Abstract
Background: Silicon based Planar Photonic Crystals (PPC) are used for the design of a 1.55 µm waveguide. Line defects are then formed in the PPC structures, by removing rows of holes, to obtain a Planar Photonic Crystal Waveguide (PPCW). Objective: First, we varied the thickness of the Silicon slab and the pore radius in order to obtain optimum design parameters leading to a large and complete bandgap. Next, we present a study of the guided modes in the PPCW for different widths of the waveguide by removing 1, 2 and 3 rows (W1, W2 and W3) of holes from the crystal. Methodology: Band structure calculations were performed using a block-iterative frequency-domain code to find the design parameters of both triangular and square photonic crystal slab lattices of air holes. The frequency domain method for Maxwell's equations in a plane-wave basis was used to calculate the dispersion relations for the guided modes for several widths of the waveguides. Results: The structure with the larger width has a much more complicated dispersion diagram. The most important difference between the three structures (W1, W2 and W3) is that in the case of the wider waveguide, several modes exist at all bandgap frequencies. Conclusion: The structures with a single line defect (W1), there are no leaky modes in the frequency range in which modes become guided. This result indicates that this structure is most preferable.
Highlights
In most previously published study, Two Dimensional (2-D) silicon based photonic crystals have been extensively studied, both theoretically and experimentally (Jamois et al, 2002)
We will carry that idea one step further, by studying structures with two-dimensional periodicity but a finite thickness. Such hybrid structures are known as photonic crystal slabs or planar photonic crystals (Kuchinsky et al, 2000)
We will show that such structures can have a Photonic Bandgap (PBG) and we will vary the thickness of the Silicon slab and the pore radius to obtain the largest possible bandgap
Summary
In most previously published study, Two Dimensional (2-D) silicon based photonic crystals have been extensively studied, both theoretically and experimentally (Jamois et al, 2002) In these structures, the dielectric constant is periodic in one plane (usually defined as the xy plane) and extends infinitely in the third direction (z direction). Line defects are formed in the PPC structures, by removing rows of holes, to obtain a Planar Photonic Crystal Waveguide (PPCW). We present a study of the guided modes in the PPCW for different widths of the waveguide by removing 1, 2 and 3 rows (W1, W2 and W3) of holes from the crystal. Methodology: Band structure calculations were performed using a block-iterative frequency-domain code to find the design parameters of both triangular and square photonic crystal slab lattices of air holes.
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