Mher Ghulinyan
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.
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A theory of light diffraction from planar quasicrystalline lattice with resonant scatterers is presented. Rich structure, absent in the periodic case, is found in specular reflection spectra, and interpreted as a specific kind of Wood anomalies, characteristic for quasicrystals. The theory is applied to semiconductor quantum dots arranged in Penrose tiling.
Topological physics in photonic systems have attracted great attentions in recent years. In this work, we theoretically study the one and two dimensional photonic quasicrystal resonator lattices characterized by the first and second Chern number, which show exotic boundary states within the photonic energy band gap. In particular, the second Chern number protected edge states has opened up new possibilities for realizing topological physics of dimensions higher than three in photonic systems, which is highly sought for. Such photonic systems can be easily experimentally realized in regular pho…
Non-Hermitian delocalization in a 2D photonic quasicrystal
本研究在十二重光子准晶实验中发现非厄米势可增强波包空间扩展的新机制，揭示非厄米准晶行为更丰富，为光子束调控等领域提供新可能。
We show that it is possible to have a topological phase in two-dimensional quasicrystals without any magnetic field applied, but instead introducing an artificial gauge field via dynamic modulation. This topological quasicrystal exhibits scatter-free unidirectional edge states that are extended along the system's perimeter, contrary to the states of an ordinary quasicrystal system, which are characterized by power-law decay. We find that the spectrum of this Floquet topological quasicrystal exhibits a rich fractal (self-similar) structure of topological "minigaps," manifesting an entirely new …
Topological insulators and topological superconductors are distinguished by their bulk phase transitions and gapless states at a sharp boundary with the vacuum. Quasicrystals have recently been found to be topologically nontrivial. In quasicrystals, the bulk phase transitions occur in the same manner as standard topological materials, but their boundary phenomena are more subtle. In this Letter we directly observe bulk phase transitions, using photonic quasicrystals, by constructing a smooth boundary between topologically distinct one-dimensional quasicrystals. Moreover, we use the same method…
Chiral photonic topological states in Penrose quasicrystals
该研究在磁光Penrose光子准晶体中发现无需Bloch能带的手性拓扑边缘态，并用实空间Bott指数±1表征其非平凡拓扑。
We introduce a novel optimization method to design the first examples of photonic quasicrystals with substantial, complete photonic band gaps (PBGs): that is, a range of frequencies over which electromagnetic wave propagation is forbidden for all directions and polarizations. The method can be applied to photonic quasicrystals with arbitrary rotational symmetry; here, we illustrate the results for 5- and 8-fold symmetric quasicrystals. The optimized band gaps are highly isotropic, which may offer advantages over photonic crystals for certain applications.
Photonic quasicrystal of spin angular momentum
本研究首次实现由自旋角动量构成的光子准晶体，构建类de Bruijn铺砌理论框架阐明其形成机制，发现新型自旋-轨道耦合效应及类相位子动力学，拓展了准晶体的应用场景。
We numerically analyze, using Finite Difference Time Domain simulations, the bandgap properties of photonic quasicrystals with a low index contrast. We compared 8-, 10- and 12-fold symmetry aperiodically ordered lattices with different spatial tiling. Our results show that tiling design, more than symmetry, determines the transmission properties of these structures.
Observation of localization of light in photonic quasicrystals of diverse symmetries
本研究利用干涉平面波创建不同旋转对称性的二维光子准晶体，实验证实了光在纯线性准晶体中的局域化现象，并发现临界深度随对称性阶数增加而减小，为非周期系统波局域化应用铺平道路。
In developing strategies of manipulating surface electromagnetic waves, it has been recently recognized that a complete forbidden band gap can exist in a periodic surface-wave photonic crystal, which has subsequently produced various surface-wave photonic devices. However, it is not obvious whether such a concept can be extended to a non-periodic surface-wave system that lacks translational symmetry. Here we experimentally demonstrate that a surface-wave photonic quasicrystal that lacks periodicity can also exhibit a forbidden band gap for surface electromagnetic waves. The lower cutoff of thi…
One of the most intriguing problems of light transport in solids is the localization that has been observed in various disordered photonic structures1-11. The light localization in defect-free icosahedral quasicrystals has recently been predicted theoretically without experimental verification10. Here we report on the fabrication of submicron-size dielectric icosahedral quasicrystals and demonstrate the results of detailed studies of the photonic properties of these structures. Here, we present the first direct experimental observation of intrinsic light localization in defect-free quasicrysta…
Stable vortices with topological charge of 3 and 4 are examined numerically and analytically in photonic quasicrystals created by interference of 5 as well as 8 beams, in the cases of cubic as well as saturable nonlinearities. These structures are experimentally realizable, including a prototypical example of a stable charge 4 vortex. Direct numerical simulations corroborate the analytical and numerical linear stability analysis predictions.
