Three-dimensional woodpile photonic crystal templates for the infrared spectral range

High-quality templates of three-dimensional woodpile photonic crystals are fabricated in photoresist SU-8 by use of femtosecond laser lithography. The samples have smooth surfaces, are mechanically stable, and are resistant to degradation under environmental and chemical influences. Fundamental and higher-order photonic stopgaps are identified in the wavelength range 2.0-8.0 microm. These templates can be used for subsequent infiltration by optically active or high-refractive-index materials.     

Various photonic crystal structures fabricated by using a top-cut hexagonal prism

We demonstrate a holographic approach for the fabrication of large-area photonic crystal (PhC) microstructures by applying a single top-cut hexagonal prism (TCHP). The interference patterns of the beams from the TCHP are calculated. Various two-dimensional PhC structures are fabricated in photo-resist films. They include symmetrical hexagonal structures, the honey-comb structure and the hexagonal structure with skewed elliptical rods. The first structures come from six-beam and symmetrical three-beam interfering. The second structure appears when the beam is incident on the TCHP obliquely. The third structure is obtained when adjacent three beams or four beams are interfered. The period can be decreased to 285 nm. SPM observations of the PhCs provide the basis for measurement of their structural parameters. A good agreement is obtained for the measured structural parameters and calculated results for the PhCs. The photonic band gaps of the hexagonal symmetrical and honeycomb structures are derived by using the plane wave method. These results reveal that, by varying the number of split beams and the incident angle, using the single TCHP PhCs, different band gaps can be achieved.     

Direct optical fabrication of three-dimensional photonic crystals in a high refractive index LiNbO3 crystal

Direct optical fabrication of 3D photonic crystals in a high refractive index LiNbO3 crystal by using the femtosecond laser-induced microexplosion method is investigated. The focal distortion, caused by the refractive index mismatch-induced spherical aberration, can be significantly reduced by using a so-called threshold fabrication method. As a result, 3D fcc photonic crystals are fabricated by stacking quasi-spherical voids layer by layer. Photonic stopgaps with suppression rates of up to 30% in the transmission spectra are observed. The angle dependence of the stopgaps is also revealed.     

Introducing CdS into two- and three-dimensional photonic crystals

SiO₂/air three-dimensional (3D) periodic structures were fabricated by removing Si layers partially from Si/SiO₂ 3D photonic crystals (PhCs) formed by using autocloning. CdS/SiO₂ 3D periodic structures were formed by introducing CdS into the SiO₂/air structures by the TEA method and photoluminescence (PL) was observed from the introduced CdS. TiO₂/air/CdS two-dimensional (2D) PhCs were also fabricated by introducing CdS into the voids of TiO₂/air 2D periodic structures, in which SiO₂ layers were partially etched out from TiO₂/SiO₂ 2D PhCs fabricated by using autocloning. PL radiating normal to the surface was measured and large polarization dependence was observed.     

Ultrafast interferometric measurements of plasmonic transport in photonic crystals

We present a novel time-domain experimental approach to the study of the dynamics of surface electromagnetic wave propagation in a two-dimensional photonic crystal. A surface plasmon polariton is launched by ultrafast laser pulses and propagates into a photonic crystal, the dynamics of which are measured by an interferometric cross-correlation method. Plasmon photonic stopgaps are characterized by a single measurement. The dispersion around the stopgaps is determined with a series of angle-resolved measurements.     

FDTD analysis of 2D triangular-lattice photonic crystals with arbitrary-shape inclusions based on unit cell transformation

A finite-difference time-domain method based on Yee’s orthogonal cell is utilized to calculate the band structures of 2D triangular-lattice-based photonic crystals through a simple modification to properly shifting the boundaries of the original unit cell. A strategy is proposed for transforming the triangular unit cell into an orthogonal one, which can be used to calculate the band structures of 2D PhCs with various shapes of inclusions, such as triangular, quadrangular, and hexagonal shapes, to overcome the shortage of plane-wave expansion method for circular one. The band structures of 2D triangular-lattice-based PhCs with hexagonal air-holes are calculated and discussed for different values of its radius and rotation angle. The obtained results provide an insight to manipulate the band structures of PhCs.     

Photonic crystal surface mode microcavities

Our recent research on surface mode optical microcavities based on two-dimensional photonic crystals (PhCs) was reviewed in this paper. We presented the design, fabrication and characterization of high quality (Q) factor surface mode microcavities. Realizations of these PhCs were based on both amorphous silicon-on-insulator (SOI) structures and crystalline SOI structures.     

