Double Refraction and Malus’ Law

A green laser pointer (3) is used as light source. In a first experiment the
polarisation of the probe laser (3) is determined. For this purpose only
one polarizer (11) is used. The laser beam is expanded (10) and passes the
polarizer (11). By means of the photodetector (2) the intensity of the light
behind the second polarizer is detected and the value is displayed on the
controller (1). For different angles of the polarizer the intensity is drawn
into a graph with polar coordinates. If the laser is linearly polarized we
should expect a graph like (A).
To make sure that the laser light is linearly polarized, one polarizer is placed behind the beam expander and turned to maximum intensity. The second polarizer is used as analyser. A angular plot of
the intensity will yield the verification of the Malus’ law (A). For the
next experiment the polarizers are oriented in such a way that the
transmitted intensity is almost zero. The quarter waveplate (14) is
placed between the polarizer. Depending on the orientation of the
waveplate we will get elliptical (B) or circular polarized light (C).

Conoscopy with a quartz

By adding the lens (9) in the beam path, the laser beam creates a focus
in the distance of its focal length and subsequently it becomes divergent
and forms a “cone”. A double refractive quartz plate (13) is placed in the
so created focal plane. The crystal is cut in such a manner that the optical
axis lies perpendicular to the surface of the plate The divergent beam
can be interpreted as a bunch of rays with different propagation angle
passing the quartz crystal. All those rays which are retarded by λ/2 will
be blocked by the next polarizer creating a beautiful pattern of dark and
bright areas on the screen (5).

Conoscopy with a calcite crystal

With a value of Δn=0.172 calcite crystal has a more than 100 times
stronger double refraction than a quartz crystal with has a value of 0.0091.
The optical axis of the calcite crystal goes
from the upper left to the lower right corner
of the crystal as shown in the picture on the
left. Therefore we need to cut the crystal in
such a way that a beam can travel from one
corner to the other. Such a crystal is mounted to a post holder to permit
the study of the much stronger conoscopic pattern on the screen.

Characterising a Pockels Cell

A Pockels cell is placed in the focal plane of a polarized and a conoscopic
beam. By inserting a polarization analyser, beautiful patterns of interference can be observed on a screen and need to be interpreted. When the
high voltage to the Pockels cell is switched on, the crystal becomes biaxial and shows other interference patterns, characteristic for such crystals
of lower symmetry. Another measurement example is the determination
of the half wave voltage. At the lowest applicable voltage the polarisation
analyser is turned to maximum intensity. The cell voltage is increased
until the transmitted intensity becomes almost zero which is the case
when the phase retardation of the cell is λ/2. In this case the cell acts as
half waveplate