A multiple scattering solution for the effective permittivity of asphere mixture

A recursive algorithm for calculating the exact solution of a random assortment of spheres is described. In this algorithm, the scattering from a single sphere is expressed in a one-sphere T matrix. The scattering from two spheres is expressed in terms of two-sphere T matrices, which are related to the one-sphere T matrix. A recursive algorithm to deduce the (n+1)-sphere T matrix from the n-sphere T matrix is derived. With this recursive algorithm, the multiple scattering from a random assortment of N spheres can be obtained. This results in an N² algorithm rather than the normal N³ algorithm. As an example, the algorithm is used to calculate the low-frequency effective permittivity of a random assortment of 18 dielectric spheres. The effective permittivity deviates from the Maxwell-Garnett result for high contrast and high packing fraction. With a high packing fraction, dielectric enhancement at low frequency is possible     

Electromagnetic scattering of finite strip array on a dielectricslab

A feast recursive algorithm is used to compute the scattering properties of a finite array of strip gratings on a dielectric slab. this algorithm has a computational complexity of O(N log² N) for one incident angle and O(N ² log N) for N incident angles. It uses plane wave basis for expanding the incident wave and the scattered wave. The scattered wave is expanded in terms of a Sommerfeld-type integral with spectral distribution along a vertical branch cut, rendering its expansion very efficient. To validate the scattering solution obtained using the recursive algorithm, comparisons with the method of moments are illustrated. The current distributions on the strips and scattering patterns are both presented. Since this algorithm has reduced computational complexity and is fast compared to other conventional methods, it can be used to analyze very large strip arrays. Scattering solution of a 50-wavelength wide strip is illustrated     

Recursive updating the eigenvalue decomposition of a covariancematrix

The author addresses the problem of computing the eigensystem of the modified Hermitian matrix, given the prior knowledge of the eigensystem of the original Hermitian matrix. Specifically, an additive rank-k modification corresponding to adding and deleting blocks of data to and from the covariance matrix is considered. An efficient and parallel algorithm which makes use of a generalized spectrum-slicing theorem is derived for computing the eigenvalues. The eigenvector can be computed explicitly in terms of the solution of a much-reduced (k ×k) homogeneous Hermitian system. The overall computational complexity is shown to be improved by an order of magnitude from O(N³) to O(N ²k), where N×N is the size of the covariance matrix. It is pointed out that these ideas can be applied to adaptive signal processing applications, such as eigen-based techniques for frequency or angle-of-arrival estimation and tracking. Specifically, adaptive versions of the principal eigenvector method and the total least squares method are derived     

Fast decoding of codes from algebraic plane curves

Improvement to an earlier decoding algorithm for codes from algebraic geometry is presented. For codes from an arbitrary regular plane curve the authors correct up to d*/2-m² /8+m/4-9/8 errors, where d* is the designed distance of the code and m is the degree of the curve. The complexity of finding the error locator is O(n^7/3 ), where n is the length of the code. For codes from Hermitian curves the complexity of finding the error values, given the error locator, is O(n²), and the same complexity can be obtained in the general case if only d*/2-m²/2 errors are corrected     

On optimum time-hopping patterns

Time-hopping patterns can be constructed from simple difference sets. By studying such constructions, it has been proven that whenever n-2, n-1, or n+1 is a prime power, then time-hopping patterns that have n terms can be constructed and are of length less than n². By computation it is shown that such patterns can have length less than n²-n^1.44 for all n⩽150. It is also shown that time-hopping patterns for n terms can have length less than n²+O(n^1.55) for all n     

pn+ junction in an implanted electroactive polymer:poly(paraphenylene)

The authors have recently shown that specific and stable n or p doping may be obtained on poly(paraphenylene), providing moderate implantation conditions with appropriate ions are used. Here they describe a pn⁺-junction made in intrinsic insulating poly(paraphenylene) (α<10^-12 Ω^-1 cm^-1) by implantation (E≃50 keV) of alkali metal ions (essentially caesium for n doping) and halogen (iodine for p doping)     

