Symmetry, Unitarity, and Geometry in Electromagnetic Scattering

Abstract

occurs between the onset of the edipse and its midpoint. This agrees qualitatively with the work of Allais' with a paraconical pendulum, where the change of azimuth increased substantially in the 6rst half of the eclipse of 30 June 1954. Both these e6ects would seem to have a gI'RvltRt1onRl bRsls which cannot-bc explained by accepted classical theory.Both our experimental 6ndings and those of Allais cause one to question whether the classical laws of gravitation hold without modi6cation. CONCLUSIONQuantitative observations made with a precise torsion pendulum show, in agreement with many earlier, less precise recordings made at Harvard since 3.953, that ' Maurice F. C. Allais, Aerospace Kng. 18, 46 (1959). the times required to traverse a 6xed. fraction of its total angular path vary markedly during the hours before the eclipse and during its 6rst half, i.e. , up to its midpoint. Also the signihcant changes in these times do not coincide exactly with the astronomically determined. onset, midpoint, and endpoint of the eclipse.These variations are too great to be explained, on the basis of classical gravitational theory, by the relative change in position of the moon with respect to the earth and sun. This leads to the same conclusion arrived. at by Allaisthat classical gravitational theory needs to be modiaed to interpret his (and our) experimental results.Moreover, the 6ndings with the torsion pendulum, the sig~~~~~n™~~~~~~~~~~0~~~perpendicularly to the geogravitic vector, seem to indicate the possibility of a 6ne structure in these observations neither predicted nor recorded using the orthodox methods of quasistationary gravitational investigations.Upon de6ning vector spherical partial waves {Q ) as a basis, a matrix equation is derived describing scattering for general incidence on objects of arbitrary shape. With no losses present, the scattering matrix is then obtained in the symmetric, unitary form 8= -Q'~P, where (perfect conductor) Q is the Schmidt orthogonalisation of Q""= (k/v) J'de p(vXReg")Xg".g, integration extending over the object surface.For quadric (separable) surfaces, Q itself becomes symmetric, e fecting considerable simplihcation. A secular equation is given for constructing eigenfunctions of general objects. Finally, numerical results are presented and compared with experimental measurements.

Surface-enhanced Raman scattering and fluorescence near metal nanoparticles

“…To this end we employ extended Mie theory, expanding the field around each of the two spheres in terms of vector spherical harmonics representing magnetic and electric multipoles, 29,30 …”

Multiple Electromagnetic Scattering from a Cluster of Spheres. I. Theory

“…According to Waterman (1971) Eq. (15) defines the matrix on the left-hand side as the inverse of the electromagnetic T-matrix for the whole cluster.…”

Applicability of Effective Medium Approximations to Modelling of Mesocrystal Optical Properties

“…The T-matrix of a particle ensemble can be composed from the T-matrixes of the components [17]. Initially, the T-matrix approach was developed in the framework of the Null-Field method [25][26][27][28] or Extended Boundary Condition method [29], and is often not distinguished from them. However, the recent developments suggest that the T-matrix formalism can also be deduced from other simulation techniques [16].…”