Raman Spectroscopy and Four-Wave Mixing in Sodium
In the 1920s, 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
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 3d3/2 and 3d5/2 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 3p1/2 and 3p3/2
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 ki 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
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