Wavelet method for computing band diagrams of 2D photonic crystals

A wavelet method is applied for the first time to the computation of band diagrams of photonic crystals (PhCs). The wavelet algorithm is described. Its numerical implementation is validated in the case of emblematic two-dimensional triangular and square lattice PhCs. Although these examples do not emphasize the full power of wavelet methods, the number of wavelets needed to achieve a prescribed accuracy is already shown to be orders of magnitude smaller than the number of waves used in the traditional plane wave method. Further extension to more complex photonic structures is discussed.     

Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps

Efficient numerical methods for analyzing photonic crystals (PhCs) can be developed using the Dirichlet-to-Neumann (DtN) maps of the unit cells. The DtN map is an operator that takes the wave field on the boundary of a unit cell to its normal derivative. In frequency domain calculations for band structures and transmission spectra of finite PhCs, the DtN maps allow us to reduce the computation to the boundaries of the unit cells. For two-dimensional (2D) PhCs with unit cells containing circular cylinders, the DtN maps can be constructed from analytic solutions (the cylindrical waves). In this paper, we develop a boundary integral equation method for computing DtN maps of general unit cells containing cylinders with arbitrary cross sections. The DtN map method is used to analyze band structures for 2D PhCs with elliptic and other cylinders.     

Improved combined wave number eigenvalue equations method for band structure calculations of metal photonic crystal

We provide the combined wave number eigenvalue equations (CWNEE) method based upon the plane-wave expansion (PWE) method to calculate and optimize the band structures of the two-dimension (2D) photonic crystals (PhCs). Compared with the traditional PWE methods for the metal PhCs, the band structures can be obtained directly using the CWNEE method, and not any extra procedures are needed to handle the folded band structures. The comparison between the CWNEE method and FDTD method in accuracy and time-consuming has been analyzed, and the results show that the CWNEE method is reliable and accurate. With the CWNEE method and the Bisection-Particle Swarm Optimization method, we optimize the large gap–midgap ratio of the 2D square lattice of square metal rods and circular metal rods. Unlike many traditional PWE method, the CWNEE method can directly calculate the band structure in the arbitrary given frequency range, and it is quite useful for calculating the defect mode of photonic crystal cavity.     

Fabrication of Two-Dimensional Photonic Crystals with Controlled Defects by Combination of Holographic Lithography and Two-Photon Polymerization

A new ternary photopolymer system is used in fabricating photonic crystals （PhCs） with controlled defects by combination of single-photon and two-photon photopolymerization. The former process can produce PhCs in one-step recording with a low-power （tens mW） continuous-wave laser at 532nm, while the latter can create desired defects. The preparation of the material, the optical setup and the preliminary experimental results are given. Compared with other methods, this approach is much more accessible and convenient for use of visible light and has advantages of making PhCs in a large scale quickly and economicaJly and introducing any defects exactly, especially for three-dimensional structures.     

Cluster coherent potential approximation for disordered photonic crystals using photonic Wannier functions

We present an investigation of disordered photonic crystals (PhCs) based on the combination of photonic Wannier functions with the concept of the coherent potential approximation (CPA). In particular, we provide the theoretical foundation of a real-space cluster CPA that is causal, enforces the proper symmetries of the effective medium, and includes effects of multiple scattering of the same and nearby defects, which is essential for strong defects. Based on this, we present results for the density of states of disordered PhCs for different types of disorder. Our results are thus relevant to such diverse areas as random lasing and the analysis of fabricational imperfections in PhCs.     

Woodpile photonic crystals composed of air columns

Silicon-based woodpile photonic crystals (PhCs) composed of air columns have a large gap/midgap ratio exceeding 20% over a wide dimensional range of the cross section of the air column when the cross section is deformed to a rectangular shape extended normal to the stacking direction. Such a PhC structure can be formed using a simple technique based on 45° dry etching. Furthermore, introducing twin air columns with small cross sections instead of corresponding mother air columns yields a defect state at the region where the columns cross. Since the fabrication process is a planar-type Si wafer process, fabricated PhCs can be easily combined with conventional electronic circuits and optical elements, such as Si waveguides and switches.     

