In photonic crystals, light propagation is forbidden in a certain wavelength range, the bandgap. In a two-dimensional crystal composed of parallel high-refractive index rods in a low-index background a line defect can be formed by removing a row of these rods, which can act as a waveguide for frequencies in the bandgap of the crystal. In order to get more insight into the main features of such waveguides we have studied a number of properties, using simulation tools based on the finite difference time domain method and a finite element Helmholtz solver. We show conceptually simple methods for determining the bandgap of the crystal as well as the dispersion of a waveguide for wavelengths in this bandgap. For practical applications, it is also important to know how much light can be coupled into the waveguide. Therefore, the coupling of light from a dielectric slab waveguide into the photonic crystal waveguide has been examined, showing that a coupling efficiency of up to 83% can be obtained between a silicon oxide slab and a waveguide in a crystal of silicon rods. Finally, calculations on an ultra-compact filter based on reflectively terminated side-branches of waveguides (similar to tuned stubs in microwave engineering) are shown and discussed.
- Numerical modelling
- Photonic bandgap crystals
- Wavelength filter
Stoffer, R., Hoekstra, H. J. W. M., de Ridder, R. M., van Groesen, E., & van Beckum, F. P. H. (2000). Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides and filters. Optical and quantum electronics, 32(6-8), 947-961. https://doi.org/10.1023/A:1007039100873