Corner states (CSs) in higher-order topological insulators (HOTIs) have recently been of great interest in both crystals and quasicrystals. In contrast to electronic systems, HOTIs have not been found in photonic quasicrystals (PQCs). Here, we systemically study the higher-order topology in the two-dimensional Thue-Morse photonic quasicrystals (TM-PQCs). Not only the topological phase transition and the non-trivial CSs with fractional charge induced by multipole moments, but also a new type of CSs are found due to the complex structure of TM-PQCs near corners. The different origins of these CS…
Multiple-beam holography has been widely used for the realization of photonic quasicrystals with high rotational symmetries not achievable by the conventional periodic crystals. Accurate control of the properties of the interfering beams is necessary to provide photonic band-gap structures. Here we show, by FDTD simulations of the transmission spectra of 8-fold quasiperiodic structures, how the geometric tiling of the structure affects the presence and properties of the photonic band-gap for low refractive index contrasts. Hence, we show an interesting approach to the fabrication of photonic q…
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.
Previous methods for determining photonic quasicrystal (PQC) spectra have relied on the use of large supercells to compute the eigenfrequencies and/or local density of states (LDOS). In this manuscript, we present a method by which the energy spectrum and the eigenstates of a PQC can be obtained by solving Maxwells equations in higher dimensions for any PQC defined by the standard cut-and-project construction, to which a generalization of Blochs theorem applies. In addition, we demonstrate how one can compute band structures with defect states in the higher-dimensional superspace with no addit…
We present a study of the lensing properties of two-dimensional (2-D) photonic quasicrystal (PQC) slabs made of dielectric cylinders arranged according to a 12-fold-symmetric square-triangle aperiodic tiling. Our full-wave numerical analysis confirms the results recently emerged in the technical literature and, in particular, the possibility of achieving focusing effects within several frequency regions. However, contrary to the original interpretation, such focusing effects turn out to be critically associated to local symmetry points in the PQC slab, and strongly dependent on its thickness a…
In this paper, we report on the first evidence of guided resonances (GRs) in aperiodically-ordered photonic crystals, tied to the concept of "quasicrystals" in solid-state physics. Via a full-wave numerical study of the transmittance response and the modal structure of a photonic quasicrystal (PQC) slab based on a representative aperiodic geometry (Ammann-Beenker octagonal tiling), we demonstrate the possibility of exciting GR modes, and highlight similarities and differences with the periodic case. In particular, we show that, as for the periodic case, GRs arise from the coupling of the incid…
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…
Optical interference holography has been proved to be a useful technique in fabricating periodic photonic crystals in which electromagnetic waves are forbidden in certain frequency bandgaps. Compared to periodic crystals quasicrystals, having higher point group symmetry, are more favourable in achieving complete bandgaps. In this report, we propose two seven-beam optical interference configurations based on the reciprocal vector space representations for quasicrystals to fabricate icosahedral quasicrystals. Interference simulations for the quasicrystals exhibit the full symmetry of an icosahed…
We present the key results from a comprehensive study of the refraction and focusing properties of a two-dimensional dodecagonal photonic ``quasicrystal'' (PQC), carried out via both full-wave numerical simulations and microwave measurements on a slab made of alumina rods inserted in a parallel-plate waveguide. We observe anomalous refraction and focusing in several frequency regions, confirming some recently published results. However, our interpretation, based on numerical and experimental evidence, differs substantially from the one in terms of ``effective negative refractive-index'' that w…
We report on the formation and development of the photonic band gap in two-dimensional 8-, 10- and 12-fold symmetry quasicrystalline lattices of low index contrast. Finite size structures made of dielectric cylindrical rods were studied and measured in the microwave region, and their properties compared with a conventional hexagonal crystal. Band gap characteristics were investigated by changing the direction of propagation of the incident beam inside the crystal. Various angles of incidence from 0 \degree to 30\degree were used in order to investigate the isotropic nature of the band gap. The…
We report the realization of an active one-dimensional Fibonacci photonic quasi-crystal via spin coating. Manipulation of the luminescence properties of an organic dye embedded in the quasi-crystal is presented and compared to theoretical simulations. The luminescence occurs via the pseudo-bandedge mode and follows the dispersion properties of the Fibonacci crystal. Time resolved luminescence measurement of the active structure shows faster spontaneous emission rate, indicating the effect of the large photon densities available at the bandedge due to the presence of critically localized states…
In this paper, we study the radiation from embedded sources in two-dimensional finite-size "photonic-quasicrystal" (PQC) slabs made of dielectric rods arranged according to a 12-fold symmetric aperiodic tiling. The results from our investigation, based on rigorous full-wave simulations, show the possibility of achieving broadside radiation at multiple frequencies, with high-directivity (e.g., 15 dB) and low-sidelobes (e.g., -12 dB). We also show that leaky waves are supported by a PQC slab, and that the beamwidth is directly proportional to the leaky-wave attenuation constant, which provides a…
Spectral Distribution of one-dimensional Photonic Quasicrystals: The Role of Irrational Numbers
本文研究了一维光子准晶体的谱分布，发现其谱结构受无理数参数β的大小影响，呈现出与β相关的线性关系。
Robust Anderson transition in non-Hermitian photonic quasicrystals
本文研究非厄米光子准晶体中的安德森相变，证明在局域非公度增益和损耗作用下，该相变对退相干效应具有鲁棒性，并通过光子网格晶格中的合成准晶体加以验证。
All-dielectric photonic quasicrystals may act as zero-refractive-index homogeneous materials despite their lack of translational symmetry and periodicity, stretching wavelengths to infinity and offering applications in light wavefront sculpting and optical cloaking.
