Slab photonic crystal demultiplexers : analysis and design

The exploitation of the superprism phenomenon for optical demultiplexing using a slab photonic crystal on the silicon on insulator platform is the main subject of this thesis. The S-vector and k-vector superprisms are considered. Design equations for the S-vector superprism demultiplexer which fully take into account the nonlinear spectral dependence of beam propagation and dispersion are introduced. This allows wide-band coarse wavelength division multiplexing (CWDM) demultiplexers to be designed. Selecting minimum prism area as a metric, the best photonic crystal lattice, design parameters and prism geometry is sought. A full 3-D modeling approach using the plane wave expansion method is employed to ensure the practicality of the design. We show that the slab 1-D photonic crystal can provide the smallest superprism. Based on our result, an area of 1367 mum2 is sufficient to resolve 4 standard CWDM channels (20nm channel spacing). We extend this approach by proposing a stratified photonic crystal which has 5 times less area for an 8 channel CWDM design.We then propose the first fully integrated k-vector superprism layout. Design rules and equations are presented and we use these to obtain the design parameters that result in a minimum prism area. We show that an optimized 1-D photonic crystal k-vector superprism with the area of less than 0.1 mm2 is sufficient to resolve 32 standard dense wavelength division multiplexing (DWDM) channels (100GHz channel spacing). The resulting chip size is approximately 4.5 times less than an equivalent etched grating demultiplexer.We also demonstrate that fast lenses can be made using slab 1-D photonic crystal with an periodicity.We introduce an analytical approximation technique for slab 1-D photonic crystals based on the weighted index method. The variational nature of the method leads to acceptable results for moderate refractive index contrast materials. The method can also be extended to 2-D cases and to nonlinear systems.The plane wave expansion (PWE) method and field matching have been combined to obtain a new method which is capable of obtaining all types of modes including the leaky modes of slab 1-D photonic crystals. The method requires fewer plane waves than the conventional PWE method but provides a better approximation. We compare our results with an accurate finite element method as a benchmark.A report of our first attempt for the fabrication, post-possessing and optical characterization of the proposed k-vector superprism demultiplexer is also presented. We recommend the development of a cladding, and more accurate fabrication procedures for future investigations