A Hestenes Spacetime Algebra Approach to Light Polarization

Sugon, Quirino M.; McNamara, Daniel J.

doi:10.1007/978-1-4612-0089-5_26

Cited by 2 publications

(2 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…are the electromagnetic field [29,31] and the space-time derivative operator, respectively. Distributing the space-time derivative operator and applying the definition of the geometric product to the nabla operator, we get…”

Section: A Maxwell's Equationmentioning

confidence: 99%

Polarization ellipse and Stokes parameters in geometric algebra

2011

View full text Add to dashboard Cite

In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.

show abstract

Section: A Maxwell's Equationmentioning

confidence: 99%

Polarization ellipse and Stokes parameters in geometric algebra

2011

View full text Add to dashboard Cite

show abstract

“…In the second section, we shall review geometric algebra and calculus within the framework of Hestenes's spacetime algebra in spacetime split form via Clifford (Dirac) algebra Cl4,0. [15,16] In the third section, we shall revisit Maxwell's equation and use it to derive the Energy-Momentum equation. We shall show that the scalar and vector parts of the latter are the two conservations laws, while the imaginary vector part is a relation for the curl of the Poynting vector.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic energy-momentum equation without tensors: a geometric algebra approach

Sugon,

McNamara

2008

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, we define energy-momentum density as a product of the complex vector electromagnetic field and its complex conjugate. We derive an equation for the spacetime derivative of the energy-momentum density. We show that the scalar and vector parts of this equation are the differential conservation laws for energy and momentum, and the imaginary vector part is a relation for the curl of the Poynting vector. We can show that the spacetime derivative of this energy-momentum equation is a wave equation. Our formalism is Dirac-Pauli-Hestenes algebra in the framework of Clifford (Geometric) algebra Cl4,0.

show abstract

A Hestenes Spacetime Algebra Approach to Light Polarization

Cited by 2 publications

References 4 publications

Polarization ellipse and Stokes parameters in geometric algebra

Polarization ellipse and Stokes parameters in geometric algebra

Electromagnetic energy-momentum equation without tensors: a geometric algebra approach

Contact Info

Product

Resources

About