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  • Articles  (7,762)
  • Springer  (4,625)
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  • Electrical Engineering, Measurement and Control Technology  (6,686)
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  • Articles  (7,762)
Publisher
Years
  • 2010-2014
  • 2005-2009  (4,061)
  • 1985-1989  (1,795)
  • 1975-1979  (1,798)
  • 1945-1949  (108)
Year
Journal
  • 1
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    Circuits, systems and signal processing 6 (1987), S. 363-387 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract For a broad class of interconnected nonlinear systems, this paper develops a complete design methodology for decentralized variable structure control. Specifically, the paper sets forth design schemes for local switching surfaces and the related local switched feedback gains which together force the original nonlinear interconnected system to behave as a reduced order interconnected equivalent system having a desired response such as stability, tracking, or prespecified eigenvalues. Also developed is a numerical algorithm for constructing the switched local feedback gains. A simple nonlinear example illustrates the control strategy.
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  • 2
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    Circuits, systems and signal processing 6 (1987), S. 391-419 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A new stabilization method of a large-scale dynamic system, consisting of a set of interconnected subsystems, is presented in this paper. The topology of the interconnected subsystems is given as a network containing nodes with only one ingoing link, and none, one, or more outgoing links. Here, when the notion “node” is used a subsystem is assumed, and the links stand for the subsystem interconnections. The stabilization method is made only by the use of local linear state feedback around each subsystem, in order to satisfy constraints given in the problem. The interconnections among the subsystems are assumed to be nonlinear, time-varying. According to the topology of the large-scale system, the method of stabilization is hierarchic, one proceeds from node to node, and is applicable from a computer standpoint. A design algorithm follows directly, and can be made using the Generate and Test method for each subsystem independently, thus enabling designers to use a computer which has a video terminal as a peripheral unit and providing a possibility for interactive applications.
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  • 3
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    Circuits, systems and signal processing 6 (1987), S. 421-447 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The estimation of covariance matrices which are structured, for example, of Toeplitz type, from measurement data is considered. The problem is considered in the context of array beamforming, and various methods of estimation are derived and compared, such comparison including consideration of the behavior of the estimate in beamforming applications.
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  • 4
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    Circuits, systems and signal processing 6 (1987), S. 449-456 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The planar least-squares inverse (PLSI) polynomials are used for stabilization of two-dimensional unstable recursive filters. In order to obtain the PLSI polynomials, the main work involved consists in forming a set of linear equations and then solving them. In this paper we present an efficient and simple method to form the necessary set of linear equations (i.e., the required coefficient matrix) for a chosen pattern and order of the desired PLSI polynomial, starting from the denominator polynomial of a two-dimensional unstable recursive filter.
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  • 5
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    Circuits, systems and signal processing 6 (1987), S. 347-362 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper shows how to use orthogonal functions to invert singular (i.e., generalized state-space) systems. The approach is to express the inverse system itself as a singular system, and then to apply the theory of orthogonal functions to convert that differential-algebraic system to a purely algebraicgeneralized Lyapunov equation whose solution yields the input of the original system given its output. Both left and right inversion are treated. Necessary and sufficient conditions for the existence and uniqueness of the generalized Lyapunov equation are derived, and a generalizedQZ algorithm is given for its efficient solution. It is also shown that the coefficients in the Walsh function expansion may be approximately found using an FFT-type butterfly network. These results provide both an extension in theory, by investigating the properties of a new Lyapunov equation, and an extension in the implementation of system inversion, by providing a scheme which applies to generalized state-space systems and uses an unconventional approach which may prove to be a useful contribution.
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  • 6
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    Circuits, systems and signal processing 6 (1987), S. I 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
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  • 7
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    Circuits, systems and signal processing 6 (1987), S. 457-470 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In digital communication networks, a special class of complex biquad recursive digital filters called orthogonal filters is increasingly being used. The separate effects of the overflow and quantization nonlinearities on these orthogonal filters' responses have been investigated [5], [6]. In this paper we examine the zero-input stability properties of the actual orthogonal filter having both overflow and quantization nonlinearities. The overflow nonlinearities considered include saturation, bit-by-bit inversion, zeroing, and modulo 2 arithmetic. The quantization techniques used may be roundoff, magnitude, or value truncation. An example demonstrates the adverse coupling effect between the overflow and quantization nonlinearities. Two criteria are therefore derived to ensure asymptotic overflowstability of the filter in the presence of quantization. These criteria have been translated to the coefficient plane; various regions corresponding to different minimum wordlengths required to ensure decoupling of the overflow and quantization phenomena have been derived.
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  • 8
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    Circuits, systems and signal processing 6 (1987), S. 471-505 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The identification problem for electromagnetic objects excited by transients is discussed. Several classes of models are reviewed, and an output error model is selected. An algorithm for solving the transient identification problem using this model is presented, and some of the issues connected with its use are considered. Examples of the application of this algorithm to electromagnetic data are given.
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  • 9
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    Circuits, systems and signal processing 6 (1987), S. 3-30 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Conditions are obtained for the cepstrum of anl 1 sequence having arbitrary support on theM-dimensional lattice to exist also as anl 1 sequence with arbitrary support. These conditions are used to show that the cepstrum of a sequence with support on a half-space will, when it exists, also have support on the same half-space. This result is used, in turn, to describe the support of the cepstrum of a sequence with bounded support on a half-space. The relationship between the existence of the cepstrum and bounded-input, bounded-output (BIBO) stability for all three of these cases is considered. Finally, the derivatives of the inversion operator, the homomorphic transform operator, and its inverse are calculated. These results are also useful in the one-dimensional case.
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  • 10
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    Circuits, systems and signal processing 6 (1987), S. 31-43 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A signal-processing software system is described which allows the simulation of systems described by block diagrams or signal-flow graphs. A high-level data-flow language describes the interconnection of the components. All configurations of interconnections are allowed, including those containing feedback. Component systems (blocks) are allowed to be multi-input, multi-output, and to be programmed in any language. Blocks are implemented as separate processes running under a UNIX2 operating system. Input and output signals are transferred between blocks via the UNIXpipe facility. Thedata type of a signal is arbitrary in the context of the compiler; within a component or system, signals and internal variables can be either floating point or fixed point. The compiler enforces strong or weak type checking of signals according to the characteristics of the blocks generating and receiving the signals. The invariance of the program to implementation data type is accomplished by the use of abstract data types. Fixed-point simulations having differing number of bits per signal and per internal variable in a block are supported. Special display software is used to allow any signal in the system to be displayed on any graphics device.
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  • 11
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    Circuits, systems and signal processing 6 (1987), S. 61-75 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Necessary and sufficient conditions are given for the solvability of fully implicit index-one and semiexplicit index-two linear time-varying semistate systems of the formA(t)x′+B(t)x=f(t). Using these solvability criteria, we establish the convergence and stability of backward difference formulas (BDF) for solvable semiexplicit index-two systems. In the algebraic variables, these methods exhibit a boundary layer of instability of length 2k, wherek is the order of the method. Finally, we show that the systems considered in this paper belong to a class of problems, solvable by BDF, which strictly contains the systems safely transformable to standard canonical form.
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  • 12
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    Circuits, systems and signal processing 6 (1987), S. 45-60 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The design of two-dimensional IIR digital filters is approached using linear-programming techniques. The problem is formulated as an approximation problem and filter frequency response characteristics are represented via the square of the magnitude of the filter transfer function. An appropriate approximation error is minimized leading to a linear problem formulation. The latter problem does not require differential correction methods for its solution, thus resulting in a computationally efficient algorithm. Stability conditions and symmetry considerations are easily accounted for. The linear programming approach assures convergence of the solution to a global minimum, among other advantages over nonlinear methods. Several examples illustrate the strength and effectiveness of the methodology.
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  • 13
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    Circuits, systems and signal processing 6 (1987), S. 77-93 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Necessary and sufficient conditions for output and state feedback stabilization are given for single-input/single-output systems. Extensions are also provided for single-input/multi-output and multi-input/single-output systems. A technique for constructing explicitly a stabilizing controller is presented, and the main differences with respect to the one-dimensional case are clarified. Finally, the existence of “intrinsically unstable” transfer functions, i.e., not allowing stabilizable realizations, is discussed.
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  • 14
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    Circuits, systems and signal processing 6 (1987), S. 95-106 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A single-parameter controlled-variable amplitude change function has been constructed for digital filtering using multiple units of a prototype filter. The limits of variation are discussed. The technique is shown to be useful not only for the reduction of errors in either the pass band or the stop band of the overall filter, but also for varying the cutoff frequency of the overall filter over a wide range. Hardware implementation problems resulting from a wide variation are shown to be overcome by a modular approach.
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  • 15
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    Circuits, systems and signal processing 6 (1987), S. 125-126 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
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  • 16
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    Circuits, systems and signal processing 6 (1987), S. 123-123 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
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  • 17
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    Circuits, systems and signal processing 6 (1987), S. 107-119 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper considers the problem of estimating the parameters of continuous-time stationary Gaussian processes with rational spectra, from uniformly sampled measurements. The sampled process is shown to be an autoregressive moving-average process, and explicit relationships between the parameters of the continuous-time and the sampled processes are derived. These relationships are then used to derive a lower bound on the variances of biased estimates of the continuous-time parameters, and on the generalized variance of such estimates. It is shown by some examples that the bound on the generalized variance depends on the sampling interval in a nonmonotonic manner. In particular, for each specific set of parameters there exists a sampling interval for which the lower bound is minimized.
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  • 18
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    Circuits, systems and signal processing 6 (1987), S. 127-137 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The identification of concurrency is a critical factor in the high-speed calculation of algorithms. This study considers maps onX, a discrete resolution space. We establish a resolution on the space of linear maps onX which exhibit compatibility with array processing. Our results are extended to the partially ordered resolution space setting. While on-line array processing motivates our study, the results also suggest efficient processing procedures for off-line applications.
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  • 19
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    Circuits, systems and signal processing 6 (1987), S. 139-151 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper describes a method for designing systolic structures with bit-level pipelining. The proposed technique starts with the signal flow graph representation of a given algorithm. A new signal flow graph rule, called the gain transfer rule is introduced to achieve bit-level pipelining. Using this approach, systolic arrays with bit-level pipelining are derived for a general recursive digital filter and a convolver. The proposed technique is quite general and has also been applied to obtain systolic structures for other problems such as vector transformation. In comparison with some previously reported designs, the new architectures are characterized by simpler basic processing cells and faster data throughput rate or smaller chip area requirements.
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  • 20
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    Circuits, systems and signal processing 6 (1987), S. 191-215 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract NON-VON is a highly parallel non-von Neumann supercomputer presently under construction at Columbia University. The basis for NON-VON's significant cost/performance advantage lies in a highly unusual application of VLSI technology to the realization of massive computational parallelism. This paper outlines the manner in which the emerging technology of VLSI circuits is employed in NON-VON to achieve this advantage. Particular emphasis is given to novel aspects of the design, layout, and operation of the NON-VON processing element, eight of which are to be embedded within each integrated circuit chip.
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    Circuits, systems and signal processing 6 (1987), S. 153-174 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Parallel sorting algorithms have been proposed for VLSI implementation. Random defects in the silicon wafer and fabrication errors render processors in the wafer faulty, and may cause these algorithms to fail despite a significant number of nonfaulty processors. This paper presents twofault-tolerant pipelined sorting algorithms that would work on a wafer comprised of faulty and nonfaulty processors. Both the algorithms useO(n) processors and requireO(n) time to sortn elements.
