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.

https://iopscience.iop.org/article/10.1088/0034-4885/75/3/036502/pdf

Exploiting aperiodic designs in nanophotonic devices

The transmission coefficients (TCs) and angularly averaged conductance for quasi-particle transport are studied for a bilayer graphene superlattice arranged according to the Fibonacci sequence. The transmission is found to be symmetric around the superlattice growth direction and highly sensitive to the direction of the quasi-particle incidence. The transmission spectra are fragmented and appear in groups due to the quasi-periodicity of the system. The average conductance shows interesting structures sharply dependent on the height of the potential barriers between two graphene strips. The low-energy conductance due to Klein transmission is substantially modified by the inclusion of quasi-periodicity in the system.

Resonant tunnelling in a Fibonacci bilayer graphene superlattice

Tunable Fano resonances in the ballistic transmission and tunneling lifetime in a biased bilayer graphene nanostructure

A study on the variation in resonant tunneling lifetime (RTL) with the applied electric field is presented for the GaAs/AlxGa1−xAs periodic multibarrier systems (MBSs). The variation shows a contrasting behavior of lifetime for quasiresonant states situated at the miniband edge and those for well inside the miniband. For fields larger than 500 kV/m, the RTL corresponding to the midband state increases with the increase in electric field, whereas it decreases with the increase in field for the states near the miniband edges. The existence of the characteristic field and the characteristic lifetime that represent the synchronization of carrier velocity associated with all the quasiresonant states is an interesting outcome of the present theoretical investigation in ballistic transport of carriers through a MBS. This synchronization results in the maximum average escape rate through the system. It has also been shown that the characteristic field corresponds to the formation of localized partial Wannier–Star...

Electric-field-induced resonant tunneling lifetime in semiconductor multibarrier systems

Resonant tunneling in GaAs/AlxGa1−xAs superlattices with aperiodic potential profiles

The effect of a uniform electric field on the resonant tunneling across multibarrier systems (GaAs/AlxGa1−xAs and GaN/AlxGa1−xN) is exhaustively explored by a computational model using exact Airy function formalism and the transfer-matrix technique. The numerical computation takes care of the common problems of numerical inefficiency and overflow associated with the Airy functions for low-applied voltages. The model presents the study of both the field-free and field-dependent tunneling across multibarrier systems using a single formalism. The current–voltage characteristics, studied for the multibarrier systems with different number of barriers, exhibit all the experimentally observed features like resonant peaks, negative differential conductivity regimes, etc. Our results have both qualitative and quantitative agreement with the reported experimental findings.

Resonant tunneling in electrically biased multibarrier systems

We present an exhaustive study on tunneling and electrical conduction in an electrically biased GaAs–AlyGa1−yAs generalized Fibonacci superlattice. The study is based on transfer matrix formalism using an Airy function approach and provides an exact calculation of the current density in the case of quasi-periodic multibarrier systems. The results suggest the use of such quasi-periodic systems in perfect band-pass or band-eliminator (of extremely low width) circuitry. We have clearly demonstrated the resonance-type peaks and negative differential conductivity regimes in such systems. It has also been found that quasi-periodicity favors sharp negative differential conductivity peaks compared to those in periodic superlattices and thus have profound importance in device applications.

Current density in generalized Fibonacci superlattices under a uniform electric field

The tunneling lifetimes of quasi-resonant states for electrons in various kinds of generalized Fibonacci and generalized Thue–Morse GaAs–AlxGa1−xAs superlattices have been evaluated numerically under variable dc bias conditions All the quasi-periodic systems have been framed using the generalized block model The variation of the lifetime at different quasi-resonant levels with respect to the external dc field undergoes a remarkable change due to the effect of quasi-periodicity The occurrence of a minimum value of the average lifetime and its dependence on quasi-periodicity have been analyzed It is shown that the low-order quasi-periodicity in the case of the generalized Fibonacci superlattice and the high-order quasi-periodicity for the generalized Thue–Morse superlattice hold promise for potential device applications The impact of an increase in the number of barriers on the tunneling lifetime has also been studied exhaustively

The effect of quasi-periodicity on the resonant tunneling lifetimes of states in electrically biased semiconductor superlattices

An exhaustive study on the energy spectrum and the wave functions of semiconductor superlattices (SLs) in the presence of saw-tooth potential, step potential and the combined potential has been carried out. The study uses a realistic model for the SL based on the periodic crystal potential of the host crystals. The application of the staircase potential results in the formation of discrete Wannier–Stark ladder (WSL) which is experimentally exploited to achieve quantum cascade laser. The conditions for the WSL in SL has been pointed out. For the purpose of comparison, the effect of these potentials on the energy spectrum and the wave functions has also been reported for a single crystal.

P. Panchadhyayee

Papers

Resonant tunneling in electrically biased multibarrier systems

Current density in generalized Fibonacci superlattices under a uniform electric field

Electric-field-induced resonant tunneling lifetime in semiconductor multibarrier systems

The effect of quasi-periodicity on the resonant tunneling lifetimes of states in electrically biased semiconductor superlattices

Role of staircase potential in the energy spectrum of a periodic system