Multiple-scattering Method Research Articles

Effects due to disorder on photonic crystal-based waveguides

Using the multiple-scattering method, we have studied the effects of various types of disorders on the performance of two-dimensional photonic crystal-based waveguides with cylindrical inclusions. The following three types of disorders are considered: (a) all cylinders are disordered; (b) only those cylinders in the boundary layer of the waveguide are disordered; and (c) all cylinders except those in the boundary layer of the waveguide are disordered. Our results show that, for both the cases of position and size randomness, the quality of the waveguide is insensitive to the type-(c) disorder, but very sensitive to type-(a) and type-(b) disorder. We thus conclude that the uniformity of the microstructures in the boundary layer of the waveguide is vital in ensuring the functionality of the waveguide.

Low-energy electron scattering by CF3Cl andCF3Br:elastic scattering and vibrational excitation

Absolute differential cross sections (DCSs) for elastic andvibrationally inelastic scattering of electrons from CF3Cl andCF3Brhave been determined by a crossed-beam experiment, in the energy range of1.5–100 eV and over the scattering angles of 15° – 130°. Therelative flow method was applied to normalize these cross sections, using helium as astandard. The present results are compared with the previous ones for CF3H, CF4 andCF3I.An effect due to a long-range interaction of polar molecules has been observed in asystematic manner in elastic DCSs below 3 eV. Broad resonance structures where thevibrational cross sections are enhanced are observed at around 7 eV in both CF3Cl andCF3Bras experimentally confirmed previously in CF3H, CF4 andCF3I.The continuum multiple-scattering method is also employed to carry out theanalysis.

Comparison of simulation methods for electronic structure calculations with experimental electron energy-loss spectra

The electronic structure of hexagonal GaN is studied using two simulation techniques in order to develop a method to interpret the fine-structure of an experimental nitrogen K-edge electron energy loss spectrum obtained using a scanning transmission electron microscope. The application of these simulation methods to the bulk spectrum is a necessary first step in developing a fundamental understanding of the effect of changes in the electronic structure on the properties of defects. It is found here that both of the techniques used, multiple scattering (MS) and density functional theory (DFT), produce excellent agreement with the experimental bulk spectrum. The MS method is limited in accuracy but efficient in time, while the DFT method is more accurate but time consuming. Through the combination of these methods, experimental energy loss spectra can be readily understood, and a means to unravel the complexities of the electronic structure can be determined.

Band gaps and elastic waves in disordered stacks: normal incidence

We present a development of previous work where we studied the reflection and transmission properties of an array of circular cylindrical voids in an elastic matrix. The voids were taken to be infinitely long, equally spaced and of the same radius. In this paper we improve the method to deal with the problems of inclusions as well as voids and study various forms of disorder within the array, as well as stack designs showing good low–pass and band–pass characteristics in transmission.

Reflectionless multichannel wavelength demultiplexer in a transmission resonator configuration

A wave demultiplexer system with N channels in a two-dimensional photonic crystal is proposed. The demultiplexer is realized by the coupling among an ultra-low-quality factor microcavity and N resonators with high-quality factor. The coupling mode theory is employed to analyze the behavior of this system. The analytic results reveal that the reflection is fully absent at the peak frequencies for all channels. The simulations obtained by multiple-scattering method and experimental results in the microwave region show that the analysis is valid. This method might also be valuable for the design of other all-optical functional circuits.

Multiple-scattering lidar retrieval method: tests on Monte Carlo simulations and comparisons with in situ measurements.