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  • 22
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    Circuits, systems and signal processing 6 (1987), S. 175-189 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract With the advent of wafer-scale integration (WSI), the placement of several “processors” on a single VLSI wafer is becoming a realistic possibility. To avoid the problems of a very low yield inherent in any silicon component of (very) large area, redundant components will be used. In this article we examine three different solutions for reconnecting the nonfaulty processors so that the resulting network is a square grid. We then present results of simulations for various percentages of faulty processors, which show that a small amount of redundancy is the interprocessors paths and a simple back-track based algorithm can produce a resulting grid that, while not necessarily optimal, includes most of the nonfaulty processors.
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    Circuits, systems and signal processing 6 (1987), S. 239-259 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Conventional random access memories are capable only of writing data into and reading data from the storage location corresponding to a given address. The availability of VLSI circuits containing hundreds of thousands of switching devices, however, has recently made practical the implementation of “active” memory chips capable of performing a range of complex operations on their stored data. Such designs are characterized by the extensive intermingling of processing and memory resources within a single chip to achieve the rapid and cost-effective parallel execution of operations relevant to such tasks as image processing, computer graphics, artificial intelligence, and database management. This paper presents a brief survey of a number of active memory chips that have been implemented or proposed, along with a more detailed examination of a particular active memory circuit, the NON-VON 3 primary processing subsystem chip.
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  • 24
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    Circuits, systems and signal processing 6 (1987), S. 217-238 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Serialization of memory access can be a critical bottleneck in shared memory parallel computers. The NYU Ultracomputer, a large-scale MIMD (multiple instruction stream, multiple data stream) shared memory architecture, may be viewed as a column of processors and a column of memory modules connected by a rectangular network of enhanced 2×2 buffered crossbars. These VLSI nodes enable the network to combine multiple requests directed at the same memory location. Such requests include a new coordination primitive, fetch- and-add, which permits task coordination to be achieved in a highly parallel manner. Processing within the network is used to reduce serialization at the memory modules. To avoid large network latency, the VLSI network nodes must be high-performance components. Design tradeoffs between architectural features, asymptotic performance requirements, cycle time, and packaging limitations are complex. This report sketches the Ultracomputer architecture and discusses the issues involved in the design of the VLSI enhanced buffered crossbars which are the key element in reducing serialization.
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    Circuits, systems and signal processing 6 (1987), S. 263-286 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Conventional frequency-domain window-leakage analysis accurately describes the leakage in the short-time Fourier transform only for stationary signals. Leakage in the time-frequency plane from concentrated transient or nonstationary signals can be effectively analyzed by use of a time-frequency window-leakage envelope with rectangular contours. This envelope is obtained from the Wigner distribution of the analysis window, with appropriate corrections for the sidelobe leakage. The time-frequency window-leakage envelope gives insight into the tradeoffs in time-frequency leakage between various windows and allows quick and accurate estimates of the leakage in the short-time Fourier transform. A simple technique for constructing signals with Wigner distributions that are linear transformations of the Wigner distribution of a known signal is developed. With this technique, windows with a variety of time-frequency orientations and leakage behavior can be developed.
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    Circuits, systems and signal processing 6 (1987), S. 287-298 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Fitting a high-order autoregressive model to data is often used to estimate the frequencies of sinusoids from their noisy measurements. This paper analyzes the asymptotic bias of the frequency estimates obtained by this method. It is shown that the bias decreases significantly with increasing model order.
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    Circuits, systems and signal processing 6 (1987), S. 299-314 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We consider the general nonstationary passive systems modeled by linearRCG (G = gyrator) networks. Such networks in general contain conventional topological degeneracies (i.e., capacitor-only loops and/or inductor-only cutsets) as well as the topological degeneracies due to gyrator positioning in the network. Our central result is the explict demonstration that the existence of topological degeneracies does not impose any obstruction to the existence of the explicit state model, which we derive under no restriction on the topology of the network. We also discuss the conditions for the existence of the state model, its unique solutions, and the continuity of the state vector. The nature of the degeneracies inherent in the formulation is highlighted and it is shown that a gyrator-only subnetwork is accountable for algebraic degeneracies. Since the nature and the existence of topological degeneracies does not have anything to do with whether the element characteristics are linear or nonlinear, passive or active, our results are easy to extend to a large class of nonlinear and/or activeRCG networks.
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    Circuits, systems and signal processing 6 (1987), S. 315-334 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper studies the behavior of motions of large-scale (LS) semistate systems (SSS) governed byP i (t)x i =M i (t,x i )x i +f i (t)+h i (t, x), i=1,2,...,s, =(x 1 T x 2 T ⋯x s T )T, where matricesP i (t) are singular. Using Lyapunov's approach and the tools for LS system analysis, a variant of attractivity and ultimate boundedness of appropriate time-variable sets are investigated. The results are based on a specific choice of the aggregate functions. It is assumed that the reduction of equations to a normal form of lower order is inconvenient. The aggregation-decomposition approach used in this paper reduces the dimensionality of an aggregate matrix of the system to the number of its systems. Motion properties of LS systems are deduced from the properties of its isolated subsystems, the character of interconnections, and the conditions imposed on the system aggregate matrix. Sufficient algebraic conditions for the above-mentioned motion properties are developed.
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    Circuits, systems and signal processing 6 (1987), S. 335-345 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper various conditions guaranteeing the ordinary, uniform, and asymptoticA-stability of semistate equations are given. These results are based on and given in terms of the semi-explicit form of a semistate equation.
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    Optical and quantum electronics 10 (1978), S. 83-93 
    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract An analysis of the role of tunnelling rays in pulse propagation in graded-index fibres is presented. Tunnelling ray attenuation is handled by using the generalized parameter technique which allows attenuation coefficients to be dispensed with and relevant families of tunnelling rays to be identified. Results are given for impulse response pulse widths and shapes. Incorporation of tunnelling ray pulse contributions into the formalism for determining optimum refractive-index profiles is presented. For most cases, tunnelling ray effects are small, but significant corrections may be necessary when measurements are made on short lengths of fibre.
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    Optical and quantum electronics 10 (1978), S. 131-138 
    ISSN: 1572-817X
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    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Fifth order non-linear processes produced by a focused beam in metal vapour have been investigated experimentally. Evidence of saturation of fifth harmonic generation by picosecond laser pulses is reported.
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    Optical and quantum electronics 10 (1978), S. 107-117 
    ISSN: 1572-817X
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    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract In this paper power coupling between two multimode optical fibres is investigated. A formalism (based on a geometrical approach) suitable for analysing any coupling configuration between fibres with any index profile and any radiance distribution is presented. The model is applied to obtain coupling losses both in uniformly excited parabolic- and step-index fibres, in the presence of all kinds of coupling errors. Numerical results of extensive utility are shown and useful asymptotic expressions of coupling efficiency, valid for small values of coupling error parameters, are derived together with some practical rules for error combination. Mention is also made of some experimental results we have obtained, which corroborate some previous assertions. The work can supply a useful tool in the design of joints and connectors between single fibres or optical cables.
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    Optical and quantum electronics 10 (1978), S. 153-161 
    ISSN: 1572-817X
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    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract The photon drag and optical rectification response fromn-type gallium phosphide containing 2.4×1016 electrons cm−3 has been studied using laser sources at 10.61 and 2.83μm. By using different contact configurations, the existence of an additional electric field term in the propagation direction has been deduced. This field is shown to arise from the spatial derivatives of the photon drag and optical rectification field components caused by absorption of the radiation. The importance of this effect in detector design is considered.
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    Optical and quantum electronics 10 (1978), S. 171-178 
    ISSN: 1572-817X
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    Notes: Abstract On the basis of the theory of coupled waves the amplitudes of the first-order diffracted waves and the diffraction efficiency is calculated for sequentially superposed phase gratings stored in dielectric reflection holograms. The investigations are restricted to the case of a fixed reference wave during recording and Bragg-angle incidence. By analogy to the transmission volume grating the coupling effects which appear between incident beams and diffracted waves give the possibility of building up beam-couplers and -splitters with certain coupling parameters determined by the recording process. Moreover, reflection gratings allow a favourable combination between coupling and reflecting properties and avoid the diffraction efficiency oscillations that are characteristic of transmission gratings. The performance of the reconstruction process with several waves simultaneously allows the tuning of the intensities of diffracted waves with dependence on amplitude or phase differences between incident beams.
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    Optical and quantum electronics 10 (1978), S. 181-183 
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    Optical and quantum electronics 19 (1987), S. 20-24 
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    Optical and quantum electronics 19 (1987), S. 29-36 
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    Notes: Abstract The stability criteria governing the behaviour of laser oscillators are becoming increasingly well understood, and it is found that for practical applications two types of criteria must usually be distinguished. For lasers in the inhomogeneous limit these two types are essentially equal, and this study explores their behaviour as the degree of inhomogeneous broadening is varied. All lasers exhibit a combination of homogeneous and inhomogeneous line broadening, and the graphical results presented here may be used for predicting or interpreting single-mode instabilities in practical oscillators with arbitrary mixed line broadening.
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    Optical and quantum electronics 19 (1987), S. 73-77 
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    Notes: Abstract The value and sign of the ultrashort pulse (USP) chirp are studied experimentally in the YAG:Nd solid-state laser using different saturable absorbers. The effects of active and passive media as well as USP parameters on the chirp are analysed. The possibility of controlling the USP chirp value by selecting the initial passive locking density is shown.
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    Optical and quantum electronics 19 (1987), S. 79-82 
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    Optical and quantum electronics 19 (1987), S. 93-107 
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    Notes: Abstract Anisotropic diffraction and self-diffraction processes in KNbO3 crystals are investigated utilizing the large elementr 51 of the electro-optic tensor. Geometrical conditions, polarization changes, phase conjugation, phase doubling and the dynamics of hologram recording are studied theoretically and experimentally. Anisotropic diffraction with equal or different frequencies for recording and reading permits the determination of photo- and dark conductivity. Further material properties are estimated on the assumption that the charge transport is governed by diffusion effects.
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    Optical and quantum electronics 19 (1987), S. 141-143 
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    Optical and quantum electronics 19 (1987), S. 169-178 
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    Notes: Abstract Analytic solutions are presented for a simple model describing situations where self-focusing and self-bonding of intense optical beams by thin non-linearly refracting media can occur. Physical optics is employed to study effects arising when a non-linear medium is placed in contact with an aperture stop. The feasibility of constructing an optical power limiter by utilizing either external self-focusing or self-bending is discussed.
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    Optical and quantum electronics 19 (1987), S. 223-229 
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    Notes: Abstract A generalized multiple-prism dispersion theory, applicable to pulse compression schemes in femtosecond dye lasers, is described. The equations can be utilized to determine the dispersive characteristics of any multiple-prism arrangement. Also, the difference in dispersive values resulting in the use of various prism materials, including ZnSe, is compared.
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    Optical and quantum electronics 19 (1987), S. 231-236 
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    Notes: Abstract Drilling of small holes into media containing O-H or C-H bonds with a 2.92μm YAIO3-Er laser is studied. In materials containing O-H bonds strong absorption allows small volumina to be heated with only marginal heat diffusion. Drilling with nearly diffraction-limited lateral resolution is achieved.
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    Optical and quantum electronics 19 (1987), S. 327-349 
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    Notes: Abstract The two-photon absorption cross-sections and excited-state absorption cross-sections of the dyes rhodamine 6G, methylene blue and fuchsin dissolved in methanol, and of the dyes safranine T, 1,3,3,1′,3′,3′-hexamethylindocarbocyanine iodide (HMICI) and 1,3,1′,3′-tetramethyl-2,2′-dioxopyrimidi-6,6′-carbocyanine hydrogen sulphate (PYC) dissolved in hexafluoroisopropanol (HFIP) are determined. The excitation is achieved with picosecond light pulses of a passively mode-locked Nd-glass laser (λL = 1.054μm). The influence of amplified spontaneous emission on the two-photon absorption dynamics is analysed.
