ABSTRACT
In this paper, we use Clifford (geometric) algebra Cl(3,0) 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.
ABSTRACT
A concave diffraction grating with a tunable radius of curvature R is fabricated by embedding a nitinol wire within an elastomeric grating replica. Curvature of the grating is controlled via the shape memory effect, where strain in the wire is recovered due to martensite-austenite phase transformations induced by resistive heating. The generated force bends the grating into a variable curvature determined by applied current. The radius of curvature for the concave grating is variable from 170 to 44 mm over a current range of 0 to 2.5 A. Actuation of R redirects the grating normal, resulting in a scanning motion of the diffracted beam.
