Group index limitations in slow-light photonic crystals

In photonic crystals the speed of light can be significantly reduced due to band-structure effects associated with the spatially periodic dielectric function, rather than originating from strong material dispersion. In the ideal and loss-less structures it is possible even to completely stop the light near frequency band edges associated with symmetry points in the Brillouin zone. Unfortunately, despite the impressive progress in fabrication of photonic crystals, real structures differ from the ideal structures in several ways including structural disorder, material absorption, out of plane radiation, and in-plane leakage. Often, the different mechanisms are playing in concert, leading to attenuation and scattering of electromagnetic modes. The very same broadening mechanisms also limit the attainable slow-down which we mimic by including a small imaginary part to the otherwise real-valued dielectric function. Perturbation theory predicts that the group index scales as 1/ϵ″ which we find to be in complete agreement with the full solutions for various examples. As a consequence, the group index remains finite in real photonic crystals, with its value depending on the damping parameter and the group-velocity dispersion. We also extend the theory to waveguide modes, i.e. beyond the assumption of symmetry points. Consequences are explored by applying the theory to W1 waveguide structures.