We review our work done for topology optimization of passive photonic crystal component parts for broadband and
wavelength dependent operations. We show examples of low-loss topology-optimized bends and splitters optimized for
broadband transmission and demonstrate the applicability of topology optimization for designing slow-light and/or
wavelength selective component parts. We also present how the dispersion of light in the slow-light regime of photonic
crystal waveguides can be tailored to obtain filter functionalities in passive devices and/or to obtain semi-slow light
having a group velocity in the range ~(c0/15 - c0/100); vanishing, positive, or negative group velocity dispersion (GVD);
and low-loss propagation in a practical ~5-15 nm bandwidth.
We report thorough investigations of photonic crystal waveguide properties in the slow light regime. The transmission and the group index near the cutoff wavelengths oscillate in phase in close analogy with the 1D photonic crystal behavior. The influence of having a finite number of periods in the photonic crystal waveguide is addressed to explain the spiky character of both the transmission and group index spectra. The profile of the slow-light modes is stretched out into the first and second rows of the holes closest to the waveguide channel. One of our strategies to ameliorate the design of photonic crystal devices is to engineer the radii of holes in these rows. A topology optimization approach is also utilized to make further improvements. The results of the numerical simulations and the optical characterization of fabricated devices such as straight waveguides with bends and couplers are presented. A nice match is found between theory and experiment.
We report on direct numerical calculations and experimental measurements of the group-index dispersion in a photonic crystal waveguide fabricated in silicon-on-insulator material. The photonic crystal is defined by a triangular arrangement of holes and the waveguide is carved out by introducing a one-row line defect. Both the numerical and experimental methods are based on the time of flight approach for an optical pulse. An increase of the group index by approximately 45 times (from 4 to 155) has been observed when approaching the cutoff of the fundamental photonic bandgap mode. Numerical 2D and 3D simulations of pulse dynamics in the waveguide made by the time-domain method shows excellent agreement with measured data in most of the band. These group index values in a photonic crystal waveguide are to the best of our knowledge the largest numbers reported so far by direct tracking of pulse propagation.