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    Optical and quantum electronics 19 (1987), S. 377-384 
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    Notes: Abstract A numerical model of passive mode-locking of dye lasers is presented, which allows the calculation of the steady state pulse parameters without any limitation to pulse energy and duration. The solutions are compared with previous analytical results based on a rate equation treatment (i.e. without considering the phase memory). The pulse evolution and the influence of cavity dumping on the steady state are discussed.
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    Optical and quantum electronics 19 (1987), S. S37 
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    Notes: Abstract Calculations are presented of bistable characteristics occurring on reflection from Fabry-Perot and distributed feedback laser amplifiers. Depending on the drive current and wavelength detuning, a variety of non-linear and bistable behaviour can be expected, including a new form of hysteresis loop not hitherto widely discussed. Switching powers and speeds are calculated for 1.5 μm InGaAsP amplifiers, and some potential applications for these effects are explored.
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    Optical and quantum electronics 19 (1987), S. S61 
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    Notes: Abstract Experiments and theory on optical feedback effects for different delay times in a system consisting of a GaAlAs-DH diode coupled to an external resonator are presented. Two hysteresis types are found, for short and long delay times. In the case of short optical delay the low-power hysteresis branch corresponds to the noise level below the lasing threshold, whereas for a long delay regular or irregular pulsations of considerable mean power occur. On the upper power level c.w. single-mode emission is dominant for both of the hysteresis types. Dynamic losses due to spectral bandwidth changes may explain the different behaviour.
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    Optical and quantum electronics 19 (1987), S. 115-121 
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    Notes: Abstract An inverse variational method for the determination of the normalized depth of a non-homogeneous surface layer in planar optical waveguides is presented. The depth is calculated from the dispersion curve of the lowest TE0 guided mode for knowna priori types of profile of the refraction index coefficientn(x). To test the accuracy of the method, linear, quadratic, step, exponential and Gaussian profiles were tested.
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    Optical and quantum electronics 19 (1987), S. 131-137 
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    Notes: Abstract Analytical expressions for the loss coefficient and the perturbed propagation constant are presented for planar leaky structures which may have media of complex refractive indices. Numerical calculations are reported for the loss variation with parameters such as the buffer refractive index, buffer thickness and superstrate refractive index.
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    Optical and quantum electronics 19 (1987), S. 203-208 
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    Notes: Abstract The theoretical study of the propagation of a bell-shaped light pulse through a saturable absorber having excited-state absorption is presented. Assuming that the pulse-width is longer than the first excited-state lifetime of the absorber, a general expression for the steady-state transmission of the absorber is obtained. It is shown that when the excited-state absorption cross-section is larger than the ground-state absorption cross-section (reverse saturable absorber) the absorber acts as a power limiter. An explicit expression for the change of temporal pulse-width in a single transit through the absorber is obtained, which shows that the pulse-width increases due to the presence of excited-state absorption. An analytical expression is presented for the optimum pulse intensity at which the maximum pulse broadening occurs.
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    Optical and quantum electronics 19 (1987), S. 237-246 
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    Notes: Abstract A theoretical model of pulse propagation through single-mode fibres is presented taking into account the combined action of self-phase modulation, stimulated Raman-scattering and the group velocity mismatch between pump and Stokes pulses. Due to the walk-off of Stokes and laser light an asymmetric pump pulse depletion resulting in considerable reshaping of laser pulses and an asymmetric self-phase modulation spectrum can be calculated and experimentally verified. A maximum laser power is found to be transferable through the fibre.
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    Optical and quantum electronics 19 (1987), S. S47 
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    Notes: Abstract The advantages to be gained from the use of optical processors and interconnects for hybrid electronic/optical signal processing networks are first presented. The physics of nonlinear diode laser amplifiers is then examined in the context of optical thresholding and logic. Specific examples of the use of these devices in simple optical processors and interconnects are proposed. The technology required for realization of arrays of laser amplifiers for the proposed applications is finally discussed.
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    Optical and quantum electronics 19 (1987), S. 289-292 
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    Notes: Abstract The first complete Monte-Carlo model of a surface light-emitting diode is presented in this paper. In the model all important phenomena (including the two-dimensional diffusion of minority carriers before their recombination in the active region and the re-emission of radiation) are taken into account. The influence of various construction parameters on the external quantum efficiency of the homojunction GaAs diode is examined.
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    Optical and quantum electronics 19 (1987), S. 313-317 
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    Notes: Abstract The modulation performance of lead-salt laser diodes suitable for mid-infrared fibre optic communication systems has been investigated. The electron and photon lifetime for a PbCdS laser have been determined to 3.1 ns and 3.3 ps, respectively. Moreover, an experiment using short lengths of fluoride fibres shows the feasibility of GHz fibre optic communication links in the mid-infrared region using lead-salt lasers if the potential ultra-low loss of mid-infrared optical fibres can be realized.
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    Optical and quantum electronics 19 (1987), S. 323-324 
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    Optical and quantum electronics 10 (1978), S. 9-15 
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    Notes: Abstract The optical processor proposed here consists basically of a coherent light source and two liquid crystal light valves, of which the first converts incoherent input patterns into coherent ones; the second operates entirely on coherent signals. It is shown that, if the valve operating point is correctly chosen and its transfer characteristic linearized, negative feedback is implemented around the second valve. The valves perform as active system components, because they modulate the source power by their driving signals. The linear dynamic range, modulation transfer function, and time transient behaviour of the system are briefly studied.
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    Optical and quantum electronics 10 (1978), S. 31-40 
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    Notes: Abstract The propagation of electromagnetic waves along a radially-inhomogeneous single-mode optical fibre with small index difference between core and cladding is studied. As in the case of the step-index fibre the propagation modes are weakly guided and their transverse fields are essentially polarized in one direction. The simple field descriptions and characteristic equation obtained here enable mode spot size and bending loss to be determined and are useful for practical design work of radially-inhomogeneous single-mode optical fibres.
