Electromagnetic scattering from an infinite elliptic metalliccylinder coated by a circular dielectric one

The scattering from an infinite elliptic metallic cylinder coated by a circular dielectric one is considered. The electromagnetic field is expressed in terms of both circular and elliptical cylindrical wave functions, which are connected with one another by well-known expansion formulas. In the special case of small h=ka/2 (a being the interfocal distance of the elliptic conductor and k the wavenumber of the dielectric coating), exact, closed-form expressions of the form S (h)=S(0)[1+g "h²+O(h⁴)] are obtained for the scattered field and the various scattering cross sections of the problem. Both polarizations are considered for normal incidence. Graphical results for various values of the parameters are given     

Two theorems on lattice expansions

It is shown that there is a tradeoff between the smoothness and decay properties of the dual functions, occurring in the lattice expansion problem. More precisely, it is shown that if g and g¯ are dual, then (1) at least one of H^1/2 g and H^1/2 g¯ is n in L²(R), and (2) at least one of Hg and g ¯ is not in L²(R). Here, H is the operator -1/(4π²)d²/(dt² )+t². The first result is a generalization of a theorem first stated by R.C. Balian (1987). The second result is new and relies heavily on the fact that, when G∈W^2,2(S) with S=[-1/2, 1/2]×[-1/2, 1/2] and G(0), than 1/G∉L ²(S)     

Scattering by an infinite circular dielectric cylinder coatingeccentrically an elliptic metallic one

The scattering of a plane electromagnetic wave by an infinite-circular dielectric cylinder, containing eccentrically an elliptic metallic one is considered. The electromagnetic field is expressed in terms of both circular and elliptical-cylindrical wave functions, connected with one another by well-known expansion formulas. Translational addition theorems for circular cylindrical wave functions are also used for the satisfaction of the boundary conditions in the dielectric cylinder. When the solution is specialized to small values of h=k₁c/2, with k₁ the wavenumber of the dielectric cylinder and c the interfocal distance of the elliptic conductor, semianalytical expressions of the form S(h)=S(0)[1+gh²+O(h ⁴)] are obtained for the scattered field and the various scattering cross sections of this configuration. Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters     

Evidence for continuous visible chemical lasing from the fast nearresonant energy transfer pumping of atomic sodium

Energy transfer from selectively formed metastable states of SiO is used to pump sodium-atom laser amplifiers at λ≈569 nm (4d²D-3p²P), λ≈616 nm (5s²S-3p² P), and λ≈819 nm (3d²D -3p²P). The a³Σ⁺ and b³Π states of SiO are generated in high yield from the Si+N₂O→SiO+N₂ reaction. The energy stored in the triplet states is transferred in a highly efficient collisional process to pump sodium atoms to their lowest excited 3d² D, 4d²D, and 5s²S states. Adopting a sequence in which high concentrations of silicon and sodium atoms are mixed and oxidized, a continuous amplification (gain condition) is monitored which suggests the creation of a population inversion among the receptor sodium-atom energy levels and forms the basis for full cavity oscillation on the Na4 d²D-3p²P transition at 569 nm     

The Zak transform and some counterexamples in time-frequencyanalysis

It is shown how the Zak transform can be used to find nontrivial examples of functions f, g∈L²(R) with f×g≡0≡F×G, where F, G are the Fourier transforms of f, g, respectively. This is then used to exhibit a nontrivial pair of functions h, k∈L²(R), h≠k, such that |h|=|k|, |H |=|K|. A similar construction is used to find an abundance of nontrivial pairs of functions h, k∈L² (R), h≠k, with |A_h |=|A_k| or with |W_h|=|W _k| where A_h, A_k and W_h, W_k are the ambiguity functions and Wigner distributions of h, k, respectively. One of the examples of a pair of h, k∈L²(R), h≠k , with |A_h|=|A_k| is F.A. Grunbaum's (1981) example. In addition, nontrivial examples of functions g and signals f₁≠f₂ such that f₁ and f₂ have the same spectrogram when using g as window have been found     

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     

VUV stimulated anti-Stokes Raman emission in inverted atomicselenium

Stimulated anti-Stokes Raman scattering at 145.7 nm in inverted Se is generated by photolysis of OCSe at 193 nm and the subsequent up-conversion of 205.1-nm pump radiation. The tuning profile is characterized with OCSe pressure, the energies and relative timing of the pump and photodissociation lasers, and CO and Ar buffer-gas pressure. The use of CO as a buffer gas is discovered to be detrimental to the anti-Stokes output. Sixteen competing stimulated emission channels are found to suppress anti-Stokes emission on exact 4p ^{4 1}S₀-4p³ 5s³ P⁰₁ pump resonance     

Sliding block codes between constrained systems

The construction of finite-state codes between constrained systems called sofic systems introduced by R. Karabed and B. Marcus (1988) is continued. It is shown that if Σ is a shift of finite type and S is a sofic system with k/n=h(S )/h(Σ), where h denotes entropy, there is a noncatastrophic finite-state invertible code from Σ to S at rate k:n if Σ and S satisfy a certain algebraic condition involving dimension groups, and Σ and S satisfy a certain condition on their periodic points. Moreover, if S is an almost finite type sofic system, then the decoder can be sliding block     

Correlation between 1/f noise and hFElong-term instability in silicon bipolar devices

