2D Periodic Structures Research Articles

Scattering and Diffraction of Electromagnetic Wave by 3D Periodic Structures with Subwavelength Scales:Self-consistent Field Approach**The project supported by National Natural Science Foundation of China

We generalize the self-consistent field approach to deal with the problem of scattering and diffraction of electromagnetic wave by multiple obstacles. We derive in a rigorous way the relevant equations for determining the local field inside the scatterers as well as the far field of light scattering and diffraction for general periodic structures. To demonstrate the applicability of this approach, we calculate the far field distribution of the light scattering by a 3D grating. The convergent solution of the scattering field for this 3D grating can be evaluated numerically. From the comparison of the amplitudes of the diffraction factor in the 3D grating and an isolated scatterer, it is shown that the multi-scattering effect in the 3D grating cannot be neglected. The multi-scattering effect depends on the structural parameters of the 3D grating, the incident angle, and the polarization direction of the illuminating light.

First proton-beam driven Rayleigh–Taylor experiments on KALIF

We have used a high-power pulsed proton beam (50 ns, 0.15–1 TW/cm 2, 1.7 MeV peak proton energy) of the Karlsruhe Light Ion Facility (KALIF) to ablatively accelerate 20–50 μm thick planar targets provided with a 2D periodic structure to velocities of ∼10 km/s. Line-imaging laser-Doppler velocimetry with high spatial (≤10 μm) and temporal (≥200 ps) resolution is employed to measure the velocity of the rear surface of the targets provided with a small-scale corrugation. From the temporal evolution of the transverse velocity profiles we obtain the feed-through of the hydrodynamic instability developing at the boundary between the condensed part of the target and the ablation plasma. We find stable acceleration during the first wave reverberation cycle. After this an exponential growth is observed at an average rate that amounts to 40–65% of the classical value. The reduction is mainly due to heat transport driven mass convection through the boundary between the condensed part of the target and the ablated plasma.

Surface acoustic waves in two-dimensional periodic elastic structures

Acoustic waves localized at the surface of two-dimensional (2D) periodic elastic structures, or 2D phononic crystals, are studied theoretically by taking account of the elastic anisotropy of constituent materials. The surface considered is perpendicular to the axis of a periodic array of cylinders embedded in a background material. The dispersion relations of the surface modes are calculated for circular cylinders of AlAs which form a square lattice in a GaAs matrix. The folding and anisotropy of the surface wave branches, as well as the existence of pseudosurface waves, are found. The stop band distributions of the surface, pseudosurface, and bulk waves are plotted in a form relevant for comparison with ultrasound imaging experiments.

Nonlinear transmission resonance in a two-dimensional periodic structure with photonic band gap

Electromagnetic wave propagation in a nonlinear two-dimensional (2D) periodic medium is investigated by numerically solving four coupled nonlinear differential equations governing wave propagation. It is found that a transmission resonance occurs at a modest level of power when such a system is illuminated with radiation with the frequency in the stop gap of the 2D periodic structure. The system exhibits optical switching from a low-transmission to a high-transmission state as one sweeps through the resonance by increasing the input power. A nonlinear eigenmode is excited within the 2D structure at the switching power. The properties of these localized solutions are also presented and discussed.

Speed of light in a 2D photonic crystal in the low-frequency limit

We consider an arbitrary 2D periodic structure in the low-frequency limit and demonstrate that it exhibits birefringence for propagation in the plane of periodicity. For polarization parallel to the cylinder axis the effective dielectric constant, ε eff is just the average of the constituents, as known. On the other hand, for in-plane polarization, ε eff is a function of the propagation direction. Numerical calculations have been performed for triangular cylinders forming a square lattice. This leads to an anisotropy as large as 20%, much in excess of anisotropy observed in natural crystals.

