Precise control of the polarization state of the beam is necessary to achieve the best performance of optical systems and optical components. Characteristics such as reflectivity, insertion loss, and beam splitting ratio are also different for different polarization states. Polarization is also important over other properties of light, as it is used to transmit signals and make sensitivity measurements. Even when the light intensity is constant, the polarization state of the beam can be used to transmit information. By demodulating the polarization state of the beam, it is possible to reveal how light is modulated after interaction with matter (magnetic, chemical, mechanical), and sensors and measurement devices can be designed based on this change in polarization state. In view of this, optical components that can filter, modify, and characterize the polarization state of a light source are valuable. The same polarization control can be achieved by taking advantage of the reflective, absorption, and transmission properties of the materials in these components. The following is a discussion of the physical phenomena that enable polarization control and the key components that utilize polarization control.
Figure 1: Description of linearly polarized waves (left) and standard symbols for linearly polarized light.
As shown in Figure 1, the direction of the electric field vibration of the light wave is perpendicular to the direction of propagation. Since the electric field is a vector quantity, it can be represented by an arrow with magnitude (length) and direction. This direction indicates the direction of polarization of the light. There are three basic polarization states: linearly polarization, circular polarization, and elliptical polarization. These three polarization terms describe the path drawn by the tip as the electric field propagates through space. Figure 1 shows a temporal snapshot of linearly polarized light, all confined to a single plane, although the electric field direction is different. Thus, at a fixed point on the z-axis, the tip of the arrow will swing up and down along a line with respect to time, and the angle of this line relative to the optical axis represents the polarization state of the line-polarized light. For circularly polarized light, the electric field vector tip forms a spiral trajectory, and for a fixed point in the z-direction, the vector rotates with time, like the second hand on a watch. Circularly polarized light can be left- or right-handed, depending on whether the direction of rotation is clockwise or counterclockwise.
Ellipsoidal polarization is the most prevalent polarization case, it is the same as circular polarization, but it differs in magnitude on the major and minor axes (for circular polarization, they are equal).
Incoherent light sources, such as lamps, LEDs, or the sun, typically emit unpolarized light, which is a random superposition of all polarization states. And the output of the laser is luminous.
It is often highly polarized, i.e., consists almost entirely of a linear polarization state. The analysis of the polarization of a laser can be simplified by decomposing the polarization state into two components in the orthogonal direction. The symbols in the upper part of the table represent unpolarized, vertically polarized, and horizontally polarized light, for the graph in the figure, vertically along the y-axis and horizontally along the x-axis. When the plane of incidence is specified (see the lower half of the table in Figure 1), the polarization component gets a specific name, s-polarization refers to the component perpendicular to the plane, and p-polarization is the component parallel to the plane. Examples depicting linearly polarized light are shown in the rest of the diagrams in this section.
Polarized light interacts with optical materials either by selectively filtering the corresponding polarization state or by converting the incident polarization state to another polarization state. This polarization control relies on a certain optical property of the material, which is manifested as having different responses to the emitted light in different polarization states. Specifically, there is birefringence for different input polarization states, that is, different polarization states of light have different refractive indexes, that is, anisotropy. This anisotropy affects the transmission and absorption properties of light, and is the main implementation mechanism for polarization devices and waveplates, as described below. In addition, even isotropic materials (with the same refractive index for different polarizations) can be selected by reflection for polarization.
The Fresnel equation describes the change in reflectivity with the angle of incidence. For linearly polarized light, the reflectivity of the s-polarized and p-polarized varies with the angle of incidence. There is an angle of incidence in which the p-rays are fully transmitted, or have zero reflection, and the s-rays are partially reflected, and this angle is known as the Brewster angle (b). This angle can be determined according to Snell's law, b = arctan(n 2 n 1). Figure 2 shows the phenomenon of light incident from air to the surface of a dielectric material at an angle of incidence b 56°. This polarization selectivity can be used to produce strongly polarized light in the laser cavity as well as for fine tuning of the output laser wavelength.
Figure 2: When the angle of incidence is equal to the Brewster angle, the corresponding polarization (left), the reflectance of the plate as a function of the angle of incidence shows that the p-polarization appears to the minimum under the Brewster angle condition.
The transmittance of a polarizer is strongly dependent on the polarization state of the incident light. Polarizers typically filter line-polarized light, so an ideal polarizer would result in 100 transmissions from one polarization component while filtering out all orthogonal components (see Figure 3). In fact, some undesirable polarization will also be transmitted. The ratio of transmittance of the transmittance of the polarized light of the target after passing through the polarizer and the transmittance of the undesirable polarized light (simply by rotating the polarizer by 90°) is defined as the extinction ratio. A higher extinction ratio indicates a higher polarization purity in the transmitted light. The difference between a polarizer and a Brewster plate is that the transmitted light in the former is highly polarized, while the latter is not (only the reflection is highly polarized).
Figure 3: Effect of polarizer on unpolarized light, which is divided into p-light and s-light (right) after passing through the Gran-laser calcite polarizer.
Polarizers rely on birefringent materials, which can exhibit polarization-dependent absorption and refraction due to the fact that the refractive index is complex. The first type of polarizer is based on the selective absorption of incident light, often referred to as a dichroic polarizer. A typical material used for this anisotropic absorption is a stretched polymer elongated silver crystal. The strong absorption axis of the material is perpendicular to the desired direction of output polarization, so that the undesirable polarization state is strongly absorbed. There is also a different type of polarizer that is based on the anisotropy of birefringent crystals, such as calcite. Depending on the crystal axis aligned by the polarization components, the birefringent crystal will produce O light or E light. These lights undergo different refractive indices and have different critical angles of total reflection, resulting in one polarization component being reflected and the other being transmitted. Two calcite prisms are placed back to back to form a rectangular optical element, and the final transmitted beam will be in the same direction as the incident beam. Depending on whether a high damage threshold and a large reception angle are required, the gap between the prisms can be either air or optically clear adhesives.
Polarizers are used to filter the incident polarization state, increase its purity, or separate the orthogonal components of a linearly polarized beam. However, the polarizer cannot be the input of light.
Polarization states are converted to different polarization states. If you want to convert the polarization state, you need an optical element called a waveplate or retarder. In order to understand how it works, it is important to understand that any polarization state, not just linear polarization, can be decomposed into orthogonal components. The difference between the polarization states is generated by the phase difference between the orthogonal components. Linear polarization has an in-phase component, i.e., there is no phase difference, but it has different amplitudes depending on its angle. Circularly and elliptically polarized components have a phase difference of 2 or quarters of a wavelength (the different components of circular polarization have the same amplitude, while the different components of elliptical polarization have different amplitudes). Therefore, in order to convert one polarization state to another, the phase difference between the two components must be controlled. This can be achieved by incident a polarized beam into a birefringent crystal, causing either the O or E waves to experience a different phase delay. How waveplates (one-part and half-waveplate) convert one polarization state to another is shown in Figure 4, an important example of polarization conversion is shown on the right side of Figure 4. A half-wave plate can rotate the angle of a linearly polarized beam to any other angle and can be used to rotate a vertically polarized laser beam to obtain horizontal polarization. In addition, waveplates and polarizers can be combined to form variable attenuators and isolators (reducing the effect of the return light on the resonator).
Figure 4: A common application for a general polarization conversion using a waveplate (left) and a half-waveplate for rotating linear polarization to twice the angle of incidence (right).