Optical Knowledge Sharing - Optical Polarization 2

2.2 Basic Polarization States

A. Elliptical Polarization

Elliptical polarization is the most fundamental polarization state. In this case, the two electric field components have a constant phase difference (one propagates faster, the other slower), and the phase difference is not an integer multiple of ( \pi/2 ). The amplitudes can be either the same or different. When viewed along the direction of propagation, the trajectory of the electric field vector’s endpoint will outline an ellipse, as shown in the figure below:

B. Linear Polarization

Linear polarization is a special form of elliptical polarization. In this case, the two electric field components have no phase difference, and the electric field vector oscillates in a single plane. When viewed along the direction of propagation, the trajectory of the electric field vector’s endpoint is a straight line. If the amplitudes of the two components are the same, this results in 45-degree linear polarization, as shown in the figure below:

C. Circular Polarization

Circular polarization is another special form of elliptical polarization. In this case, the two electric field components have a 90-degree phase difference and the same amplitude. When viewed along the direction of propagation, the trajectory of the electric field vector’s endpoint is a circle, as shown in the figure below:

2.3 Classification of Light Sources by Polarization

Light emitted directly from ordinary light sources is an irregular collection of countless polarized lights, so it is not possible to observe any preferred direction of light intensity directly. This type of light, which has the same intensity in all directions of vibration, is called natural light. It has randomly varying polarization states and phase differences, including all possible vibration directions perpendicular to the direction of light propagation, and does not exhibit polarization. Common examples of natural light include sunlight and light from household bulbs.

Completely polarized light has a stable electromagnetic wave oscillation direction, with the two components of the electric field having a constant phase difference. It includes the aforementioned linearly polarized light, elliptically polarized light, and circularly polarized light.

Partially polarized light contains components of both natural light and polarized light. For example, the laser beams we often use are neither completely polarized nor unpolarized, so they belong to partially polarized light. To quantify the proportion of polarized light in the total light intensity, the concept of the Degree of Polarization (DOP) is introduced. It is the ratio of the intensity of polarized light to the total light intensity, ranging from 0 to 1, where 0 indicates unpolarized light and 1 indicates completely polarized light. Additionally, the Degree of Linear Polarization (DOLP) is the ratio of the intensity of linearly polarized light to the total light intensity, and the Degree of Circular Polarization (DOCP) is the ratio of the intensity of circularly polarized light to the total light intensity. In everyday life, light emitted from common LED lights is also partially polarized light.

2.4 Conversion Between Polarization States

Many optical components can affect the polarization state of a light beam. These effects can sometimes be desired by the user and sometimes not. For example, when a light beam is reflected, its polarization state usually changes. Taking natural light as an example, after being reflected off a water surface, it becomes partially polarized light. As long as the light beam is not reflected or does not pass through any polarizing medium, its polarization state remains stable.

To quantitatively change the polarization state of a light beam, polarizing optical components can be used. For example, a quarter-wave plate is a common polarizing component made of birefringent crystal material, with a fast axis and a slow axis. It can delay the phase of the electric field vector parallel to the slow axis by ( \pi/2 ) (90°), while the electric field vector parallel to the fast axis experiences no delay. Thus, when linearly polarized light with a 45-degree polarization angle is incident on a quarter-wave plate, the transmitted light beam becomes circularly polarized light, as shown in the figure below. First, a linear polarizer converts natural light into linearly polarized light, and then the linearly polarized light passes through the quarter-wave plate, becoming circularly polarized light, with no change in light intensity. Similarly, when the light beam propagates in the reverse direction, circularly polarized light with a 45-degree polarization angle incident on the quarter-wave plate becomes linearly polarized light.

Using an integrating sphere mentioned in previous articles, linearly polarized light can be converted into unpolarized light. When linearly polarized light enters the integrating sphere, it undergoes multiple reflections inside the sphere, disrupting the vibration of the electric field. This results in unpolarized light at the output end of the integrating sphere.

2.5 P-Polarized Light, S-Polarized Light, and Brewster’s Angle

P-polarized light and S-polarized light are both linearly polarized light with perpendicular polarization directions. They are meaningful when considering the reflection and refraction of light beams. As shown in the figure below, when a light beam is incident on a surface, forming reflected and refracted beams, the plane formed by the incident light beam and the normal is defined as the plane of incidence. P-polarized light (from the German word “Parallel”) is light with a polarization direction parallel to the plane of incidence, while S-polarized light (from the German word “Senkrecht”) is light with a polarization direction perpendicular to the plane of incidence.

P-Polarized and S-Polarized Light 

Under normal circumstances, when natural light is reflected and refracted at the interface of a dielectric, the reflected and refracted light are both partially polarized. Only when the angle of incidence is at a specific angle, the polarization state of the reflected light is completely S-polarized (perpendicular to the plane of incidence), and the polarization state of the refracted light is almost entirely P-polarized (parallel to the plane of incidence). This specific angle of incidence is called Brewster’s angle. When light is incident at Brewster’s angle, the reflected light and refracted light are perpendicular to each other. Utilizing this characteristic, linearly polarized light can be generated.