Fabrication of submicrometre 3D periodic structures composed of Si/SiO2

The successful fabrication of 3D periodic structures composed of two transparent materials in the submicrometre range is reported for the first time. The material system comprises a-Si (n=3.26) and SiO/sub 2/ (n=1.46), and sputter-etching leads to 'high-fidelity' layer-to-layer propagation of a concave-convex pattern.

Optical bistability and hysteresis in a two-dimensional periodic structure fabricated in Fe doped LiNbO 3

Optical bistability and hysteresis is observed experimentally with a nolinear two-dimensional (2D) periodic structure. The structure is a 2D volume index grating created in LiNbO 3:Fe crystal through hologram recording and subsequent fixing techniques. No external feedback is provided. A strong intensity-dependent photovoltaic effect in LiNbO 3:Fe material provides nonlinear coupling for the excited fields within the 2D periodic structure.

Observation of new two-dimensional periodic structures in the confined regions of the reconstructed Pt(100) surface

New 2D periodic structures have been observed by STM in the regions of the reconstructed Pt(100) surface which are confined by domain boundaries or lattice steps. These structures can be seen only in a very narrow energy window near the Fermi level, and they are strongly correlated to the original atomic arrangements of the surface. These structures arise most probably from a modification in the distribution of the electronic density of states which is strongly coupled to the ion cores of the surface to produce a periodic shift in the atomic rearrangements in order to minimize the strain and free energy of the surface.

DNA nanoconstructions

The control of structure on the nanometer scale is central to nanotechnology. We are pursuing this end with synthetic DNA, whose sequence is selected by sequence symmetry minimization algorithms, so that it can form branched junctions. These structures can be ligated together in the same way that linear DNA is ligated in molecular cloning. Ligating branched structures generates stick figures whose edges consist of double helical DNA and whose vertices are branch points. We have built a DNA molecule whose helix axes have the connectivity of a cube. The vertices are separated by two helical turns of DNA; hence the plectonemic nature of DNA makes this molecule a hexacatenane, each of whose cyclic strands corresponds to a face. We have developed a solid-support-based procedure to implement these constructions. Using the solid-support-based methodology we have constructed a molecule whose helix axes have the connectivity of a truncated octahedron. This figure contains 14 faces, of which six are ideally square and eight are hexagonal; this Archimedean polyhedron contains 24 vertices and 36 edges. Control of topology is strong in this system, but control of three-dimensional (3D) structure remains elusive. Our key aim is the formation of prespecified two-dimensional and 3D periodic structures. Applications envisioned include nanomanipulators and scaffolding for molecular electronic devices.

Photonic band gaps in three dimensions: New layer-by-layer periodic structures

A new three-dimensional (3D) periodic dielectric structure constructed with layers of dielectric rods of circular, elliptical, or rectangular shape is introduced. This new structure possesses a full photonic band gap of appreciable frequency width. At midgap, an attenuation of 21 dB per unit cell is obtained. This gap remains open for refractive indices n ≥ 1.9. Furthermore, this new 3D layer structure potentially has the additional advantage that it can be easily fabricated using conventional microfabrication techniques on the scale of optical wavelengths.

Photonic band structure investigation of two-dimensional Bragg reflector mirrors for semiconductor laser mode control

A theoretical study that follows the lines of previous photonic band structure investigations has been undertaken in search of a two-dimensional (2D) periodic dielectric structure that exhibits a certain type of photonic band structure for application as an external feedback mirror for laser diode arrays and broad-area devices. Instead of looking for an absolute band gap for a band of frequencies, we are particularly interested in structures that exhibit only stop bands, i.e., bands with a narrow extent in both frequency and angle. This type of reflecting structure, which can also be termed a 2D Bragg reflector, could provide improved mode control for both longitudinal and transverse characteristics of the modes for these devices. Our study, which employed photonic band structure calculational methods, showed that square lattice dielectric structures exhibit such stop bands for both TE and TM waves and could be used as photonic band structure mirrors to induce better mode control.

