Raman and photoluminescence

Next we´ll take a look at some essentials of Raman and photoluminescence.

Simulated time-resolved emission spectrum example

In the next few images we show simulated data to illustrate key differences between Raman and photoluminescence emissions. Here we consider an imaginary molecule (or an ensemble of them), having been hit by an excitation laser pulse of 500 ps duration (full width at half maximum). The absolute values on the vertical axis don’t matter, but the time (ps) and the Raman Shift (cm-1) axes are essential.

Figure 2 Time-resolved SIMULATED Raman spectrum produced by a laser pulse of 500 ps temporal width. The temporal pulse position and width are identical to the laser pulse’s. The laser pulse itself (at Raman shift 0) is not shown – simulating the case where good spectral filters have been installed to block it completely.

Figure 3 Time-resolved SIMULATED photoluminescence spectrum produced by a laser pulse of 500 ps temporal width. Note the temporally long “tail” of emission occurring well after the excitation.

Figure 4 Time-resolved SIMULATED emission spectrum produced by a laser pulse of 500 ps temporal width. This spectrum is simply the sum of the Raman and photoluminescence spectra.

Simulated illustration of time-gating

In Figure 4 we see the (simulated) actual optical pulse that would be landing on the detector in due course. The following images illustrate the results when both laser pulse duration and the gate width are gradually decreased. The simulated molecule’s physical properties (most importantly, luminescence lifetime) are always the same. Note the changes in the scale of the time axis.

Figure 5. Conventional CW Raman spectrum of the SIMULATED molecule, computed by setting the time gate width to infinite.

Figure 6. Left: Gated spectrum with 2 ns gate width and 1 ns excitation pulse width of the SIMULATED molecule. Right: As the arrows indicate, the blue curve on the right is the emission pulse’s temporal profile at the position of the Raman peak, whereas the red curve is the temporal profile at a position next to it, containing only photoluminescence contribution.

Figure 7. Gated spectrum with 0.5 ns gate width and 0.25 ns excitation pulse width of the SIMULATED molecule.

Figure 8. Gated spectrum with 100 ps gate width and 50 ps excitation pulse width of the SIMULATED molecule.

Figure 9. Gated spectrum with 20 ps gate width and 10 ps excitation pulse width of the SIMULATED molecule. The residual (photo)luminescence, explicitly indicated here, is the part that occurs simultaneously with the Raman pulse and therefore is not rejected by gating.

The noise in the simulation is modeled as pure shot noise distributed according to Poisson statistics. This is often very close to the actual measurement noise if there is no drastic fluctuation in the sample. If photon shot noise is the limiting factor, then pulsed excitation and gated detection have a fundamental and straightforward advantage over conventional CW Raman spectrometry: the rejection of luminescence shot noise. This physical fact is illustrated in the above simulations, where the contrast of the Raman bands increases steadily with shortening pulse and gate.

Some physical background

We will review some basics of the theory of photoluminescence and Raman scattering on the molecular level, starting from a couple of qualitative Perrin-Jablonski energy diagrams (Figure 10).

Figure 10. Schematic overview of molecular energy levels involved in Raman scattering and fluorescence (Perrin-Jablonski diagrams)

The quantum-mechanical energy levels sketched in Figure 10 are to be interpreted as follows: S0 and S1, denoted by black horizontal lines are the ground state and first excited state of a valence electron. The lighter blue lines are associated with vibrational states of the molecule’s atoms with respect to each other. In other words, they denote the vibrational energy levels that can be probed by Raman spectroscopy or IR absorption spectroscopy. In this simple example, it is assumed that the molecules are initially in the ground state i.e. state of lowest electronic and vibrational internal energy. Incoming photons (Excitation) then interact with the molecules. To give a slightly less abstract impression of the process, Figure 11 depicts in a schematic way the relevant electronic orbitals of a simple molecule.

Figure 11. Schematic examples illustrating the electronic S0 and S1 orbitals around a diatomic molecule. The orbitals describe the probability distribution of the “position of the electron”, a darker color indicating larger probability. While in S1, the electron “orbits” the molecule faster and therefore spends more time far away from the center than while in S0.

