A "poor man's approach" to modelling of micro-structured optical fibres

Based on the scalar Helmholtz equation and the finite-difference approximation, we formulate a matrix eigenvalue problem for the calculation of propagation constants, beta(omega), in micro-structured optical fibres. The method is applied to index-guiding fibres as well as air-core photonic bandgap fibres, and in both cases qualitatively correct results are found. The strength of this approach lies in its very simple numerical implementation and its ability to find eigenmodes at a specific eigenvalue, which is of great interest, when modelling defect modes in photonic bandgap fibres.Comment: 9 pages including 5 figures. Accepted for Journal of Optics A: Pure and Applied Optic

Limits of slow-light in photonic crystals

While ideal photonic crystals would support modes with a vanishing group velocity, state-of-the art structures have still only provided a slow-down by roughly two orders of magnitude. We find that the induced density of states caused by lifetime broadening of the electromagnetic modes results in the group velocity acquiring a finite value above zero at the band gap edges, while attaining superluminal values within the band gap. Simple scalings of the minimum and maximum group velocities with the imaginary part of the dielectric function or, equivalently, the linewidth of the broadened states, are presented. The results obtained are entirely general and may be applied to any effect which results in a broadening of the electromagnetic states, such as loss, disorder, finite-size effects, etc. This significantly limits the reduction in group velocity attainable via photonic crystals.Comment: 5 pages, 3 figures, accepted for Physical Review

Imposing high-symmetry and tuneable geometry on lanthanide centres with chelating Pt and Pd metalloligands

Exploitation of HSAB preferences allows for high-yield, one-pot syntheses of lanthanide complexes chelated by two Pd or Pt metalloligands, [MII(SAc)4]2− (SAc− = thioacetate, M = Pd, Pt). The resulting complexes with 8 oxygen donors surrounding the lanthanides can be isolated in crystallographically tetragonal environments as either [NEt4]+ (space group: P4/mcc) or [PPh4]+ (space group: P4/n) salts. In the case of M = Pt, the complete series of lanthanide complexes has been structurally characterized as the [NEt4]+ salts (except for Ln = Pm), while the [PPh4]+ salts have been structurally characterized for Ln = Gd–Er, Y. For M = Pd, selected lanthanide complexes have been structurally characterized as both salts. The only significant structural difference between salts of the two counter ions is the resulting twist angle connecting tetragonal prismatic and tetragonal anti-prismatic configurations, with the [PPh4]+ salts approaching ideal D4d symmetry very closely (φ = 44.52–44.61°) while the [NEt4]+ salts exhibit intermediate twist angles in the interval φ = 17.28–27.41°, the twist increasing as the complete 4f series is traversed. Static magnetic properties for the latter half of the lanthanide series are found to agree well in the high temperature limit with the expected Curie behavior. Perpendicular and parallel mode EPR spectroscopy on randomly oriented powder samples and single crystals of the Gd complexes with respectively Pd- and Pt-based metalloligands demonstrate the nature of the platinum metal to strongly affect the spectra. Consistent parametrization of all of the EPR spectra reveals the main difference to stem from a large difference in the magnitude of the leading axial term, B02, this being almost four times larger for the Pt-based complexes as compared to the Pd analogues, indicating a direct Pt(5dz2)–Ln interaction and an arguable coordination number of 10 rather than 8. The parametrization of the EPR spectra also confirms that off-diagonal operators are associated with non-zero parameters for the [NEt4]+ salts, while only contributing minimally for the [PPh4]+ salts in which lanthanide coordination approximates D4d point group symmetry closely.LHD acknowledges support from NSF-CCT EMT 08-517. (08-517 - NSF-CCT EMT

Failure of standard approximations of the exchange coupling in nanostructures

We calculate the exchange coupling for a double dot system using a novel, numerically exact yet efficient technique, based on finite-element methods. Specifically, we evaluate the exchange coupling both for a quasi-one and a two-dimensional system, also including an applied magnetic field. Our numerical results provide a stringent test for standard approximation schemes (e.g., Heitler-London, Hund-Mulliken, Hubbard), and they show that the standard methods do not have reliable predictive power for real quantum-dot systems.Comment: 7 pages, 4 figure

Enhanced circular dichroism via slow-light in dispersive structured media

Circular dichroism (CD) is in widespread use as a means of determining enantiomeric excess. We show how slow-light phenomena in dispersive structured media allow for a reduction in the required optical path length of an order of magnitude. The same ideas may be used to enhance the sensitivity of CD measurements while maintaining the same optical path length through the sample. Finally, the sensitivity may be enhanced in frequency regimes where CD data is typically not accessible due to a modest chiral response of the enantiomers.Comment: 4 pages, 4 figure

On the Job Search and the Wage Distribution

Estimates of the structural parameters of a job separation model derived from the theory of on-the-job search are reported in this paper. Given that each employer pays the same wage to observably equivalent workers but wages are dispersed across employers, the theory implies that an employer's separation flow is the sum of an exogenous outflow unrelated to the wage paid and a job-to-job flow that decreases with the employer's wage. The specification estimated allows worker search effort to depend on the wage currently earned. The empirical results imply that search effort declines with the wage paid, as the theory predicts, using Danish IDA data for the years 1994-1995. Furthermore, the estimates for the full sample and four occupational sub-samples explain the employment effect, defined as the horizontal difference between the distribution of wages earned and the distribution of wages offered.

Fundamental limitations to gain enhancement in periodic media and waveguides

A common strategy to compensate for losses in optical nanostructures is to add gain material in the system. By exploiting slow-light effects it is expected that the gain may be enhanced beyond its bulk value. Here we show that this route cannot be followed uncritically: inclusion of gain inevitably modifies the underlying dispersion law, and thereby may degrade the slow-light properties underlying the device operation and the anticipated gain enhancement itself. This degradation is generic; we demonstrate it for three different systems of current interest (coupled resonator optical waveguides, Bragg stacks, and photonic crystal waveguides). Nevertheless, a small amount of added gain may be beneficial