Showing papers in "Bell System Technical Journal in 1964"
TL;DR: In this paper, the field configurations and propagation constants of a hollow circular waveguide made of dielectric material or metal for application as an optical waveguide were determined and the increase of attenuation due to curvature of the axis was also determined.
Abstract: The field configurations and propagation constants of the normal modes are determined for a hollow circular waveguide made of dielectric material or metal for application as an optical waveguide. The increase of attenuation due to curvature of the axis is also determined. The attenuation of each mode is found to be proportional to the square of the free-space wavelength λ and inversely proportional to the cube of the cylinder radius a. For a hollow dielectric waveguide made of glass with v = 1.50, λ = 1μ, and a = 1 mm, an attenuation of 1.85 db/km is predicted for the minimum-loss mode, EH 11 . This loss is doubled for a radius of curvature of the guide axis R ≈, 10 km. Hence, dielectric materials do not seem suitable for use in hollow circular waveguides for long distance optical transmission because of the high loss introduced by even mild curvature of the guide axis. Nevertheless, dielectric materials are shown to be very attractive as guiding media for gaseous amplifiers and oscillators, not only because of the low attenuation but also because the gain per unit length of a dielectric tube containing He-Ne “masing” mixture at the right pressure can be considerably enhanced by reducing the tube diameter. In this application, a small guide radius is desirable, thereby making the curvature of the guide axis not critical. For λ = 0.6328μ and optimum radius a = 0.058 mm, a maximum theoretical gain of 7.6 db/m is predicted. It is shown that the hollow metallic circular waveguide is far less sensitive to curvature of the guide axis. This is due to the comparatively large complex dielectric constant exhibited by metals at optical frequencies. For a wavelength λ = 1μ and a radius a = 0.25 mm, the attenuation for the minimum loss TE 01 mode in an aluminum waveguide is only 1.8 db/km. This loss is doubled for a radius of curvature as short as R ≈ 48 meters. For λ = 3μ and a = 0.6 mm, the attenuation of the TE 01 mode is also 1.8 db/km. The radius of curvature which doubles this loss is approximately 75 meters. The
1,482 citations
TL;DR: In this paper, a generalization of the generalized prolate spheroidal wave functions is presented, and the eigenvalues of both (i) and (ii) are studied in detail.
Abstract: In two earlier papers∗ in this series, the extent to which a square-integrable function and its Fourier transform can be simultaneously concentrated in their respective domains was considered in detail. The present paper generalizes much of that work to functions of many variables. In treating the case of functions of two variables whose Fourier transforms vanish outside a circle in the two-dimensional frequency plane, we are led to consider the integral equation $\gamma \varphi(x) = \int_{0}^{1} J_{N}(cxy) \sqrt{cxy} \varohi(y) dy. \qquad \eqno{\hbox{(i)}}$ It is shown that the solutions are also the bounded eigenfunctions of the differential equation $(1-x^{2}){d^{2}\varphi \over dx^{2}} - 2x {d \varphhi \over dx} +\left(x-c^{2}x^{2} + {{1 \over 4} - N^{2} \over x^{2}}\right) \varphi = 0. \qquad \eqno{\hbox{(ii)}}$ a generalization of the equation for the prolate spheroidal wave functions. The functions ϕ (called “generalized prolate spheroidal functions”) and the eigenvalues of both (i) and (ii) are studied in detail here, and both analytic and numerical results are presented. Other results include a general perturbation scheme for differential equations and the reduction to two dimensions of the case of functions of D > 2 variables restricted in frequency to the D sphere.
755 citations
TL;DR: By using a large number of stages, these designs achieve a far greater combinatorial efficiency than has been attained heretofore.
