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 (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, 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 (or rotational) 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 intensities

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

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

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 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 ${\displaystyle I_{p}}$ 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 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 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 similarly 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 associated with a specific vibrational (or rotational) transition. 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 Raman gain coefficient's value drops, 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 to the difference in wavelengths.

Study of molecular conformational structures

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 indicates the different conformational structures of the same molecule.

Material composition analysis

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 allows for the determination of the composition's stoichiometric relations.

Microscopy

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.

Ultrafast microscopy

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