Deterministic Aperiodic Arrays Research Articles

Nonlocal topological insulators: Deterministic aperiodic arrays supporting localized topological states protected by nonlocal symmetries

The properties of topological systems are inherently tied to their dimensionality. Indeed, higher-dimensional periodic systems exhibit topological phases not shared by their lower-dimensional counterparts. On the other hand, aperiodic arrays in lower-dimensional systems (e.g., the Harper model) have been successfully employed to emulate higher-dimensional physics. This raises a general question on the possibility of extended topological classification in lower dimensions, and whether the topological invariants of higher-dimensional periodic systems may assume a different meaning in their lower-dimensional aperiodic counterparts. Here, we demonstrate that, indeed, for a topological system in higher dimensions one can construct a one-dimensional (1D) deterministic aperiodic counterpart which retains its spectrum and topological characteristics. We consider a four-dimensional (4D) quantized hexadecapole higher-order topological insulator (HOTI) which supports topological corner modes. We apply the Lanczos transformation and map it onto an equivalent deterministic aperiodic 1D array (DAA) emulating 4D HOTI in 1D. We observe topological zero-energy zero-dimensional (0D) states of the DAA-the direct counterparts of corner states in 4D HOTI and the hallmark of the multipole topological phase, which is meaningless in lower dimensions. To explain this paradox, we show that higher-dimension invariant, the multipole polarization, retains its quantization in the DAA, yet changes its meaning by becoming a nonlocal correlator in the 1D system. By introducing nonlocal topological phases of DAAs, our discovery opens a direction in topological physics. It also unveils opportunities to engineer topological states in aperiodic systems and paves the path to application of resonances associates with such states protected by nonlocal symmetries.

Hyperuniformity and wave localization in pinwheel scattering arrays

We investigate the structural and spectral properties of deterministic aperiodic arrays designed from the statistically isotropic pinwheel tiling. By studying the scaling of the cumulative integral of its structure factor in combination with higher-order structural correlation analysis we conclude that pinwheel arrays belong to the weakly hyperuniformity class. Moreover, by solving the multiple scattering problem for electric point dipoles using the rigorous Green's matrix theory, we demonstrate a clear transition from diffusive transport to localization behavior. This is shown by studying the Thouless number as a function of the scattering strength and the spectral statistics of the scattering resonances. Surprisingly, despite the absence of sharp diffraction peaks, clear spectral gaps are discovered in the density of states of pinwheel arrays that manifest a distinctive long-range order. Furthermore, the level spacing statistics at large optical density exhibits a sharp transition from level repulsion to the Poisson behavior, consistently with the onset of the wave localization regime. Our findings reveal the importance of hyperuniform aperiodic structures with statistically isotropic k-space for the engineering of enhanced light-matter interaction and localization properties.

Comparative study of transparent display using aperiodic arrays of Si–SiO2 core–shell nanoparticles

In this paper, the different arrays of core–shell nanoparticles are investigated to propose a high-quality transparent display. In this work, we compare the optical properties of the different types of deterministic aperiodic arrays in a visible range. To realize this idea, the Si–SiO2 core–shell nanoparticle is used, and with varying radius and distance between nanoparticles, the transparency and contrast of the proposed transparent monitor are investigated. By comparing the deterministic aperiodic and periodic arrays, we show that the Fibonacci structure can achieve a higher scattering rate as well as narrow bandwidth. We use the array of nanoparticles based on the Fibonacci configuration by an appropriate lattice constant to obtain a very sharp scattering profile. We use the Finite-Difference Time-Domain numerical method to simulate and calculate the optical properties of the deterministic aperiodic and periodic arrays of nanoparticles. Finally, we demonstrate the effect of several nanoparticles on the bandwidth, peak of scattering, and absorption cross-section.

Effect of morphology of nanoparticles on performance of transparent display

Nanoparticles based transparent display is one of the most successful methods to realize transparent monitors. Also, an array of nanoparticles, especially aperiodic arrangements, plays an important role in this case. Normally, when one talks about nanoparticles, the spherical morphology appears in mind, in which it is possible to implement different morphology for nanoparticles. In this paper, six different classes of morphologies with various arrangements, such as periodic array and deterministic aperiodic arrays, have been investigated to propose a high-performance transparent display. We compare different morphologies of Si–SiO2 nanoparticles at RGB (Red, Green, Blue) wavelengths in different types of arrays to find the highest scattering cross-section. Our calculations and figure of merit depending on the optical properties of nanoparticles, such as the resonance wavelength, the extinction, scattering and absorption cross-section, and the scattering to absorption ratio (SAR). We will show that in the proposed structures, there are suitable parameters to provide higher scattering cross-section as well as narrow bandwidth in which that is equivalent to introduce the maximum transparency and contrast ratio of transparent monitor. We use the Finite-Difference Time-Domain (FDTD) numerical method to simulate and calculate the deterministic aperiodic and periodic arrays of nanoparticles. Finally, we obtain the absorption and scattering cross-sections for six classes of nanoparticles: Cube, Sphere, Disk, Oblate ellipse, Prolate ellipse, and Pyramid into aperiodic and periodic arrays.