Abstract: A rearrangeable connecting network is one whose permitted states realize every assignment of inlets to outlets — that is, one in which it is possible to rearrange existing calls so as to put in any new call. In the effort to provide adequate telephone service with efficient networks it is of interest to be able to select rearrangeable networks (from suitable classes) having a minimum number of crosspoints. This problem is fully resolved for the class of connecting networks built of stages of identical square switches arranged symmetrically around a center stage: roughly, the optimal network should have as many stages as possible, with switches that are as small as possible, the largest switches being in the center stage; the cost (in crosspoints per inlet) of an optimal network of N inlets and N outlets is nearly twice the sum of the prime divisors of N, while the number of its stages is 2×−1, where x is the number of prime divisors of N, in each case counted according to their multiplicity. By using a large number of stages, these designs achieve a far greater combinatorial efficiency than has been attained heretofore.
315 citations
TL;DR: In this article, conditions under which the response to an arbitrary set of initial conditions approaches zero (i.e., the zero vector) as t → ∞ for all initial conditions were derived.
Abstract: Let e N denote the set of N-vector-valued functions of t defined on [0, ∞) such that for any real positive number y, the square of the modulus of each component of any element is integrable on [0, y], and let L 2N (0, ∞) denote the subset of e N with the property that the square of the modulus of each component of any element is integrable on [0, ∞). In the study of nonlinear physical systems, attention is frequently focused on the properties of one of the following two types of functional equations $\eqalignno{g &= f + KQf \cr g &= Kf + Qf}$ in which K and Q are causal operators, with K linear and Q nonlinear, g e e N , and f is a solution belonging to e N . Typically, f represents the system response and g takes into account both the independent energy sources and the initial conditions at t = 0. It is often important to determine conditions under which a physical system governed by one of the above equations is stable in the sense that the response to an arbitrary set of initial conditions approaches zero (i.e., the zero vector) as t → ∞. In a great many cases of this type, g belongs to L 2N (0, ∞) and approaches zero as t → ∞ for all initial conditions, and, in addition, it is possible to show that if f e L 2N (0, ∞), then f(t) → 0 as t → ∞. In this paper we attack the stability problem by deriving conditions under which g e L 2N (0, ∞) and f e e N imply that f e L 2N (0, ∞). From an engineering viewpoint, the assumption that f e L N is almost invariably a trivial restriction. As a specific application of the results, we consider a nonlinear integral equation that governs the behavior of a general control system containing linear time-invariant elements and an arbitrary finite number of time-varying nonlinear elements. Conditions are presented under which every solution of this equation belonging to e N in fact belongs to L 2N (0, ∞) and approaches zero as t → ∞.
238 citations
TL;DR: In this paper, it was proved that a condition similar to the Nyquist criterion guarantees the stability of a large class of feedback systems containing a single time-varying nonlinear element.
Abstract: It is proved that a condition similar to the Nyquist criterion guarantees the stability (in an important sense) of a large class of feedback systems containing a single time-varying nonlinear element. In the case of principal interest, the condition is satisfied if the locus of a certain complex-valued function (a) is bounded away from a particular disk located in the complex plane, and (b) does not encircle the disk.
225 citations
TL;DR: Permutation decoding as a n eans of error control is evaluated for the binary symmetric channel and for the switched telephone network as represented by experimental data and is found to be extremely effective on the binary symmetry channel and of very doubtful value on the present telephone network.
Abstract: A symmetry of a systematic code is a permutation of bit positions in each code word (the same permutation is applied to all code words) which preserves the code as a whole. Permutation decoding makes use of these symmetries to build up a decoding algorithm for the code. It is difficult to find an appropriate set of symmetries for a code picked at random. For cyclic codes the problem is somewhat easier, and for some special cyclic codes it is solved completely in this paper. For these codes, at least, it is evident that permutation decoding is easy to implement and inexpensive compared with other decoding schemes. Permutation decoding as a n eans of error control is evaluated for the binary symmetric channel and for the switched telephone network as represented by experimental data. It is found to be extremely effective on the binary symmetric channel and of very doubtful value on the present telephone network.