Properties, applications and fabrication of photonic crystals with ring-shaped holes in silicon-on-insulator

We show that photonic crystals with ring-shaped holes (RPhCs) exhibit superior properties compared to conventional photonic crystals (PhCs). At low air-fill factors RPhCs can have a larger bandgap than conventional PhCs. Moreover, RPhC waveguides with both high group index and small group velocity dispersion can be designed. RPhC waveguides are also more sensitive to external refractive index changes, which is attractive for sensor applications. Finally we set up a procedure to pattern RPhCs in silicon-on-insulator.     

Air waveguide in a hybrid 1D and 2D photonic crystal hetero-structure

An air waveguide in hybrid one-dimensional photonic crystal and two-dimensional photonic crystal slab hetero-structure is designed. Light propagating in air waveguide can be confined by two-dimensional photonic crystal slab in x-y plane and one-dimensional photonic crystal films in z direction. Theoretical calculations show that air waveguide in the hetero-structure can achieve some functions as 3D PhCs but could be made more easily than 3D PhCs.     

纳米压印制备的光子晶体结构对AlGaN基材料深紫外出光效率的提高

通过利用阳极氧化铝的方法制备高度有序的光子晶体结构作为纳米压印模板,将大面积光子晶体图案转移到了样品表面,解决了国际上小尺寸光子晶体制备困难的问题。采用纳米压印的方法在AlGaN基样品表面上制备了290 nm的周期光子晶体结构,并将表面具有光子晶体结构的AlGaN基样品正面出光强度提高121%。偏振特性的实验结果表明六角排列的孔状光子晶体将原来朝向样品侧面传播的TE偏振光偏折转向正面,从而增加光抽取效率,改变出光偏振度。指出远场角分辨图案的变化归因于光子晶体对出光的衍射和Bragg散射效果。实验中采用的创新性工艺可以用来制备具有高出光效率的深紫外发光二极管。     

Relationship between group velocity and symmetry of photonic crystals

Group velocity (GV) of eigenmode is a crucial parameter to explain the extraordinary phenomena about light propagation in photonic crystals (PhCs). To study relationships between group velocity and symmetry of PhCs, a new general expression of GV in PhCs made up of non-dispersive material is introduced. Based on this, the GVs of eigenmodes of PhCs, especially those of degenerate eigenmodes at highly symmetric points in the first Brillouin zone, are discussed. Some interesting results are obtained. For example, the summation of degenerate eigenmodes' GVs is invariant under the operations of wave vector ${{\bm K}}$-group $M_{{\bm K}} $. In addition, some numerical results are presented to verify them.     

Fabrication and annealing analysis of three-dimensional photonic crystals

Three-dimensional face-centered-cubic (fcc) photonic crystals (PhCs) are fabricated on quartz substrate using vertical deposition technique, and followed by annealing in a temperature range of 200-700 °C. The monodispersed SiO₂ microspheres with a diameter of 220 nm in colloidal solution are synthesized using tetraethylorthosilicate as a precursor material. The as grown opal structure exhibits a strong photonic band gap (PBG) around 450 nm in the transmission spectrum. We find that the position of PBG peak in the spectrum is relevant to incident angle of light. Moreover, it is very sensitive to annealing temperature. It quickly shifts to short wavelength direction with annealing temperature increasing. The effect results from the decrease in refraction index due to the moisture evaporation in silica microspheres.     

Negative refraction in photonic crystals

We demonstrate that light propagation in strongly modulated 2D/3D photonic crystals (PhCs) becomes refraction-like in the vicinity of the photonic bandgap, which is contrary to the fact that light propagation in weakly modulated PhCs is very different from refraction and thus the definition of refraction index becomes meaningless. Such a crystal behaves like a material having an effective refractive index controllable by the band structure. This situation is analogous to the effective-mass approximation in electron-band theory. The propagation states having a negative effective index exhibit unusual properties, such as mirror-like imaging effect, image-transfer effect. These properties are confirmed by finite-difference time-domain simulations.     

Photonic Band Gap Properties of Three-Dimensional SiO2 Photonic Crystals

Three-dimensional SiO2 photonic crystals （PhCs） are fabricated on quartz substrates by the vertical deposition method. Scanning electron microscopy measurement reveals that the samples exhibit an ordered close-packed arrangement of SiO2 spheres. It is found that the position of the [111] photonie band gap （PBG） shifts to a long wavelength （red shift） with increasing sphere size. Gap broadening effects are observed due to the presence of defects in the samples. Moreover, the optical properties of the PBG are very sensitive to the annealing temperature. Our results indicate that the optical properties of the PBG can be easily tuned in the visible region by appropriate experimental parameters, which will be useful for practical applications of PhC optical devices.