Ralph Torres physics undergrad at ateneo. doing theory & ai safety research.

Ateneo theory

Posted 2024-06-01

goal

output

R. Torres, Q. Sugon, and C. Bennett, Interference of two circularly polarized far-field dipole radiation: energy and momentum density computations via geometric algebra (unpublished, w. 2021), proposal

In this paper, we revisit the two-source interference problem by employing two circularly polarized electric dipoles as sources. We formulate the electromagnetic interference by establishing an expression for the dipole in the far-field radiation zone via geometric algebra. This expression describes the electromagnetic field as a unified mathematical object in the form of the sum of electric field and imaginary magnetic field in spherical coordinates. We then calculate the energy and momentum densities resulting from the interference. The computation allows us to construct the intensity profile and interference pattern of the two-dipole system which are then to be compared to the findings in the interference literature.

This paper is essentially an extension of the geometric algebra formulation by [10]. The electromagnetic wave in that formulation is propagating through planar wave fronts, whereas in this paper, it propagates through spherical wave fronts. We may verify the results of [10] by approximating the spherical wave fronts as planar since the former is locally flat geometrically speaking. The scope of this paper restricts us to the formulation of the electromagnetic field expression only for the circularly polarized case. However, a possible extension to the more general elliptical case is being considered. We also restrict to the electromagnetic waves propagating through the far-field region of the dipole as the near-field zone contains non-radiative terms in the electromagnetic field expression.

[10]: M. W. C. Sze, Q. M. Sugon, and D. J. McNamara, “Oblique superposition of two elliptically polarized lightwaves using geometric algebra: is energy–momentum conserved?”, 12 (2010).