A comparison of the absorbed power for periodic, disordered and deterministic aperiodic arrays of Silver nanoparticles

The comparison between the optical properties of ordered and disordered metallic nanoparticles (NP) on the top of a silicon substrate has been studied. Such structures have been used to enhance the performance of optoelectronic devices, by exploiting the properties of the metallic NPs and their interaction with each other. This comparative study has been carried out using the Finite Difference Time Domain (FDTD) numerical analysis. Here, we report the role of distributed NP’s on a silicon substrate and the electric field coupling between them. A slab of silicon substrate with a size of the micrometer range has been taken. Several metallic NPs have been distributed on the surface of the silicon. This structure has been studied for both periodic and disordered arrays of metallic nanoparticles. These NP’s have been chosen as silver for which they exhibit strong localized surface plasmon resonance (LSPR). Total absorbed power has also been studied. The structure is illuminated by a plane wave source with a wavelength range that varies between 300 nm to 800 nm.

Quasiperiodic plasmonic concentrators for enhanced light absorption in ultra-thin film solar cells

ABSTRACTThis report will demonstrate broadband, wide-angle, and polarization-insensitive absorption enhancement in ultra-thin films resting on metal substrates that have been etched with arrays of shallow sub-wavelength cylindrical holes. Absorption enhancement will be studied as a function of array geometry, with particular emphasis given to quasiperiodic arrays (a class of deterministic aperiodic arrays that were originally developed to tessellate 2-D planes with regular polygons). Through simulations and experimental data, it was found that absorption enhancement is heavily dependent on the rotational symmetry of the pattern of holes, as well as the inter-hole distance.

Spatial and spectral detection of protein monolayers with deterministic aperiodic arrays of metal nanoparticles

Light scattering phenomena in periodic systems have been investigated for decades in optics and photonics. Their classical description relies on Bragg scattering, which gives rise to constructive interference at specific wavelengths along well defined propagation directions, depending on illumination conditions, structural periodicity, and the refractive index of the surrounding medium. In this paper, by engineering multifrequency colorimetric responses in deterministic aperiodic arrays of nanoparticles, we demonstrate significantly enhanced sensitivity to the presence of a single protein monolayer. These structures, which can be readily fabricated by conventional Electron Beam Lithography, sustain highly complex structural resonances that enable a unique optical sensing approach beyond the traditional Bragg scattering with periodic structures. By combining conventional dark-field scattering micro-spectroscopy and simple image correlation analysis, we experimentally demonstrate that deterministic aperiodic surfaces with engineered structural color are capable of detecting, in the visible spectral range, protein layers with thickness of a few tens of Angstroms.

Plasmonic Nanogalaxies: Multiscale Aperiodic Arrays for Surface-Enhanced Raman Sensing

The accurate and reproducible control of intense electromagnetic fields localized on the nanoscale is essential for the engineering of optical sensors based on the surface-enhanced Raman scattering (SERS) effect. In this paper, using rigorous generalized Mie theory (GMT) calculations and a combined top-down/bottom-up nanofabrication approach, we design and experimentally demonstrate approximately 10(8) spatially averaged, reproducible SERS enhancement in deterministic aperiodic arrays of Au nanoparticles with different length scales. Deterministic aperiodic arrays of 200 nm diameter nanocylinders are first fabricated using electron-beam lithography on quartz substrates, and smaller size (30 nm diameter) Au nanoparticles are subsequently positioned by in situ Au reduction at regions of maximum field enhancement. These multiscale structures, which we call "plasmonic nanogalaxies", feature a cascade enhancement effect due to the strong electromagnetic interactions of small satellite nanoparticles with localized fields in aperiodic arrays of nanocylinders. The development of SERS substrates based on aperiodic arrays with different length scales provides a novel strategy to engineer plasmon-enhanced biosensors with chemical fingerprinting capability.