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Birefringence of crystals can
modify the Polarization State of light which is very useful in many
applications. This type of optical components are called
birefringent wave plates or retardation plates (or just wave plates or
retarders for short).
The velocities of the extraordinary and ordinary
rays through the birefringent materials vary inversely with their
refractive indices. The difference in velocities gives rise to a phase
difference when the two beams recombine. In the case of an incident
linearly polarized beam this is given by a=2pd(ne-no)/l(a-phase
difference; d-thickness of waveplate; ne,
no-refractive indices of extraordinary
and ordinary rays respectively; l-wavelength). At any specific wavelength
the phase difference is governed by the thickness of the waveplate. Red Optronics provides the following
waveplates: octadic-wave
(l/8), quarter-wave (l/4), half-wave
(l/2) and full-wave (l) plates. Half
Wave Plate The half wave plate can be used to rotate the
polarization state of a plane polarized light as shown in Figure 1.
 Suppose a plane-polarized wave is normally incident on a
wave plate, and the plane of polarization is at an angle q with
respect to the fast axis, as shown. After passing through the plate,
the original plane wave has been rotated through an angle 2q.
A half-wave plate is very handy in rotating
the plane of polarization from a polarized laser to any other
desired plane (especially if the laser is too large to rotate).
Most
large ion lasers are vertically polarized. To obtain
horizontal polarization, simply place a half-wave plate in the beam
with its fast (or slow) axis 45° to the vertical. The l/2 plates can also change left
circularly polarized light into right circularly polarized light or
vice versa. The thickness of half waveplate is such that the phase
difference is 1/2 wavelength (l/2, Zero order) or certain
multiple of 1/2-wavelength [(2n+1)l/2, multiple
order].
Quarter Wave Plate
Quarter wave plate are used to
turn plane-polarized light into circularly  polarized light and vice
versa. To do this, we must orient the wave plate so that equal
amounts of fast and slow waves are excited. We may do this by
orienting an incident plane-polarized wave at 45° to the fast (or
slow) axis, as shown in Figure 2. When a l/4 plate is double passed, i.e.,
by mirror reflection, it acts as a l/2 plate and rotates the plane
of polarization to a certain angle, i.e., 90°. This scheme is widely
used in isolators, Q-switches, etc.
The thickness
of the quarter waveplate is such that the phase difference is 1/4
wavelength (l/4, Zero order) or certain multiple of
1/4-wavelength [(2n+1)l/4, multiple order].
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