Diffusion and noise in GaAs material and devices

The variation of the diffusion coefficient D(E) versus the electric field strength E is determined at 300 K in n-type GaAs (N_D=3×10^-17 cm^-3 ), using pulsed high-frequency noise measurements. D(E) is found to increase slightly at low field, then to decrease down to one tenth of its ohmic value near the threshold field. Long (⩾4 μm) real n⁺-n-n⁺ Gunn diodes, with an arbitrary doping profile, can be modeled. Comparisons are made, and excellent agreement is found, between experimental and theoretical characteristics of two real diodes, with notch and with gradual doping profiles. The doping profile N_D(x ) is shown to have a considerable influence on the diode behavior, in regard to the electric field profile as well as the noise characteristics. Using the impedance field method, the noise current is modeled and found to by very sensitive in the D(E) variation law, in particular in the range of 2.5-4 kV/cm. The agreement between the experimental noise and the computed noise of real diodes is quite satisfactory when using the D(E) determined     

Decoding algebraic-geometric codes up to the designed minimumdistance

A simple decoding procedure for algebraic-geometric codes C _Ω(D,G) is presented. This decoding procedure is a generalization of Peterson's decoding procedure for the BCH codes. It can be used to correct any [(d*-1)/2] or fewer errors with complexity O(n³), where d * is the designed minimum distance of the algebraic-geometric code and n is the codelength     

The sublinear relationship between index change and carrier densityin 1.5 and 1.3 μm semiconductor lasers

The carrier-induced index change was measured using a novel injection-reflection technique in combination with differential carrier lifetime data. The observed relation between index change and injected carrier density at bandgap wavelength is nonlinear and is approximately given by δn_act=-6.1×10^-14 ( N)^0.66 for a 1.5-μm laser and δn _act=-1.3×10^-14 (N)^0.68 for a 1.3-μm laser. The carrier-induced index change for a 1.3-μm laser at 1.53-μm wavelength is smaller and is given by δn _act=-9.2×10^-16 (N)^0.72      

Full Newton and constraint methods for semilinear signal modeling

The authors derive an expression for the Hessian matrix of the variable projection functional (VPF) and implement the Hessian using QR factorization. This is incorporated into a full Newton variable projection (FNVP) algorithm for estimating parameters in semilinear signals. They introduce a deflation technique for constraining the VPF to contain known basis vectors. For modeling exponential signals, the computational cost of the FNVP algorithm is shown to vary linearly with N, the size of the data vector, while other algorithms vary as N² or N log ₂ N     

Schottky diodes of Au on GaAs1-xSbx/GaAs n-Nheterostructures grown by MBE

Au Schottky barrier heights on molecular-beam-epitaxial grown n-GaAs_1-xSb_x/N-GaAs heterostructures with x up to 0.26 have been studied. It was found that φ_bn=0.9-1.77x+2.89x², or φ_bn≈0.77E_g-0.20 for x<0.26. The pinning position of the Fermi level with respect to the valence-band edge for x<0.26 takes the form of E _pin=-0.52x+0.53 eV, which also appears to be valid for an x value up to 1.0     

Bulk and surface properties of amorphous hydrogenated fluorinatedsilicon grown from SiF4 and H2

A detailed study of the growth of amorphous hydrogenated fluorinated silicon (a-Si:H, F) from a DC glow discharge in SiF₄ and H₂ is discussed. The electrical properties of the films can be varied over a very wide range. The bulk properties of the best films that were measured included an Urbach energy E_u =43 meV, a deep-level defect density N_s=1.5×10¹⁵ cm^-3, and a hole drift mobility of 8×10^-3 cm² V^-1 s^-1, which reflects a characteristic valence band energy of 36 meV. It was found that E_u, N _s, and the density of surface states N_ss are related to each other. Under the deposition condition of the films with the best bulk properties, N_ss reaches its highest value of 1×10¹⁴ cm^-2. It is suggested that in growth from SiF₄/H₂, the density of dangling bonds at the growing surface is very sensitive to the deposition conditions     

The fast multipole method (FMM) for electromagnetic scatteringproblems

The fast multipole method (FMM) developed by V. Rokhlin (1990) to efficiently solve acoustic scattering problems is modified and adapted to the second-kind-integral-equation formulation of electromagnetic scattering problems in two dimensions. The present implementation treats the exterior Dirichlet problem for two-dimensional, closed, conducting objects of arbitrary geometry. The FMM reduces the operation count for solving the second-kind integral equation from O(n³) for Gaussian elimination to O(n^4/3) per conjugate-gradient iteration, where n is the number of sample points on the boundary of the scatterer. A sample technique for accelerating convergence of the iterative method, termed complexifying k, the wavenumber, is also presented. This has the effect of bounding the condition number of the discrete system; consequently, the operation count of the entire FMM (all iterations) becomes O(n^4/3). Computational results for moderate values of ka, where a is the characteristic size of the scatterer, are given     