160 citations
TL;DR: The results of measurements at moderate to high magnetic fields on a large number of nonmagnetic ion substituted yttrium iron garnets suggest that intrasublattice interactions play an important role in determining their spontaneous magnetizations and Curie temperatures as mentioned in this paper.
Abstract: The results of measurements at moderate to high magnetic fields on a large number of nonmagnetic ion substituted yttrium iron garnets suggest that intrasublattice interactions play an important role in determining their spontaneous magnetizations and Curie temperatures. It is shown that the system {Y 3−x Ca x }[Fe 2 ](Fe 3−x Si x )O 12 is continuously related to the system {Y 3−x Ca x }[Zr x Fe 2−x ](Fe 3 )O 12 or {Y 3 }[Sc x Fe 2−x ](Fe 3 )O 12 . It is concluded that in these systems the tetrahedral-tetrahedral (d-d) antiferromagnetic interactions are stronger than octahedral-octahedral (a-a) antiferromagnetic interactions. The changes in magnetic structure from an ideal ferrimagnet, yttrium iron garnet, to an end-member in which there are at least short-range antiferromagnetic interactions (i.e., in {Ca 3 }[Fe 2 ](Si 3 )O 12 or a hypothetical {YCa 2 }[Zr 2 ](Fe 3 )O 12 ) should bear an analogy to the crystal chemical changes. It is therefore proposed that when substitution is made exclusively in one sublattice, the moments of the Fe3+ ions in that sublattice remain parallel (as in the Yafet-Kittel theory), while the weakened average a-d interactions and the intrasublattice interactions lead to random canting of the Fe3+ ion moments of the other. This tendency occurs as soon as substitution begins. On continued substitution, a point is reached beyond which canting increases much more rapidly with increasing substitution. In this region, the intrasublattice interactions dominate the a-d interactions, but it is probable that the canting continues to be random.
151 citations
TL;DR: In this article, the focusing power of a positive lens is described by the difference in phase angle between a ray on the tube axis and a ray at arbitrary distances from this axis and also as the second derivative of the phase angle on the axis of the tube.
Abstract: If a cool gas is blown into a hot tube, it acts as a positive lens which will focus a light beam passing through the tube. Using a theory presented in Ref. 3, we give curves which show the temperature distribution in the tube as a function of the distance from the tube axis and also as a function of the distance along the axis. The focusing power of the lens is described by the difference in phase angle between a ray on the tube axis minus a ray at arbitrary distances from this axis and also as the second derivative of the phase angle on the axis of the tube. The phase curves, as a function of distance r from the tube axis, follow very closely an r2 dependence. Expressions are given for the focal length of the lens. The power consumption of the lens is discussed, and a figure of merit is defined as focusing power per watt. The gas used for this lens should be selected such that (n − 1)/k is as large as possible (where n is the index of refraction, k the heat conductivity of the gas). Using CO 2 and a ¼-inch ID tube 5 inches long heated 20°C above the incoming gas, a focal length of 5 feet with a power consumption of 0.325 watt is calculated; the focal length is inversely proportional to power consumption within certain limits.
103 citations
TL;DR: A scheme for duplicating control equipment and a description of circuit and program facilities for taking advantage of this duplication to detect, to automatically recover from, and to analyze troubles are described.
Abstract: The No. 1 electronic switching system has a much higher concentration of control than previous telephone systems. This makes the task of providing continuous telephone service more challenging than ever. It is important that troubles be detected almost instantaneously, before many calls are affected. The main subjects of this article are (1) a scheme for duplicating control equipment and (2) a description of circuit and program facilities for taking advantage of this duplication to detect, to automatically recover from, and to analyze troubles.
93 citations
TL;DR: In this paper, a natural algebraic and combinatorial approach to the study of rearrangeable networks is described, with attention centered principally on two-sided networks built of stages of square crossbar switches, each stage having N inlets and N outlets.
Abstract: In the interest of providing good telephone service with efficient connecting networks, it is desirable to have at hand a knowledge of some of the combinatorial properties of such networks One of these properties is rearrangeability: a connecting network is rearrangeable if its permitted states realize every assignment of inlets to outlets, or alternatively, if given any state x of the network, any inlet idle in x, and any outlet idle in x, there is a way of assigning new routes (if necessary) to the calls in progress in x so that the idle inlet can be connected to the idle outlet A natural algebraic and combinatorial approach to the study of rearrangeable networks is described, with attention centered principally on two-sided networks built of stages of square crossbar switches, each stage having N inlets and N outlets The approach is based in part on the elementary theory of permutation groups The principal problem posed (and partly answered) is this: What connecting networks built of stages are rearrangeable? Sufficient conditions, including all previously known results, are formulated and exemplified
84 citations
TL;DR: The space groups for these structures have been put into a form convenient for use, as have the other two sets of space groups as mentioned in this paper, and the tables are available on request from the Circulation Manager, Bell System Technical Journal, Bell Telephone Laboratories, Incorporated, 463 West Street, New York 14, N. Y.
Abstract: The law-energy electron diffraction work of L. H. Germer, J. J. Lander, A. U. MacRae, J. Morrison and others is resulting in new information about surface structures. These three-dimensional structures have periodicity only in two dimensions. The 230 triperiodic space groups are not applicable to the solution of these structures. The 17 strictly two-dimensional groups do not admit the existence of a third dimension and may therefore not be appropriate for these structures which are not strictly planar. The useful space groups for these structures are the 80 diperiodic groups in three dimensions. Nowhere in the literature have these been put into a form convenient for use, as have the other two sets of space groups. This has now been done and the tables are available on request from the Circulation Manager, Bell System Technical Journal, Bell Telephone Laboratories, Incorporated, 463 West Street, New York 14, N. Y. Sample tables are given in this paper.
TL;DR: A number of schemes in which gases can be made to guide a light beam have recently been in vestigated as mentioned in this paper, where the major problem is to avoid losses in transmission systems for light.
Abstract: Development of systems for long-distance communications using laser beams is of considerable current interest. A major problem is to avoid losses in transmission systems for light. Losses by scattering and absorption in solid transmission schemes arc likely to be large. By using gases as the media that guide the light beam, such losses should be minimized. A number of schemes in which gases can be made to guide a light beam have recently been in vestigated.
TL;DR: In this paper, the authors extended the transmission line matrix formalism for describing the transfer properties of microwave networks to the electromagnetic fields associated with optical masers, and the spontaneous emission noise of the optical maser was examined and shown to be amenable to a thermal description.
Abstract: The transmission line matrix formalism so useful for describing the transfer properties of microwave networks is extended to the electromagnetic fields associated with optical masers. The spontaneous emission noise of the optical maser is examined and shown to be amenable to a thermal description. Taking the point of view, well accepted at microwave frequencies, that a weakly nonlinear oscillator is a saturated amplifier of noise, the power and linewidth of the noise radiation emitted by the optical maser is calculated using the transmission line formalism. The significant parameters for any optical maser are shown to be the frequency, the single-pass gain of the maser medium, the effective mirror reflectivity and the population ratio. The pre-oscillation characteristics of the maser are examined and the reason for the extremely sharp oscillation threshold of the gas masers is discussed. Some observations concerning semiconductor optical masers are also made.
TL;DR: In this article, a model is presented which permits a theoretical calculation of the power spectrum of these fluctuations and satisfactorily predicts the features of spectra computed from experimental fading data except for an observed rise at low frequencies.