A multiple-field-of-view (MFOV) lidar measurement and solution technique has been developed to exploit the retrievable particle extinction and size information contained in the multiple-scattering contributions to aerosol lidar returns. We describe the proposed solution algorithm. The primary retrieved parameters are the extinction coefficient at the lidar wavelength and the effective particle diameter from which secondary products such as the extinction at other wavelengths and the liquid-water content (LWC) of liquid-phase clouds can be derived. The solutions are compared with true values in a series of Monte Carlo simulations and with in-cloud measurements. Good agreement is obtained for the simulations. For the field experiment, the retrieved effective droplet diameter and LWC for the available seven cases studied are on average 15% and 35% (worst case) smaller than the measured data, respectively. In the latter case, the analysis shows that the differences cannot be attributed solely to lidar inversion errors. Despite the limited penetration depth (150-300 m) of the lidar pulses, the results of the studied cases indicate that the retrieved lidar solutions remain statistically representative of measurements performed over the full cloud extent. Long-term MFOV lidar monitoring could thus become a practical and economical option for cloud statistical studies but more experimentation on more varied cloud conditions, especially for LWC, is still needed.

Propagation of water waves through finite periodic arrays of vertical cylinders

We study the transmission of water waves propagating in finite-size two-dimensional periodic structures which consist of bottom-mounted cylinders using the multiple-scattering method. Complete band gaps exist between the first and the second bands in square and triangular periodic structures, as well as one modeled on a graphite atomic lattice. We investigate the dependence of the band edges on the filling fraction. The graphite-type structure shows the band gap at a lower filling fraction than the others. Therefore, the graphite-type structure may be more suitable for practical coastal protection. We also calculate the first-order force on cylinders located along the symmetry direction.

Non-Rayleigh distribution of reflected speckle intensities from localized states inside the gap of disordered photonic crystals

The field distributions of reflected speckles arising from localized states inside the gap of disordered photonic crystals in two dimensions were studied through numerical simulations using the multiple-scattering method. The statistics of the Lyapunov exponent of the transmitted waves were also studied. Similar to the case of disordered photonic crystals in one dimension, two types of localized states were found depending on the degree of disorder and the frequency inside the gap. Our simulation results indicate that the reflection statistics depend on whether or not the localized states are of the normal type. They also depend on whether the reflected angles are in the Bragg direction or not. For the non-Bragg angles, we found that the intensity distribution arising from the normal-type localized states follows Rayleigh statistics, in agreement with random matrix theory. However, deviations from Rayleigh statistics were found for second type of localized states. The crossover behavior from non-Rayleigh to Rayleigh statistics was studied as a function of the degree of disorder. By separating the field into coherent and diffuse parts, we have studied the statistics of field and phase distributions for both diffuse and total fields as well as their speckle contrasts. It is found that the crossover behavior is very similar to behavior in ballistic to diffusive wave propagation for the transmitted waves and can be described by the random-phasor-sum model (RPS). For the Bragg angle, non-Rayleigh statistics were found for both kinds of localized states. The statisics are sensitive to the degree of disorder. It is found that both the RPS and K distribution have limited ranges of validity in this case.

Multiple-scattering and DV-Xα theoreticaldetermination of the local structure of SO2/Pd(111)

We have calculated the sulfur 1s near-edge x-ray absorptionfine-structure (NEXAFS) spectra of SO2 adsorbed onPd(111) in terms of the multiple-scattering cluster andself-consistent field DV-Xα method. The physical originof the resonances in the NEXAFS spectra has been unveiled. Bythe multiple-scattering calculation we have for the first timeidentified two weak features appearing in S K-shell NEXAFS ofSO2/Pd(111), which locate near the π* andσ* resonances respectively. Meanwhile, aself-consistent DV-Xα cluster calculation has beenperformed to confirm the above conclusion. Our calculationresults for the local structure of SO2/Pd(111) arebroadly in agreement with those of Fourier-transform analysis ofthe surface-extended x-ray absorption fine structure.

