One-dimensional Periodic Structure Research Articles

Coupled periodic magnetic nanostructures (invited)

The static and dynamic properties of coupled one-dimensional (1D) and two-dimensional (2D) periodic Ni80Fe20 structures fabricated using deep ultraviolet lithography were systematically studied using broadband ferromagnetic resonance spectroscopy, magneto-optical Kerr effects measurements, and magnetic force microscopy. We have probed the influence of dipolar coupling on the spin configurations and magnetization reversal mechanisms in three different types of magnonic crystals, namely, a 1D chain of coupled ellipsoids arranged in two basic configurations (elements coupled along the major or minor axis) and a 2D noncollinear array of rectangular elements. We observed that the “collective” modes present in the spin wave spectrums for the array are significantly dependent on the geometrical parameters of the magnetic elements, as well as on their arrangement. For instance, the eigenmodes corresponding to the linear chain of ellipsoidal elements are considerably shifted when compared to a continuous film due to the varying demagnetizing field. However, for 2D periodic magnetic structures in which the elements are arranged in a “C” cell configuration with each unit cell comprising of three rectangular elements, we observed the presence of two distinct eigenmodes that vary with the magnitude and orientation of the applied field.

Extending the zero-effective-phase photonic bandgap by one-dimensional ternary photonic crystals

A novel method to enlarge the zero-effective-phase bandgap has been presented in the one-dimensional photonic crystals by sandwiching the third material between the two single-negative materials to form a one-dimensional ternary periodic structure. The band-edges formula for the one-dimensional ternary photonic crystal is derived based on the effective-medium theory and the expressions of the upper and lower frequency limits for the ternary photonic crystals are obtained. Then two schemes to enlarge the zero-effective-phase bandgaps are put forward. Moreover, the angular- and polarization-dependences of the photonic bandgap are investigated. Finally, the role of the dispersion in the sandwiched layer on the bandgap extending has been discussed and two schemes are also presented to enlarge the zero-effective-phase photonic bandgap.

Absorptive photonic crystals in 1D

Light propagation in one-dimensional (1D) periodic structures (photonic crystals),including absorption, is studied analytically. Oblique incidence on a slab with an arbitrarycomplex valued refractive index is treated. The transfer matrix method and Braggconditions are modified accordingly. The propagation in a sinusoidal absorptive crystal iscomputed as an example.

Metamaterial-Based Millimeter-Wave Switchable Leaky Wave Antennas for On-Chip Implementation in Gaas Technology

A planar, metamaterial-based, one-dimensional periodic structure that can be switched between multiple states is numerically investigated. It can be fabricated at low cost in gallium-arsenide (GaAs) technology for antenna-on-chip and system-on-chip millimeterwave applications. The device radiates in the leaky wave region and its radiation pattern can be changed by switching between states in addition to changing the frequency, over a wide bandwidth. It can also be employed to obtain nearly identical radiation patterns at different frequencies due to its reconfigurability. This digitally programmable device presents dynamic shifting of the band-gap by as much as 80 GHz. Tunability is obtained by externally controlled FET switches, directly integrated into the device in the GaAs substrate. The switches dynamically change reactive loads imposed by N rectangular patches in each unit cell, positioned below a microstrip line, allowing the device to switch between 2 N states. A representative CAD model is presented, giving closer attention towards the requirements of commercial GaAs monolithic MMIC fabrication processes. Interesting radiation characteristics of this leaky wave antenna are presented and discussed.

BROAD OMNIDIRECTIONAL REFLECTOR IN THE ONE-DIMENSIONAL TERNARY PHOTONIC CRYSTALS CONTAINING SUPERCONDUCTOR

A method to enlarge the omnidirectional photonic bandgaps (PBGs) has been presented in the one-dimensional photonic crystals by sandwiching a superconductor layer between two dielectric materials to form a one-dimensional ternary periodic structure. The angle- and thickness-dependence of these PBGs have been investigated in detail, and then the thermally-tunability of these omnidirectional PBGs by controlling external temperature of the superconductor is discussed. It is shown that these omnidirectional PBGs can be extended markedly in the one-dimensional ternary photonic crystal and the gap width or the wavelength range can also be tuned by varying external temperature.

New Formula for Evaluating the Number of Unit Cell of a Finite Periodic Structure Considered as Infinite Periodic One

This paper presents a modeling and an analysis of one-dimensional periodic structure composed of a cascade connection of N cells considered as infinite. The ABCD matrix representations with the Floquet analysis have been used to derive the dispersion relation and input impedance of infinite periodic structure. The transmission matrix for the N identical cascaded cells has been successfully used to obtain an efficient and easy-to-use formula giving the necessary number of cells such that they can be considered infinite. As an illustrative example, the formula is applied and verified to finite size TL periodically loaded with obstacles. Scattering parameters and the input impedance of the structure are expressed and plotted.

