Brillouin Light Scattering Spectroscopy, or BLS, is an experimental technique that involves scattering monochromatic light, e.g. that from a laser, off of thermally excited phonons and measuring the shift in frequency of the scattered light. This technique allows experimenters to study important properties of the material, for example elastic constants such as the Young's modulus, or thermodynamic properties such as phase changes. The technique is essentially non-destructive and is used to study many different types of materials such as semiconductors, nanoporous materials such as porous silicon, and carbon nanotubes.
Thermal excitations in a crystal lattice give rise to phonons which are essentially quantized sound waves, rather analogous to photons, which are quantized electromagnetic waves. These (acoustic) phonons act like quantum mechanical particles and carry momentum as well as energy. When photons scatter off of phonons energy and momentum must be conserved, and the result is that the scattered photons have a different wavelength and frequency, corresponding to different momentum and energy. The classical interpretation of this result is that the light scattering off of fluctuations in pressure experience Doppler shifting. Light scattered from approaching waves are shifted towards narrower wavelengths while light scattered from receding waves are shifted towards broader wavelengths.
Viewed as a quantum mechanical process, a photon travelling through the medium may either produce a phonon by exciting the lattice (known as the Stokes process), and thus lose energy, or absorb a phonon from the lattice (known as the Anti-Stokes process) and gain energy.
Phonons can be characterized according to their propagation modes as well as their range of motion. For example, Rayleigh surface waves, surface acoustic waves or SAWs give rise to surface modes which are essentially ripples along the surface of the medium. Surface modes are the only type of modes that can be studied in great detail in opaque media, or media opaque to the wavelength of light being used. Bulk modes travel inside the medium and are mostly studied in transparent media. There are both longitudinal and transverse modes to consider. To study surface modes in transparent media, samples must first be coated with a thin film of metal such as gold or aluminum, thin enough so as not to perturb the scattering mechanism, but thick enough to allow scattering to take place. Experiments may be done with various film thicknesses in order to extrapolate results to zero film thickness.
To gain an understanding of how Brillouin scattering can be used to study material properties, consider probing surface phonons with laser light incident at an angle θ from normal incidence of the material's surface. Photons incident on the material may either be reflected from the material or scattered diffusely in all directions. If we make use of a backscattering arrangement in which we collect photons that are scattered 180° back towards the incident light we can greatly simplify further calculations.
An incident photon has angular frequency ωi and wavevector ki which points in the direction of propagation, and has magnitude |ki| = 2π/λi. The incident photon has momentum pi =
hki and energy Ei = hωi. Similarily, the scattered photon has momentum ps = hks and energy Ei = hωi. Finally, the phonon has angular frequency Ω and wavevector Q, with momentum pp = hQ and energy Ep = hΩi. The phonon wavevector lies in the plane of the medium since it's constrained to move on this surface.
We require that momentum be conserved in the plane of the surface, so that:
pisinθ ± ps = - pssinθ.
kisinθ ± Q = - kssinθ.
We also require that energy be conserved, so that:
ωi ± Ω = &omegas.
In each case + Q or + Ω corresponds to absorbing a phonon while - Q or - Ω corresponds to creating one. Now, ± Ω = ωs - ωi = Δω. Furthermore, since the wavelength of light is much shorter than that of the phonon, we can make the approximation that kf ≅ - ki. So:
± Ω = Δω
Q = 2 kisinθ
Now the phonon travels at speed v, and Ω = v Q, so Q = Ω / v, and we get that
Δω = ± 2 v kisinθ
Thus if we measure the frequency shift Δω at various angles θ, we can plot Δω against sinθ to obtain a slope of 2 ki v. Knowing ki we can then determine v, the velocity of sound in the medium.
One can generally analyze the scattered light using a Fabry-Perot interferometer, needed because of the high frequency resolution required to distinguish the inelastically scattered light from the elastically scattered light that did not interact with phonons. A frequency spectrum will typically contain a broad central peak corresponding to the elasically scattered light, with two smaller peaks placed symmetrically on either side corresponding to phonon creation and anihilation.
Once v is determined, and if the density of the material is known, the material's Young's modulus can be determined. Also, the frequency shift is dependent on the orientation of the crystal plane with respect to the incident light. By performing the experiment at various azimuthal angles as well as incident angles, other elastic constants such as C11, C12 and C44 can be determined.