Aperiodic Environments Research Articles

Wave Transport and Localization in Prime Number Landscapes

In this paper, we study the wave transport and localization properties of novel aperiodic structures that manifest the intrinsic complexity of prime number distributions in imaginary quadratic fields. In particular, we address structure-property relationships and wave scattering through the prime elements of the nine imaginary quadratic fields (i.e., of their associated rings of integers) with class number one, which are unique factorization domains (UFDs). Our theoretical analysis combines the rigorous Green’s matrix solution of the multiple scattering problem with the interdisciplinary methods of spatial statistics and graph theory analysis of point patterns to unveil the relevant structural properties that produce wave localization effects. The onset of a Delocalization-Localization Transition (DLT) is demonstrated by a comprehensive study of the spectral properties of the Green’s matrix and the Thouless number as a function of their optical density. Furthermore, we employ Multifractal Detrended Fluctuation Analysis (MDFA) to establish the multifractal scaling of the local density of states in these complex structures and we discover a direct connection between localization, multifractality, and graph connectivity properties. Finally, we use a semi-classical approach to demonstrate and characterize the strong coupling regime of quantum emitters embedded in these novel aperiodic environments. Our study provides access to engineering design rules for the fabrication of novel and more efficient classical and quantum sources as well as photonic devices with enhanced light-matter interaction based on the intrinsic structural complexity of prime numbers in algebraic fields.

Aperiodic Photonics of Elliptic Curves

In this paper we propose a novel approach to aperiodic order in optical science and technology that leverages the intrinsic structural complexity of certain non-polynomial (hard) problems in number theory and cryptography for the engineering of optical media with novel transport and wave localization properties. In particular, we address structure-property relationships in a large number (900) of light scattering systems that physically manifest the distinctive aperiodic order of elliptic curves and the associated discrete logarithm problem over finite fields. Besides defining an extremely rich subject with profound connections to diverse mathematical areas, elliptic curves offer unprecedented opportunities to engineer light scattering phenomena in aperiodic environments beyond the limitations of traditional random media. Our theoretical analysis combines the interdisciplinary methods of point patterns spatial statistics with the rigorous Green’s matrix solution of the multiple wave scattering problem for electric and magnetic dipoles and provides access to the spectral and light scattering properties of novel deterministic aperiodic structures with enhanced light-matter coupling for nanophotonics and metamaterials applications to imaging and spectroscopy.

Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays

In this paper we explore the potential of one-dimensional and two-dimensional deterministic aperiodic plasmonic arrays for the design of electromagnetic coupling and plasmon-enhanced, sub-wavelength optical fields on chip-scale devices. In particular, we investigate the spectral, far-field and near-field optical properties of metal nanoparticle arrays generated according to simple deterministic sequences characterized by fractal Fourier spectra. Additionally, we will consider the case of flat Fourier-transform sequences, which reproduce the behavior of purely random systems to an arbitrary degree of accuracy. Based on the coupled dipole approach (CDA) and finite difference time domain (FDTD) simulations, we study the radiative (long-range) and quasi-static (short-range) electromagnetic coupling in deterministic aperiodic plasmon arrays of metal nanoparticles. In addition, we investigate the local field enhancement and the enhancement scaling in periodic and aperiodic arrays with increasing degree of complexity. We believe that the accurate control of electromagnetic coupling and sub-wavelength field enhancement in deterministic aperiodic environments will enable novel nanodevice applications in areas such as field-enhanced nanosensors, engineered SERS substrates and optical nano-antenna arrays.

Light-Emitting Silicon Nanocrystals and Photonic Structures in Silicon Nitride

In this paper, we review our main results on the optical and electrical properties of light-emitting silicon nanocrystals (Si-ncs) obtained from the thermally induced nucleation in amorphous silicon-rich nitride (SRN) films deposited either by plasma-enhanced chemical vapor deposition (PE-CVD) or magnetron sputtering. In particular, we discuss the Si-ncs microscopic light emission mechanism combining the optical data with the first-principle calculations of the absorption/emission Stokes shifts and recombination lifetimes. In addition, we report on the electrical injection characteristics of simple p-i-n device structures showing efficient bipolar transport and room temperature electroluminescence, and demonstrate efficient energy sensitization of erbium (Er) ions from the Si-ncs embedded in the SRN matrices. We further show that the light-emitting nanocrystals in SRN can be embedded in aperiodic photonic environments, where the localized optical modes can be used to significantly enhance the Si-ncs emission intensity at different emission wavelengths. These results suggest that the Si-ncs embedded in the SRN matrices have a large potential for the fabrication of optically active photonic devices based on the Si technology

Persistence of oviposition rhythm in individuals of Drosophila melanogaster reared in an aperiodic environment for several hundred generations.

The oviposition rhythm of individual flies of Drosophila melanogaster from a population maintained in an aperiodic environment (with light, temperature, humidity, and other factors which could provide time cues, kept constant) for several hundred generations was assayed in constant light (LL), in light/dark (LD 12:12 hr) cycle, and in constant darkness (DD). More than 50% of the flies assayed exhibited rhythmicity in oviposition in all three light regimes. The results indicate that the phenomenon of egg laying is rhythmic in individual D. melanogaster females and is controlled by an endogenous time keeping mechanism. The persistence of the oviposition rhythm in a large proportion of individuals in the population after several hundred generations of rearing in a constant environment strengthens the view that possessing biological clocks may confer some intrinsic fitness advantage even to organisms living in aperiodic environments. J. Exp. Zool. 290:541-549, 2001.

Comparative study of the critical behavior in one-dimensional random and aperiodic environments

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents omega>0. At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as t ~ log^{1/omega}. Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of omega, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities.