Photonic crystal waveguide

In the present invention, an optical device having a waveguide structure includes a photonic band structure region, the photonic band structure region comprising a first region having a first refractive index and an array of sub-regions having a second refractive index, the array of subregions being arranged in a Fibonacci spiral pattern. The present invention can also be applied to optical fibers.The Fibonacci spiral pattern and can be found in nature in the arrangement of the seeds of a sunflower and in pine kernels. The Fibonacci pattern is an optimal packing system for the sub-regions surrounding a central cavity region.