Abstract: Fluctuations in received signal amplitude occur during mobile communications because of the motion of the mobile station through the spatial standing-wave pattern resulting from the interaction of direct and reflected signals. A model is presented which permits a theoretical calculation of the power spectrum of these fluctuations and satisfactorily predicts the features of spectra computed from experimental fading data except for an observed rise at low frequencies. The model is based on the geometry of the reflections from nearby randomly placed vertical plane reflectors. Vertical polarization is assumed. Both the standing-wave pattern and the Doppler shift view of fading are used to obtain nearly identical results. The detailed shape and in particular the sharp cutoff frequency of the spectrum are shown to depend crucially on the angle a between the direction of vehicle motion and the direction to the fixed station. Detailed comparisons are made of theoretical spectra with experimental spectra representing a range of the angle α. The collection, digitization, calibration, plotting, and digital processing to obtain power spectra of actual recorded fading waveforms are described.
TL;DR: In this paper, a bilinear z transformation is used to preserve the essential amplitude characteristics of the continuous filter over the frequency range between zero and one-half the sampling frequency.
Abstract: A design procedure is presented for readily obtaining sampled-data filter representations of continuous filters. The procedure utilizes the bilinear z transformation and preserves the essential amplitude characteristics of the continuous filter over the frequency range between zero and one-half the sampling frequency. It is shown that the procedure can yield meaningful sampled-data filter designs for many of those filters where the standard z transform cannot be used directly.
TL;DR: In this paper, a periodic sequence of lens-like focusers separated by gaps is solved for a periodic series of lenses-like focussers, and the field configurations of the modes and their propagation constants, as well as the transmission and cutoff bands, are calculated.
Abstract: Maxwell's equations are solved for a periodic sequence of lens-like focusers separated by gaps. Each focuser consists of an arbitrarily thick slab of dielectric in which the dielectric constant tapers off radially with different quadratic laws in two perpendicular directions. Since there are no limitations on the thickness of the slabs, the solutions cover the complete gamut from a sequence of infinitely thin lenses with astigmatism to a continuous dielectric waveguide, and from spherical to cylindrical lenses. The field configurations of the modes and their propagation constants, as well as the transmission and cutoff bands, are calculated. Any arbitrary input field distribution can then be expanded in terms of the normal modes, and the expansion determines the field everywhere. Formulas derived for sequences of weak lenses turn out to give very good results even for lenses whose thickness and separation are equal to the focal length.
TL;DR: In this article, the rate equations of Statz and De Mars giving the time development of the inversion and photon number in a maser or laser are discussed analytically with the aid of a mechanical analogy in which a particle moves in a potential well under the influence of a viscous damping force.
Abstract: The rate equations of Statz and De Mars giving the time development of the inversion and photon number in a maser or laser are discussed analytically with the aid of a mechanical analogy in which a particle moves in a potential well under the influence of a viscous damping force. The coordinate of this particle is analogous to the logarithm of the light output of the laser, and the amplitude, period, and damping of the motion can be directly related to the parameters of the rate equations. Simple analytic approximations are developed for all of the quantities of experimental interest in the spiking pattern of a laser. Four relationships are given, which do not contain any of the rate equation parameters, whereby a spike pattern can be tested to determine if it is consistent with the usual rate equations. Systematic procedures are described for extracting all of the information contained in spike patterns.
TL;DR: The frequency, field patterns, and losses of the resonant modes of spherical mirror optical resonators can be obtained to good accuracy as the solutions of the integral equations of Fresnel diffraction theory as mentioned in this paper.
Abstract: The frequencies, field patterns, and losses of the resonant modes of spherical mirror optical resonators can be obtained to good accuracy as the solutions of the integral equations of Fresnel diffraction theory. By a simple transformation of the variables and parameters of the integral equations, we have found certain families of resonators which have the same diffraction loss at each mirror, and whose field patterns are scaled versions of each other. In the case of the infinite strip resonator, this reduces from five to three the number of parameters necessary to specify the losses and mode patterns.
TL;DR: The new hardware and software designs required to adapt a No. 1 ESS to a store and forward system are outlined with emphasis on the techniques used to get large system capacity, continuous reliable operation, and flexible service features.
