Hyper-Raman scattering is a three-photon process, the system is excited with two photons (ω_{i}) and emits one photon at the frequency 2ω_{i} ± ω.
Hyper-Raman or hyperpolarizability tensors
The hyperpolarizability (β) is a third range tensor, it contains 27 independet components collected in a 9x3 matrix:
Taking into account that the tensor is symmetric in the last two indeces ( β_{ijk} = β_{ikj} ) the number of independent componentes of β can be reduced from 27 to 18:
On the other hand, the components which are experimentally relevant are those with k = i.
Porto notation
It is a way to indicate the configuration of the Hyper-Raman scattering experiment. This notation expresses the orientation of the crystal with reference to the polarization of the laser in both the exicitation and analysing directions. The Porto notation, for Hyper-Raman scattering, consists of five letters:
A(BCD)E
A ≡ The direction of the propagation of the incident light (k_{i}).
B ≡ The direction of the polarization of the scattered light (E_{s}).
C and D ≡ The direction of the polarization of the incident light (E_{i}).
E ≡ The direction of the propagation of the scattered light (k_{s}).
Example: X(ZYY)Y
In this case, the direction of the propagation of the incident light is along the X direction while the direction of the scattered light is along the Y direction. The direction of the polarization of the incident lights is along the Y direction while the direction of the polarization of the scattered light is along the Z direction.
Back scattering geometry
One of the possible geometries which can be carried out in a Hyper-Raman scattering experiment is the back scattering geometry. In this geometry, the direction of the propagation of the incident and scattered light is the same but their senses are opposite. On the other hand, the propagation and polarization of the incident and scattered light must be ortogonal.
k_{i} = -k_{s}
k_{i} ⊥ E_{i} and k_{s} ⊥ E_{s}
Examples of back scattering geometry configurations:
-X(ZYY)X
-Z(YXX)X
-Y(XZZ)Y
...
Right angle scattering geometry
Right angle scattering geometry is another experimental configuration for Hyper-Raman scattering. In this geometry, the propagation and polarization of the incident and scattered light must be ortogonal.
k_{i} ⊥ E_{i}
k_{s} ⊥ E_{s}
Examples of right angle scattering geometry configuration: