Modal transmission-line theory of three-dimensional periodic structures with arbitrary lattice configurations

The scattering of waves by multilayered periodic structures is formulated in three-dimensional space by using Fourier expansions for both the basic lattice and its associated reciprocal lattice. The fields in each layer are then expressed in terms of characteristic modes, and the complete solution is found rigorously by using a transmission-line representation to address the pertinent boundary-value problems. Such an approach can treat periodic arbitrary lattices containing arbitrarily shaped dielectric components, which may generally be absorbing and have biaxial properties along directions that are parallel or perpendicular to the layers. We illustrate the present approach by comparing our numerical results with data reported in the past for simple structures. In addition, we provide new results for more complex configurations, which include multiple periodic regions that contain absorbing uniaxial components with several possible canonic shapes and high dielectric constants.     

Reductive silylation and alkylation of phthalimides

Preparative electrochemical reduction of N-methylphthalimide in dry acetonitrile and in the presence of dimethylsulfate or trimethylchlorosilane lead to bis-lactams by dimerization at the carbonyl group. 1, 3-Bis-trimethylsilyloxy-2-methylisoindole is formed instead using a large excess of silylating agent. An analogous isoindole derivative is obtained from reduction of N-phenylphthalimide. A mechanism accounting for the formation of one or two electron products under different alkylating conditions is discussed.     

Robust discrete-time minimum-variance filtering

The bounded-variance filtered estimation of the state of an uncertain, linear, discrete-time system, with an unknown norm-bounded parameter matrix, is considered. An upper bound on the variance of the estimation error is found for all admissible systems, and estimators are derived that minimize the latter bound. We treat the finite-horizon, time-varying case and the infinite-time case, where the nominal system model is time invariant. In the special stationary case, where it is known that the uncertain system is time invariant, we provide a robust filter for all uncertainties that still keep the system asymptotically stable     

Design considerations for planar Schottky barrier diodes

The cut-off frequency of the simplest planar Schottky diode on a uniformly doped n-layer of GaAs is derived. The theoretical results are given as functions of doping concentration and layer thickness with the specific contact resistance as parameter. An improved planar diode structure is presented with several short Schottky contact fingers connected in parallel. Experimental values ranging from 100 to 300 GHz agree with the calculated values when parasitic capacitances are taken into account.     

Crystal chemistry of γ-(Zn, Me)3(PO4)2 solid solutions

A number of γ-(Zn,$\text{Me}$)₃(PO₄)₂ solid solutions with the “γ-Zn₃(PO₄)₂” structure have been prepared and equilibrated at about 1070 K ($\text{Me}\text{= Mg, Mn, Fe, Co, Ni, Cu, and Cd}$). Approximate homogeneity ranges are given. The monoclinic unit cell dimensions have been accurately determined from Guinier-Hägg photographs. The structure contains five- and six-coordinated cations. Correlations between homogeneity ranges, unit cell dimensions, cation radii and cation distributions are pointed out, and the phases are also compared with isotypic (Mg,$\text{Me}$₃(PO₄)₂ and (Co,$\text{Me}$)₃(PO₄)₂ solid solutions.     

Grating diffraction and Wood's anomalies at two-dimensionally periodic impedance surfaces

We address the problem of plane-wave scattering and Wood's anomalies at two-dimensional (2-D) periodic surfaces by employing a simplified grating model given by a planar surface whose impedance varies sinusoidally along two orthogonal directions. We obtain a rigorous solution to the corresponding boundary-value problem in terms of an infinite set of coupled recurrence equations. When truncated for computational purposes, this solution is in the form of a banded matrix, which we solve by direct methods and also by a highly efficient iterated matrix procedure. Numerical results are presented for symmetric and nonsymmetric incidence cases, and we show that certain diffracted fields do not depolarize in the former case. The expected Wood's anomalies of both Rayleigh and leaky-wave types are confirmed, and their location in wavelength space is numerically demonstrated for 2-D periodic configurations.     

Average variability of the radiation reflected by vegetated surfaces due to differing irradiations

The average variability of the reflected radiation field due to differing distributions of the irradiation in case of a savannah was given in a previous paper. In this paper, equivalent results are given for three more surfaces: bog, pasture land, and coniferous forest. Because the results are rather similar, mean values for vegetated surfaces can be derived. They indicate a change of the reflected radiance by $\text{± 1\%}$ per degree change of the solar zenith angle and per 10% change of the optical depth of the atmosphere.