“Fractional Photonics”: designing light transport in complex aperiodic media

Space-time fractional transport equations are integro-differential equations with power-law kernels that naturally account for the non-local and memory effects that become important in strongly non-homogeneous environments.In this talk I will discuss the applications of fractional calculus methods to photonics, with emphasis on the physics of multiple light scattering in structurally-complex, aperiodic optical structures and metamaterials. I will focus on our recent results on tunable, sub-diffusive photon transport of ultra-short pulses a across deterministic aperiodic media with multifractal energy spectra and critical mode localization. I will discuss fractional photon diffusion in the presence of optically amplifying media, thus generalizing Letokhov’s treatment of non-resonant uniform random structures to disordered media with arbitrary correlations. The concept of a “fractional random laser” will be introduced along with detailed predictions on its laser threshold and dynamical behavior. The combination of fractional calculus with photonic devices represents a novel and effective approach for the engineering of complex optical structures with anomalous photon transport and amplification properties leading to enhanced light-matter interaction across multiple spectral bands.