# polarization techniques

This application note describes short polarized light, delay, and some of the tools used to manipulate the polarization state of light. Also included are descriptions of component combinations that represent common light manipulation tools such as optical isolators, light attenuators, polarization rotators, and variable beamsplitters.

#### light polarization

In classical physics, light of a single color is described by an electromagnetic field in which electric and magnetic fields oscillate at a frequency (ν) related to wavelength (λ) as shown in the equation

C= λν

Where c is the speed of light. Visible light, for example, has wavelengths from 400 to 750 nm.

An important property of optical waves is their polarization state. A vertically polarized wave is one in which the electric field is only along the z-axis when the wave is propagating along the y-axis (Figure 1A). Similarly, a horizontally polarized wave is one in which the electric field is only along the x-axis. Any polarization state propagating along the y-axis can be superimposed on vertically and horizontally polarized waves with a certain relative phase. The amplitude of the two components is determined by projections of the direction of polarization along the vertical or horizontal axis. For example, light polarized at 45° to the xz plane is the same in amplitude and phase for both vertically and horizontally polarized light (Figure 1B).

Circularly polarized light is generated when a linear electric field component is λ/4 out of phase with the orthogonal component, as shown in Fig. 1C.

Elliptically polarized light represents an arbitrary phase shift between the two electric field components as shown in Figure 1D.

We produce linearly polarized light when we send unpolarized light through a polarizing medium whose axis coincides with the desired linear polarization. When this polarized light is passed through a second polarizer, only the components that are parallel to the polarization axis can escape while the orthogonal component is absorbed. When vertically polarized light is transmitted through a polarizer aligned at 45°, the amplitude of the exiting light is reduced by a factor of 1/lambda/2 and the intensity by 50% of the original intensity. When vertically polarized light is sent through a horizontally aligned polarizer, no component of the original light is parallel to the direction of polarization and no light escapes.

#### delay

Another useful tool for manipulating polarized light is the phase retarder. The phase delay is achieved by making the optical path length for one of the orthogonal polarizations different from the other.

#### Lambda/4 plate

When the orthogonal electric field components are equivalent, a phase shift in one component results in circularly polarized light, as shown in part C of FIG. Retarders that cause this shift are referred to as "Lamda/4 plate". They have the unique property of converting elliptically polarized light to linearly polarized light or converting linearly polarized light to circularly polarized light when the fast axis of the quarter-wave plate is 45° to the incident plane of polarization. This is done using birefringent uniaxial materials with two different indices of refraction. Light polarized along the direction of smaller index travels faster and hence this axis is called the fast axis. The other axis is the slow axis.

The alignment of lambda/4 plates is achieved using a linear polarizer and mirror as shown in FIG. Using a polarizing beam splitter, vertically polarized light is directed through an Lmada/4 plate onto a mirror. When the angle between the fast axis of the quarter-wave plate and the plane of polarization is 45°, the reflected light has a polarization that is 90° to the polarization of the original source. This maximizes the light at B and minimizes the light at reference point A as shown in Figure 2.

#### Lambda/2 plate

A retarder that produces a λ/2 phase shift is known as a "Lamda/2 plate". Lambda/2 plates can rotate the polarization of linearly polarized light to twice the angle between the fast axis of the retarder and the plane of polarization. If the fast axis of a lambda/2 plate is placed at 45° to the plane of polarization, a polarization rotation of 90° results.
When circularly polarized light is passed through a half-wave plate, the “handedness” of the polarization changes. This corresponds to shifting the horizontal polarization in figure C by one λ.

#### Optical isolators

Retarders used in conjunction with polarizers offer many useful devices. For example, optical isolation can be achieved by combining a linear polarizer with a lambda/4 plate. By correctly aligning this plate with the linear polarizer, linearly polarized light is converted to circularly polarized light. Because circularly polarized light exhibits a shift in “handedness” upon specular reflection, the reflected light is now linearly polarized and rotated 90° relative to the light exiting the isolator. Horizontally polarized light incident on a vertically aligned polarizer will be rejected.

#### Optical Attenuators

An optical attenuator is constructed by combining two linear polarizers and a half-wave plate. The input and output polarizers are crossed so that no light passes through them. However, inserting the half-wave plate allows light to pass through the device. The amount of light is determined by the angle between the optical axis of the incident polarizer and the half-wave plate. By placing the optical axis of the half-wave plate at a 45° angle to the incoming polarizer, maximum transmission is achieved. Align the optical axis of the half-wave plate with one of the two
The optical axes of the input or output polarizer provide the minimum transmission. How close the minimum is to zero transmission depends on the quality of the polarizers and the half-wave
disk used in the device.
By replacing the half-wave plate with a device that varies the polarization, such as a B. a variable retarder, a variable attenuator is created. This configuration is shown in Figure 4. If we orient the fast axis of the variable retarder at 45° to the input polarizer and modulate the delay between half-wave and full-wave, the transmission will vary between maximum and minimum, creating an optical shutter chopper.

#### polarization rotator

A simple polarization rotator consists of a half-wave plate in linearly polarized light. By rotating the half-wave plate, the polarization is rotated by twice the angle of the fast axis of the half-wave plate with the plane of polarization, as shown in Figure 5A. We achieve variable polarization rotation by aligning the fast axis of a variable retarder at 45° to the incoming polarization and following this component with a lambda/4 plate with its slow axis aligned with the incoming polarization, as shown in Figure 5B. The amount of rotation achieved depends on the amount of delay exhibited by the first retarder. The polarization axis is rotated through an angle that is half the phase shift provided by the variable retarder.