Page 363 - Electrical Properties of Materials

Electro-optic, photorefractive, and nonlinear materials 345

13.4 Electro-optic, photorefractive, and nonlinear materials
Before talking more about applications, I shall first review some properties of
materials which make them suitable components for devices.
In electro-optic materials, the application of an electric field will affect the
index of refraction that an optical wave ‘sees’. Note that waves with different
electric polarizations are differently affected. The exact relationships are given
by tensors, a subject I am reluctant to enter, but if you are interested you can
attempt Exercise 13.6. Let me just say that the dielectric tensor (which relates
the three components of the electric field to the three components of the dielec-
tric displacement) has nine terms, and each of these terms may depend on the
three components of the electric field. Thus, altogether, the electro-optic tensor
has 27 components (only 18 if the symmetry of the dielectric tensor is taken
into account). There is no need to worry. In practice, usually, only one of the
numerous components is needed, and the effect may be presented in the form,

1 r is the electro-optic coefficient.

= rE . (13.1)
r
2
Since r = n , the change in refractive index may be written as
1 3
n =– n rE . (13.2) Note that r may be positive or
2
negative depending on crystal ori-
Taking LiNbO 3 as an example, n = 2.29, and for a certain orientation of the entation.
–1
crystal we have r =3.08 × 10 –11 mV . With reasonable voltages, one may
–1
6
obtain an electric field of about 10 Vm , causing a change in the refractive
–4
index of n =1.86 × 10 . It does not seem a lot, but it is more than enough
for a number of applications. The indices of refraction and the electro-optic
coefficients for some often used materials are given in Table 13.2.
The essential thing to remember is that in electro-optic crystals the refract-
ive index, and consequently the propagation of the wave, may be changed by
applying an electric field.
The properties of electro-optic materials are dependent, of course, on dir-
ection, but since the aim is no more than to give a general idea of the
ranges involved, only the largest components are listed for each material. The
wavelengths at which these values were measured are also indicated.

Table 13.2 Properties of electro-optic materials

Substance Wavelength Electro-optic Index of Static
(μm) coefficient refraction dielectric
–1
(10 –12 mV ) constant
Bi 12 SiO 20 0.514 2.3 2.22 56
BaTiO 3 0.514 820 2.49 4300
CdTe 1.0 4.5 2.84 9.4
GaAs 1.15 1.43 3.43 12.3
KNbO 3 0.633 380 2.33 50
LiNbO 3 0.633 32.6 2.29 78
ZnO 0.633 2.6 2.01 8.15