Direct Energy, 2018a

3 PYROELECTRICS AND ELECTRO-OPTICS 65
3.4. The rst gure below shows the displacement ux density
a function of the strength of an appliedelectric eldintensity
in a non-electro-optic material.
displacement ux density
∣ −→ ∣
D
∣ −→ ∣
E
∣ −→ D
as
∣ −→ E ∣
The secondgure below shows the
∣ as a function of the strength of an
appliedelectric eldintensity ∣ in a ferroelectric electro-optic material.
The solidline corresponds to an unpoledmaterial. The dotted
line corresponds to the material after it has been poled in the â z direction,
andthe dashedline corresponds to the material after it has
been poledin the −â z direction.
(a) For the non-electro-optic material, ndthe relative permittivity,
ɛ r . Also ndthe magnitude of the material polarization, −→ P.
(b) Assume the ferroelectric electro-optic material is poledby a
strong external electric eld, andthen the eldis removed. Find
∣ after the exter-
the magnitude of the material polarization
nal eldis removed.
∣ −→ ∣
P
(c) Assume the ferroelectric material is poledin the −â z direction by
a strong external eld, and then the eld is removed. A dierent
external electric eldgiven by −→ E = 100â z
V
m
is applied. Find
the approximate relative permittivity of the material.
−→ DinC/m
2
400 · ɛ 0
200 · ɛ 0
100
−→ EinV/m