On-chip Group and Phase Velocity Control for Classical and Quantum Optical Devices

We present group and phase velocity control for the photonic integrated circuits with an emphasis on two-dimensional photonic crystal devices in this thesis. We describe the theory, analytical and numerical designs, and experimental characterization of silicon nanophotonic devices both in classical and quantum space. These devices which include negatively refractive photonic crystals, coherently interacting nano-resonators, power splitters, and interferometers provide phase-delay and time-delay tunability that lead to new functionalities in photonic integrated circuits for on-chip information processing, optical computation and communications. The high performance designs are all compatible with CMOS fabrication processes and can be easily integrated for infrared telecommunication applications. Here, we study photonic crystals in terms of the wavelengths at which they are transparent as well as they have a band-gap. This is particularly important in this work as most of the research on photonic crystals to date has focused more on the band gaps, ignoring effects that occur in transparent wavelengths. We show that a number of applications such as zero-phase delay lines and adjustable filters can be realized based on their polarization-dependent properties and nontrivial phase effects in the transparent region and dynamic storage of light can be achieved via optical analogue of electromagnetically induced transparency in an originally non-transmitting wavelength region