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.

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.

We present experimental observations of nonlinear propagation effects in an integrated AlGaAs waveguide filter. We demonstrate pulse shaping, pulse compression, and the production of gap solitons within the stop band of the grating for switching powers of approximately 130 W . This nonlinear behavior is associated with the counterbalancing effects of self-phase modulation and the large dispersion effects introduced by the grating itself.

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