Multiple-scattering studies of the near edge X-ray absorption fine structure of the Cl-passivated Ge(1 1 1) surface

The multiple-scattering cluster method has been employed to calculate the chlorine 1s near edge X-ray absorption fine structure (NEXAFS) of the Cl-passivated Ge(1 1 1) surface. The physical origins of the resonances in NEXAFS have been unveiled. It is shown that the most important resonance is attributed to the photoelectron scattering between the central chlorine and the top most germanium atom which is just below the core excited chlorine. Our studies confirm the atop Cl–Ge monochloride structure and show that the Cl–Ge bond length is equal to 2.15±0.05 Å, in good agreement with the previous extended X-ray absorption fine structure results and ab initio calculations.

Photonic bandgaps in two-dimensional short-range periodic structures

Through simulations and experiments we found considerable photonic bandgaps (PBGs) in two-dimensional structures with short-range periodicity (SRP) and without any spatial symmetry. A multiple-scattering method is used in our numerical investigations. Our experiments are performed in the microwave region with a microwavevector network analyser. The short-range periodic structures used in the investigations are produced through the arrangement of four certain basic units in a Fibonacci sequence in two dimensions. It is interesting that the PBG positions and widths are invariant for different translational cutouts and for different thickness of these SRP structures, showing that the PBG properties of the structures under consideration are decided by their SRP and not by their patterns. The physics behind the results is explored.

A comparative study of electron and positron scattering from molecules. IV. CH3Cl, CH3Br, and CH3I molecules

An experimental study of electron and positron scattering from CH3Cl, CH3Br, and CH3I molecules has been carried out, and total cross sections (TCSs) for both projectiles were determined. Several strong structures due to resonances in the TCSs have been observed for electron impact, while weak but not negligible structures have also been seen for positron impact. A strong variation for the dominant resonance peak seen at around 10 eV was found to depend on a type of halogen atoms, and a detailed study of this dependence on molecular species has been performed to understand the origin and nature of these resonances. The continuum multiple-scattering method has been employed for the analysis of experimental results in addition to the evaluation of the elastic cross section. For larger halogen atoms, TCSs tend to possess larger magnitudes at energies above 100 eV than for smaller halogen atoms suggesting that the halogen atoms in fact dominate the dynamics, and their magnitudes increase in the order of CH3I>CH3Br>CH3Cl. A comparative study of CH4 was also performed to provide insight on the effects of molecular geometrical structure and electronic state.

Photonic band gaps of AB3 and B3structures of metallodielectric spheres

Using the vector-wave multiple-scattering method we have calculatedthe photonic band structures of AB3 and B3 crystals composedof perfect metal spheres in air. It is shown that AB3 photoniccrystal contains a large photonic band gap and B3 photonic crystalhas more than one gap when the filling ratio of metal spheres exceedsa threshold. The multiple photonic gaps of the B3 structure areuseful in the design of optical multi-channel perfect mirrors and opticalmulti-band filters in the microwave regime.

Bridging two ways of describing final-state interactions in A(e,e′p) reactions

We outline a relativistic and unfactorized framework to treat the final-state interactions in quasi-elastic A(e,e'p) reactions for four-momentum transfers Q$^{2} \gtrsim 0.3$ (GeV/c)$^{2}$. The model, which relies on the eikonal approximation, can be used in combination with optical potentials, as well as with the Glauber multiple-scattering method. We argue that such a model can bridge the gap between a typical ``low'' and ``high-energy'' description of final-state interactions, in a reasonably smooth fashion. This argument is made on the basis of calculated structure functions, polarization observables and nuclear transparencies for the target nuclei $^{12}$C and $^{16}$O.

Effects of Ta on the magnetic structure of permalloy

In permalloy (Py) based heterostructures Ta has deleterious effects on the magnetic properties resulting in magnetic dead layers. Using the Korringa–Kohn–Rostoker coherent potential approximation method, it is shown that the average moment of Py (Ni0.8Fe0.2) is rapidly quenched by Ta substitutional additions. Locally self-consistent multiple-scattering method calculations for large supercell models of Py0.9Ta0.1 show that Ta additions also result in substantial fluctuations in the size of the local moments. The configuration dependent reductions in the local moments are larger for Ni than for Fe sites and are the largest for Ni sites closest to Ta.

