Two-dimensional Periodic Structures Research Articles

Two-Dimensional Organization of Single Crystal ZnO Nanopillars

ABSTRACTPeriodically ordered ZnO nanopillar arrays were fabricated by a combination of soft templates created by e-beam lithography and an electrochemical process. Growth at 90 °C in an aqueous solution ensured compatibility with the polymethyl methacrylate used as a template material. We demonstrate that individual ZnO nanopillars with diameters around 100 nm can be precisely placed in desired locations to form two-dimensional periodic structures. This approach provides a new method for design and fabrication of ZnO photonic materials. The process is compatible with standard microfabrication techniques and may have potential applications in the manufacture of photonic and optoelectronic devices.

Surface nanoscale periodic structures in congruent lithium niobate by domain reversal patterning and differential etching

We report on the fabrication and characterization of one- and two-dimensional periodic structures down to 200 nm size, in congruent lithium niobate crystal samples. Periods from 2μm to 530 nm are investigated. Interference photolithography is used to obtain short pitch insulating gratings, and subsequent electric-field poling, at the overpoling regime, is performed for periodic domain inversion. Nanoscale structures are obtained by selective chemical etching, and topographic investigations are performed by atomic force microscope. The fabricated structures are attractive in nonlinear optics for short-wavelength conversion and in the field of photonic crystals for Bragg and band-gap applications.

On the potential of connected stars as auxetic systems

Auxetic materials and structures exhibit the unexpected behaviour of getting wider when stretched and thinner when compressed. This behaviour requires the structures (the internal structure in the case of materials) to have geometric features, which must deform in a way that results in the structure expanding when stretched. This paper assesses the potential for auxetic behaviour of a novel class of two-dimensional periodic structures which can be described as “connected stars” as they contain star-shaped units of different rotational symmetry which are connected together to form two-dimensional periodic structures. These structures will be studied through a technique based on force-field based methods (the EMUDA technique) and it will be shown that some, but not all, of these structures can exhibit auxetic behaviour. An attempt is made to explain the reasons for the presence or absence of a negative Poisson's ratio in these systems.

Magnetostatic spin waves in two-dimensional periodic structures (magnetophoton crystals)

Series of experiments are carried out to study the propagation of magnetostatic spin waves in ferromagnetic films containing 2D periodic structures formed by etched apertures. For spin waves, such films are analogous to photon crystals (namely, magnetophoton or magnon crystals). The spectra of waves transmitted through the structure display features associated with a change in the spin homogeneity due to etching or radiation loss, as well as with Bragg reflection effect or the emergence of forbidden gaps in the spectrum of propagating waves.

Optical patterning in azobenzene polymer films

Thin azobenzene polymer films show a very unusual property, namely optically induced material transport. The underlying physics for this phenomenon has not yet been thoroughly explained. Nevertheless, this effect enables one to inscribe different patterns onto film surfaces, including one- and two-dimensional periodic structures. Typical sizes of such structures are of the order of micrometers, i.e. related to the interference pattern made by the laser used for optical excitation. In this study we have measured the mechanical properties of one- and two-dimensional gratings, with a high lateral resolution, using force-distance curves and pulse force mode of the atomic force microscope. We also report on the generation of considerably finer structures, with a typical size of 100 nm, which were inscribed onto the polymer surface by the tip of a scanning near-field optical microscope used as an optical pen. Such inscription not only opens new application possibilities but also gives deeper insight into the fundamentals physics underlying optically induced material transport.

Artificially integrated synthetic rectangular waveguide

A synthetic rectangular waveguide (SRW), which consists of two electrical sidewalls and two parallel periodical structures placed at the top and bottom surfaces of the waveguide, is presented. The SRW is made by multilayered integrated circuit processes, which typically have large ratios of SRW lateral dimensions to substrate thickness. Two theoretical methods, finite-element method and deembedding of composite structure consisting of SRW and mode converters, are applied to investigate the propagation characteristics of the SRW. Application of the dispersion characteristics of the two-dimensional periodical structures coupled with appropriate mode converter designs leads to results in SRW designs supporting TE/sub 10/, TM/sub 00/, and TM/sub 10/ modes. Measurements and the two theoretical approaches indicate that the slow-wave factor is 4.9 and Q-factor is 260 at 6.85 GHz for the TE/sub 10/ mode propagation with a cutoff frequency of 4.10 GHz (0.348 factor of cutoff frequency of conventional rectangular waveguide using the same material and dimensions). The theoretical data show the TM/sub 00/ mode to have a slow-wave factor of 1.8, Q-factor of 187.6 at 11.4 GHz, and cutoff frequency of 10.2 GHz. The TM/sub 10/ mode has a slow-wave factor of 1.98, Q-factor of 187.6 at 12.5 GHz, and cutoff frequency of 10.4 GHz.

