D. M. Beggs

Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells

The bandstructures of two-dimensional photonic crystals with octagonal quasicrystalline unit cells have been calculated. The existence of photonic band-gaps in such structures is demonstrated, and results showing the variation of the spectral position and width of the photonic band-gaps with the size of the unit cell and filling fraction within the unit cell are presented.

Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap

Transmission and reflection of light in disordered two-dimensional photonic crystals with an incomplete photonic band-gap have been modelled for various levels of disorder. It is found that ballistic and scattered light display different behaviours as a function of the disorder parameter. For ballistic light, the dependence of the transmission coefficient on the disorder parameter exhibits a threshold-like behaviour, whereas the transmission of scattered light increases rapidly for small disorder. Unlike for photonic crystals with a complete band-gap, the minimum of the transmission for scattered light does not coincide with the centre of the photonic band-gap, and Fabry–Perot-type oscillations can be seen within the photonic band-gap.

Etched Bragg reflectors as two-dimensional photonic crystals

We have studied GaAs/oxidized AlAs (AlOx) Bragg reflectors with etched air grooves running parallel to the growth direction. Such structures possess periodic modulation of the refractive index in two dimensions, and we have found that they have a photonic band gap for E-polarized modes over a large range of parameters of the structure, and can support complete photonic band-gaps for both E- and H-polarizations for a more restricted range of values of the parameters. Also, for certain parameter values of the etched Bragg reflector, the total density of states in a wide spectral region is reduced by factor of up to 20 compared to an effective medium characterized by the mean dielectric constant.

Propagation of electromagnetic waves through a system of randomly placed cylinders : the partial scattering wave resonance.

Propagation of electromagnetic waves through a system of randomly placed cylinders has been modelled. It was found that there is a dip in the ballistic transmission spectra for both the E and H polarizations, which is associated with scattering of the partial wave with angular momentum equal to zero by a single cylinder.

Stability of Photonic Band Gap in the Presence of Disorder

The photonic eigenmodes near a band gap of a type of one‐dimensional disordered photonic crystal have been investigated statistically. For the system considered, it is found that the tail of the density of states entering the band gap is characterized by a certain penetration depth, which is proportional to the disorder parameter. A quantitative relation between the relative penetration depth, the relative width of the photonic band gap and the disorder has been found. It is apparent that there is a certain level of disorder below which the probability of the appearance of photonic eigenstates at the centre of the photonic band gap essentially vanishes.

The interaction of quantum well excitons with evanescent EM waves and the spectroscopy of waveguide polaritons

A transfer matrix method has been used to calculate the dispersion relations of planar dielectric waveguides (WGs) containing quantum well (QW) excitons. It is found that WG polaritons are formed, whose dispersion displays the classic anti‐crossing behaviour at the exciton resonance frequency. For a QW placed at the anti‐node of the fundamental TE mode of the WG considered, the Rabi‐splitting is calculated to be 6.55meV, with WG polaritons of lifetime ∼ 7 ps, corresponding to a displacement along the WG axis of ∼ 0.5 mm. A smaller splitting of the polariton modes (4.7 meV) was found for the case of the QW placed in the cladding of the WG.

Interaction of quantum well excitons with evanescent plane electromagnetic waves

A formalism based on non-local dielectric response theory and Green function techniques has been developed to describe the interaction of quantum well excitons with an evanescent optical wave of a planar waveguide. Reflection spectra of a system in which a quantum well placed behind a dielectric interface at which light experiences total internal reflection have been calculated. It is shown that the spectral feature corresponding to the exciton resonance becomes much more pronounced if the angle of incidence is close to the critical angle of total internal reflection. The concept of a generalized Snell law has been applied to provide simplification of the formalism.