We present experimental scattering data at microwave frequencies on a structured metamaterial that exhibits a frequency band where the effective index of refraction (n) is negative. The material consists of a two-dimensional array of repeated unit cells of copper strips and split ring resonators on interlocking strips of standard circuit board material. By measuring the scattering angle of the transmitted beam through a prism fabricated from this material, we determine the effective n, appropriate to Snell's law. These experiments directly confirm the predictions of Maxwell's equations that n is given by the negative square root of epsilon.mu for the frequencies where both the permittivity (epsilon) and the permeability (mu) are negative. Configurations of geometrical optical designs are now possible that could not be realized by positive index materials.

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Experimental Verification of a Negative Index of Refraction

Recent advances in the field of nonlinear optical phenomena are reviewed with particular empphasis placed on such topics as parametric oscillation self-focusing and trapping of laser beams, and stimulated Raman, Rayleigh, and Brillouin scattering. The optical frequency radiation is treated classically in terms of the amplitudes and phases of the electromagnetic fields. The interactions of light waves in a mterial are then formulated in terms of Maxwell's equations and the electric dipole approximation. In this method, non-linear susceptibility tensors are introdueed which relate the induced dipole moment to a power series expansion in field strengths. The tensor nature and the frequency dependence of the nonlinearity coefficients are considered. The various experimental, observations are described and interpreted in terms of this formalism.

https://ieeexplore.ieee.org/iel5/5/31089/01447053.pdf

Nonlinear optics

In this paper, potential‐dependent transformations are used to transform the four‐component Dirac Hamiltonian to effective two‐component regular Hamiltonians. To zeroth order, the expansions give second order differential equations (just like the Schrodinger equation), which already contain the most important relativistic effects, including spin–orbit coupling. One of the zero order Hamiltonians is identical to the one obtained earlier by Chang, Pelissier, and Durand [Phys. Scr. 34, 394 (1986)]. Self‐consistent all‐electron and frozen‐core calculations are performed as well as first order perturbation calculations for the case of the uranium atom using these Hamiltonians. They give very accurate results, especially for the one‐electron energies and densities of the valence orbitals.

Relativistic regular two‐component Hamiltonians

This paper gives the 2010 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. The 2010 adjustment takes into account the data considered in the 2006 adjustment as well as the data that became available from 1 January 2007, after the closing date of that adjustment, until 31 December 2010, the closing date of the new adjustment. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2010 set replaces the previously recommended 2006 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.

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CODATA Recommended Values of the Fundamental Physical Constants: 2006

Quantum electrodynamical corrections to the fine structure of helium

The real part of the refractive index $n(\ensuremath{\omega})$ of a nearly transparent and passive medium is usually taken to have only positive values. Through an analysis of a current source radiating into a 1D ``left-handed'' material (LHM)---where the permittivity and permeability are simultaneously less than zero---we determine the analytic structure of $n(\ensuremath{\omega})$, demonstrating frequency regions where the sign of $\mathrm{Re}[n(\ensuremath{\omega})]$ must, in fact, be negative. The regime of negative index, made relevant by a recent demonstration of an effective LHM, leads to unusual electromagnetic wave propagation and merits further exploration.

/pdf/negative-refractive-index-in-left-handed-materials-114edb9z6s.pdf

Negative Refractive Index in Left-Handed Materials

A general discussion of the free-electron lasers (FEL's) with variable parameter wigglers is presented with a view towards their potential for the production of high power optical radiation at reasonable efficiency. The theoretical analysis is based upon a one-dimensional relativistic Hamiltonian formulation and is developed in a manner to take advantage of the analogy between the FEL process and radio frequency accelerators. Three promising operational modes are identified and analyzed. The first may be thought of as an electron decelerator and is thought to have the most promise for single-pass devices. Both oscillator and amplifier configurations are studied. The second is based upon adiabatic trapping and detrapping, intended to reduce the spread in electron energy typically induced by the FEL process. The third is based upon the method of phase area displacement. It has the advantage of wide gain bandwidth and small induced energy spread, and is thought to have the most promise for storage ring applications. Generally speaking, it is found that high peak power is intrinsic to these modes of operation. Potential problems from parasitic oscillations analogous to the stimulated Raman effect are analyzed, and some others arising from transverse inhomogeneity are identified.

Free-electron lasers with variable parameter wigglers

A simple and convenient approximation is obtained for the multiphoton energy-transfer processes which accompany the scattering of a charged particle by a scattering potential in the presence of a strong external electromagnetic field. It is expressed in terms of the differential elastic-scattering cross section combined with known functions, and is valid when the scattering potential is weak or when the wave frequency is small. A detailed form of the classical limit is obtained.

/pdf/charged-particle-scattering-in-the-presence-of-a-strong-4aao53wx4e.pdf

Charged-Particle Scattering in the Presence of a Strong Electromagnetic Wave

The question of whether the entire hadronic electromagnetic current operator can be identical with a linear combination of the renormalized field operators for the known neutral vector mesons ρ0, φ0, and ω0 is investigated in the context of a Lagrangian field theory. It is found that such an identity is completely consistent with gauge invariance, provided that these mesons are coupled only to conserved currents. The general renormalization problem of the strong interactions of these vector mesons is discussed. It is shown that the proposed identity between the hadronic electromagnetic current and the renormalized meson fields can be related to the possible identity between the unrenormalized currents generating the neutral vector mesons and those generating the photon; furthermore, this proposed identity leads to an exact relation between the entire O(e2) hadronic contribution to the photon propagator and the renormalized propagators of the neutral vector mesons, and such a relation implies, among other consequences, that to O(e2) and neglecting leptonic contributions, the ratio of the unrenormalized charge e0 and the renormalized charge e is finite. Various experimental applications are given. In particular, the analysis of φ−ω mixing and their leptonic decay rates is made independently of the approximate validity of the SU3 symmetry.

Norman M. Kroll

Papers

Quantum electrodynamical corrections to the fine structure of helium

Negative Refractive Index in Left-Handed Materials

Free-electron lasers with variable parameter wigglers

Charged-Particle Scattering in the Presence of a Strong Electromagnetic Wave

Neutral Vector Mesons and the Hadronic Electromagnetic Current