X-ray absorption near-edge structure of selenium inthe Cu-In-Se system

The x-ray absorption near edge structure (XANES) of selenium is investigatedin the crystals with compositions from the pseudobinary cut lineCu2Se-In2Se3. This includes CuInSe2, indium-rich ternary compounds (Cu2In4Se7,CuIn3Se5, CuIn5Se8, CuIn7Se11) and α-In2Se3. The absorption at the K andL3/L2edges of selenium has been measured using synchrotron radiation. Twotheoretical approaches are used to the interpretation of the experimentaldata: the band structure calculation and the real-space multiple-scattering(RSMS) method. In the first one, the angular momentum projected densities ofstates at Se sites are calculated for CuInSe2 and α-In2Se3 for the energies upto 17 eV above the conduction band minimum by the LMTO-ASA method. The RSMSapproach represented by the FEFF8 code is used to calculate the XANES spectrafor the phases with tetragonal symmetry. Clusters up to 160 atoms are used inthe calculations. The influence of different structural factors on theselenium XANES is studied.

Photonic gap in amorphous photonic materials

Two-dimensional amorphous photonic materials are created, which do not possess any long-range order but have only short-range order. Our calculation of the multiple-scattering method shows that, for S-polarized waves, these materials have photonic gap that is independent of incident directions. Even though the detailed structures of amorphous photonic materials are different with each other, they possess a common photonic gap, if only they have the same short-range order. Based on our studies it may be confirmed that, for S-polarized waves, the first band gap of photonic crystals comes mainly from the short-range order, while the higher-order band gaps are related to the long-range order. The measured transmission spectrum of an amorphous photonic material agrees perfectly with the calculation.

Surface states in two-dimensional metallodielectric photonic crystals studied by a multiple-scattering method

We present a multiple-scattering method in conjunction with supercell calculations to study the electromagnetic surface states in two-dimensional metallodielectric photonic crystals. In the case of dielectric photonic crystals with cylindrical scatterers, this method is able to produce surface states inside a partial or full gap for p-polarized waves, similar to those found previously by using the method of plane-wave expansion. However, in two different systems of metallodielectric photonic crystals we have studied here, we do not find surface states. This is true for both perfect metal and metal with a Drude-like dielectric function. The absence of surface states may be attributed to the expulsion of electric field from the surface into the homogeneous medium due to the presence of metallic component, making the formation of surface unfavorable.

Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals

A recent publication [Nature (London) 404, 740 (2000)] claimed that absolute photonic gaps can be realized in 12-fold quasicrystalline arrangement of small airholes in a matrix of silicon nitride or glass. The result is rather surprising since silicon nitride $(n=2.02)$ and in particular, glass $(n=1.45)$ have rather low refractive index. In this work, we have studied the transmission properties of the same systems by using the multiple-scattering method. We found that the 12-fold triangle-square tiling is indeed very good for the realization of photonic gaps and we found absolute gaps in systems with airholes in dielectric, dielectric cylinders in air, and metal cylinders in air. However, for the case of air-holes in a dielectric background, absolute gaps appear only when the dielectric contrast is sufficiently high, and both silicon nitride and glass have refractive indices below the threshold.

Electron and positron scattering from CF 3I molecules below 600 eV: a comparison with CF 3H

The total cross-sections (TCSs) for electron and positron scattering from CF 3I molecules have been studied experimentally. A theoretical analysis based on the continuum multiple-scattering (CMS) method has been performed to understand the origin of resonances and the elastic cross-sections. The present TCS for electron scattering is found to be larger by about 20% than that of T. Underwood-Lemons, D.C. Winkler, J.A. Tossel, J.H. Moore [J. Chem. Phys. 100 (1994) 9117] although the general shape agrees well in the entire energy studied. The difference in the cross-sections for CF 3I and CF 3H is explained by the sizes and the dipole moments of these molecules.