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Pockels effect
Demonstratingthe Pockels effectin a conoscopic beam path
Objects of the experiment
To identify the optical axis of the birefringent crystal of the Pockels cell in a conoscopic beam path.
To demonstrate the
Pockels effect in a conoscopic beam path.
To measure the half-wave voltage of the Pockels cell.
The Pockels effect
The
Pockels effect is the name given to the occurrence ofbirefringence and to the change in existing birefringence phe-nomena in an electric field linearly proportional to the electricfield strength. It is related to the
Kerr effect, although in thelatter case the birefringence increases exponentially with theelectric field strength. For reasons of symmetry, the Pockelseffect can only occur in crystals with no inversion center,whereas the Kerr effect can occur in all substances.
When the direction of the light beam and the optical axis ofbirefringence are perpendicular to each other, we call this a"transverse configuration" (see Fig. 1). The electric field isapplied in the direction of the optical axis. For Pockels cells in
Schematic diagram of a Pockels cell in transverse configu-
the transverse configuration, lithium niobate (LiNbO
Lithium niobate crystals are optically uniaxial, negatively
Diagram of a conoscopic beam path for demonstrating
birefringent and have the main refractive indexes
n
the ordinary beam, and
ne = 2.20 for the extraordinary beam(measured using the wavelength of the He-Ne laser, l =632.8 nm.
Birefringence in a conoscopic beam path
The proof of birefringence in a conoscopic beam path isdescribed in numerous optics textbooks. A crystal with plane-parallel cut faces is illuminated with a divergent, linearlypolarized light beam, and the light passing through it is ob-served behind a perpendicularly aligned analyzer (see Fig. 2).
The optical axis of the birefringence is clearly apparent in theinterference image, as it is indicated by the symmetry in itsvicinity. In this experiment, the optical axis is parallel to the
entrance and exit surfaces; this is why the interference patternconsists of two sets of hyperbolas [1] which are rotated by 908with respect to one another. The real axis of the first hyperbolaset is parallel to the optical axis, while that of the second setis perpendicular to the optical axis.
LD Physics Leaflets
1 High-voltage power supply, 10 kV . . .
1 He-Ne laser, linearly polarized . . . .
1 Polarization filter . . . . . . from
1 Optical bench, 1 m, standard cross-section
1 Translucent screen . . . . . . .
1 Safety connection lead, red . . . .
1 Safety connection lead, blue . . . .
1 Safety connection lead, 10 cm . . . .
The dark lines of the interference image are caused by light
Interference pattern in the conoscopic beam path with the
rays for which the difference between the optical paths of the
optical axis of the crystal in the direction of the arrow. The
extraordinary and the ordinary partial beam in the crystal is an
numbers represent the path difference between the ordi-
integral multiple of the wavelength. These light rays retain their
nary and the extraordinary partial beam. Thus for example
original linear polarization after passage through the crystal,
the lines with the value +1(−1) have the path difference
and are extinguished in the analyzer. The light rays reaching
the center of the interference image are normally incident onthe surface of the crystal. For these rays, the path differencebetween the extraordinary and the ordinary partial beam is
D =
d ⋅ (
no −
ne),
where
d = 20 is the thickness of the crystal in the direction of
The Pockels effect magnifies or reduces the difference of the
the beam. The path difference corresponds to approximately
main refractive indices
no –
ne, depending on the sign of the
2800 wavelengths of the laser light used. however, D is not
applied voltage. This in turn alters the difference D – m ⋅ l, and
usually precisely a whole multiple of l, but rather lies between
thus the position of the dark interference lines. If the so-called
two values, Dm = m ⋅ l and Dm+1 = (m + 1) ⋅ l. The dark lines
half-wave voltage
Up is applied, the value of D is changed by
in the first hyperbola set thus correspond to the path differ-
one-half wavelength. The dark interference lines shift to the
ences Dm+1, Dm+2, Dm+3, etc., and those of the second set to
positions of the bright lines, and vice versa. This process
Dm, Dm−1, Dm−2, etc. (Fig. 3). The position of the dark lines, or
repeats itself each time the voltage is increased by
Up.
better their distance from the center, depends on the magni-tude of the difference between D and m ⋅ l.
Safety note
The He-Ne laser fulfills the German technical standard
Carry out all measurements in a darkened room.
"Safety Requirements for Teaching and Training Equip-
Do not insert the rods of the optical components all the way in
ment – Laser, DIN 58126, Part 6" for class 2 lasers. When
the optics riders, so that subsequent fine adjustment of the
the precautions described in the Instruction Sheet are
height can be carried out.
observed, experimenting with the He-Ne laser is not
Fig. 4 shows the experiment setup; the position of the left edge
of each optics rider is given in cm.
Never look directly into the direct or reflected laserbeam.
Do not exceed the glare limit (i. e. no observer should
Setting up the optical components:
feel dazzled).
