Polarization States of Lasers: A Comprehensive Analysis of s/p Polarization and o/e Rays

The polarization state of a laser essentially describes the vibration direction of the electric field vector. In optical and optical communication systems, the two most common polarization classification systems are:

 

● s/p polarization (senkrecht/parallel): Used to describe the behavior of light at interfaces

● o/e Rays (ordinary/extraordinary): Used to describe the propagation of light in anisotropic materials

 

These two systems are often mixed in engineering applications, but from a physical perspective, they correspond to two completely different constraint mechanisms and belong to different levels of description systems.

 

Engineering-Level Understanding: Differences Between the S Polarization and P Polarization

 

s-Polarization and p-Polarization (Interface Coordinate System)

 

Definition Criterion: Incident plane: A plane jointly determined by the propagation direction of light and the normal of the interface.

 

 

When the incident angle meets a specific condition (i.e., Brewster's angle, which is approximately 56° for glass), the reflected light becomes completely s-polarized, and the refracted light consists of p-polarized light and partial s-polarized light. This phenomenon is used in the design of laser resonators to reduce reflection loss.

 

① s-Polarization (senkrecht polarization, vertical polarization)

 

Electric field direction: Perpendicular to the incident plane

Equivalent understanding: The electric field is parallel to the interface

 

Memory aid: senkrecht (German for "perpendicular") → perpendicular to the incident plane

 

② p-Polarization (parallel polarization)

 

Electric field direction: Lies within the incident plane

 

Memory aid: parallel → within the incident plane

 

Core Characteristics:

o-Ray and e-Ray (Crystal Coordinate System)

 

Definition Criterion: Crystal optical axis and its dielectric anisotropy.

 

 

① o-Ray (ordinary ray)

 

Refractive index: Independent of the propagation direction (constant)

 

Propagation characteristics:

 

● Satisfies the conventional law of refraction

● The direction of the wave vector is consistent with the direction of energy propagation

 

② e-Ray (extraordinary ray)

 

Refractive index: Varies with the propagation direction

 

Propagation characteristics:

 

● Determined by anisotropy

● The direction of energy propagation (Poynting vector) is generally not completely consistent with the direction of the wave vector

 

 

 

Unity of Physical Nature: Perspective from Maxwell's Equations

 

The two types of polarization can be unified into one sentence:

 

The polarization state is the eigenstate of Maxwell's equations under specific constraint conditions.

 

 

Two types of constraints correspond to two types of polarization:

 

 

Nature of s/p Polarization

 

■ At the interface, the electromagnetic field must satisfy:

 

● Continuity of the tangential component of the electric field

● Continuity of the tangential component of the magnetic field

 

■ Under this constraint, the electromagnetic field is naturally decomposed into two decoupled modes:

 

● TE mode (corresponding to s-polarization)

● TM mode (corresponding to p-polarization)

 

s/p polarization is the result of eigen-decomposition determined by boundary conditions.

 

Nature of o/e Rays

 

■ In anisotropic media:

 

● The dielectric constant is a tensor

● The electric field must satisfy: D = ε · E

 

■ From this, a set of allowed propagating eigenpolarization states is obtained:

 

● o-Ray

● e-Ray

 

o/e Rays are the eigenpropagation modes determined by the material's dielectric tensor.

 

Unified Core Conclusion:

Why the s/p Polarization and o/e Rays Cannot Be Mixed

 

 

Summary in one sentence: s/p polarization is a "description method" of polarization, while o/e Rays are the "intrinsic existence form" of polarization.

 

Practical Significance in Coupling Scenarios Such as Optical Communication/Silicon Photonics/CPO

 

Interface Problems → Use s/p Polarization

 

● Silicon photonics grating coupling

● Chip end-face coupling

● Optical coating and reflection control

● FAU optical coupling

 

Focus: Coupling efficiency + Polarization Dependent Loss (PDL) + Reflection loss

 

Material/Device Problems → Use o/e Rays

 

● Lithium niobate modulators

● Polarizing Beam Splitters (PBS)

● Waveplates and polarization controllers

● Polarization-maintaining fibers

 

System-Level Problems (e.g., CPO / Optical Engine)

 

In practical systems, the following usually exist simultaneously:

 

● Interface effects (s/p polarization)

● Material anisotropy (o/e Rays)

● Waveguide mode evolution

 

The final polarization behavior is jointly determined by "boundary conditions + material properties".

 

Final Summary

 

Within the framework of electromagnetic theory: The polarization state is the eigenstate of Maxwell's equations under specific constraints.

 

● Interface constraints → s/p polarization

● Material constraints → o/e Rays

 

 

The two correspond to two different physical mechanisms: external boundaries and internal materials, belonging to different levels of description systems and cannot be directly mixed.

 

In one sentence: All polarization problems essentially boil down to one question: Under given constraints, in what directions can the electric field stably exist?