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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.
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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.
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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.
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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 dno – dne 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 ⋅ (dn o − dne), refractive indexes no – ne increases or decreases due to thePockels effect, depending on the polarity of the voltage.
dno – dne = 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 LD DIDACTIC GmbH ⋅ Leyboldstrasse 1 ⋅ D-50354 Hürth ⋅ Phone (02233) 604-0 ⋅ Telefax (02233) 604-222 ⋅ E-mail: [email protected] by LD DIDACTIC GmbH Printed in the Federal Republic of Germany Technical alterations reserved

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