This paper describes Meep, a popular free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetism. In particular, we focus on aspects of implementing a full-featured FDTD package that go beyond standard textbook descriptions of the algorithm, or ways in which Meep differs from typical FDTD implementations. These include pervasive interpolation and accurate modeling of subpixel features, advanced signal processing, support for nonlinear materials via Padé approximants, and flexible scripting capabilities. PACS

Nanoelectromechanical systems (NEMS) hold promise for a number of scientific and technological applications. In particular, NEMS oscillators have been proposed for use in ultrasensitive mass detection, radio-frequency signal processing, and as a model system for exploring quantum phenomena in macroscopic systems. Perhaps the ultimate material for these applications is a carbon nanotube. They are the stiffest material known, have low density, ultrasmall cross-sections and can be defect-free. Equally important, a nanotube can act as a transistor and thus may be able to sense its own motion. In spite of this great promise, a room-temperature, self-detecting nanotube oscillator has not been realized, although some progress has been made. Here we report the electrical actuation and detection of the guitar-string-like oscillation modes of doubly clamped nanotube oscillators. We show that the resonance frequency can be widely tuned and that the devices can be used to transduce very small forces.

Magnesium diboride differs from ordinary metallic superconductors in several important ways, including the failure of conventional models to predict accurately its unusually high transition temperature, the effects of isotope substitution on the critical transition temperature, and its anomalous specific heat. A detailed examination of the energy associated with the formation of charge-carrying pairs, referred to as the 'superconducting energy gap', should clarify why MgB(2) is different. Some early experimental studies have indicated that MgB(2) has multiple gaps, but past theoretical studies have not explained from first principles the origin of these gaps and their effects. Here we report an ab initio calculation of the superconducting gaps in MgB(2) and their effects on measurable quantities. An important feature is that the electronic states dominated by orbitals in the boron plane couple strongly to specific phonon modes, making pair formation favourable. This explains the high transition temperature, the anomalous structure in the specific heat, and the existence of multiple gaps in this material. Our analysis suggests comparable or higher transition temperatures may result in layered materials based on B, C and N with partially filled planar orbitals.

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We present a study of the superconducting transition in MgB2 using the ab-initio pseudopotential density functional method and the fully anisotropic Eliashberg equation. Our study shows that the anisotropic Eliashberg equation, constructed with ab-initio calculated momentum-dependent electron-phonon interaction and anharmonic phonon frequencies, yields an average electron-phonon coupling constant λ = 0.61, a transition temperature Tc = 39K, and a boron isotope-effect exponent αB = 0.31 with a reasonable assumption of µ * = 0.12. The calculated values for Tc, λ, and αB are in excellent agreement with transport, specific heat, and isotope effect measurements respectively. The individual values of the electron-phonon coupling λ( k, k ′ ) on the various pieces of the Fermi surface however vary from 0.1 to 2.5. The observed Tc is a result of both the raising effect of anisotropy in the electron-phonon couplings and the lowering effect of anharmonicity in the relevant phonon modes.Although MgB 2 is a readily available sp-bonded material, superconductivity in this material with a transition temperature of T c = 39 K was found only very recently [1]. This relatively high T c has motivated many studies, as has the observation that the detailed superconducting properties of MgB 2 show significant deviations from those calculated using the standard BCS model. The isotope effect exponent for boron α B is reduced substantially from the conventional value for sp metals [2,3], and the average electron-phonon coupling strength λ obtained from specific heat measurement [4,5] seems too small to justify the high T c . In addition, specific heat measurements [4,5], tunneling [6] and photoemission [7] spectra, and point-contact spectroscopy [8,9] show low energy excitations suggesting a secondary gap. Theoretical calculations show that the Fermi surface has several pieces and is very anisotropic [10], and that the electron-phonon coupling is dominated by the in-plane B-B stretching modes (E 2g ) [10][11][12] which have a large anharmonicity [13,14]. The electron-phonon interaction varies strongly on the Fermi surface [14,15], and a twoband model suggests a multigap scenario [14]. However, there has not yet been a quantitative, first-principles calculation of T c including the full variation of the electronphonon interaction on the Fermi surface and the anharmonicity of the phonons to help confirm the phononmediating pairing mechanism for superconductivity in MgB 2 .In this letter, we present T c and isotope-effect exponents for MgB 2 obtained by solving the k and ω dependent Eliashberg equation. It is shown that the anisotropy (i.e., the electronic-state dependence) of the electronphonon interaction on the Fermi surface is strong enough to raise T c to 39K even though the interaction is weakened by the anharmonicity of the phonons as compared to the harmonic case. In addition, it is shown that the anharmonicity of the phonons reduces α B to 0.31. These results show that conventional phonon-mediated electron pairing theory can explai...

Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (pixelization). We show that accuracy can be significantly improved by using a subpixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory and compare it with other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.

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