Symmetry Considerations for Closed Loop Photonic Crystal Coupled Resonators

Waveguide coupling to closed loop coupled-resonator optical waveguides is explored. By coupling a CROW chain back on itself, a reduction in individual resonant linewidth is achieved making these slow light modes more conducive to periodic filters toward novel frequency-comb integration. Through numerical simulation by finite-difference time-domain methods, the importance of waveguide symmetry conditions for coupling is illustrated. The impact of unit cavity mode symmetry strongly impacts the necessary coupling geometry to both cavities and waveguides. Design insight into different waveguide coupling schemes is provided while aiming to achieve transmission of the resonant structure exhibited by the isolated resonator.