Two-dimensional Photonic Quasicrystals Research Articles

Photonic bandgaps of different unit cells in the basic structural unit of germanium-based two-dimensional decagonal photonic quasi-crystals

Based on the infrared optical material germanium, in the basic structural unit of a two-dimensional decagonal photonic quasi-crystal, photonic bandgaps of four square unit cells with a scattering radius in the range of [0,0.3a] have been calculated within two cases of construction (i.e., air cylinders arranged in germanium and germanium cylinders arranged in air) by using the plane wave expansion method. In considering the Bragg-like scattering effect in two-dimensional photonic quasi-crystals as the elastic collision in physics, we put forward the photonic bandgap impact function F=q(1)q(2)q(3)επr(2) for the first time, to the best of our knowledge. A certain unit cell structure shares some similar photonic bandgap properties with a periodic structure. For a certain structure of the unit cell, the center frequency change trends of the photonic bandgap and the type of photonic bandgap generated are not related with the period of the photonic crystal, but with the relative dielectric constant and the construction, respectively. Different unit cell structures own different photonic bandgap structures. This occurs because the high degree of rotational symmetry of the quasi-periodic structure and weak long-range order of the basic structural unit lead to different Bragg-like scattering effects within the unit cell structures.

Negative refraction and localized states of a classical wave in high-symmetry quasicrystals

Recently, negative refraction of electromagnetic waves in periodic photonic crystals has been demonstrated experimentally and sub-wavelength images observed. A theoretical and experimental investigation is reported of the electromagnetic wave transport in high-symmetry photonic quasicrystals (QCs). It is shown that negative refraction can appear in these transparent quasicrystalline photonic structures. It is interesting that highly symmetric two-dimensional photonic QCs possess a universal feature for non-near-field focus of two kinds of polarized waves (S wave and P wave). That is, the non-near-field focus for two kinds of polarized waves can be realized by using flat lenses, which consist of some high-symmetric two-dimensional photonic QCs with the same structures and parameters. In addition, some two-dimensional and three-dimensional localized states in defect-free photonic QCs have been found. It is evident that these unusual localized states can be explored by means of electron energy loss spectroscopy.

Resonant transmission of electromagnetic waves through two-dimensional photonic quasicrystals

We present numerical simulations of electromagnetic millimeter-wave propagation in a two-dimensional lattice of dielectric rods arranged in a tenfold Penrose tiling. We find (i) isotropic photonic band gap as expected for quasicrystals and (ii) localized states. We demonstrate that the high frequency edge of the second band gap is characterized by a very small refractive index (fast light). We study the transmission of electromagnetic waves in the frequency range corresponding to fast light and demonstrate that it is related to tunneling through localized states. We use the fast light phenomenon to design a focusing device—a planoconcave lens.

Complete band gaps in two-dimensional photonic quasicrystals

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.

Fabrication of Si-based two-dimensional photonic quasicrystals by using multiple-exposure holographic lithography

Two-dimensional (2D) photonic quasicrystal (PQC) template patterns have been fabricated by using multiple-exposure holographic lithography (MHL). The MHL technique is based on Lloyd’s mirror setup using interference of two equivalent beams, which is an excellent method for fabricating periodic structures of a large area. The 2D PQC array shows various sizes and shapes with a change in the incident angle (θ) and rotation angle (γ) of the multiple-exposure beams. In addition, the filling factor (η), which is a very important factor for optical characteristic of 2D PQCs, was controlled by the exposure time (τ). The fabricated PQCs showed eight-, ten-, and 12-fold patterns with high-order rotational symmetries. Diffraction patterns using 632.8 nm HeNe laser were also observed with n-rotation symmetry for the corresponding n-fold PQCs. After fabricating the PQCs, reactive-ion etching of the silicon wafer was performed with 50-nm-thick chromium (Cr) as a mask in CF4/O2 plasma to a 1.3 μm depth. The authors confirmed that fabrication of n-fold 2D PQCs in a large area with suitable optical characteristics could be controlled by some parameters of MHL.

Two-dimensional photonic quasicrystals by single beam computer-generated holography

Recently important efforts have been dedicated to the realization of a new kind of photonic crystals, known as photonic quasicrystals, in which the lack of the translational symmetry is compensated by rotational symmetries not achievable by the conventional periodic crystals. Here we show a novel approach to their fabrication based on the use of a programmable Spatial Light Modulator encoding Computer-Generated Holograms. Using this single beam technique we fabricated Penrose-tiled structures possessing rotational symmetry up to 23-fold, and a two-dimensional Thue-Morse structure, which is an aperiodic structure not achievable by multiple beam holography.

Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals

By using the sparse-matrix canonical-grid method, we performed large-scale multiple-scattering calculations to study band-edge states in large-sized two-dimensional photonic quasicrystals. We find that the band-edge states evolve in an abrupt and irregular way when the sample size is increased. New states with reduced symmetries can emerge at the band edge in large samples. Strong multifractal behaviors in the wave functions are also observed. Our findings unveil important differences between quasiperiodic and periodic systems at band edges.

Properties of microcavities in two-dimensional photonic quasicrystals with octagonal rotational symmetry

It is now well established that two-dimensional structures with dielectric variations based on quasicrystalline tilings are able to support photonic band gaps. Here, we have investigated the properties of the localized defect modes with frequencies within the photonic band gap for a certain kind of two-dimensional octagonal photonic quasicrystal with lattice vacancies breaking the quasi-periodic symmetry. The eigenfrequencies of such localized modes are given as a function of filling fractions for four distinct microcavity designs, and the electromagnetic field profiles of the localized modes are explored. The calculations of the eigenfrequencies and electromagnetic field profiles were performed using a supercell approximation in a plane wave method.

Wave and defect dynamics in nonlinear photonic quasicrystals

Quasicrystals are unique structures with long-range order but no periodicity. Their properties have intrigued scientists ever since their discovery and initial theoretical analysis. The lack of periodicity excludes the possibility of describing quasicrystal structures with well-established analytical tools, including common notions like Brillouin zones and Bloch's theorem. New and unique features such as fractal-like band structures and 'phason' degrees of freedom are introduced. In general, it is very difficult to directly observe the evolution of electronic waves in solid-state atomic quasicrystals, or the dynamics of the structure itself. Here we use optical induction to create two-dimensional photonic quasicrystals, whose macroscopic nature allows us to explore wave transport phenomena. We demonstrate that light launched at different quasicrystal sites travels through the lattice in a way equivalent to quantum tunnelling of electrons in a quasiperiodic potential. At high intensity, lattice solitons are formed. Finally, we directly observe dislocation dynamics when crystal sites are allowed to interact with each other. Our experimental results apply not only to photonics, but also to other quasiperiodic systems such as matter waves in quasiperiodic traps, generic pattern-forming systems as in parametrically excited surface waves, liquid quasicrystals, and the more familiar atomic quasicrystals.

The Ga-Nitride/air Two-Dimensional Photonic Quasi-crystals Fabricated on GaN-based Light Emitters

ABSTRACTThe two-dimensional (2D) Ga-nitride/air photonic quasi-crystals (PQC) were successfully fabricated by the technique of focused Ga ion beam (FIB) milling on GaN based epitaxial wafers. The effects of the PQC on the current injected edge emitting GaN-based light emitters were investigated. The quasi-crystal structures studied in this work are based on square-triangular tiling with 8-fold or 12-fold symmetry. The air hole diameter in the different PQC patterns was varied from 95nm up to 1200nm, the filling factor of air hole was in the range of 10% to 50% and the depth of the hole was 90nm to 370nm, respectively. Among these, the nearest center-to-center distance of the holes and/or the lattice constant was reached to be 170nm. The photonic quasi-crystals on the GaN-based light emitters demonstrated a two to three factor of magnitude enhancement of surface extractive emission. The blocking of the propagation of planar-guided modes by the photonic quasi-crystals was observed. By comparison of symmetry effect among the triangular lattice PC and PQCs, it was found that the GaN-based photonic quasi-crystal (PQC) with 12-fold symmetry provided a much favorable enhancement of the extractive light emission over that of triangle lattice PC and 8-fold symmetric PQC as well.

The design of two-dimensional photonic quasicrystals by means of a Fourier transform method

The design of two-dimensional photonic quasicrystals by means of a Fourier transform method

The design of two-dimensional photonic quasicrystals by means of a Fourier transform method

The design of two-dimensional photonic quasicrystals by means of a Fourier transform method

The design of two-dimensional photonic quasicrystals by means of a fourier transform method

We report a method of designing aperiodic photonic quasicrystals. The method is based on the recognition that the Fourier transform of the dielectric structure has a direct influence on the mode spectrum, and can be chosen to enhance the properties of the system. The diffraction of light by, and the band structure of, such modified photonic quasicrystals is investigated and compared to the properties of conventional photonic quasicrystals.

Two-dimensional penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes

We report measurements of the diffraction pattern of a two-dimensional photonic quasicrystal structure. Using a set of plane waves defined by the diffraction pattern we introduce a theoretical approach for the calculation of the band structure which captures the rotational and inflational properties of the quasicrystal. Based on this model we find that the density of modes of the quasicrystal displays a fractal character and a depleted region analogous to the band gap in a periodic system.