Photonic band gaps in periodic dielectric structures: The scalar-wave approximation

Using a plane-wave expansion method we have computed the band structure for a scalar wave propagating in periodic lattices of dielectric spheres (dielectric constant e, ) in a uniform dielectric background (e&). All of the lattices studied (simple cubic, bcc, fcc, and diamond) do possess a full band gap. The optimal values of the filling ratio f of spheres and of the relative dielectric contrast for the existence of a gap are obtained. The minimum value of the relative dielectric contrast for creating a gap is also obtained. These results are applicable to the problem of classical-wave propagation in composite media and relevant to the problem of classical-wave localization. I. INTRODUCTION Recently, there has been growing interest' in the studies of the propagation of electromagnetic (EM) waves in three-dimensional (3D) periodic andlor disordered dielectric structures (photonic band structures). The reasons for this interest are both fundamental and practical. The possibility of the observation of Anderson localization of EM waves in disordered dielectric structures, where the strong el-el interaction effects entering the electron-localization problem are absent, is of fundamental interest. ' Also in analogy to the case of electron waves propagating in a crystal, classical EM waves traveling in periodic dielectric structures will be described in terms of photonic bands with the possibility of the existence of frequency gaps where the propagation of EM waves is forbidden. The potential applications of such photonic band gaps are very interesting. It has been suggested that the inhibition of spontaneous emission in such gaps can be utilized to substantially enhance the performance of semiconductor lasers and other quantum electronic devices. Photonic band-gap materials can also find applications in frequency-selective mirrors, bandpass filters and resonators. Moreover, electromagnetic interaction governs many properties of atoms, molecules and solids. The absence of EM modes inside the photonic gap can lead to unusual physical phenomena. For example, atoms or molecules embedded in such a material can be locked in excited states if the photons to be emitted to release the excess energy have frequency within the forbidden gap. In addition, John has proposed that Anderson localization of light near a photonic band gap might be achieved by weak disordering of a periodic arrangement of spheres. It is therefore, very important to obtain structures with a frequency gap where the propagation of EM waves is forbidden for all wave vectors. Yablonovitch and Gmitter have demonstrated the soundness of the basic idea of photonic bands in 3D periodic structures in an experiment using microwave frequencies, where the periodic structures can be fabricated by conventional machine tools. In addition, a photonic gap in a face-centeredcubic (fcc) dielectric structure was reported. During the same period, theoretical studies of the propagation of EM waves in 3D periodic structures began. ' At first, the photonic band structures have been examined theoretically in the scalar-wave approximation ' in which the vector nature of the EM field is ignored. It soon became apparent' that not so many aspects of the experimental photon bands in periodic dielectric structures can be understood in terms of scattering of scalar waves. However, the scalar-wave approach is directly applicable to the scattering of acoustic waves, an area of equally active interest and to the localization of acoustic waves. ' ' Recently, by expanding the EM fields with a plane-wave basis set, Maxwell's equations were solved exactly, ' taking the vector nature of the EM field fully into account. Comparison of the calculated' ' results of the fcc structure with experiment indicated that, while the experimental data and theory agree very well over most of the Brillouin zone, there are two symmetry points (8' and U) where the experiment indicates a gap, while calculations show that propagating modes exist. It is now believed that the fcc structure does not possess a full photonic band gap in the lowest bands, instead there is a region of low density of states rather than a forbidden frequency gap.

Pinning and the size of grains in high-T c ceramics

We have investigated the dependence of the intergranular local critical current density j c on temperature for ceramic YBCO samples using the contactless method based on the measurement of surface impedance of samples. It was found that there is an the unusual behaviour of the function j c( T). It has a local maximum at some temperature. To understand the nature of this maximum we have investigated theoretically the interaction between single vortex and Josephson ceramic medium. This interaction was studied in the framework of 2D periodic structure model with different period a. It was shown that the ratio of maximal difference of energy for different states to the period a has a maximum when the parameter a is an order of the Josephson penetration depth λ j . The experimental results can be explained qualitatively on the base of this theory.

