Stimulated Raman spectroscopy

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, that is, its lowest electronic energy level. Then, it simultaneously absorbs both pump and Stokes photons, which causes a vibrational (or rotational) 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 (or rotational) state other than the ground state. The virtual state, which is actually a superposition of probability tails of real states, cannot be occupied by the molecule. However, for a simultaneous absorption of two photons, it 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 (or rotational) state and the ground state, the probability for a transition due to this stimulated process is enhanced by orders of magnitude.

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. These changes in the beams intensities are described by the following rate equations

${\displaystyle {\frac {dI_{S}}{dz}}=g_{R}I_{p}I_{S}-\alpha I_{S},}$

${\displaystyle {\frac {dI_{p}}{dz}}=-{\frac {\omega _{p}}{\omega _{S}}}g_{\mathrm {R} }I_{p}I_{S}-\alpha I_{p},}$

where, ${\displaystyle I_{p}}$ and ${\displaystyle I_{S}}$ are the pump and Stokes beams intensities, respectively, ${\displaystyle \omega _{p}}$ and ${\displaystyle \omega _{S}}$ are the pump and Stokes angular frequencies, respectively, ${\displaystyle z}$ is the coordinate along which the beams propagate, ${\displaystyle g_{R}}$ is the Raman gain coefficient, and ${\displaystyle \alpha }$ is the loss coefficient. The loss coefficient is an effective coefficient that might account for loses 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 ${\displaystyle I_{p}}$ and ${\displaystyle I_{S}}$. The second term is equivalent to the amount of intensity lost and is thus dependent only on ${\displaystyle I_{S}}$. The second rate equation describes the change in pump beam intensity, its form is quite 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 ${\displaystyle -\omega _{p}/\omega _{S}}$. This factor reflects the fact that each photon (as opposed to intensity units) lost from the pump beam due to SRS is gained by the Stokes beam.

In most cases, the experimental conditions support two simplifying assumptions: (1) photon loss along the Raman interaction length, ${\displaystyle \Delta z}$, is negligible. Mathematically this corresponds to

${\displaystyle \alpha /g_{R}\ll I_{p},I_{S}}$

and (2) the change in beam intensity is linear; mathematically this corresponds to

${\displaystyle g_{R}\cdot \Delta z\cdot Max(I_{p},I_{S})\ll 1}$.

Accordingly, the SRS signal, that is, the intensity changes in pump and Stokes beams is approximated by

${\displaystyle \Delta I_{S}\simeq g_{\mathrm {R} }I_{p,0}I_{S,0}\Delta z,}$

${\displaystyle \Delta I_{p}\simeq -{\frac {\omega _{p}}{\omega _{S}}}g_{\mathrm {R} }I_{p,0}I_{S,0}\Delta z,}$

where ${\displaystyle I_{p,0}}$ and ${\displaystyle I_{S,0}}$ are the initial pump and Stokes beams intensities, respectively. As for the Raman interaction length, in many cases this length can be evaluated in a similar fashion to the evaluation of the Rayleigh length as

${\displaystyle \Delta z=4\pi n\omega _{0}^{2}/(\lambda _{p}+\lambda _{S})}$.

Here, ${\displaystyle n}$ and ${\displaystyle \omega _{0}}$ are the averaged refractive index and beam waist, respectively, and ${\displaystyle \lambda _{p}}$ and ${\displaystyle \lambda _{S}}$ are the pump and Stokes wavelengths, respectively.

Every molecule has some characteristic Raman shifts, each associated with a specific vibrational (or rotational) transition of the molecule. The relation between a Raman shift, ${\displaystyle \Delta \omega }$, and the pump and Stokes photon wavelengths is given by

${\displaystyle \Delta \omega [\mathrm {cm} ^{-1}]=\left({\frac {1}{\lambda _{p}[\mathrm {nm} ]}}-{\frac {1}{\lambda _{S}[\mathrm {nm} ]}}\right)\times {\frac {[10^{7}\mathrm {nm} ]}{[\mathrm {cm} ]}}}$

When the difference in wavelengths between both lasers is close to some Raman transition, the Raman gain coefficient ${\displaystyle g_{R}}$ receives values on the order of ${\displaystyle 10^{-30}[\mathrm {cm} ^{2}/\mathrm {molecule} \cdot \mathrm {sr} ]}$ resulting with an efficient SRS. As this difference starts to differ from a specific Raman transition the value of the Raman gain coefficient drops down and the process becomes increasingly less efficient and less detectable.

An SRS experimental setup includes two laser beams (usually co-linear) 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 (shown in the equation above) applies only on the difference in wavelengths.

Works in this field were done both in the Cina[3] and Bar[4][5] groups. Each conformer is associated with a slightly different SRS spectral signature. Detection of these different landscapes is an indication of the different conformational structures of the same molecule.

Here, the SRS signal dependence on the concentration of the material is utilized. Measuring different SRS signals, associated with the different materials in the composition, allow for the determination of the stoichiometric relations of the composition.

Stimulated Raman scattering (SRS) microscopy allows non-invasive label-free imaging in living tissue. In this method, pioneered by the Xie group,[6] a construction of an image is obtained by performing SRS measurements over some grid, where each measurement adds a pixel to the image.

Employing femtosecond laser pulses, as was done in the Katz, Silberberg,[7] and Xie[8] groups, allows for an instant generation of a very large portion of the spectral signature by a single laser pulse. The broad signal is a result of the width of the laser band as dictated by the uncertainty principle, which determines an inverse proportion between the uncertainty in time and uncertainty in frequency. This method is far faster than traditional microscopy methods as it circumvents the need in long and time-consuming frequencies scanning.