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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The most common types of waveplates are quarter-wave plates (λ/4 plates) and half-wave plates (λ/2 plates), where the difference of phase delays between the two linear polarization directions is π/2 or π, respectively, corresponding to propagation phase shifts over a distance of λ / 4 or λ / 2, respectively.

Some important cases are:

• When a light beam is linearly polarized, and the polarization direction is along one of the axes of the waveplate, the polarization remains unchanged.

• When the incident polarization does not coincide with one of the axes, and the plate is a half-wave plate, then the polarization stays linear, but the polarization direction is rotated. For example, for an angle of 45° to the axes, the polarization direction is rotated by 90°.

• When the incident polarization is at an angle of 45° to the axes, a quarter-wave plate generates a state of circular polarization. (Other input polarizations lead to elliptical polarization states.) Conversely, circularly polarized light is converted into linearly polarized light.

Within a laser resonator, two quarter-wave plates around the gain medium are sometimes used for obtaining single-frequency operation (→ twisted-mode technique). Inserting a half-wave plate between a laser crystal and a resonator end mirror can help to reduce depolarization loss. The combination of a half-wave plate and a polarizer allows one to realize an output coupler with adjustable transmission.

Many waveplates are made of crystalline quartz (SiO₂), as this optical material exhibits a wide wavelength range with very high transparency, and can be prepared with high optical quality. Other possible materials (to be used e.g. in other wavelength regions) are calcite (CaCO₃), magnesium fluoride (MgF₂), sapphire (Al₂O₃), mica (a silicate material), and some birefringent polymers.

There are optical devices which are somewhat related to waveplates:

• Fresnel rhomb retarders and other types of prism retarders have the same basic function as waveplates, but exploit polarization-dependent phase changes during total internal reflection. This principle allows broadband (achromatic) operation.

• A Babinet–Soleil compensator, containing a pair of birefringent wedges, can be used as a waveplate with a variable degree of retardation. Other versions of tunable waveplates such as the Berek compensator are based on variable tilting of birefringent plates.

• There are various types of fiber polarization controllers with similar functions.

• Electro-optic crystals and liquid crystal devices can be used to make electrically controllable waveplates, also called active retarders.

Video source link: https://www.youtube.com/watch?v=cwTDaXC3UbI