Comments on ``Differential cross section for Aharonov-Bohm effect with nonstandard boundary conditions''

We show that the violation of rotational symmetry for differential cross section for Aharonov-Bohm effect with nonstandard boundary conditions has been known for some time. Moreover, the results were applied to discuss the Hall effect and persistent currents of fermions in a plane pierced by a flux tube.Comment: 4 pages, plain latex, Author URL http://www.amolf.nl/external/wwwlab/atoms/theory/, replaced with final versio

Inward and Outward Integral Equations and the KKR Method for Photons

In the case of electromagnetic waves it is necessary to distinguish between inward and outward on-shell integral equations. Both kinds of equation are derived. A correct implementation of the photonic KKR method then requires the inward equations and it follows directly from them. A derivation of the KKR method from a variational principle is also outlined. Rather surprisingly, the variational KKR method cannot be entirely written in terms of surface integrals unless permeabilities are piecewise constant. Both kinds of photonic KKR method use the standard structure constants of the electronic KKR method and hence allow for a direct numerical application. As a by-product, matching rules are obtained for derivatives of fields on different sides of the discontinuity of permeabilities. Key words: The Maxwell equations, photonic band gap calculationsComment: (to appear in J. Phys. : Cond. Matter), Latex 17 pp, PRA-HEP 93/10 (exclusively English and unimportant misprints corrected

Resonance-Induced Effects in Photonic Crystals

For the case of a simple face-centered-cubic photonic crystal of homogeneous dielectric spheres, we examine to what extent single-sphere Mie resonance frequencies are related to band gaps and whether the width of a gap can be enlarged due to nearby resonances. Contrary to some suggestions, no spectacular effects may be expected. When the dielectric constant of the spheres $\epsilon_s$ is greater than the dielectric constant $\epsilon_b$ of the background medium, then for any filling fraction $f$ there exists a critical $\epsilon_c$ above which the lowest lying Mie resonance frequency falls inside the lowest stop gap in the (111) crystal direction, close to its midgap frequency. If $\epsilon_s <\epsilon_b$, the correspondence between Mie resonances and both the (111) stop gap and a full gap does not follow such a regular pattern. If the Mie resonance frequency is close to a gap edge, one can observe a resonance-induced widening of a relative gap width by $\approx 5$.Comment: 14 pages, 3 figs., RevTex. For more info look at http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm

How many orthonormal bases are needed to distinguish all pure quantum states?

We collect some recent results that together provide an almost complete answer to the question stated in the title. For the dimension d=2 the answer is three. For the dimensions d=3 and d>4 the answer is four. For the dimension d=4 the answer is either three or four. Curiously, the exact number in d=4 seems to be an open problem

Photonic crystals of coated metallic spheres

It is shown that simple face-centered-cubic (fcc) structures of both metallic and coated metallic spheres are ideal candidates to achieve a tunable complete photonic bandgap (CPBG) for optical wavelengths using currently available experimental techniques. For coated microspheres with the coating width to plasma wavelength ratio $l_c/\lambda_p \leq 10$ and the coating and host refractive indices $n_c$ and $n_h$, respectively, between 1 and 1.47, one can always find a sphere radius $r_s$ such that the relative gap width $g_w$ (gap width to the midgap frequency ratio) is larger than 5% and, in some cases, $g_w$ can exceed 9%. Using different coatings and supporting liquids, the width and midgap frequency of a CPBG can be tuned considerably.Comment: 14 pages, plain latex, 3 ps figures, to appear in Europhys. Lett. For more info on this subject see http://www.amolf.nl/research/photonic_materials_theory/moroz/moroz.htm