Mount the He-Ne laser, the 5-mm lens
(a) and the 50-mm
lens
(b). Carefully turn the laser and the 5-mm lens and
adjust their heights so that optimum illumination of the
50-mm lens is achieved.
Set up the translucent screen at a suitable distance, andattach a piece of white paper to the screen.
LD Physics Leaflets
b) Demonstrating the Pockels effect:
Experiment setup for demonstrating the Pockels effect
(a) Lens, f = 5 mm
Return the pointer on the Pockels cell to the initial position
(b) Lens, f = 50 mm
(+458 or −458 with respect to the analyzer).
(c) Pockels cell
Slowly increase the voltage
U (do not exceed 2 kV!) and
(pointer position: ± 458 with respect to analyzer)
observe the changes in the interference pattern.
(d) Polarization filter as analyzer
(pointer position: ± 90
Reduce the voltage to 0 V, connect the plus-socket of the
8 to polarization direction of laser)
high-voltage power supply to the ground socket andreverse the connections on the Pockels cell.
Set up the polarization filter as the analyzer and vary the
Once again, increase the voltage
U (do not exceed 2 kV!)
direction of polarization until you obtain the minimum in-
and observe the changes in the interference pattern.
tensity on the screen.
Add the Pockels cell to the assembly and slide it into the
c) Determining the half-wave voltage:
exact position of the minimum beam cross-section. Ob-serve the screen and make sure that light reflections on the
Set the voltage to
U = 0 V and mark the dark lines of the
interior surfaces of the crystal and the plate capacitor in the
interference pattern on the piece of paper using a green
Pockels cell are avoided.
Turn the pointer by either +458 or −458 with respect to the
Slowly increase the voltage
U and record each value at
which the bright and dark interference lines are exactlycongruent with the markings on the piece of paper.
Adjust the height of the laser, the 5-mm lens and, if neces-sary, the Pockels cell as well until the center of the hyper-bola sets in the interference pattern is in the center of thefield of view.
Measuring example and evaluation
If necessary, turn the Pockels cell on the rod axis.
a) Demonstrating birefringence:
When the Pockels cell is rotated around the axis of the light
Connect the Pockels cell to the left output of the high-volt-
beam, the interference image turns as well. In this case, the
age power supply (max. short-circuit current 100 mA); be
real axis of the first hyperbola set is always parallel to the
sure to connect the minus-socket to the ground socket.
optical axis of the crystal (indicated by the direction of the
Turn the potentiometer of the power supply all the way to
the left; then switch on the high-voltage power supply andactivate the left-hand output with the selector button.
Maximum bright-dark contrast is achieved when the anglebetween the optical axis and the analyzer is ± 458. The screenis dark when the optical axis is parallel or perpendicular to the
Carrying out the experiment
a) Demonstrating birefringence:
b) Demonstrating the Pockels effect:
Compare the position of the hyperbola set in the interfer-
When the voltage has the correct polarity, the dark interference
ence pattern with the position of the pointer on the Pockels
lines of the first hyperbola set (real axis of the hyperbolas
parallel to the optical axis of the crystal) move toward the
Slowly vary the position of the pointer on the Pockels cell
center as the voltage increases, while those of the second
and note the changes in the interference pattern.
hyperbola set move away from the center.
LD Physics Leaflets
The two hyperbolas with the path difference Dm+1 = (m + 1) ⋅ l
At the values for the voltage
U given in Table 1, the intensity of
move to the center at a voltage
U1 (see Fig. 5); thus, the center
the lines at the marked points in the interference pattern
is dark. When the voltage is increased further, the two hyper-
change from bright to dark, as the path difference between the
bolas change over to the second hyperbola set and there
ordinary and the extraordinary partial beam changes by one-
become continuously larger. At a voltage
U2 the next two
half the wavelength. The difference between these voltages is
hyperbolas move across the center to the other hyperbola set,
the half-wave voltage Up. This has a value of approx. 0.5 V.
the following two at a voltage
U3 and so on. The interval
The change in the birefringence d
no – d
ne after applying the
between the voltages
U1,
U2 and
U3 corresponds to twice the
half-wave voltage is very small. Using equation (I), we can
half-wave voltage (see below).
When the polarity of the voltage is reversed, the hyperbolas
move in the opposite direction. Thus, the difference of the main
=
d ⋅ (d
n
o − d
ne),
refractive indexes
no –
ne increases or decreases due to thePockels effect, depending on the polarity of the voltage.
d
no – d
ne = 16 ⋅ 10–16
c) Determining the half-wave voltage:
Table 1: Measurement results for determination of the half-wave voltage
Brightness on translucent
screen at the markedlocation
M. Born and E. Wolf,
Principles of Optics, Pergamon Press
Changes in the conoscopic interference image due to
the Pockels effect; the respective hyperbola of the inter-ference order m + 1 are emphasized with bold lines
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