Fano profiles in transmission spectra of terahertz radiation through one-dimensional periodic metallic structures

The transmission properties of broadband terahertz radiation through one-dimensional periodic metallic structures are investigated experimentally, and the obtained results are explained theoretically. Characteristic minima known as Wood’s anomalies are observed in the transmission spectra. The measured line shapes, the so-called Fano profiles, are caused by the coupling between resonant surface plasmons excited on the metallic grating and nonresonant diffraction orders. Numerical simulations using classical electrodynamics are in good agreement with the experiments.

Optomechanics of liquid crystals for dynamical optical response of photonic structures

We show that the mechanical effect of light on the orientational ordering of the crystallineaxis of a mesophase can be used to control the dynamics of the optical response of liquidcrystal infiltrated photonic structures. The demonstration is made using a one-dimensionalperiodic structure whose periodicity is broken by the presence of a nematic liquid crystaldefect layer. In this study we report on output light polarization and/or intensity dynamicsthat depend on the initial molecular ordering and incident light wavelength and intensity.

Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures

The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.

Anomalous patterned scattering spectra of one-dimensional porous silicon photonic crystals

Far-field secondary emission spectra of one-dimensional periodic photonic structures based on porous silicon show characteristic co-focal rings centered close to the structure plane normal. The rings appear when the frequency of picosecond excitation laser pulses is tuned to the edges of the fourth photonic band gap. They can be clearly distinguished from the typical reflected and transmitted light in the oblique incidence geometry. The rings number is dependent on the excitation frequency and the incidence angle. We explain these anomalous spectral features of porous silicon structures by the spectral filtering of light elastically scattered inside the photonic structure by the narrow photonic bands. The elastic scattering of light due to the photonic disorder in the structure causes the appearance of secondary waves propagating in any direction. But only those waves which fall into the allowed photonic bands penetrate through the whole structure and move through its front or back surfaces. The observed patterned secondary emission is an example of efficient photonic engineering by simple means of multilayer porous silicon structures.

Group-index engineering in silicon corrugated waveguides

We demonstrate group-index engineering in a one-dimensional periodic silicon structure consisting of a deep-etched laterally corrugated waveguide with circular holes patterned onto its wide section. Our theoretical analysis, supported by experimental results, shows that the first-order optical mode can propagate inside the Brillouin zone with a relatively high group index over a wide frequency range. Nearly constant group index as high as 13.5 over a wavelength range of approximately 14 nm is experimentally demonstrated in a 50-microm-long waveguide.

A Perturbation Approach for Predicting Wave Propagation in One-Dimensional Nonlinear Periodic Structures

Wave propagation in one-dimensional nonlinear periodic structures is investigated through a novel perturbation analysis and accompanying numerical simulations. Several chain unit cells are considered featuring a sequence of masses connected by linear and cubic springs. Approximate closed-form, first-order dispersion relations capture the effect of nonlinearities on harmonic wave propagation. These relationships document amplitude-dependent behavior to include tunable dispersion curves and cutoff frequencies, which shift with wave amplitude. Numerical simulations verify the dispersion relations obtained from the perturbation analysis. The simulation of an infinite domain is accomplished by employing viscous-based perfectly matched layers appended to the chain ends. Numerically estimated wavenumbers show good agreement with the perturbation predictions. Several example chain unit cells demonstrate the manner in which nonlinearities in periodic systems may be exploited to achieve amplitude-dependent dispersion properties for the design of tunable acoustic devices.

The slowing of light in one-dimensional hybrid periodic and non-periodic photoniccrystals

Studied in the present paper are the transmission properties, the group velocity, the totalphase, the phase time and the slowing-down factor of one-dimensional periodic photonicbandgap structures. The effects of the periodicity and non-periodicity of photonicstructures and of the number of layers on the slowing down of light in these structures arealso discussed. The group velocity of non-periodic (Fibonacci, Thue–Morse and Cantor)and hybrid (periodic/non-periodic) photonic bandgap structures are studied and comparedto those of periodic structures. We show that the slowing-down factors at the edge of thebandgaps are higher for the hybrid (periodic/non-periodic) multilayer systems.The proposed structures have been modelled using the transfer matrix method.

Slow-light transmission in one-dimensional periodic structures

We have analyzed the transmission properties of pulses through one-dimensional periodic structures in order to systematically explore the best conditions to achieve the maximum delay with the minimum possible distortion. In the absence of absorption and no layer variation, the transmission coefficient $t_N$ can be well approximated by a sum of Lorentzian resonances. The ratio between their width $\Gamma_{\rm r}$ and their separation $\Delta\omega_{\rm r}$ is a crucial parameter to characterize the distortion of the transmitted pulse. For typical values of the parameters used in telecommunications and high index of refraction contrasts $n_2 / n_1$, the distortion of the transmitted pulse is unacceptably large for frequencies near the edge of the transmission window. We estimate fractional delays achievables in terms of the central frequency used and the pulse bandwidth.

