polarizer may be inserted, as shown. The analyzer, oriented at 90?
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to the polarizer, prevents any
light from being transmitted when no voltage is applied to the electro-optic material. When the
corre
ct volta
ge is applied to the dev
ice, the direc
tion of the polari
zati
on is rotated by 9
0?
. Then the
light will pass
through the analyzer.
Fig. 2
Schematic diagram of the operation of a modulator based
on the electro-optic effect. In this configuration, the voltage is
applied parallel to the direction of light propagation.
Two types of electro-optic effect have been used: the Kerr electro-optic effect, which is shown by
liquids such as nitrobenzene,
and the Pockels electro-optic effect,
shown by crystalline m
aterials
such as ammonium dihydrogen phosphate or lithium niobate. Some early electro-optic devices used
nitrobenzene, but the liquid tends to polymerize in the presence of the intense laser light. Modern
electro-optic modulators use the Pockels effect. The electro-optic modulators are often called
Pockels cells.
The orien
tatio
n of the polari
zer and ana
lyz
er at 45?
to the vert
ical, as show
n in Figure 1, is a
common configuration, used with many commercial modulators. But the orientation depends on the
particular material used and on the direction in which the crystal has been cut. The manufacturer&#;s
instructions should be consulted to ensure proper orientation of the modulator and the directions of
the pass axes for
the polarizer and analyzer.
With the dire
ctio
n of polarizat
ion at 45?
to the verti
cal direc
tion, the pola
rizat
ion vect
or is
composed of two perpendicular components of equal intensity, one vertical and one horizontal. The
crystalline element is oriented with its axes in a specified orientation (which depends on the
crystalline sy
mmetry of the particular material). The applied voltage
induces birefringence in the
crystal
, so
that the two
components of polarization travel with
different velocities inside the crystal.
This induced birefringence is the basis of the electro-optic effect.
The two components travel
in the same direction
through the crystal and do not
become physically
separated. But the two components, in phase as they enter the crystal, emerge with different phases.
As they traverse the crystal, they accumu
late a phase difference,
which depends on the
distance
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traveled and on the applied voltage. When the beams emerge from the crystal, the polarization of
the combined single beam depends on the accumulated phase difference. If the phase difference is
one-half wav
elength, the pol
arization is rota
ted by
90?
from its original
direction. This by
itself
does not change the intensity of the beam. But, with the analyzer, the transmission of the entire
system varie
s,
according to
T
=
T
0
sin
2
(p D
nL
/l ) Equation 1
where
T
is the transmission,
T
0
the intrinsic transmission of the assembly, taking into account all the
losses, D
n
the birefringence (that is, the difference in refractive index for the two polarizations),
L
the length of the crystal, and l the wavelength of the light. The birefringence is an increasing
function of the applied voltage, so that the transmission of the device will be an oscillatory function
of applied voltage.
The maximum transmission occurs when
D
n
= l /2
L
Equation 2
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