Self-organized photonic time quasicrystal from a single imposed clock
研究通过单一时钟在非线性介质中自组织出时间准晶体，利用非线性介质自身选择准周期性时间秩序，展现相位动态和离散频谱组合。
2D dielectric photonic quasicrystals can be designed to show isotropic band gaps. The system here studied is a quasiperiodic lattice made of silicon dielectric cylinders arranged as periodic unit cell based on a decagonal approximant of a quasiperiodic Penrose lattice. We analyze the bulk properties of the resulting lattice as well as the bright states excited in the gap which correspond to localized resonances of the electromagnetic field in specific cylinder clusters of the lattice. Then we introduce a controlled shear deformation which breaks the decagonal symmetry and evaluate the width re…
We study theoretically the transmission spectra in one-dimensional photonic quasicrystals, made up of SiO$_2$($A$) and TiO$_2$($B$) materials, organized following the Octonacci sequence, where the $n$th-stage of the multilayer $S_{n}$ is given by the rule $S_{n}=S_{n-1}S_{n-2}S_{n-1}$, for $n\geq 3$ and with $S_{1}=A$ and $S_{2}=B$. The expression for transmittance was obtained by employing a theoretical calculation based in the transfer-matrix method. To normally incident waves, we observe that, for a same generation, the transmission spectra for TE and TM waves are equal, at least qualitativ…
Exploring Aperiodic Order in Photonic Time Crystals
该论文提出分析非周期有序光子时间准晶体的理论框架，推广迹映射方法至时间域，以Thue-Morse序列为例研究能带与波传输，揭示多尺度光谱响应和局域化效应，为先进光子器件发展提供见解。
One-dimensional Thue-Morse (ThMo) lattices are examples of self-similar structures that exhibit bandgap phenomena. ThMo multilayers may also possess fractal photonic bandgaps that give rise to large omnidirectional reflectance and light emission enhancement effects. Two-dimensional (2D) ThMo aperiodic quasicrystals possess interesting properties for photonic applications too. Here we demonstrate the experimental fabrication of large area 2D ThMo lattices into polymeric substrates at nanometer scale by electron beam lithography (EBL). Far field diffraction patterns of the experimental Thue-Mors…
Aubry-André transition in photonic time quasicrystals
该研究证实光子时间准晶体中存在Aubry-André转变，其发生在动量迁移率边处，该转变将光按波数分为传播与停止增长的分量，拓展了Aubry-André转变的适用域。
Non-Hermitian photonic time quasicrystal
本研究提出非厄米光子时间准晶体，通过复相位延拓实现体放大率整数相位锁定，连接Avila加速度与可观测光响应，实现量子化放大与光谱选择。
Observation of Light Localization at the Edges of Quasicrystal Waveguide Arrays
该研究在径向裁剪的Penrose准晶波导阵列中观测到边缘光的线性与非线性局域，揭示截短半径对局域的影响，实验验证了飞秒刻写阵列中的局域态及向边缘孤子的功率依赖转变，为准周期光子系统截短诱导局域提供首个实验证据。
High-harmonic spectroscopy of mobility edges in one-dimensional quasicrystals
本文提出利用高次谐波产生探测一维准晶体的局域化转变与迁移率边，并引入偶极迁移率分类非线性光学区域。
The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i) quasicrystals exhibit nontrivial topological properties and (ii) these properties are attributed to dimensions higher than that of the quasicrystal. Specifically, we show, both theoretically and experimentally, that one-dimensional quasicrystals are assigned two-dimensional Chern numbers and, respectively, exhibit topologically protected boundary states equivale…
Second harmonic generation in a two dimensional nonlinear quasi-crystal is demonstrated for the first time. Temperature and wavelength tuning of the crystal reveal the uniformity of the pattern while angle tuning reveals the dense nature of the crystal's Fourier spectrum. These results compare well with theoretical predictions showing the excellent uniformity of the crystal and suggest that more complicated ``nonlinear holograms'' should be possible.
Quasicrystals are nonperiodic structures having no translational symmetry but nonetheless possessing long-range order. The material properties of quasicrystals, particularly their low-temperature behavior, defy easy description. We present a compact optical setup for creating quasicrystal optical potentials with 5-fold symmetry using interference of nearly co-propagating beams for use in ultracold atom quantum simulation experiments. We verify the optical design through numerical simulations and demonstrate a prototype system. We also discuss generating phason excitations and quantized transpo…
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