Numerical evaluation of parabolic cylinder functions

The numerical evaluation of the parabolic cylinder functions D _p(z) in two cases is described. Case I is for the argument z=xe^-iπ/4, with x real, and the order p=-1/2+iy, with y real. Case II is for z arbitrary, but p an integer. These cases are of special importance in the analysis of wave scattering from a parabolic cylinder. Expressions for D_p(z) are presented which are numerically accurate and efficient     

New ternary line codes based on trellis structure

The trellis coding technique is applied to line-coded baseband digital transmission systems. For R=n/n+1(n=1,2,3) coding rates, a new codeword assignment model is proposed to accomplish basic requirements for line coding in which each length n binary data sequence is encoded into a length n+1 ternary (+,0,-) line codeword chosen among the code alphabet with 2ⁿ⁺² elements. Assuming Viterbi decoding, the system error performance is improved by increasing the free Euclidean distance between coded sequences. A new algorithm is given for the calculation of the free distance between line-coded sequences so obtained. For R=1/2 and R=3/4 rates, the analytical error performance upper bounds are derived. The power spectral densities of the new line codes are also calculated and compared with those of known line codes     

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     

A simple interferometric method for monitoring mode hopping intunable external-cavity semiconductor lasers

The mode-hopping events in a 1.3-μm grating-tuned external-cavity laser are analyzed on the basis of interferometric measurements. The average frequency of mode hopping for a 7.5-cm external-cavity laser is estimated and is expressed as f_c =2.7×10⁶×exp [-1.7/(I/I _th-1)] (hertz) for 0.07⩽(I/I_th -1)⩽0.8 (I=injection current and I_th =threshold current). The mode-hopping monitoring signal was negatively fed back to the laser using an automatic control circuit which maintained single-mode operation while the wavelength of the grating external-cavity laser was tuned     

Multiple quantum well optical modulator structures using surfaceacoustic wave induced Stark effect

Multiple-quantum-well (MQW) optical modulator structures using the quantum-confined Stark effect (QCSE) manifested by the application of an electric field induced by a propagating surface acoustic wave (SAW) are proposed. The magnitudes of the parallel E_∥ and perpendicular E_⊥ electric-field components are computed to determine the electroabsorption and change of index of refraction for the AlGaAs-GaAs system. The proposed structures are shown to be less cumbersome than conventional p-i-n configurations used to impress E. In addition, an enhanced performance Bragg modulator/switch which utilizes the QCSE as well as the acoustic phase grating produced by the SAW beam is described     

Grating degeneration technique and sandwich structures forholographic N×N passive star couplers

Design for an efficient N×N passive integrated optical star coupler are proposed. The concepts of grating degeneration and sandwich structures are presented. The techniques and their combinations can significantly reduce the number of gratings required by the coupler and thus make it possible to build holographic N×N star couplers with recording materials of a moderate dynamic range     

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     

Reliability evaluation of a limited-flow network in terms ofminimal cutsets

Many systems can be regarded as flow networks whose arcs have discrete and multi-valued random capacities. The probability of the maximum flow at each various level and the reliability of such a flow network can be calculated in terms of K-lattices which are generated from each subset of the family of all MCs (minimal cutsets). However the size of such a family 2^m-1 (m=number of MCs) grows exponentially with m. Such a flow network can be considered as a multistate system with multistate components so that its reliability can be evaluated in terms of upper boundary points of each level d (named d-MCs here). This work presents an algorithm to generate all d-MCs from each MC for each system capacity level d. The new algorithm is analyzed and compared with the algorithm given by J. Xue (1985). Examples show how all d-MCs are generated; the reliability of one example is computed     

Light-to-input nonlinearities in an R-LED series network

The light-to-current (L-I) and light-to-voltage (L-V) differential nonlinearities in the simple network of a customary LED and an external resistor R in series are analyzed and calculated theoretically and compared with experimental data. Particular emphasis is placed on the influence of the log-arithmetic slope ν of the L-I characteristic and the bias current I upon the ratio of the corresponding nonlinearity parameters. It is thus deduced that, for a given optical power P, over superlinear portions of the L-I curve (ν>1) the L-I linearity is typically better than its corresponding L-V linearity. On the contrary, when the L-I dependence is sublinear (ν<1) the voltage driving scheme may ensure for the R-LED network, or the LED alone, a local L-V response much more linear than the L-I response, provided that appropriate (optimum) I and/or R values are chosen     

More on the decoder error probability for Reed-Solomon codes

A combinatorial technique similar to the principle of inclusion and exclusion is used to obtain an exact formula for P_E (u), the decoder error probability for Reed-Solomon codes. The P_E(u) for the (255, 223) Reed-Solomon code used by NASA and for the (31, 15) Reed-Solomon code (JTIDS code) are calculated using the exact formula and are observed to approach the Qs of the codes rapidly as u gets large. An upper bound for the expression |P_E(u)/ Q-1| is derived and shown to decrease nearly exponentially as u increases     

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

The scattering from an infinite, circular, perfectly conducting cylinder coated by an elliptic dielectric cylinder 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 is the interfocal distance of the elliptic dielectric and k its wavenumber), exact, closed-form expressions of the form S(h)=S(0)[1+gh ²+O(h⁴)] are obtained for the scattered field and the various scattering cross sections. Both polarizations are considered for normal incidence. Graphical results for various values of the parameters are given     

