Direct Energy, 2018a

3 PYROELECTRICS AND ELECTRO-OPTICS 59
n eo =
( 1
+ γ ∣ −→ E ∣ + s ∣ −→ E ∣ 2 −1/2
+ ...)
(3.12)
ɛ r x
[ ( 1
∣ ∣∣ −→
∣ ∣ ∣∣ ∣∣ −→
∣ )]
∣∣
2 −1/2
1+γɛ r x E + sɛr x E + ... (3.13)
ɛ r x
n eo =
n eo = n x
[1+γn 2 x ∣ −→ E ∣ + sn 2 x ∣ −→ E ∣ 2 −1/2
+ ...]
(3.14)
The quantityof Eq. 3.14 in brackets can be approximated using the binomial
expansion and keeping onlythe rst terms.
(
1+γn 2 x ∣ −→ E ∣ + sn 2 x ∣ −→ E ∣ 2 −1/2
+ ...)
≈
(
1 − 1 2 γn2 x
∣ −→ E
∣ − 1 2 sn2 x ∣ −→ E ∣ 2)
(3.15)
Finally, the overall index of refraction can be written as a polynomial expansion
of the strength of the external electric eld [10, p. 698].
n eo ≈ n x
(1 − 1 2 γn2 x ∣ −→ E ∣ − 1 2 sn2 x ∣ −→ E ∣ 2) (3.16)
The Pockels electro-optic eect is called the linear electro-optic eect while
the Kerr eect is called the quadratic eect due to the form of the equation
above.
3.3.2 Electro-Optic Eect in Crystalline Materials
As with the piezoelectric eect, we can determine which crystalline insulating
materials will exhibit the Pockels eect bylooking at the symmetries
of the material. To determine if a crystal can show the Pockels eect, determine
the crystal structure, identify the symmetries, and determine its
crystal point group. The Pockels eect occurs in noncentrosymmetric materials,
materials with a crystal structure with no inversion symmetry. Of
the 32 crystal point groups, 21 of these groups may exhibit the Pockels
electro-optic eect. For materials in these crystal point groups, χ (2) and
the Pockels coecient γ are nonzero. These 21 groups are also the piezoelectric
crystal point groups [10, ch. 18], and they are listed in Table 2.2.
In some crystalline materials which belong to these crystal point groups,
the Pockels eect is nonzero but too small to be measurable.
From Table 2.2 we can see that all materials that are piezoelectric are
also Pockels electro-optic and vice versa. Also, all materials that are pyroelectric
are piezoelectric but not the other wayaround. Thus, if a device is