The serpentine optical waveguide: Engineering the dispersion relations and the stopped light points

We present a study a new type of optical slow-light structure comprising a serpentine shaped waveguide were the loops are coupled. The dispersion relation, group velocity and GVD are studied analytically using a transfer matrix method and numerically using finite difference time domain simulations. The structure exhibits zero group velocity points at the ends of the Brillouin zone, but also within the zone. The position of mid-zone zero group velocity point can be tuned by modifying the coupling coefficient between adjacent loops. Closed-form analytic expressions for the dispersion relations, group velocity and the mid-zone zero v_g points are found and presented.