We determine the range of thicknesses and refractive indices for which omnidirectional reflection from quasiperiodic multilayers occurs. By resorting to the notion of area under the transmittance curve, we assess in a systematic way the performance of the different quasiperiodic Fibonacci multilayers.
We have designed, optimized, fabricated and characterized highly reflective quasi-omnidirectional (angular range of $0-60^\circ$) multilayered structures with a wide spectral range. Two techniques, chirping (a continuous change in thicknesses) and stacking of Bragg-type sub-structures, have been used to enhance the reflectance with minimum thickness for a given pair of refractive indices. Numerical calculations were carried out employing the transfer matrix method and we optimized the design parameters to obtain maximal reflectance averaged over different spectral ranges for all angles. We fab…
We theoretically investigate the possibility of realizing a nonlinear all-optical diode by using the unique features of quasiperiodic 1D photonic crystals. The interplay between the intrinsic spatial asymmetry in odd-order Thue-Morse lattices and Kerr nonlinearity, combined with the unconventional field localization properties of this class of quasiperiodic sequences, gives rise to sharp resonances that can be used to give a polarization-insensitive, nonreciprocal propagation with a contrast close to unity for low optical intensities.
Photonic bandgap design is one of the most basic ways to effectively control the interaction between light and matter. However, the traditional photonic bandgap is always dispersive (blueshift with the increase of the incident angle), which is disadvantageous to the construction of wide-angle optical devices. Hypercrystal, that the photonic crystal with layered hyperbolic metamaterials (HMMs), can strongly modify the bandgap properties based on the anomalous wavevector dispersion of the HMM. Here, based on phase variation compensation between HMM and isotropic dielectric layers, we propose for…
We measured and calculated transmission spectra of two-dimensional quasiperiodic photonic crystals (PCs) based on a 5-fold (Penrose) or 8-fold (octagonal) symmetric quasiperiodic pattern. The photonic crystal consisted of dielectric cylindrical rods in air placed normal to the basal plane on vertices of tiles composing the quasiperiodic pattern. An isotropic photonic band gap (PBG) appeared in the TM mode, where electric fields were parallel to the rods, even when the real part of a dielectric constant of the rod was as small as 2.4. An isotropic PBG-like dip was seen in tiny Penrose and octag…
The light propagation through a stack of two media with different refractive indices, which are aligned according to different quasiperiodic sequences determined by metallic means, is studied using the transfer matrix method. The focus lies on the investigation of the influence of the underlying quasiperiodic sequence as well as the dependence of the transmission on the frequency, the incidence angle of the light wave and different ratios of the refractive indices. In contrast to a periodically aligned stack we find complete transmission for the quasiperiodic systems for a wide range of differ…
The surface of thin-film solar cells can be tailored with photonic nanostructures to allow light trapping in the absorbing medium. This in turn increases the optical thickness of the film and thus enhances their absorption. Such a coherent light trapping is generally accomplished with deterministic photonic architectures. Here, we experimentally explore the use of a different nanostructure, a disordered one, for this purpose. We show that the disorder-induced modes in the film allow improvements in the absorption over a broad range of frequencies and impinging angles.
Waves propagating in certain one-dimensional quasiperiodic lattices are known to exhibit a sharp localization transition. We theoretically predict and experimentally observe that the localization of light in one-dimensional photonic quasicrystals may be followed by a second delocalization transition for some states on increasing quasiperiodic modulation strength - an example of a reentrant transition. We further propose that this phenomenon can be qualitatively captured by a dimerized tight-binding model with long-range couplings.
