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Guide to Polarized Light Principles: Definitions, Applications, and Why Distinguishing P-Polarized a


I. P-polarized light and S-polarized light are two types of linearly polarized light defined based on the orientation of light polarization relative to the plane of incidence (the plane formed by the incident light ray and the normal to the interface).

1. Key Reference: The Plane of Incidence
First, imagine a beam of light striking the interface between two media at an angle (e.g., from air into glass).
The incident ray and the normal line to the interface (perpendicular to the interface) form a plane called the “plane of incidence.”
2. Definition of P-polarized and S-polarized Light
P-polarized light: Full name Parallel-polarized light.
Polarization direction: Its electric vector is parallel to the incident plane.
Mnemonic: P = Parallel.

S-polarized light: Full name Senkrecht-polarized light (perpendicular polarization). “Senkrecht” is German for “perpendicular.”
Polarization direction: Its electric vector is perpendicular to the incident plane.
Mnemonic: S = Senkrecht / Perpendicular.
Visual Understanding: Extend your right hand. Your thumb represents the direction of light propagation, while the other four fingers represent the vibration direction of the electric vector. If the vibration oscillates “up and down” within the plane defined by your thumb and the normal line, it is P-polarized light. If it oscillates “side to side” (perpendicular to this plane), it is S-polarized light.

II. Why Distinguish Between P-Polarized and S-Polarized Light?

Because they behave very differently when interacting with a medium interface. This difference is primarily reflected in their reflectance and transmittance.
1. Differences in Reflectance - Fresnel Formulas
The Fresnel formulas describing reflection and refraction at an interface are given separately for P-polarized and S-polarized light.
Generally, under non-normal incidence, the reflectivity of S-polarized light is always higher than that of P-polarized light.
This implies that when non-polarized light (containing all polarization directions) strikes at an angle, the reflected light contains a greater proportion of S-polarized light. Consequently, the reflected light becomes partially polarized (predominantly S-polarized).
2. Brewster's Angle - A Critical Phenomenon
This is a unique property of P-polarized light.
There exists a specific angle of incidence known as Brewster's angle.
When light strikes at Brewster's angle, the reflectivity of P-polarized light becomes zero! All P-polarized light energy is refracted into the second medium.
The reflected light at this point is 100% S-polarized.
Application: This is one of the simplest methods to generate fully linearly polarized light (e.g., camera polarizing filters utilize this principle to eliminate glare reflections from glass or water surfaces).
3. Phase Shift Differences
During reflection, P-polarized and S-polarized light may undergo different phase shifts (e.g., from 0 to π), particularly during total internal reflection. This is crucial for designing optical films and waveguides.

III. Key Application Areas

Polarization Devices
1. Polarization-Splitting Prism:
By exploiting the difference in reflectivity between P-polarized and S-polarized light on a dielectric film, this device completely separates P-polarized and S-polarized light within a beam, outputting them in two distinct directions.
2. Brewster Window:
Used in laser cavities, a window positioned at the Brewster angle exhibits negligible loss for P-polarized light, enabling highly polarized P-polarized laser output.
3. Thin-Film Optics and Anti-Reflection/Enhancement Coatings:
When designing anti-reflection coatings for optical lenses, both P-polarized and S-polarized light must be considered simultaneously to optimize performance at the design angle.
Mirrors (e.g., those within laser cavities) must also exhibit high reflectivity for both P-polarized and S-polarized light.
4. Ellipsometry:
By measuring changes in the amplitude ratio and phase difference between P-polarized and S-polarized light after reflection from a sample surface, this technique enables extremely precise determination of thin-film thickness and optical constants.

Summary Comparison Table

Properties
P-polarized light (parallel polarization)
S-polarized light (perpendicular polarization)
Definition
Electric vector oscillation direction parallel to the incident plane
Electric vector oscillation direction perpendicular to the incident plane
Reflectivity
Generally low, zero at the Brewster angle
Always higher than P-polarized light
Brewster angle
Reflected light completely disappears
Reflected light is 100% S-polarized
Phase Shift
May exhibit specific phase jumps upon reflection, differing from S-polarized light
May exhibit specific phase jumps upon reflection, differing from P-polarized light
Primary Applications
Generating linearly polarized light (Brouistein window), low-loss transmission
Generating linearly polarized light (reflection), polarization splitting


In summary, the distinction between P-polarized and S-polarized light provides the fundamental framework for analyzing light-interface interactions (reflection, refraction, interference). Whenever an optical system involves oblique incidence, the independent behavior of these two polarization states must be considered.
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