Disorder in coupled-resonator optical waveguides

Disorder in coupled-resonator optical waveguides (CROWs) is modeled by exploiting the concept of the characteristic impedance of a periodic slow-light waveguide. Every imperfection in the CROW structure is modeled as an impedance discontinuity, and the related backreflection is evaluated by using well-known reflection rules. We demonstrate that backreflections induced by disorder scale with the square of the slowing factor and the square of the disorder parameter, both independently of the specific structure. The method is simple and accurate, holds even when the slowing factor of the CROW is modified by disorder, and can be applied to any slow-light structure where the characteristic impedance can be defined. Theoretical and numerical results are supported by an experimental investigation showing the effects of increasing disorder on both frequency and time domain responses of a ring resonator CROW. Pulse envelope distortions due to distributed backreflections along the disordered CROW arise as one of the main limiting factors for applications based on CROWs.