Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Stokes’ Theorem and Its Applications

Stokes’ Theorem and Its Applications

Stokes’ Theorem provides a fundamental connection between the circulation of a vector field along a closed boundary and the cumulative rotational behavior across the surface it encloses. For a smooth three-dimensional surface with an oriented boundary curve, this theorem offers a unified way to relate motion along the edge to local rotational effects distributed over the surface.Mathematical FormulationThe theorem states that the circulation of a vector field along a closed curve is equal to...

Stokes' Law

Stokes' Law

Viscous forces, like friction, are intermolecular forces that resist the relative motion of molecules over each other. When a solid body moves through a liquid, viscous forces drag it in the opposite direction. The force's magnitude depends on the solid's shape and size, as well as its speed and the liquid's coefficient of viscosity, density and temperature.
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only for low Reynolds...

Divergence and Stokes' Theorems

Divergence and Stokes' Theorems

The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write numerous physical laws...

General State of Stress

General State of Stress

The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...

Transformation of Plane Stress

Transformation of Plane Stress

Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's faces...

Relation between Mathematical Equations and Block Diagrams

Relation between Mathematical Equations and Block Diagrams

In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Femtosecond-laser-induced shockwaves in water generated at an air-water interface.

Optics express·2013

Same author

Angular distribution of diffuse reflectance from incoherent multiple scattering in turbid media.

Applied optics·2013

Same author

Energy transfer between laser filaments in liquid methanol.

Optics letters·2012

Same author

Multiple scattering effects on the remote sensing of the speed of sound in the ocean by Brillouin scattering.

Applied optics·2010

Same author

Angular distribution of the forward light scattering from a quartz fiber.

Applied optics·2010

Same author

Empirical equation for the index of refraction of seawater.

Applied optics·2010

Same journal

Multifunctional reconfigurable terahertz metasurface based on vanadium dioxide phase transition: achieving broadband absorption and efficient polarization conversion.

Applied optics·2026

Same journal

High-Q-factor electromagnetically induced transparency utilizing quasi-bound states in the continuum in an all-dielectric terahertz metasurface.

Applied optics·2026

Same journal

Automated stitching interferometry for high-precision metrology of X-ray mirrors.

Applied optics·2026

Same journal

Experimental demonstration of an approach to designing a metal-dielectric DBR resonant cavity structure.

Applied optics·2026

Same journal

High-precision wavefront reconstruction from a single-shot interferogram using a physics-driven hybrid feature calibration network.

Applied optics·2026

Same journal

Ultra-high-Q Fano resonance based on coupled topological corner states in Kagome photonic crystals.

Applied optics·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 14, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Relationships between elements of the Stokes matrix.

E S Fry, G W Kattawar

|March 25, 2010

Summary

This summary is machine-generated.

Stokes matrices, though having sixteen elements, are defined by four amplitudes and three phase differences. These relationships offer crucial consistency checks for experimental measurements of light scattering.

More Related Videos

In Situ Measurement of Vacuum Window Birefringence using 25Mg+ Fluorescence

In Situ Measurement of Vacuum Window Birefringence using ²⁵Mg⁺ Fluorescence

Published on: June 13, 2020

Related Experiment Videos

Last Updated: Jun 14, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

In Situ Measurement of Vacuum Window Birefringence using 25Mg+ Fluorescence

In Situ Measurement of Vacuum Window Birefringence using ²⁵Mg⁺ Fluorescence

Published on: June 13, 2020

Area of Science:

Optics
Light Scattering
Polarimetry

Background:

Stokes matrices describe the polarization state of light.
Sixteen elements define a Stokes matrix, derived from fundamental scattering amplitudes and phase differences.
Relationships exist between these elements under specific scattering conditions.

Purpose of the Study:

To explore the fundamental relationships between the elements of a Stokes matrix.
To identify how these relationships change when considering ensembles of particles.
To provide a framework for validating experimental polarimetry data.

Main Methods:

Analysis of the mathematical structure of the Stokes matrix.
Derivation of relationships based on scattering theory for single particles.
Investigation of the impact of incoherent summation of Stokes matrices from particle ensembles.

Main Results:

Nine independent relationships connect the sixteen elements of a Stokes matrix for single-particle scattering.
For ensembles of particles, these relationships transform into six one-way inequalities.
These inequalities serve as essential consistency checks for experimental data.

Conclusions:

The inherent relationships within Stokes matrices are robust.
The derived inequalities provide a powerful tool for verifying experimental measurements in polarimetry.
This work simplifies the interpretation of complex scattering phenomena.