# Ateneo Geometric Algebra Group publishes in JOSA A 2010: Oblique superposition of two elliptically polarized lightwaves using geometric algebra: is energy–momentum conserved?

Michelle Wynne C. Sze, Quirino M. Sugon, Jr., and Daniel J. McNamara, “Oblique superposition of two elliptically polarized lightwaves using geometric algebra: is energy–momentum conserved?,” J. Opt. Soc. Am. A 27, 2468-2479 (2010). doi:10.1364/JOSAA.27.002468

Abstract

In this paper, we use Clifford (geometric) algebra Cl3,0 to verify if electromagnetic energy–momentum density is still conserved for oblique superposition of two elliptically polarized plane waves with the same frequency. We show that energy–momentum conservation is valid at any time only for the superposition of two counter-propagating elliptically polarized plane waves. We show that the time-average energy–momentum of the superposition of two circularly polarized waves with opposite handedness is conserved regardless of the propagation directions of the waves. And, we show that the resulting momentum density of the superposed waves generally has a vector component perpendicular to the momentum densities of the individual waves.

© 2010 Optical Society of America

History
Original Manuscript: July 29, 2010
Manuscript Accepted: September 18, 2010
Revised Manuscript: September 12, 2010
Published: October 22, 2010

Ateneo Physics News Notes:

• Michelle Wynne C. Sze finished her B.S. in Physics at the Ateneo de Manila University last March 2010.  She started doing research on the geometric algebra paper last 2nd semester of 2010, while taking her elective course on “Calculus on Manifolds for Physicists” under Dr. Quirino Sugon Jr.   Her undergraduate thesis, however, is not on theoretical physics but on experimental physics under Dr. Raphael Guerrero of the Ateneo Photonics Laboratory.  Their work was published in Applied Optics 2010 with Jose Ramon A. Batiller as co-author: Deformable curvature and beam scanning with an elastomeric concave grating actuated by a shape memory alloy. Ms. Sze is currently taking her M.S. in Physics at the University of Physics–Diliman.
• Dr. Quirino M. Sugon Jr. is a faculty of the Ateneo Physics Department.  He coordinates the Ateneo Geometric Algebra Group $(GA)^{2\dagger}$ and the Kyushu University’s Space Environment Research Center (SERC) Subcenter at Manila Observatory.  Dr. Sugon works as a postdoctoral student of Fr. Daniel J. McNamara, S.J.
• Fr. Daniel J. McNamara, S.J. is currently on leave as a Professor of the Ateneo Physics Department.  He is presently teaching at the Ateneo de Davao University.  He is also the Associate Director for Research at the Manila Observatory.

Brylle Mark Carriaga (BS Ps ’10), Michelle Wynne Sze (BS Ps ’10), Dr. Quirino Sugon Jr., and Artoni Ang (BS Ps ’10) during a Physics Undergraduate Thesis defense last February 2010 at the Padre Faura Hall, Room F-318. On the left background is Mr. Jerry Barretto (Ph.D. in Physics, Candidate).