Guided-wave intensity modulators using amplitude-and-phaseperturbations

A theoretical analysis of intensity modulation in coupled waveguides and Mach-Zehnder interferometers is reported. Simultaneous phase and amplitude perturbations Δn+ιΔk are considered. Predictions are made about the performance of electrooptic GaAs and InP modulators controlled by the free-carrier effect (ΔN) or by the Franz-Keldysh effect (ΔE ). The phase-dominant condition Δn>5Δk is optimal. The predicted depth of modulation is greater than that of conventional loss-modulators over a range of ΔN or ΔE     

Efficient algorithm for reliability of a circular consecutive-k-out-of-n:F system

The time complexities of previously published algorithms for circular consecutive-k-out-of-n:F systems are O (nk²) and O(nk). The authors propose a method to improve the original O(nk² ) algorithm, and hence derive an O(nk) algorithm     

An efficient communication structure for distributed commitprotocols

To maintain consistency in a distributed database environment, the transactions must be executed atomically. The standard algorithm for ensuring an atomic execution is called the distributed commit protocol. The two-phase commit protocol and its variations, the well-known protocols used for this purpose, are characterized by successive rounds of message exchange, among all the sites of the database, at the time a transaction enters into a completion phase. The performance of these protocols is given by a complexity measure that depends on the communication structure of the protocol. Given N sites, the worst-case complexity of a commit protocol is O(N²). A communication structure called maximal binomial structure (MBS) is presented, for which the complexity of the protocol is O(N×log³ N). A lower bound for this complexity is also given, which is O(N×log² N). Protocols using the MBS remain symmetric. A scheme for an arbitrary expansion of the MBS to allow communication among a large number of sites is proposed. For the expanded system, the protocol complexity is also shown to be O(N×log³ N ). These structures are shown to be superior to other known structures     

Reliability polynomial for a ring network

A mathematical model is developed for the reliability of a system made up of m unreliable nodes arranged in a ring. The model can be used to calculate the reliability of single-ring networks in which the network recovery mechanism depends on bypassing failed stations, but link signal power margins are inadequate to overcome losses due to more than n bypass switches in series. Computational complexity is 0(n²m+nm²/2) in time, and 0(m²/2) in memory requirements     

Recursive T-matrix algorithms for the solution ofelectromagnetic scattering from strip and patch geometries

Two recursive T-matrix algorithms are presented and their reduced computational complexities and reduced memory requirements are demonstrated. These algorithms are applied to the problem of electromagnetic scattering from conducting strips and patches with canonical geometries. The geometries are reminiscent of finite-sized frequency selective surfaces. Computational complexities of O( N²) and O(N^7/3) and memory requirements of O(N) and O(N ^4/3) are shown to be feasible for two-dimensional and three-dimensional geometries, respectively. The formulation uses only two components of the electric field. Therefore, the vector electromagnetic problem of scattering from three-dimensional patch geometries can be solved using scalar addition theorems for spherical harmonic wave functions. For a two-dimensional strip problem, both TM and TE polarizations can be solved simultaneously using this formulation. Numerical scattering results in the form of radar cross sections (RCS) are validated by comparison with the method of moments     

On the reduction in multiplicative complexity achieved by thepolynomial residue number system

The polynomial residue number system is known to reduce the complexity of polynomial multiplication from O(N² ) to O(N). A new interpretation of this complexity reduction is given in the context of associative algebras over a finite field. The new point of view provides a clearer understanding of the Chinese remainder theorem     

Restoration of color images by multichannel Kalman filtering

A Kalman filter for optimal restoration of multichannel images is presented. This filter is derived using a multichannel semicausal image model that includes between-channel degradation. Both stationary and nonstationary image models are developed. This filter is implemented in the Fourier domain and computation is reduced from O(Λ ³N³M⁴) to O(Λ³N³M² ) for an M×M N-channel image with degradation length Λ. Color (red, green, and blue (RGB)) images are used as examples of multichannel images, and restoration in the RGB and YIQ domains is investigated. Simulations are presented in which the effectiveness of this filter is tested for different types of degradation and different image model estimates