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    Optical and quantum electronics 10 (1978), S. 17-29 
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    Notes: Abstract A two-dimensional real waveguide having a parabolic distribution of dielectric permittivity in the core region, flanked by cladding layers of constant refractive index is proposed as a model for a class of stripe-geometry injection lasers. The model is analysed by a series-solution method and results are given in terms of plots of normalized propagation constant, near-field filling factor, and far-field half-angle, all versus normalized frequency. These results are compared with those for the alternative models of (a) a homogeneous core waveguide, and (b) a medium whose dielectric permittivity varies quadratically with position throughout the whole of space. Apart from the series-solution method which was employed, a survey is included of other techniques available for analysing this waveguide model. These include perturbation theory, variational analysis, an exact solution of the scalar wave equation, and the WKB approximation.
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    Optical and quantum electronics 10 (1978), S. 53-60 
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    Notes: Abstract A ray theory based on the time-independent Fokker-Planck equation and the integration of time along ray trajectories provides analytical expressions for the average arrival time and spread of optical pulses propagating in randomly distorted, multimode, optical fibres. A clear physical picture emerges from the theory. The analytical expressions obtained for 〈t〉 and 〈t 2〉 coincide with the ones obtained by Olshansky from coupled-mode theory. The 〈t 3〉 and 〈t 4〉 moments of the impulse response are also calculated. Simple closed-form formulae are given for the step-index slab. The coupling between all modes is effectively taken into account in our ray theory.
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    Optical and quantum electronics 10 (1978), S. 61-82 
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    Notes: Abstract If light comes from a fixed direction and is to be collected onto an absorbing body which is approximately a point or a straight line, it is well known that a mirror of parabolic profile serves the purpose efficiently. If the light is diffuse, or its direction of incidence variable, or if the absorber is not approximately a point or a straight line, the parabola is less useful. This paper describes various particular collecting problems of this more general sort, together with efficient solutions for them, mainly by means of mirrors. The subject represents a corner of geometric optics little explored until recently, in which the notion of image formation scarcely appears. A unifying principle is the invariance of the ‘Lagrange-Helmholtz’ invariant, which is related to Liouville's theorem of Hamiltonian mechanics, and there is a unifying method of construction of the mirror profiles by means of string.
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    Optical and quantum electronics 10 (1978), S. 119-129 
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    Notes: Abstract Frequency stabilization using ‘mobile’ resonances is compared with that employing frequency modulation. Analogy with radio-frequency experiments leads to an optimization of the error signal. Offsets occuring in each case are discussed and additional offsets due to asymmetry are evaluated.
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    Notes: Abstract The influence of bulk losses and bulk dispersion on the propagation properties of surface waves in a radially inhomogeneous optical fibre is investigated numerically. The fibre is assumed to consist of a homogeneous cladding of either infinite or finite extent and a radially inhomogeneous core of higher permittivity. Bulk losses and dispersion in the core and cladding materials are presented by frequency-dependent complex permittivities. Power series expansions for the electromagnetic field quantities in the core have been used and the attenuation and the phase coefficients for the lower order modes have been calculated numerically. Results are presented for two different permittivity profiles, viz. the parabolic profile and the cubic spline profile, the cladding being of infinite extent in this case. Also, the influence of a finite cladding diameter on the numerical results is discussed.
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    Optical and quantum electronics 10 (1978), S. 139-151 
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    Notes: Abstract A simple model for the description of intracavity measurements of narrow absorption lines, developed in a previous paper [5], is generalized to include the effect of an inhomogeneous, in addition to the homogeneous, contribution to the laser line. Moreover, the standing wave effect which was previously treated only near threshold, is now properly studied well above threshold. It is shown that mode competition increases strongly, in the case of a large number of standing waves falling within the homogeneous laser line width, when one passes from the near threshold region to a high excitation level. The enhancement factor, however, is nearly independent of the intensity. Consideration is also given to the case of running waves.
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    Optical and quantum electronics 10 (1978), S. 163-170 
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    Notes: Abstract A composition-dependent single Sellmeier oscillator model, developed for predicting the refractive index against composition behaviour for the three binary glass systems, SiO2-B2O3, SiO2-P2O5 and SiO2-GeO2, is extended to a double Sellmeier oscillator model. The inclusion of both composition-dependent u.v. and i.r. terms in the Sellmeier equation has enabled the wavelength dispersive properties of optical glass fibres; refractive index, material dispersion and profile dispersion, to be computed for any composition, in any one of these three binary glasses. Theoretical calculations, for particular compositions, of material and profile dispersions are compared with experimental measurements on fibres of the same compositions, fabricated by chemical vapour deposition.
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    Optical and quantum electronics 10 (1978), S. 179-180 
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    Optical and quantum electronics 10 (1978), S. 184-185 
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    Optical and quantum electronics 10 (1978), S. 186-187 
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    Optical and quantum electronics 10 (1978), S. 195-203 
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    Notes: Abstract In the present paper the two-photon fluorescence (TPF) quenching produced by ruby lasers in dye is calculated on the basis of an electronic energy level system adapted for the special conditions of Rhodamine 6G. The model used here takes into consideration the action of competing one-photon processes. It will be shown that the reversed profile of TPF quenching in the overlap region is produced by the superposition of pulses with a time-dependent fluctuating phase as well as with a determinate quadratically time-dependent phase.
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    Optical and quantum electronics 10 (1978), S. 211-221 
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    Notes: Abstract A simplified theory for the performance of a digital optical receiver is developed. The receiver sensitivity is calculated in terms of circuit parameters, received and equalized pulse shapes, photodiode parameters and bit-rate. An excellent agreement between this theory and a more complicated analysis by Personick [4] is demonstrated. It is shown that the receiver sensitivity may be improved by launching reduced-width pulses into the fibre, particularly if fibre bandwidth is a significant limitation. Reduced-width pulses bring benefits in source power consumption and lifetime, and in timing recovery.
