Stimulated Raman spectroscopy
Stimulated Raman spectroscopy, also referred to as stimulated Raman scattering, is a form of spectroscopy employed in physics, chemistry, biology, and other fields. The basic mechanism resembles that of spontaneous Raman spectroscopy: a pump photon, of the angular frequency, which is scattered by a molecule has some small probability of inducing some vibrational transition, as opposed to inducing a simple Rayleigh transition. This makes the molecule emit a photon at a shifted frequency. However, SRS, as opposed to spontaneous Raman spectroscopy, is a third-order non-linear phenomenon involving a second photon—the Stokes photon of angular frequency —which stimulates a specific transition. When the difference in frequency between both photons resembles that of a specific vibrational transition the occurrence of this transition is resonantly enhanced. In SRS, the signal is equivalent to changes in the intensity of the pump and Stokes beams. The signals are typically rather low, of the order of a part in, thus calling for modulation-transfer techniques: one beam is modulated in amplitude, and the signal is detected on the other beam via a lock-in amplifier. Employing a pump laser beam of a constant frequency and a Stokes laser beam of a scanned frequency allows for unraveling the molecule's spectral fingerprint. This spectral fingerprint differs from those obtained by other spectroscopy methods, such as Rayleigh scattering, as the Raman transitions confer different exclusion rules than those that apply to Rayleigh transitions.
History
The phenomenon of SRS was accidentally discovered by Woodbury and Ng in 1962. In their experiment, they introduced a Kerr cell containing nitrobenzene into a ruby laser cavity to study Q-switching processes. This resulted in a strong emission at a wavelength in the IR region that could not be associated with the characteristic wavelengths of the ruby gain medium. At first, this was explained as luminescence. Only at a later stage was this interpreted correctly as the first experimental observation of SRS. A year later, Garmire et al. introduced a two-wave mixing framework to describe SRS. These pioneering works opened a new avenue of research and were followed by many theoretical and experimental works in the field of SRS.Principle
Qualitative description
The principle of SRS can be intuitively understood by adopting the quantum mechanical description of the molecule's energy levels. Initially, the molecule lies in the ground state, its lowest electronic energy level. Then, it simultaneously absorbs both pump and Stokes photons, which causes a vibrational transition with some probability. The transition can be thought of as a two-step transition where, in the first step, the molecule is excited by the pump photon to a virtual state, and in the second, it is relaxed into a vibrational state other than the ground state. The virtual state, a superposition of real states' probability tails, cannot be occupied by the molecule. However, the simultaneous absorption of two photons might provide a coupling route between the initial and final states. When the energy difference between both pump and Stokes photons matches the energy difference between some vibrational state and the ground state, the probability for a transition due to this stimulated process is enhanced by orders of magnitude.Quantitative description
Each photon that undergoes SRS is shifted in color from pump to Stokes color. Thus, the SRS signal is proportional to the decrease or increase in the pump, or Stokes beams intensities, respectively. The following rate equations describe these changes in the beams intensitieswhere, and are the pump and Stokes beams intensities, respectively, and are the pump and Stokes angular frequencies, respectively, is the coordinate along which the beams propagate, is the Raman gain coefficient, and is the loss coefficient. The loss coefficient is an effective coefficient that might account for losses due to a variety of processes such as Rayleigh scattering, absorption, etc. The first-rate equation describes the change in Stokes beam intensity along the SRS interaction length. The first term on the right-hand side is equivalent to the amount of intensity gained by the Stokes beam due to SRS. As SRS involves both beams, this term is dependent both on and. The second term is equivalent to the amount of intensity lost and is thus dependent only on. The second rate equation describes the change in pump beam intensity; its form is similar to the former. The first term on the right-hand side of the second equation equals its counterpart from the first equation up to a multiplicative factor of. This factor reflects that each photon lost from the pump beam due to SRS is gained by the Stokes beam.
In most cases, the experimental conditions support two simplifying assumptions: photon loss along the Raman interaction length,, is negligible. Mathematically, this corresponds to
and the change in beam intensity is linear; mathematically, this corresponds to
Accordingly, the SRS signal, that is, the intensity changes in pump and Stokes beams, is approximated by
where and are the initial pump and Stokes beams intensities, respectively. As for the Raman interaction length, in many cases, this length can be evaluated similarly to the evaluation of the Rayleigh length as
Here, and are the averaged refractive index and beam waist, respectively, and and are the pump and Stokes wavelengths, respectively.
Every molecule has some characteristic Raman shifts associated with a specific vibrational transition. The relation between a Raman shift,, and the pump and Stokes photon wavelengths is given by
When the difference in wavelengths between both lasers is close to some Raman transition, the Raman gain coefficient receives values on the order of resulting with an efficient SRS. As this difference starts to differ from a specific Raman transition, the Raman gain coefficient's value drops, and the process becomes increasingly less efficient and less detectable.
An SRS experimental setup includes two laser beams of the same polarization; one is employed as pump and the other as Stokes. Usually, at least one of the lasers is pulsed. This modulation in the laser intensity helps to detect the signal; furthermore, it helps increase the signal's amplitude, which also helps detection. When designing the experimental setup, one has great liberty when choosing the pump and Stokes lasers, as the Raman condition applies only to the difference in wavelengths.