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     

Coupling coefficients for partially meltback trapezoidal gratings

In distributed-feedback or distributed Bragg reflector lasers, the coupling coefficient K describing the grating feedback strength is an important parameter which must be optimized. The author presents a simple way to take into account the grating deformation likely to occur during regrowth and computes corresponding coupling coefficients for optimum first- and second-order, dry- and wet-etched gratings. He shows that meltback has little effect on K as long as the grating depth remains unchanged. Because of their V-groove-like shape, wet etched gratings are very meltback-sensitive. Therefore, it is concluded that dry-etched gratings must be preferred to avoid coupling coefficient degradation during regrowth     

Comments on `Electromagnetic wave scattering by an infinite planemetallic grating in case of oblique incidence and arbitrarypolarization'

In a previous paper by K. Uchida et al. (see ibid., vol.36, no.3, p.415-22, 1988) it is claimed that in the case of an arbitrary polarized plane wave incident on a strip grating, it is necessary to investigate the quasi-two-dimensional problem where the separation into transverse magnetic (TM) and transverse electric (TE) waves is, in general, impossible. It is shown here that although in general, arbitrarily polarized incident wave case decomposition into TE and TM waves is impossible, it is possible to divide any electromagnetic field into two orthogonal components; (1) fast polarization where an H-field component parallel to the strips is zero and (2) slow polarization where an E-field component parallel to the strips is zero     

Temperature sensitivity of phase-matched second-harmonic generationin LiIO3

Measurements were made of the temperature dependence (between 23 and 65°C) of the phase-matching angle &thetas;_pm for type I frequency doubling of 1064-nm laser light in lithium iodate (LiIO₃). The measured value of d&thetas;_pm/dT is -14.7±1 μrad/°C, which corresponds to a thermal sensitivity β_T =0.24±0.02 cm^-1/°C for this process. Also calculated is a value of d&thetas;_pm/dT using experimentally determined thermooptic data available in the literature. The calculated value of d&thetas;_pm/dT is -31±18 μrad/°C using literature values of n and dn/dT for LiIO₃. The extreme sensitivity of the calculated value of d&thetas;_pm/dT to small errors in the thermooptic coefficients may be the reason for this discrepancy     

A generalized recursive algorithm for wave-scattering solutions intwo dimensions

A generalized recursive algorithm valid for both the E _z and H_z wave scattering of densely packed scatterers in two dimensions is derived. This is unlike previously derived recursive algorithms which have been found to be valid only for E_z polarized waves. In this generalized recursive algorithm, a scatterer is first divided into N subscatterers. The n-subscatterer solution is then used to solve the (n+n')-subscatterer solution. The computational complexity of such an algorithm is found to be of O (N²) in two dimensions while providing a solution valid for all angles of incidence. This is better than the method of moments with Gaussian elimination, which has an O(N³) complexity     

Balancing sets of vectors

For n>0, d⩾0, n≡d (mod 2), let K(n, d) denote the minimal cardinality of a family V of ±1 vectors of dimension n, such that for any ±1 vector w of dimension n there is a v∈V such that |v- w|⩽d, where v-w is the usual scalar product of v and w. A generalization of a simple construction due to D.E. Knuth (1986) shows that K(n , d)⩽[n/(d+1)]. A linear algebra proof is given here that this construction is optimal, so that K(n, d)-[n/(d+1)] for all n≡d (mod 2). This construction and its extensions have applications to communication theory, especially to the construction of signal sets for optical data links     

Vector sets for exhaustive testing of logic circuits

(L, d)-universal sets are useful for exhaustively testing logic circuits with a large number of functional components, designed so that every functional component depends on at most d inputs. Randomized and deterministic constructions of ( L, d)-universal test sets are presented, and lower and upper bounds on the optimal sizes of such sets are proven. It is also proven that the design of an optimal exhaustive test set for an arbitrary logic circuit is an NP-complete problem     

A study of single-phase to three-phase cycloconverters using PSPICE

A single-phase-to-three-phase cycloconverter system operating from a 50 Hz input has been simulated under various loading conditions using a PSPICE circuit simulator. The Giacolleto SCR model has been modified. Detailed waveforms of load voltage, load current, and current of various semiconductor-controlled rectifiers (SCRs) have been plotted. It has been demonstrated that for low and medium L/R loads a simple constant firing angle sequence works well, whereas the cosine wave crossing method (CWCM) seems to be optimum for high L/R loads. Theoretical results are validated with the experimental results     

Binary [18,11]2 codes do not exist-Nor do [64,53]2 codes

A binary, linear block code C with block length n and dimension n is commonly denoted by [n, k] or, if its minimum distance is d, by [n, k,d]. The code's covering radius r(C) can be defined as the smallest number r such that any binary column vector of length (n-k) can be written as a sum of r or fewer columns of a parity-check matrix of C. An [n,k] code with covering radius r is denoted by [n,k]r. R.A. Brualdi et al., (1989) showed that l(m,r) is defined to be the smallest n such that an [n,n-m]r code exists. l(m,2) is known for m⩽6, while it is shown by Brualdi et al. that 17⩽l(7,2)⩽19. This lower bound is improved by A.R. Calderbank et al. (1988), where it is shown that [17,10]2 codes do not exist. The nonexistence of [18,11]2 codes is proved, so that l(7,2)=19. l[7.2)=19 is established by showing that [18,11]2 codes do not exist. It is also shown that [64,53]2 codes do not exist, implying that l(11,2)⩾65