Brillouin Spectroscopy

Brillouin spectroscopy is an empirical spectroscopy technique which allows the determination of elastic moduli of materials. The technique uses inelastic scattering of light when it encounters acoustic phonons in a crystal, a process known as Brillouin scattering, to determine phonon energies and therefore interatomic potentials of a material. The scattering occurs when an electromagnetic wave interacts with a density wave, photon-phonon scattering. Brillouin spectroscopy is an empirical spectroscopy technique which allows the determination of elastic moduli of materials. The technique uses inelastic scattering of light when it encounters acoustic phonons in a crystal, a process known as Brillouin scattering, to determine phonon energies and therefore interatomic potentials of a material. The scattering occurs when an electromagnetic wave interacts with a density wave, photon-phonon scattering. This technique is commonly used to determine the elastic properties of materials in mineral physics and material science. Brillouin spectroscopy can be used to determine the complete elastic tensor of a given material which is required in order to understand the bulk elastic properties. Brillouin spectroscopy is similar to Raman spectroscopy in many ways; in fact the physical scattering processes involved are identical. However, the type of information gained is significantly different. The process observed in Raman spectroscopy, Raman scattering, involves high frequency molecular rotational and vibrational modes. Information relating to modes of vibration, such as the six normal modes of vibration of the carbonate ion, (CO3)2−, can be obtained through a Raman spectroscopy study shedding light on structure and chemical composition, whereas Brillouin scattering involves the scattering of photons by low frequency phonons providing information regarding elastic properties. Optical phonons measured in Raman spectroscopy have wavenumbers on the order of 10 –10000 cm−1 , while phonons involved in Brillouin scattering are on the order of 0.1 – 6 cm−1. This order of magnitude difference becomes obvious when attempting to run Raman spectroscopy vs. Brillouin spectroscopy experiments. In Brillouin scattering, and similarly Raman scattering, both energy and momentum are conserved in the relations: Where ω and k are the angular frequency and wavevector of the photon, respectively. While the phonon angular frequency and wavevector are Ω and q. Subscripts i and s correspond to incident and scattered waves. The first equation is the result of the application of the conservation of energy to the system of the incident photon, the scattered photon, and the interacting phonon. Applying conservation of energy also sheds light upon the frequency regime in which Brillouin scattering occurs. The energy imparted on an incident photon from a phonon is relatively small, generally around 5-10% that of the photon’s energy. Given an approximate frequency of visible light, ~1014 GHz, it’s easy to see that Brillouin scattering generally lies in the GHz regime. The second equation describes the application of conservation of momentum to the system. The phonon, which is either generated or annihilated, has a wavevector which is a linear combination of the incident and scattered wavevectors. This orientation will become more apparent and important when the orientation of the experimental setup is discussed.