Dispersion in photonic crystals

Abstract

Investigations on the dispersive properties of photonic crystals, modified scattering in ring-resonators, monolithic integration of vertical-cavity surface-emitting lasers and advanced data processing techniques for the finite-difference time-domain method are presented. Photonic crystals are periodic mesoscopic arrays of scatterers that modify the propagation properties of electromagnetic waves in a similar way as natural crystals modify the properties of electrons in solid-state physics. In this thesis photonic crystals are implemented as planar photonic crystals, i.e., optically thin semiconductor films with periodic arrays of holes etched into them, with a hole-to-hole spacing of the order of the wavelength of light in the dielectric media. Photonic crystals can feature forbidden frequency ranges (the band-gaps) in which light cannot propagate. Even though most work on photonic crystals has focused on these band-gaps for application such as confinement and guiding of light, this thesis focuses on the allowed frequency regions (the photonic bands) and investigates how the propagation of light is modified by the crystal lattice. In particular the guiding of light in bulk photonic crystals in the absence of lattice defects (the self-collimation effect) and the angular steering of light in photonic crystals (the superprism effect) are investigated. The latter is used to design a planar lightwave circuit for frequency domain demultiplexion. Difficulties such as efficient insertion of light into the crystal are resolved and previously predicted limitations on the resolution are circumvented. The demultiplexer is also fabricated and characterized. Monolithic integration of vertical-cavity surface-emitting lasers by means of resonantly enhanced grating couplers is investigated. The grating coupler is designed to bend light through a ninety-degree angle and is characterized with the finite-difference time-domain method. The vertical-cavity surface-emitting lasers are fabricated and characterized. A purely theoretical section of the thesis investigates advanced data processing techniques for the finite-difference time-domain method. In particular it is shown that an inner product can be used to filter out specific photonic crystal modes or photonic crystal waveguide modes (Bloch-modes). However it is also shown that the numerical accuracy of this inner product severely worsens for Bloch modes with very low group velocities.