R. A. Abram

Heavily doped semiconductors and devices

High carrier concentrations and the fluctuations in random potential resulting from ionized impurities alter the density of states and electron wavefunctions in heavily doped semiconductors. The theoretical and experimental work on these effects is reviewed, special attention being paid to the consequences for the optical and transport properties. Semiconductor devices are often heavily doped and the influence of heavy doping is illustrated in the injection laser and bipolar transistor, which also serve as investigative tools.

Tamm plasmon polaritons: Slow and spatially compact light

We report on the first experimental observation of Tamm plasmon polaritons (TPPs) formed at the interface between a metal and a dielectric Bragg reflector (DBR). In contrast to conventional surface plasmons, TPPs have an in-plane wavevector less than the wavevector of light in vacuum, which allows for their direct optical excitation. The angular resolved reflectivity and transmission spectra of a GaAs∕AlAs DBR covered by Au films of various thicknesses show the resonances associated with the TPP at low temperatures and room temperature. The in-plane dispersion of TTPs is parabolic with an effective mass of 4×10−5 of the free electron mass.

Electronic structure calculations on nitride semiconductors

A series of calculations have been performed on group-III nitrides (GaN, AlN and InN) in both zinc-blende and wurtzite structures. Three different levels of computation have been performed in an integrated programme of study: first-principles total energy calculations, semi-empirical pseudopotential calculations and calculations. Bandstructures are obtained from each method in a consistent manner, and used to provide effective masses and parameters for planned work on the electronic structure of alloys and quantum well heterostructures.

Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals

We report the measurements of the diffraction pattern of a two-dimensional Penrose-tiled photonic quasicrystal, obtained by etching air cylinders in a silica substrate, and the modelling of the light propagation and dispersion relations of photons inside such a structure. The calculated transmission spectra exhibit dips whose positions are insensitive to the direction of propagation and whose depth increases with increasing structure length. An approach is developed for the calculation of the dispersion relations which is based on a set of reciprocal vectors defined by the diffraction pattern. The dispersion curves exhibit gap-like features at frequencies corresponding to the dips in the transmission spectra.

Hybrid states of Tamm plasmons and exciton polaritons

Channeling of exciton polaritons in the plane of semiconductor microcavities can be achieved by the deposition of metallic mesas on the top of the semiconductor structure. We show theoretically that the regime of strong coupling between cavity polaritons and Tamm surface plasmons is possible in such structures. The effect is favorable for the spatial confinement of polaritons and the formation of hybrid one-dimensional plasmon-polariton modes.

Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure

We report measurements of the diffraction pattern of a two-dimensional photonic quasicrystal structure and use the set of plane waves defined by the diffraction pattern as the basis of a theoretical approach to calculate the photonic band structure of the system. An important feature of the model is that it retains the essence of the rotational and inflational properties of the quasicrystal at all levels of approximation: properties lost in approximate models which artificially introduce elements of periodicity. The calculated density of modes of the quasicrystals is found to display a weakly depleted region analogous to the bandgap that occurs in a periodic system. The calculated transmission spectra for different polarizations and directions of propagation show features that correlate with the behaviour of the density of modes.

Band gap narrowing due to many-body effects in silicon and gallium arsenide

The authors present a theoretical study of band gap narrowing due to many-body effects in silicon and gallium arsenide at zero temperature. A principal aim of the paper is to give a detailed description of a self-energy approach to the band gap narrowing problem and the use of the plasmon pole approximation for dielectric response in the self-energy formalism. The particular problems arising from multiple and anisotropic bands, and direct and indirect band gaps are considered. Numerical results are presented for electrons, holes and an electron-hole plasma in both Si and GaAs. For the case of electrons in Si where reliable theoretical results already exist the results are seen to agree well with the earlier work. Also the theory of band gap narrowing in the electron-hole plasma case is found to be compatible with established independent work on electron-hole droplets. The results described in this paper are expected to be relevant to heavily doped or highly excited semiconductors and electronic devices based on these although it is recognized that the theory as it stands does not include impurity disorder effects.

Bragg reflectors for cylindrical waves

A transfer matrix method is developed to calculate the electromagnetic field in a dielectric structure with circular cylindrical symmetry. The equations for the reflection and transmission coefficients of cylindrical waves from a single cylindrical boundary between two dielectrics and from a cylindrical multilayered structure are obtained. For a single dielectric interface, enhanced reflection at small interface radii and the analogue of the Brewster effect are predicted and investigated. The design of an optimized cylindrical Bragg reflector (CBR) for cylindrical waves is proposed and its optical properties are studied. It is found that the thicknesses of the layers in the CBR must be different, to provide the adjustment of the phase of the waves, that are reflected from the interfaces at different radii.

The coupling of light‐emitting diodes to optical fibers using sphere lenses

The use of a truncated sphere of high‐refractive‐index material is proposed as a lens designed to improve the coupling efficiency between a light‐emitting‐diode source and an optical fiber. A method of calculating the coupling efficiency for such lens systems is described. Numerical results for the variation of efficiency with lens parameters are presented and discussed for coupling to a fiber bundle with a numerical aperture of 0.14. Improvements of two orders of magnitude in the coupling efficiency over that attainable with the close coupling geometry are predicted.

Two-dimensional Penrose-tiled photonic quasicrystals : diffraction of light and fractal density of modes.

Abstract We report measurements of the diffraction pattern of a two-dimensional photonic quasicrystal structure. Using a set of plane waves defined by the diffraction pattern we introduce a theoretical approach for the calculation of the band structure which captures the rotational and inflational properties of the quasicrystal. Based on this model we find that the density of modes of the quasicrystal displays a fractal character and a depleted region analogous to the band gap in a periodic system.