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    Optical and quantum electronics 10 (1978), S. 233-242 
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    Notes: Abstract The influence of the spectral width on the modulation behaviour of semiconductor injection lasers has been investigated theoretically on the basis of multimode rate equations. Analytical expressions are derived yielding an effective rate of spontaneous emission for a suitable description of dynamic characteristics of injection lasers. This effective emission rate may drastically exceed the total rate of spontaneous emission into the lasing modes. In the case of large signal modulation it has been shown that a large modulation depth as required for PCM-transmission also yields a considerable spectral broadening.
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    Optical and quantum electronics 10 (1978), S. 270-272 
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    Optical and quantum electronics 10 (1978), S. 273-276 
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    Optical and quantum electronics 10 (1978), S. 279-282 
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    Optical and quantum electronics 10 (1978), S. 283-291 
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    Notes: Abstract A novel method is proposed for selecting a single longitudinal mode in lasers with homogeneously broadened gain medium. Mode selection is achieved by the interaction of the standing cavity wave between the gain medium and a spatially saturated absorber. The theory is treated in detail for various geometric configurations including examples of important laser systems under continuous-wave operation, such as dye lasers.
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    Optical and quantum electronics 10 (1978), S. 323-330 
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    Notes: Abstract Mode coupling coefficients and coupling lengths are determined for multimode fibres with general index distributions in the case where random bending is the main cause of mode coupling. It is shown that the product of the coupling length and the coupling-induced loss is determined only by the shape of the index distribution, and that the coupling length of the focusing fibre is about four times longer than that of the step-index fibre when the coupling-induced losses of both fibres are equal.
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    Optical and quantum electronics 10 (1978), S. 341-351 
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    Notes: Abstract A single expression is presented for the power transmission coefficient of both step- and graded-index fibres, which is uniformly valid for all weakly tunnelling and refracting rays. Its accuracy is demonstrated in a comparison of the corresponding power attenuation coefficient for the step-index fibre with solutions to the electromagnetic boundary value problem.
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    Optical and quantum electronics 10 (1978), S. 361-363 
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    Optical and quantum electronics 10 (1978), S. 367-381 
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    Notes: Abstract The progress of ultra high-speed photography using electron-optical devices is surveyed with special reference to recent work in the USSR. In some applications time resolutions of better than 1 ps are obtainable. The ultimate limits of streak camera techniques are discussed. Finally, systems for X-ray chronography are described.
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    Optical and quantum electronics 10 (1978), S. 353-360 
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    Notes: Abstract A detailed analysis of a symmetric cladded slab waveguide having a parabolic refractive-index profile in the core is carried out. Two techniques, one based on the step-index approximation and the other on the WKB approximation, are used to obtain the dispersion curves and the field plots for both the even and odd TE and TM-modes. An example of the practical relevance of the structure studied is given.
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    Optical and quantum electronics 10 (1978), S. 331-340 
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    Notes: Abstract Through numerical solution of the Schrödinger equation we illustrate the influence of laser modulation upon the excitation of anN-level system irradiated by simultaneous laser pulses. We show that amplitude modulation, applied to a Gaussian statistical distribution of detunings, creates a sideband structure to the excitation-reaction profile which can enhance the excitation over that for monochromatic excitation.
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    Optical and quantum electronics 10 (1978), S. 364-366 
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    Optical and quantum electronics 10 (1978), S. 441-444 
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    Optical and quantum electronics 10 (1978), S. 475-482 
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    Notes: Abstract The characteristics of graded-index optical fibres with power-law core profile and homogeneous cladding have been studied using perturbation theory. Analytical expressions are derived for the cut-off frequency, propagation constant and, in the case of leaky modes, the attenuation coefficient of an arbitrary mode on such a fibre. For the case of monomode fibres, excellent agreement is found with existing theoretical results for the propagation constant of the HE11 mode and cut-off frequency of the TE01 mode.
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    Optical and quantum electronics 10 (1978), S. 459-474 
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    Notes: Abstract The field problem for DH stripe lasers is solved, using a two-dimensional model; the field variation perpendicular to the junction plane is found from a slab model, whereas the transverse variation is calculated using a method applicable to any complex permittivity profile. The origin of transverse variations in the permittivity is described by including current spreading, temperature variations and the carrier profile. The permittivity is used directly and not fitted by a parabola or a step. The fact that a large fraction of the intensity may be propagating in then-andp-layers, is taken into account by introduction of an effective permittivity. The model is applied to a practical example, and the threshold current is found as a function of active-layer thickness and stripe width. It is described how the model can be used both below and above the threshold.
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    Optical and quantum electronics 10 (1978), S. 483-493 
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    Notes: Abstract A technique is described for obtaining deep spatial modulation of laser beams. A phase modulator at one plane in the beam path can yield amplitude modulation at a later plane with little loss in power. Explicit formulae are derived for the field distributions of the modulated beams, and applications are considered.
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    Optical and quantum electronics 19 (1987), S. 59-64 
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    Notes: Abstract The statistical properties of the phase difference between the two interfering partially correlated and partially developed speckle fields were studied experimentally as a function of the intensity correlation coefficient. The gaussian statistics are assumed for the formation of speckle fields in the diffraction region and the correlation coefficient between the two speckle intensities is used to evaluate the phase difference. The standard deviation of the phase difference can be uniquely determined in the fully developed speckle field from the correlation coefficient of the two speckle intensities. However, it was found in the partially developed speckle field that the standard deviation of the phase difference between the two speckle fields cannot be uniquely determined from the correlation coefficient of the two speckle intensities.
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    Optical and quantum electronics 19 (1987), S. 109-113 
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    Notes: Abstract Measurements were made of the random polarization fluctuations of conventional single-mode fibres of five optical fibre cables installed in the city of Berlin (West). The measurements were performed with the aid of a semiconductor laser, the frequency (f) of which was 227.3 THz (wavelength 1320 nm). Such preliminary studies are very important for optically coherent transmission over cables not maintaining the polarizations. The signal intensity fluctuations as the fibre output can be represented both as a function of time and by the related spectral power density.