SUBWAVELENGTH PERIODIC RIPPLE FORMATION ON GaN SURFACE BY FEMTOSECOND LASER PULSES

The formation of femtosecond pulsed laser-induced periodic surface structure on GaN is reported for the first time (to our knowledge) in this paper. It has been found that the formation of the laser-induced ripples is very much dependent and quite sensitive to the laser conditions of the incident laser beam energy fluence and pulse numbers. Possibly due to the unique property of high-defect density of GaN material, the process window for laser-induced ripple formation is quite narrow compared to other materials such as InP , GaP , Al 2 O 3 etc. Nevertheless, through finely adjusting laser beam fluence and pulse number, subwavelength periodic ripples could be formed on the GaN surface. The formation of such periodic two-dimensional structures was attributed to optical interference of the incident laser light with scattered waves from a surface disturbance. Photoluminescence emission could still be detected on the GaN ripple area, indicating little degradation of GaN optical property after femtosecond laser processing. The femtosecond laser-induced ripple structure has potential applications in the fabrication of nanostructures for the GaN -based devices.

Spin-glass properties of an Ising antiferromagnet on the Archimedean(3,122)lattice

We investigate magnetic properties of a two-dimensional periodic structure with Ising spins and antiferromagnetic nearest-neighbor interaction. The structure is topologically equivalent to the Archimedean $(3,{12}^{2})$ lattice. The ground state energy is degenerate. In some ground states, the spin structure is translationally invariant, with the same configuration in each unit cell. Numerical results are reported on specific heat and static magnetic susceptibility against temperature. Both quantities show maxima at temperature $T>0$. They reveal some sensitivity on the initial state in temperatures where the Edwards--Anderson order parameter is positive. For zero temperature and low frequency of the applied field, the magnetic losses are negligible. However, the magnetization curve displays some erratic behavior due to the metastable states.

Influence of Humidity on Electrical Characteristics of Self-Assembled Porous Silica Low-k Films

The influence of humidity on the dielectric constant and leakage current of self-assembled porous silica films which have two-dimensional hexagonal periodic porous structures was investigated quantitatively by proposing a new water adsorption model. The amount of adsorption was calculated by the modified Rayleigh model, where molecules are assumed to be adsorbed on the inner surface of cylindrical porous silica structures and form a dispersal concentric double-layer dielectric cylinder system. The amount of calculated by the proposed model was consistent with the measured dielectric constant and thermogravimetry data. It suggests that inner-surface coverage of the cylindrical porous silica wall with a hydrophobic group is the most effective way to suppress water adsorption. Hexamethyldisilazane as a surface coverage molecule was introduced to the periodic cylindrical porous silica film and the leakage current was suppressed by a factor of even below 0.5% relative humidity, resulting in the improvement of time-dependent dielectric breakdown lifetime by a factor of 30.

Femtosecond pulsed laser-induced periodic surface structures on GaN/sapphire

Femtosecond pulsed laser-induced periodic surface structure on GaN/sapphire is reported in this paper. It was found that the period of the laser-induced ripples was much dependent on the incident laser fluence. Through finely adjusting laser fluence and pulse number, uniform ripples could be formed on the sapphire surface. We attributed the formation of such periodic two-dimensional structures to optical interference of the incident laser light with scattered waves from a surface disturbance. Also, it was found that the GaN capping layer played a very important role in forming the periodic structures on the sapphire surface.

Surface Plasmon Interference Nanolithography

A new nanophotolithography technique based on the interference of surface plasmon waves is proposed and demonstrated by using computer simulations. The wavelengths of the surface plasmon waves at metal and dielectric interfaces can reach the nanometer scale while their frequencies remain in the optical range. As a result, the resolution of this surface plasmon interference nanolithography (SPIN) can go far beyond the free-space diffraction limit of the light. Simulation results show that one-dimensional and two-dimensional periodical structures of 40-100 nm features can be patterned using interfering surface plasmons launched by 1D gratings. Detailed characteristics of SPIN such as field distribution and contrast are also investigated.

Fabrication of polymer photonic crystals using nanoimprint lithography

Dense two-dimensional periodic photonic bandgap structures are produced inpoly(methyl methacrylate) thin films using nanoimprint lithography (NIL). The stamporiginal was made by electron beam lithography. Then, a high versatility of theprocess was achieved by fabricating copies of the stamp original via NIL, whichenables varying and optimizing both fill factors and aspect ratios independently.For reliable stamp copying over the whole structural areas, the nanorheologicalbehaviour had to be considered. Using those stamp copies, polymeric photonic bandgap structures with an aspect ratio as high as 2 were successfully replicated.

Peculiarities of mode spectrum in two-dimensional Bragg structures

The fundamental difference in the eigenmode spectrum for traditional one-dimensional (1D) periodical Bragg structures and novel two-dimensional (2D) periodical Bragg structures of planar and coaxial geometry is discussed. In the case of 1D Bragg structures, the eigenmode frequencies are located outside the Bragg reflection zone while for 2D Bragg structures the highest Q-factor modes are located just near to the frequency of Bragg resonance and the mechanism for the formation of these modes is related to the coupling of the longitudinal and transverse propagating wave fluxes. The main eigenmode possesses a Q-factor which substantially exceeds the Q-factor of the other modes even in the case when the system transverse size is much greater than the wavelength that encourage the use of 2D Bragg structures for mode selection in powerful oscillators with oversized microwave systems.

Band gaps and the electromechanical coupling coefficient of a surface acoustic wave in a two-dimensional piezoelectric phononic crystal

In this paper we analyze the phononic band structure of bulk and surface waves in a two-dimensional periodic structure consisting of an array of piezoelectric cylinders in an isotropic background material. The explicit formulations of the bulk wave and the surface wave dispersion relations in such a structure are derived based on the plane wave expansion method. The band gaps and the electromechanical coupling coefficients for surface acoustic waves propagating in such a structure are calculated. The influences of material and geometrical anisotropy as well as the filling fraction on the electromechanical coupling coefficients are discussed, and some silent features are drawn. The results of this research may serve as an important reference for studying surface acoustic wave devices consisting of phononic structures.

Excitation of two-dimensional soliton matrices by fundamental Gaussian beams

The excitation of two-dimensional periodic structures of fields of the first and second radiation harmonics due to the modulation instability of fundamental Gaussian beams is studied in a medium with a quadratic nonlinearity. The distances are found at which soliton matrix structures with a specified period are formed and destroyed. Optical gratings formed due to nonlinear aberration of broad Gaussian beams are considered.

A two-dimensional photonic structure made from a conjugated, fluorescent polymer

We report the fabrication of a two-dimensional periodic structure made from the conjugated, fluorescent polymer poly(p-phenylene vinylene), PPV, by direct-write near-field lithography of a photosensitive precursor of the conjugated polymer. The precursor film is illuminated with ultraviolet radiation using the apertured fibre of a home-built scanning near-field optical microscope (SNOM), and unexposed areas are subsequently dissolved in methanol. The fully conjugated polymer is obtained by thermal conversion under vacuum. The structure is approximately 10 mu m x 10 mu m, and consists of 30 nm tall pillars on a 330 nm periodicity lattice. We present a calculation of the photonic properties and propose that structures made with the method investigated here are promising candidates for photonic crystal lasers. We also report the results of preliminary investigations aimed at increasing the pillar height.

Effective Index Method for Modelling Sub-Wavelength Two-Dimensional Periodic Structures

An approximate method is here proposed for modelling two-dimensional sub-wavelength periodic structures. The method is based on the effective index method, where the two-dimensional problem structure is split on two one-dimensional problems, which can be solved by conventional tools. It provides in a natural way the biaxial character of a two-dimensional periodic structure with different period along different directions. The method has been tested by comparing the effective refractive index provided by more exact algorithms with the one provided by the effective index method, showing quite good agreement. Also, the EIM has been used to simulate the reflectance and transmittance behaviour of pyramidal profiles, showing also good agreement with the results supplied by exact calculations using RCWA technique. The main advantages of the method are that it is easy to implement, and the short computational time required to model a given structure.

Theory and experimental investigaion of flexural wave propagation in thin rectangular plate with periodic structure

With the idea of the phononic crystals, a thin rectangular plate with two-dimensional periodic structure is designed. Flexural wave band structures of such a plate with infinite structure are calculated with the plane-wave expansion (PWE) method, and directional band gaps are found in the ΓX direction. The acceleration frequency response in the ΓX direction of such a plate with finite structure is simulated with the finite element method and verified with a vibration experiment. The frequency ranges of sharp drops in the calculated and measured acceleration frequency response curves are in basic agreement with those in the band structures. Thin plate is a widely used component in the engineering structures. The existence of band gaps in such periodic structures gives a new idea in vibration control of thin plates.

Rapid fabrication of large-area periodic structures containing well-defined defects by combining holography and mask techniques

We demonstrate a promising method to fabricate large-area periodic structures with desired defects by using the combination of multiple-exposure two-beam interference and mask-photolithography techniques. Multiple-exposure of two-beam interference pattern at 325 nm into a positive AZ-4620 (or a negative SU-8) photopolymerizable photoresist is used to form a square and hexagonal two-dimensional periodic structures. Desired defects are introduced in these structures by irradiating the sample with one beam of the same laser through a mask in which the design of defects is patterned. A 1cm x 1cm periodic structures with the lattice constant as small as 365nm embedding several kinds of defect, such as waveguide or Mach-Zehnder, was obtained by employing this combination technique. It shows that the proposed combination technique is useful for mass production of photonic crystal optoelectronics devices.

Self-Organization of Nanoislands on the Surface of Silicon and Gallium Arsenide Single Crystals Stimulated by Spatially Periodic Laser Radiation Fields

Four interfering laser beams acting upon the surface of silicon and gallium arsenide single crystals stimulate the self-organization of nanoislands, which is manifested by the development of processes controlling the size of islands in a two-dimensional periodic structure formed on the sample surface. The influence of the polarization of interfering beams on the character of this self-organization has been studied. Islands with lateral dimensions from 60 to 100 nm and a height of 6–12 nm have been obtained. The lateral dimensions of nanoislands are 5–10 times smaller than the period of a standing wave of the laser radiation field, which is explained by the influence of elastic stresses developed at the crystal surface.