A simple formula for the L-gap width of a face-centered-cubic photonic crystal

The width $\triangle_L$ of the first Bragg's scattering peak in the (111) direction of a face-centered-cubic lattice of air spheres can be well approximated by a simple formula which only involves the volume averaged $\epsilon$ and $\epsilon^2$ over the lattice unit cell, $\epsilon$ being the (position dependent) dielectric constant of the medium, and the effective dielectric constant $\epsilon_{eff}$ in the long-wavelength limit approximated by Maxwell-Garnett's formula. Apparently, our formula describes the asymptotic behaviour of the absolute gap width $\triangle_L$ for high dielectric contrast $\delta$ exactly. The standard deviation $\sigma$ steadily decreases well below 1% as $\delta$ increases. For example $\sigma< 0.1$ for the sphere filling fraction $f=0.2$ and $\delta\geq 20$. On the interval $\delta\in(1,100)$, our formula still approximates the absolute gap width $\triangle_L$ (the relative gap width $\triangle_L^r$) with a reasonable precision, namely with a standard deviation 3% (4.2%) for low filling fractions up to 6.5% (8%) for the close-packed case. Differences between the case of air spheres in a dielectric and dielectric spheres in air are briefly discussed.Comment: 13 pages, 4 figs., RevTex, two references added. For more info see http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm

Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices

We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a viable alternative to the plane-wave method to analyze the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we reproduce the main features of the spectrum obtained by the plane wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eights and ninth bands if the dielectric constant $\epsilon_s$ of spheres is lower than the dielectric constant $\epsilon_b$ of the background medium. If $\epsilon_s> \epsilon_b$, no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast $\epsilon_b/\epsilon_s$ for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of an fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.Comment: 19 pages, 6 figs., plain latex - a section on coated spheres, two figures, and a few references adde

A superconvergent representation of the Gersten-Nitzan and Ford-Webber nonradiative rates

An alternative representation of the quasistatic nonradiative rates of Gersten and Nitzan [J. Chem. Phys. 1981, 75, 1139] and Ford and Weber [Phys. Rep. 1984, 113, 195] is derived for the respective parallel and perpendicular dipole orientations. Given the distance d of a dipole from a sphere surface of radius a, the representations comprise four elementary analytic functions and a modified multipole series taking into account residual multipole contributions. The analytic functions could be arranged hierarchically according to decreasing singularity at the short distance limit d ---> 0, ranging from d^{-3} over d^{-1} to ln (d/a). The alternative representations exhibit drastically improved convergence properties. On keeping mere residual dipole contribution of the modified multipole series, the representations agree with the converged rates on at least 99.9% for all distances, arbitrary particle sizes and emission wavelengths, and for a broad range of dielectric constants. The analytic terms of the representations reveal a complex distance dependence and could be used to interpolate between the familiar d^{-3} short-distance and d^{-6} long-distance behaviors with an unprecedented accuracy. Therefore, the representations could be especially useful for the qualitative and quantitative understanding of the distance behavior of nonradiative rates of fluorophores and semiconductor quantum dots involving nanometal surface energy transfer in the presence of metallic nanoparticles or nanoantennas. As a byproduct, a complete short-distance asymptotic of the quasistatic nonradiative rates is derived. The above results for the nonradiative rates translate straightforwardly to the so-called image enhancement factors Delta, which are of relevance for the surface-enhanced Raman scattering.Comment: 30 pages including 6 figure

Rashba effect in 2D mesoscopic systems with transverse magnetic field

We present semiclassical and quantum mechanical results for the effects of a strong magnetic field in Quantum Wires in the presence of Rashba Spin Orbit coupling. Analytical and numerical results show how the perturbation acts in the presence of a transverse magnetic field in the ballistic regime and we assume a strong reduction of the backward scattering interaction which could have some consequences for the Tomonaga-Luttinger transport. We analyze the spin texture due to the action of Spin Orbit coupling and magnetic field often referring to the semiclassical solutions that magnify the singular spin polarization: results are obtained for free electrons in a twodimensional electron gas and for electrons in a Quantum Wire. We propose the systems as possible devices for the spin filtering at various regimes.Comment: 12 pages, 12 figures, to appear in Phys. Rev.