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    Optical and quantum electronics 19 (1987), S. 139-140 
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    Optical and quantum electronics 19 (1987), S. 123-129 
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    Notes: Abstract Noise measurements on high-transimpedance amplifiers suitable for long-wavelength OTDRs give results higher than is predicted by normal noise models. Consequently, we have developed two useful techniques to measure independently the noise contribution of the JFET and the feedback resistor to the overall amplifier noise. p ]Our results show that the noise of the JFET is in accordance with an accurate theoretical model for such a device. In contrast, the noise from the feedback resistor is much higher than is predicted from the normal resistance-capacitance model for such a component. This increase results from the distributed nature of high-ohmic resistors. Our results indicate that both choice of resistor manufacturer and individual selection of a resistor from a specific manufacturer are warranted. By selecting a low-noise resistor we demonstrate a 500-MΩ transimpedance amplifier with an input equivalent noise current of 13.8 pA. In comparison, the same amplifier with a noisy resistor had an input equivalent noise current of 23 pA. p ]We use our results to show that a reasonable value of the input equivalent noise current of a low-noise photodiode-amplifier combination is 20 pA.
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    Optical and quantum electronics 19 (1987), S. 179-190 
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    Notes: Abstract The behaviour of a cylindrical single-mode optical fibre piezoceramic phase modulator was investigated in the frequency range below resonance. The integral and differential phase modulation efficiencies are reported for different geometrical dimensions of the modulator and for various piezoelectric ceramic materials. p ]The results obtained show that a phase-modulation depth in excess of ≪ can be easily achieved using commercially available piezoelectric cylinders, with driving voltage amplitude as low as 5 V.
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    Optical and quantum electronics 19 (1987), S. 191-200 
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    Notes: Abstract The time-independent diffusion equation that describes an optical power flow in an axially perturbed multimode fibre with a lossy cladding is solved. On this basis the attenuation of plastic-clad silica (PCS) fibres depending on cladding loss, mode coupling due to fibre perturbation, launching conditions and fibre length is investigated by means of computer modelling. This involves not only attenuation properties of PCS fibres by themselves, but also how they are ‘seen’ by the backscattering measurement technique.
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    Optical and quantum electronics 19 (1987), S. 259-264 
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    Notes: Abstract The distortion correction of a CO2-laser radiation wavefront is studied by using forward resonant parametric scattering in gaseous SF6 and retrace after retroreflection from a mirror.
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    Optical and quantum electronics 19 (1987), S. S1 
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    Notes: Abstract Recent progress in the study of both absorptive and dispersive bistability in semiconductor injection lasers is reported. Inhomogeneously excited semiconductor lasers as an absorptive case, and laser diode optical amplifiers and optical injection locking systems of laser diodes as dispersive cases, are described. Applications of bistable semiconductor lasers, such as optical memories, optical regenerative amplifiers and all-optical switching, are also discussed.
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    Optical and quantum electronics 10 (1978), S. 1-8 
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    Notes: Abstract This paper points out that, in impulse response calculations by the method of Gloge and Marcatili, the condition that the equal propagation constant lines and the equal group delay lines coincide is not satisfied except for a power law index profile. The group delay time is derived in this paper, by a perturbation method. The optimum index profile is determined from the measured refractive indices data of several doped silica glasses. It is found that (1) the optimum value of the fourth order coefficient is not so different from the value which minimizes the modal dispersion, except in the short wavelength region, (2) the wavelength which minimizes the total dispersion is near 1.30μm and (3) a B2O3 doped fibre has a small profile dispersion and a small total r.m.s. width.
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    Optical and quantum electronics 10 (1978), S. 41-51 
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    Notes: Abstract A model for the analysis of the bandwidth along an optical transmission line is suggested and tested on the Post Office experimental link. It is found that optical equalization is a real effect that has been observed in practice and that the degree of equalization is affected by only two major factors. These are the degree of mode coupling in the route and the functional relationship between mode delay and mode number. Finally a procedure for the optimization of the bandwidth of a link is suggested and tested.
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    Optical and quantum electronics 10 (1978), S. 503-507 
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    Notes: Abstract The properties of a volume-phase hologram of the reflection type are studied in the case when the reference and object waves are beams of finite width. Numerical results are obtained by considering a sufficiently large number of terms in a previously derived infinite series solution. The results reproduce Kogelnik's one-dimensional theory [1] when the thickness of the hologram is small in comparison with the widths of the beams but otherwise the finiteness of the recording beams leads to significant variations in the amplitude of the reconstructed beam.
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    Optical and quantum electronics 10 (1978), S. 515-520 
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    Notes: Abstract High intensity laser irradiation of a plasma can accelerate the electrons to relativistic velocities. For circularly polarized light the refractive index,n, of the collisionless plasma is then a time-independent function of laser and plasma frequency as well as laser peak intensity; but for linearly polarized light,n (i.e., the wave or phase velocity of the wave in units of the speed of light in vacuum) also becomes a periodic function of time. The deeper the wave penetrates the plasma the higher becomes the multiplicity of values ofn. This means that the laser radiation transforms inside the plasma into several nonlinear waves with periodically changing phase velocities.
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    Optical and quantum electronics 10 (1978), S. 521-526 
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    Notes: Abstract Impulse responses of a wide class of multimode optical fibres with near-optimum index profiles are investigated. The index profile is described by three parameters: the power law exponentα, the magnitude and the width of a dip at the centre of the core. It is found that for overcompensated profiles (α〈α opt) a moderate dip decreases the r.m.s. dispersion. Leaky modes are found to improve the dispersion characteristics for fibres with a dip in the index profile. Impulse response measurements are interpretated to give information about the index profile.
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    Optical and quantum electronics 10 (1978), S. ii 
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