Suppression of localization in Kronig-Penney models with correlated disorder

Fano interference governs wave transport in disordered systems

Light localization in disordered systems and Bragg scattering in regular periodic structures are considered traditionally as two entirely opposite phenomena: disorder leads to degradation of coherent Bragg scattering whereas Anderson localization is suppressed by periodicity. Here we reveal a non-trivial link between these two phenomena, through the Fano interference between Bragg scattering and disorder-induced scattering, that triggers both localization and de-localization in random systems. We find unexpected transmission enhancement and spectrum inversion when the Bragg stop-bands are transformed into the Bragg pass-bands solely owing to disorder. Fano resonances are always associated with coherent scattering in regular systems, but our discovery of disorder-induced Fano resonances may provide novel insights into many features of the transport phenomena of photons, phonons, and electrons. Owning to ergodicity, the Fano resonance is a fingerprint feature for any realization of the structure with a certain degree of disorder.

Understanding localization and delocalization phenomena is important for studying wave propagation in many types of disordered photonic systems. Here, a theoretical study of one-dimensional photonic crystal structures reveals the importance of Fano interference in wave transport in the presence of disorder.

Exploiting aperiodic designs in nanophotonic devices

In this work we consider the role of aperiodic order-order without periodicity-in the design of different optical devices in one, two and three dimensions. To this end, we will first study devices based on aperiodic multilayered structures. In many instances the recourse to Fibonacci, Thue-Morse or fractal arrangements of layers results in improved optical properties compared with their periodic counterparts. On this basis, the possibility of constructing optical devices based on a modular design of the multilayered structure, where periodic and quasiperiodic subunits are properly mixed, is analyzed, illustrating how this additional degree of freedom enhances the optical performance in some specific applications. This line of thought can be naturally extended to aperiodic arrangements of optical elements, such as nanospheres or dielectric rods in the plane, as well as to three-dimensional photonic quasicrystals based on polymer materials. In this way, plentiful possibilities for new tailored materials naturally appear, generally following suitable optimization algorithms. Then, we present a detailed discussion on the physical properties supporting the preferential use of aperiodic devices in a number of optical applications, opening new avenues for technological innovation. Finally we suggest some related emerging topics that deserve some attention in the years to come.

Metal-insulator transition in an aperiodic ladder network: an exact result

We prove that a tight-binding ladder network composed of atomic sites with on-site potentials distributed according to the quasiperiodic Aubry model can exhibit a metal-insulator transition at multiple values of the Fermi energy. For specific values of the first and second neighbor electron hopping, the result is obtained exactly. With a more general model, we numerically calculate the two-terminal conductance. The numerical results corroborate the analytical findings.

Effect of nonlinear interactions on resonant states of the random dimer model

A simple Kronig-Penney model for 1D mesoscopic systems with δ peak potentials is used to study numerically the effect of non-linear interaction on the resonant states of the random dimer model. It is shown that the nonlinear interaction increases or decreases the width of the resonances depending on both its sign and strength. The resonance width ΔE is a power law decaying with the system size as L(-γ). The exponent γ decreases linearly with the nonlinear interaction strength when the dimer impurity concentration increases. The resonance energy states, in these systems, are shifted depending on the kind of interaction. Further investigations are provided on the effect of nonlinearity on conductance fluctuations near the resonances.