We study the presence of dark and bright modes in a planar metamaterial with a double rod unit cell introducing geometric asymmetry in rod lengths. The dark mode displays a Fano-type resonance with a sharp asymmetric profile, rendering it far more sensitive than the bright mode to slight variations of the dielectric environment. This peculiar feature may envisage the possible application of the asymmetric dimer metamaterial as an optical sensor for chemical or biological analysis, provided that the effect of material losses on the dark mode quality factor is properly taken into account.

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The planetary bodies are more of a spheroid than they are a sphere thereby making it necessary to describe motions in a spheroidal coordinate system. Using the oblate spheroidal coordinate system, a more approximate and realistic description of motion in these bodies can be realized. In this paper, we derive the Riemannian acceleration for motion in oblate spheroidal coordinate system using the golden metric tensor in oblate spheroidal coordinates. The Riemannian acceleration in the oblate spheroidal coordinate system reduces to the pure Newtonian acceleration in the limit of c 0 and contains post-Newtonian correction terms of all orders of c −2 . The result obtained thereby opens the way for further studies and applications of the motion of particles in oblate spheroidal coordinate system.

The existing theories of gravitation are founded mostly on the Euclidean theoretical Physics in which the influence of gravitational field is ignored. In this paper we derive the Newton’s dynamical gravitational field equation based upon the great metric tension in which the influence of gravitation is consider.