A complement to the theory of Lohmann-type computer holograms

The introduction by Lohmann and co-workers of the detour phase method in realizing synthetic holograms has been an important step in the history of computer generated holography. In 1969, Brown and Lohmann proposed an improvement to their method: they used true phase and amplitude coding at the center of the diffracting aperture instead of periodically sampled phases and amplitudes. We present a mathematical analysis of this procedure and examine the approximation related to its practical realization.     

Truncation rules for modelling discontinuities with Galerkin method in electromagnetic theory

It is well known that apparently similar discretization schemes of Maxwell's equations in Fourier series may provide very different convergence performances because of truncation. We argue that this work performed in grating theory can be applied to other electromagnetic theories relying on expansions over series different from Fourier series. This generalization is supported by an intuitive argument and by a simple numerical example with Hermite–Gauss functions.     

A numerical study of the problem of diffraction at a locally deformed plane wave-guide

We present a rigorous solution for the problem of diffraction at a locally deformed plane wave-guide. This method can be applied to the study of mode coupling and mode conversion.     

Photon confinement in photonic crystal nanocavities

The quest for enhanced light‐matter interactions has enabled a tremendous increase in the performance of photonic‐crystal nanoresonators in the past decade. State‐of‐the‐art nanocavities now offer mode lifetime in the nanosecond range with confinement volumes of a few hundredths of a cubic micrometer. These results are certainly a consequence of the rapid development of fabrication techniques and modeling tools at micro‐ and nanometric scales. For future applications and developments, it is necessary to deeply understand the intrinsic physical quantities that govern the photon confinement in these cavities. We present a review of the different physical mechanisms at work in the photon confinement of almost all modern PhC cavity constructs. The approach relies on a Fabry‐Perot picture and emphasizes three intrinsic quantities, the mirror reflectance, the mirror penetration depth and the defect‐mode group velocity, which are often hidden by global analysis relying on an a posteriori analysis of the calculated cavity mode. The discussion also includes nanoresonator constructs, such as the important micropillar cavity, for which some subtle scattering mechanisms significantly alter the Fabry‐Perot picture.     

Mode solvers for very thin long–range plasmonic waveguides

We present two mode solvers applied to a very thin long–range plasmonic waveguide. We compare the guided mode complex effective index obtained either applying a Fourier modal method or calculating density of guided modes using the Green’s dyad technique. We achieve good agreement for both effective indices and mode profiles. We also observe a different behaviour compared to long–range surface plasmon supported by thicker films.     

Anomalous low-temperature behavior of the Co dimers in the oxo-halide CoSb2O3Br2

We report the synthesis, crystal structure determination, magnetic and low-temperature structural properties of a new cobalt antimony oxo-bromide. CoSb₂O₃Br₂ crystallizes in the triclinic crystal system, space group P−1, with the following lattice parameters: a=5.306(3) Å, b=7.812(4) Å, c=8.0626(10) Å, α=88.54(3)°, β=82.17(3)°, γ=80.32(4)°, and Z=2. The crystal structure was solved from single crystal X-ray data and refined on F², R₁=3.08. The structure consists of layers made up by three building blocks, [CoO₄Br₂], [SbO₃Br], and [SbO₃] that are connected via edge- and corner-sharing so that structural Co-Co dimers are formed. The layers have no net charge and are only weakly connected by van der Waals forces to adjacent layers. Above ∼25 K the magnetic susceptibility is independent of the magnetic field and can be very well described by a Curie-Weiss law. Below 25 K the susceptibility passes through a maximum and decreases again that is typical for the onset of long-range antiferromagnetic correlations. Long-range antiferromagnetic ordering is observed below T_N∼9 K indicating substantial inter-dimer exchange coupling between Co-Co dimers within the layers. However, according to the heat capacity results only a minute fraction of the entropy is associated with the long-range ordering transition. The phonon anomalies observed for T<6 K in Raman scattering and an anomaly in the specific heat point to a structural instability leading to a loss of inversion symmetry at lowest temperatures.     

Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task

Modal reflection, transmission and loss of deeply etched Bragg waveguide gratings were modelled by six European laboratories using independently developed two-dimensional (2D) numerical codes based on four different methods, with very good mutual agreement. It was found that (rather weak) material dispersion of the SiO₂/Si₃N₄ system does not significantly affect the results. The existence of lossless Floquet–Bloch modes in deeply etched gratings was confirmed. Based on reliable numerical results, the physical origin of out-of-plane losses of 1D or 2D photonic band gap structures in slab waveguides is briefly discussed.     

Modelling leaky photonic wires: A mode solver comparison

We present results from a mode solver comparison held within the frameworkof the European COST P11 project. The structure modelled is a high-index contrast photonic wire in silicon-on- insulator subject to substrate leakage. The methods compared are both in-house developed and commercial, and range from effective index and perturbation methods, over finite-element and finite-difference codes, beam propagation methods, to film mode matching methods and plane wave expansion methods.     

Bragg waveguide grating as a 1d photonic band gap structure: COST 268 modelling task

Modal reflection, transmission and loss of deeply etched Bragg waveguide gratings were modelled by six European laboratories using independently developed two-dimensional (2D) numerical codes based on four different methods, with very good mutual agreement. It was found that (rather weak) material dispersion of the SiO₂/Si₃N₄ system does not significantly affect the results. The existence of lossless Floquet-Bloch modes in deeply etched gratings was confirmed. Based on reliable numerical results, the physical origin of out-of-plane losses of 1D or 2D photonic band gap structures in slab waveguides is briefly discussed.     

Inhibition, enhancement, and control of spontaneous emission in photonic nanowires

We experimentally investigate the spontaneous emission (SE) rates of single InAs quantum dots embedded in GaAs photonic nanowires. For a diameter leading to the optimal confinement of the fundamental guided mode HE11, the coupling to HE11 dominates the SE process and an increase of the SE rate by a factor of 1.5 is achieved. When the diameter is decreased, the coupling to this mode vanishes rapidly, thus allowing the coupling to the other radiation modes to be probed. In these conditions, a SE inhibition factor of 16, equivalent to the one obtained in state-of-the-art photonic crystals, is measured. These results, which are supported by fully vectorial calculations, confirm the potential of photonic nanowires for a nearly perfect, broadband SE control.