Accelerated life tests with high-temperature storage and electric aging for n⁺-p-n silicon planar transistors were carried out. Current gain h_FE increases monotonously with time during the tests, and the h_FE drift is correlated with initial measured 1/f noise in the transistors, i.e. the drift amount significantly increases with the increase of noise level. The correlation coefficient of relative drift Δh_FE /h_FE and 1/f noise spectral density S_iB(f) is far larger than that of Δ h_FE/h_FE and initial DC parameters of the transistors. A quantitative theory model for the h _FE drift has been developed and explains the h _FE drift behavior in the tests, which suggests that the h _FE drift and 1/f noise can be attributed to the same physical origin, and both are caused by the modulation of the oxide traps near the Si-SiO₂ interface to Si surface recombination. 1/f noise measurement, therefore, may be used as a fast and nondestructive means to predict the long-term instability in bipolar transistors     

1/f noise in MODFETs at low drain bias

The 1/f noise in normally-on MODFETs biased at low drain voltages is investigated. The experimentally observed relative noise in the drain current S_I/I² versus the effective gate voltage V_G=V_GS-V_off shows three regions which are explained. The observed dependencies are S_I/I²∝V_G ^m with the exponents m=-1, -3, 0 with increasing values of V_G. The model explains m =-1 as the region where the resistance and the 1/f noise stem from the 2-D electron gas under the gate electrode; the region with m=0 at large V_G or V_GS≅0 is due to the dominant contribution of the series resistance. In the region at intermediate V_G , m=-3, the 1/f noise stems from the channel under the gate electrode, and the drain-source resistance is already dominated by the series resistance     

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     

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     

Optimality property of the Gaussian window spectrogram

It is shown that for any signal x(t) the minimum of ∫_-∞^∞∫_-∞ ^∞ [(t-t_x)²+(f-f _x)²] S_x^(w)(t , f) dt df over all normalized time-windows w(t) is achieved by the Gaussian window w(t)=2^1/4 exp (-πt²). Here (t_x, f _x) is the center of gravity of the signal x(t ), S_x^(w) (t, f) is the spectrogram of x(t) due to the window w( t), and the double integral is a measure of the spread of S _x^(w) (t, f) around (t _x, f_X) in the time-frequency plane     

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     

Increase of the order of approximation and improvement of theinterface conditions for the method of lines

A formalism for improving the convergence of the method of lines is presented. This formalism was developed for analyzing waveguide structures used in integrated optics and reduces the discretization error to O(h⁴). The interface conditions between different dielectrics are taken into account. Excellent convergence is demonstrated for the slab waveguide     

A chemically driven visible laser transition using fastnear-resonant energy transfer

Evidence is obtained which demonstrates the potential for developing purely chemical visible lasers based on rapid near-resonant energy transfer from metastable excited triplet states of germanium and silicon monoxide (a³Σ⁺,b ³Π) to select metal atoms. In this study, the Group IIIA metal atoms were chosen as the energy receptors for the energy transfer-pump sequence. Excited triplet states were generated from the Ge-O₃, Ge-N₂, Si-N₂O, and Si-NO₂ reactions; the bulk of the experimental results was obtained with a germanium-based system. The energy stored in the long-lived triplet states is transferred to pump X²P_1/2 thallium, indium, and gallium atoms to their lowest lying ² S_1/2 states. The authors observe a system of temporal behavior which suggests the creation of a population inversion producing a gain condition and forming the basis for full cavity oscillation on the Tl 7²S_1/2-6P _3/2 transition at 535 nm     

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     

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     

Design of bipolar imaging devices (BASIS): analysis of random noise

A design methodology for a bipolar imaging device, the base-stored image sensor (BASIS), has been established by theoretical analysis and experimental verification for random noise. The random noise in BASIS is dominated by the shot noise in readout and transient reset operation. The theoretical analysis has been carried out by introducing the probability density functions for these operations. The readout noise depends on the base-to-collector junction capacitance C_bc , the emitter common current gain h_FE, the storage capacitor C_T, and the emitter voltage V _E. The reset noise has been confirmed to be given by thermal noise. The theoretical results coincide well with the experimental results obtained by TEG devices. An expression for the S/N ratio has been derived theoretically. It is found that h_FE should be made as large as possible and ( C_bc+C_be) as small as possible to improve the S/N ratio for random noise, where C _be is the base-to-emitter junction capacitance     

On the optimality and stability of exponential twisting in MonteCarlo estimation

Estimation of the large deviations probability p_n =P(S_n⩾γn) via importance sampling is considered, where S_n is a sum of n i.i.d. random variables. It has been previously shown that within the nonparametric candidate family of all i.i.d. (or, more generally, Markov) distributions, the optimized exponentially twisted distribution is the unique asymptotically optimal sampling distribution. As n→∞, the sampling cost required to stabilize the normalized variance grows with strictly positive exponential rate for any suboptimal sampling distribution, while this sampling cost for the optimal exponentially twisted distribution is only O(n ^1/2). Here, it is established that the optimality is actually much stronger. As n→∞, this solution simultaneously stabilizes all error moments of both the sample mean and the sample variance estimators with sampling cost O(n^1/2 ). In addition, it is shown that the embedded parametric family of exponentially twisted distributions has a certain uniform asymptotic stability property. The technique is stable even if the optimal twisting parameter(s) cannot be precisely determined