| We investigate the properties of integrated dielectric filters for the purposes of on-chip routing of photons. We started with the use of high quality factor tunable photonic crystal nanobeam cavities and moving on to examine a new class of reflection based reverse designed filters that maintain the footprint of a waveguide while allowing for arbitrary amplitude and phase response.;Photonic crystal nanobeam cavities are shown to exhibit high quality factors while maintaining a strong coupling to the feeder waveguide. This leads to two-fold advantages. The localized and strongly interacting light within the highly confined cavity modes allows for significant tuning to take place while only affecting a small physical area. The nanobeam cavities are also shown to have high quality factor TE and TM modes, a property that allows for interesting applications in nonlinear optics. As a case study, we examine using graphene to modulate the signal transmitted through nanobeam cavities. We show that by flooding graphene with free carriers we can electrically effect the optical properties of the nanobeam cavity.;We examine several methods for mechanical tuning of coupled photonic crystal nanobeam cavities, starting from capacitive force actuation, moving onto gradient force manipulation, and finally ending in optomechanical motion. The gradient force will facilitate high speeds and will work with insulators such as nitrides or diamond. Optomechanical actuation will display the advantage of light-light control without electrical signals being involved, although it will suffer from disadvantages such as constant power consumption and in silicon will still be affected non-linear heating mechanisms.;Finally we will examine the theory behind, and many applications of arbitrary amplitude filters that are achieved by periodic width modulation in waveguides. We examine ways of improving the reverse design method to maintain better fidelity with target design spectra as well as examining some of the challenges in actually achieving arbitrary design such as moving toward sharper resonances. Additionally, we look at applications in ultra-fast pulse shaping and look for methods that will allow for dynamic or quasi-static applications. |
