index of refraction is such that this phase matching condition cannot be met. The parametric four-wave emission will be suppressed. When we excite the atom off resonance, the phase matching requirement may be met; however, because the indices of refraction are different for each wavelength, this requirement will cause the emitted photons to propagate at an angle from the path of the incident light. This results in a cone of light emitted form the sodium vapor. No light of the scattered wavelengths may be emitted along the axis of the laser beam.  Click here to view some data from our four-wave mixing experiment.

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