In the Non-fluorescent case the excitation photon’s energy is not sufficient to raise the valence electron to even the first excited state. In other words, the molecule cannot absorb the photon into its electronic shell structure. However, Raman scattering and Rayleigh scattering can still occur, since these phenomena do not require absorption as a precursor.
In the Fluorescent case we still have the same excitation wavelength, but a different molecule with a different set of electronic and vibrational energy levels. Now the photon may be absorbed by the molecule, raising it to an energy level defined by: 1) the electron resides in the S1 state and 2) the molecule as a whole is in some transient vibrational state. The electronic absorption phenomenon is fast (femtoseconds) due to low inertia, so to speak, of electrons. The subsequent relaxation dynamics that the molecule and its surroundings go through in order to “relax” the molecule to the lowest vibrational level while staying electronically in the S1 level take typically less than 100 ps. After this relaxation, the molecule’s valence electron is just waiting to return to the S0 state. This return, which entails the molecule losing internal energy, can occur either by emitting a new photon (Fluorescence) or non-radiatively by giving up the energy to the surrounding molecules (heating). As depicted, the wavelength of the fluorescence photon varies according to the vibrational energy level that the molecule ends up upon emission. This, combined with various broadening mechanisms, produces the typically quite featureless spectral shape of fluorescence. The mean lifetime of the S1 state determines the decay time of the fluorescence “glow” produced by an ensemble of molecules after a short excitation pulse. For more comprehensive and detailed physical picture of photoluminescence, see (Valeur & Berberan-Santos, 2013).
The mechanism of Raman scattering (Long, 2002) is different from the photoluminescence mechanism described above. There are a few different models, both classical and quantum-mechanical, that help to picture the essential properties of the phenomenon. In the most rudimentary quantum picture, only the initial and final states of the system are considered. We now consider the Stokes type of Raman scattering where the scattered photon’s energy is less than that of the excitation photon. In the initial state, our system is composed of the excitation photon and the molecule in ground state. In the final state, the system is composed of the Raman photon and the molecule in some nonzero vibrational state. What happens between these states is dismissed, but it is assumed that from start to finish, the process takes only on the order of picoseconds (this assumption is phenomenologically legitimate based on a huge number of measurement results). The emitted photon’s energy is the excitation photon’s energy minus the final vibrational energy of the molecule. In other words, the molecule has transitioned from the lowest vibrational state to some upper vibrational state, having been induced to do so by the electromagnetic perturbation provided by the excitation photon. Not all such transitions are “allowed” but it is required that the vibrational states and the polarization of the photon fulfil certain symmetry. It is these restrictions, in addition to interatomic bond lengths and strengths, that define the Raman spectrum of a molecule and also enable polarization-sensitive measurements.
The anti-Stokes Raman scattering is otherwise analogous with the Stokes type, but the molecule starts from a nonzero vibrational state and ends up in the ground state. This time the scattered photon’s energy is the sum of the excitation photon’s energy and the vibrational energy given up by the molecule. The positions of the anti-Stokes peaks in the emission spectrum are a mirror image of the Stokes peaks with respect to the laser line. The peak intensities depend on the populations of the upper vibrational states, i.e. temperature of the molecule ensemble.
A given molecule’s Raman scattering and photoluminescence mechanisms differ drastically in their response to excitation laser’s central wavelength and spectral linewidth. The spectral shape of fluorescence is unaffected by these parameters (as long as the photon energies are sufficient for absorption, but also not too high). On the other hand, the Raman spectrum as a whole follows any changes in the laser’s center wavelength, and the emission lines directly reflect the line shape of the laser. Raman bands are in effect broadened and shifted versions of the laser line.

References
Long, D. A. (2002). The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules. Chichester: Wiley-Blackwell.
Valeur, B.;& Berberan-Santos, M. N. (2013). Molecular Fluorescence – Principles and Applications. Weinheim: Wiley-VCH.