Page 279 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Interacting Subsystems
7.5 Phonon-Photon
The coupling of lattice deformations to light will be accentuated in the
following by two effects showing the static and dynamic behavior of the
interaction.

7.5.1 Elasto-Optic Effect
In a homogeneous material the coupling of an external electric field to
εε ε ε
the material manifests itself through the dielectric constant as indi-
cated in Section 4.1. The dielectric constant is a tensorial quantity with
components ε , and is therefore related to the crystal symmetry. Note
ij
that the dielectric tensor is symmetric. Distortion in the material will
change the dielectric tensor and therefore affect the properties of light
travelling through a crystal.

The index of refraction for an isotropic material, as it is applied in Sec-
tion 4.3.1, is simply the square root of the dielectric constant n = . ε
This gives rise to a change of the speed of light in material. As we know
that the dielectric property of a material is a tensorial quantity and that
this tensor is symmetric, there must be a speed of light related to the
polarization of the electromagnetic wave. We remember from linear alge-
bra that any symmetric tensor may be transformed in his proper coordi-
nate system, where the bases are give by its eigenvectors and its
eigenvalues are called the dielectric constants of the principle axes. So
depending on the symmetry of the crystal there may be up to three differ-
ent light propagation velocities. Therefore, the simple consideration with
the square root above in general holds for any principle direction involv-
ing the respective dielectric constants of the axes.

Any change in the dielectric properties of the material will effect the
components ε . These changes may result from strains internal to the
ij
material caused by an external load. Let us denote the strain, as given in
Chapter 2, by S in order not to confuse with the dielectric tensor.
ij
Remember that this is also a symmetric tensorial quantity. The relation

276 Semiconductors for Micro and Nanosystem Technology