Observation of modulated spontaneous emission of Rhodamine 6G in low refractive index contrast 1D-periodic gelatin film

The modulation of the spontaneous emission of Rhodamine 6G has been observed in one-dimensional periodic dielectric structure of dichromated gelatin film with refractive index contrast as low as 0.01. The spontaneous emission is enhanced at the band edges and inhibits in the band gap, which agree well with the theoretical analysis on the redistribution of the fractional local density of optical states.

含各向异性无磁左手介质周期结构中的光子带隙研究

We demonstrate a photonic band gap (PBG) from one-dimensional (1D) periodic structures created by a double-layer unit cell with an air layer and an anisotropic nonmagnetic left-handed metamaterial (LHM) layer whose permittivity elements are partially negative. The requirements imposed on the materials and structures to realize a PBG are derived when the frequency is above or below the cutoff frequency, and the transmission properties of the PBG are discussed by utilizing 4x4 transfer-matrix method with dispersive semiconductor metamaterial.

The experimental investigation of the discrete mode in the zero-average-refractive-index gap

We experimentally investigate the discrete mode in the zero-average-refractive-index gap (the zero-n—gap) of the one-dimensional periodical structures containing left-handed materials (LHMs) and right-handed materials (RHMs). When the discrete mode conditions are satisfied in the zero-n gap, there are no discrete propagating modes, but the zero-n—gap completely vanishes. This behavior is attributed to the dispersive property of LHMs and RHMs. In addition, the theoretical expectation of the discrete modes with no sidelobes in the zero-n—gap never occurs in experiment because the LHMs is intrinsically dispersive.

Quenched random disorder and x-ray scattering in smectic elastomers

In this work we examine layer fluctuations in a smectic elastomer with quenched random disorder induced by crosslinks. The system is analyzed in a continuum model and crosslinks are introduced as a random field in a macroscopic picture. In the case of small deformations and replica symmetry the intensity profile for x-ray scattering along the layer normal was determined for layer displacements smaller than the layer separation. In this regime it is predicted that for large enough crosslink densities the first-order diffraction pattern of the solid assumes a characteristic squared-Lorentzian form, showing a decay of short-range order over a length scale of 20 nm. Crosslinks are observed to disorder the system by decreasing the correlation length, which we show not to be a consequence of the random field. The coupling to random crosslinks is predicted to retard the decrease in the correlation length and hence found to stabilize the one-dimensional periodic layer structure against thermal fluctuations. The dependence of the correlation length on the crosslink density leads us to propose an estimate for the percolation limit of a smectic elastomer network.

Photovoltaic Performance Enhancement in Dye-Sensitized Solar Cells with Periodic Surface Relief Structures

One-dimensional and two-dimensional periodic TiO2 relief structures were incorporated in dye-sensitized solar cells. The periodic TiO2 structures were fabricated using surface relief gratings photoinscribed on azobenzene functionalized polymer films as templates and TiO2 sol-gel solution. Enhancement of power conversion of the solar cells made with the relief TiO2 structures was achieved. This enhancement suggests that the relief TiO2 structures can offer efficient light-trapping with the increased effective optical-path length in the solar cells.

A wavelet-based model of one-dimensional periodic structure for wave-propagation analysis

In this paper, a wavelet-based method is developed for wave-propagation analysis of a generic multi-coupled one-dimensional periodic structure (PS). The formulation is based on the periodicity condition and uses the dynamic stiffness matrix of the periodic cell obtained from finite-element (FE) or other numerical methods. Here, unlike its conventional definition, the dynamic stiffness matrix is obtained in the wavelet domain through a Daubechies wavelet transform. The proposed numerical scheme enables both time- and frequency-domain analysis of PSs under arbitrary loading conditions. This is in contrast to the existing Fourier-transform-based analysis that is restricted to frequency-domain study. Here, the dispersion characteristics of PSs, especially the band-gap features, are studied. In addition, the method is implemented to simulate time-domain wave response under impulse loading conditions. The two examples considered are periodically simply supported beam and periodic frame structures. In all cases, the responses obtained using the present periodic formulation are compared with the response simulated using the FE model without the periodicity assumption, and they show an exact match. This validates the accuracy of the periodic assumption to obtain the time- and frequency-domain wave responses up to a high-frequency range. Apart from this, the proposed method drastically reduces the computational cost and can be implemented for homogenization of PSs.