Quantum walk is a key operation in quantum computing, simulation, communication and information. Here, we report for the first time the demonstration of quantum walks and localized quantum walks in a new type of optical fibers having a ring of cores constructed with both periodic and quasiperiodic Fibonacci sequences, respectively. Good agreement between theoretical and experimental results have been achieved. The new multicore ring fibers provide a new platform for experiments of quantum effects in low-loss optical fibers which is critical for scalability of real applications with large-size …
Topological Pumping Through a Localized Bulk in a Photonic Hofstadter System
The Pennsylvania State University(宾夕法尼亚州立大学);Amherst College(阿默斯特学院);Massachusetts Institute of Technology(麻省理工学院);RPTU University Kaiserslautern-Landau(凯泽斯劳滕-兰道莱布尼茨技术大学)
Structural hierarchy and complex 3D architecture are characteristics of biological photonic designs that are challenging to reproduce in synthetic materials. Top-down lithography allows for designer patterning of arbitrary shapes, but is largely restricted to planar 2D structures. Self-assembly techniques facilitate easy fabrication of 3D photonic crystals, but controllable defect-integration is difficult. In this paper we combine the advantages of top-down and bottom-up fabrication, developing two techniques to deposit 2D-lithographically-patterned planar layers on top of or in between invers…
The propagation of s- and p-polarized light through quasiperiodic multilayers, consisting of layers with different refractive indices, is studied by the transfer matrix method. In particular, we focus on the transmission coefficient of the systems in dependency on the incidence angle and on the ratio of the refractive indices. We obtain additional bands with almost complete transmission in the quasiperiodic systems at frequencies in the range of the photonic band gap of a system with a periodic alignment of the two materials for both types of light polarization. With increasing incidence angle…
In this chapter, first we will address principal aspects of 1D quasiperiodicity with a particular focus on 1D Fibonacci chains. Further, the rest of the chapter will be dedicated to the electromagnetic counterpart of 1D Fibonacci structures as a relatively simplest case of the large class of photonic quasicrystals.
Originally emerged within the context of string and quantum field theory, and later fruitfully extrapolated to photonics, the algebraic transformations of quantum-mechanical supersymmetry were conceived in the space realm. Here, we introduce a paradigm shift, demonstrating that Maxwell's equations also possess an underlying supersymmetry in the time domain. As a result, we obtain a simple analytic relation between the scattering coefficients of a large variety of time-varying optical systems and uncover a wide new class of reflectionless, three dimensional, all-dielectric, isotropic, omnidirec…
We investigate the optical transmission spectra for $s$-polarized (TE) and $p$-polarized (TM) waves in one-dimensional photonic quasicrystals on a quasiperiodic multilayer structure made up by alternate layers of SiO$_{2}$ and \textit{metamaterials}, organized by following the Octonacci sequence. Maxwell's equations and the transfer-matrix technique are used to derive the transmission spectra for the propagation of normaly and obliquely incident optical fields. We assume Drude-Lorentz-type dispersive response for the dielectric permittivity and magnetic permeability of the metamaterials. For n…
In the recent years, there has been a drive towards the realization of topological phases beyond conventional electronic materials, including phases defined in more than three dimensions. We propose a way to realize 2nd Chern number topological phases with photonic crystals simply made up of defect resonators embedded within a regular lattice of resonators. In particular, through a novel quasiperiodic spatial modulations in the defect radii, a defect lattice possessing topologically nontrivial Chern bands with non-abelian berry curvature living in four-dimensional synthetic space is proposed. …
We report on the first experimental evidence of guided resonances (GRs) in photonic crystal slabs based on aperiodically-ordered supercells. Using the Ammann-Beenker (quasiperiodic, 8-fold symmetric) tiling geometry, we present our study on the fabrication, experimental characterization, and full-wave numerical simulation of two representative structures (with different filling parameters) operating at near-infrared wavelengths (1300-1600 nm). Our results show a fairly good agreement between measurements and numerical predictions, and pave the way for the development of new strategies (based, …
Quasiperiodic lattices have recently been shown to be a non-trivial topological phase of matter. Charge pumping -- one of the hallmarks of topological states of matter -- was recently realized for photons in a one-dimensional (1D) off-diagonal Harper model implemented in a photonic waveguide array. The topologically nontrivial 1D Fibonacci quasicrystal (QC) is expected to facilitate a similar phenomenon, but its discrete nature and lack of pumping parameter hinder the experimental study of such topological effects. In this work we overcome these obstacles by utilizing a family of topologically…
We perform full 3D topology optimization (in which "every voxel" of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc (including diamond), bcc, and simple-cubic lattices. Even without imposing the constraints of any fabrication process, the resulting optimal gaps are only slightly larger than previous hand designs, suggesting that current photonic crystals are nearly optimal in this respect. However, optimization can discover new structures, e.g. a new fcc structure with the same sy…
Analytic representation formulas and power series are developed describing the band structure inside non-magnetic periodic photonic three-dimensional crystals made from high dielectric contrast inclusions. Central to this approach is the identification and utilization of a resonance spectrum for quasiperiodic source-free modes. These modes are used to represent solution operators associated with electromagnetic and acoustic waves inside periodic high contrast media. A convergent power series for the Bloch wave spectrum is recovered from the representation formulas. Explicit conditions on the c…