Page 280 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Phonon-Photon
for the change of the dielectric tensor ∆ε
the literature [7.19] ij due to strain can be found in
∆ε = – ε P ε S (7.92)
il ij jkmn kl mn
Acousto- The fourth order tensor P that mediates between strain and dielectric
jkmn
Optic Tensor tensor changes is called the acousto-optic tensor. Its values are specific
for the respective material under investigation.

We restrict the following discussion to cubic crystal lattices. In such sym-
metries the dielectric tensor has only diagonal elements of the same mag-
nitude and thus behaves like in an isotropic material, where we write
ε = ε δ , where we have δ = 0 for i ≠ j and δ = 1 for i = j as
ij r ij ij ij
usual. Inserting this into (7.92) we obtain a much simpler equation
2
∆ε = – ε P S (7.93)
il r ilmn mn
For a cubic material like GaAs the acousto-optic tensor has only three
non vanishing components out of 81. Those are [7.19] P = – 0.165 ,
1111
P = – 0.140 , and P = – 0.072 . Note that in this way the above
2222 2323
isotropic behavior of the dielectric constant vanishes and we have to deal
instead with a tensor. This also implies that the refractive index is no
longer simply the square root of the dielectric constant but rather gets
dependant on how the electromagnetic is polarized and what its propaga-
tion direction is. We will not go into detail how to calculate the changes
in the refractive index. A description can be found in [7.12]. We notice
that there is an effect that couples elastostatic properties to optics and
thus gives rise to various applications for monitoring these properties or
modulating light propagation through a crystal.

7.5.2 Light Propagation in Crystals: Phonon-Polaritons
Let us describe the electromagnetic field by the Maxwell equations and
the polarization by an equation of motion for undamped oscillators with

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