Three-dimensional periodicity and twelvefold rotational symmetry.

Two 3D periodic structures are introduced based on so-called {ital T} polyhedrons. These structures can be used as mathematical models to describe the VNi alloys system in order to explain the twelvefold rotational symmetry in electron-diffraction patterns of VNi alloys. The 3D atomic models of the VNi alloy are first presented in this paper.

Analysis of the scattering and guidance of a two-dimensionally periodic metal grating structure by spectral domain method

The scattering and guidance of electromagnetic waves from a two-dimensionally (2D) periodic metal grating structure are investigated here. With the spectral domain analysis the dispersion characteristics for this structure are obtained. Properly taking into account the hybrid mode nature of the propagation problem the effects of mode coupling betweenTE andTM modes are examined. Numerical results will provide us valuable information for the design of new devices in 2D periodic structure, particularly in millimeter-wave frequency range, such as antennas, filters, couplers and distributed reflectors.

General solution theory for Schrödinger's equation in arbitrary 2D-periodic spatial structures II. The synthesis of global solutions by layer composition

After the first step in the assembly of boundary controlled monolayers method, namely the monolayer boundary value problem, was dealt with in a preceding article, here the synthesis of the original 2D-periodic spatial structure by means of the “layer composition process” is investigated. Since the convergence properties of this process are most appropriately discussed in terms of generalized Bloch waves, these are first analyzed in full detail; special interest is here paid to a “current sum rule,” which proves to be fundamental for characterizing the asymptotic behavior of the reflection and transmission operators of the synthesized structure. As an illustrating example, it is finally shown how to calculate global solutions to Schrödinger's equation for a semi-infinite crystal structure (with real physical surface) which match the correct asymptotic boundary data in both the vacuum region and the interior of the crystal deeply in the bulk.

General solution theory for Schrödinger's equation in arbitrary 2D-periodic spatial structures I. The monolayer problem

The electronic states in arbitrary spatial structures exhibiting 2-dimensional translational symmetry are most efficiently determined within a 3-step concept: First, for any single monolayer the structure is composed of, the (physically relevant) solutions to Schrödinger's equation are characterized and parametrized by means of appropriately chosen boundary data. Then, the original structure is synthesized by applying the “layer composition process,” and finally the electronic wave functions describing the underlying physical situation in the whole structure are obtained by adjusting them to the respective asymptotics (assembly of boundary controlled monolayers method). Envisaging the monolayer problem in this paper, the existence and uniqueness of both weak and strong solutions is shown. While weak solutions lead to a variational characterization, which is useful for estimating the quality of numerical approximations, the conception of strong solutions yields a realization of the monolayer Schrödinger operator in the Hilbert space L 2, the spectral properties of which are not only of practical interest (calculation of band structures) but also prove to be crucial for the convergence of the layer composition process (as will be shown in a subsequent article).

General solution theory for Schrödinger's equation in arbitrary 2D-periodic spatial structures. II. The synthesis of global solutions by layer composition: Gerhard Wachutka. Sektion Physik der Universität München, and Siemens Research Laboratories, D-8000 Munich 83, Federal Republic of Germany

General solution theory for Schrödinger's equation in arbitrary 2D-periodic spatial structures. II. The synthesis of global solutions by layer composition: Gerhard Wachutka. Sektion Physik der Universität München, and Siemens Research Laboratories, D-8000 Munich 83, Federal Republic of Germany

A structure registry condition for the interaction energy between two solids

The interaction energy between two periodic crystals obeys a structure registry condition. When the 2D periodic structures in the atomic planes parallel to the surfaces of the two crystals are not coincident, the energy contribution which accounts for the discrete characteristics of the solids along these planes vanishes. The remaining continuum potential is then unable to discriminate between the atomic distribution of surface atoms when one crystal is laterally translated with respect to the other. This registry condition leads to drastic changes in the interaction energy between two ionic crystals and can be responsible for the disappearance of specific structural properties in solids.