Abstract: This paper is an introduction to the No. 1 electronic switching system, a new general-purpose switching system developed for use in the Bell System. Organization and objectives of the system are outlined to provide a background for the detailed technical papers which follow.
TL;DR: In this paper, a pair of coupled nonlinear differential equations is given which describes the reduction of gain in a traveling-wave maser due to high-power signals, and the integral in closed form is obtained for two cases of interest.
Abstract: A pair of coupled nonlinear differential equations is given which describes the reduction of gain in a traveling-wave maser due to high-power signals. Integrals in closed form are obtained for two cases of interest. The first applies to pulsed optical amplifiers where no replacement of stored energy occurs during a signal pulse. The result is a pulse sharpening phenomenon; i.e., the leading edge of an input pulse is amplified by the original full gain while later parts of the signal experience reduced gain. The second case is that of steady-state gain saturation in the presence of a continuous pumping process. The results describe the observed gain compression of microwave ruby traveling-wave masers.
TL;DR: In this article, a set of studies has been undertaken to develop guidelines for the design and operation of communications networks with automatic alternate routing, and compared the engineered costs and overload capability of networks using several alternate routing configurations, and employing a number of different operating and control procedures.
Abstract: A set of studies has been undertaken to develop guidelines for the design and operation of communications networks with automatic alternate routing. Comparisons are made of engineered costs and overload capability of networks using several alternate routing configurations, and employing a number of different operating and control procedures. The traffic model selected consists of a 34-node network abstracted from the U.S. telephone toll network, with basic load levels obtained from field data. The overload evaluations were made using a simulation program prepared for the IBM 7090 computer.
TL;DR: In this article, it was shown that Au-n-type GaAs rectifying contacts are majority carrier rectifiers of the Schottky type and that these diodes may be characterized by a Richardson constant of 20-60 amp/cm2 deg2 and barrier heights of 1.03, 0.97 and 0.91 volts.
Abstract: Evidence is presented to show that Au-n-type GaAs rectifying contacts are majority carrier rectifiers of the Schottky type. These diodes may be characterized by a Richardson constant of 20–60 amp/cm2 deg2 and barrier heights of 1.03, 0.97 and 0.91 volts, corresponding to the 〈111〉, $\langel \overline{111}\rangle)$ and 〈110〉 orientations of GaAs substrate. GaAs Schottky barrier varactor diodes constructed on epitaxial films may be designed to yield a high cutoff frequency. Performance calculations in a practical case yield a “dynamic quality factor” of 50 at 6 gc under favorable conditions. A “dynamic quality factor” of about 20 at 6 gc should be obtainable with present fabrication technology.
TL;DR: In this paper, a digital method of deflecting a light beam using n optical modulators and n uniaxial crystals to provide 2n positions of the beam is described.
Abstract: A digital method of deflecting a light beam using n optical modulators and n uniaxial crystals to provide 2n positions of the beam is described. The input-output relations for one special configuration are derived. Optical problems and limitations are investigated and, in particular, it is found that the upper limit to the density of positions is about 106/sq. in. Presently available modulators are considered, and it is found that a KDP modulator has a power limitation above 1 mc operation for a total number of positions of about 70,000. Finally, the applications of the method as a semipermanent memory, a PCM decoder, and a digital delay line are briefly considered.
TL;DR: The optimum decision scheme obtained consists in comparing, with a predetermined threshold k, a quadratic form in the received waveform x(t), which may be regarded as a generalization of the “correlation detection” in the case of binary sure signals in noise.
Abstract: The problem of optimum reception of binary Gaussian signals is to specify, in terms of the received waveform, a scheme for deciding between two alternative covariance functions with minimum error probability. Although a considerable literature already exists on the problem, an optimum decision scheme has yet to appear which is both mathematically rigorous and convenient for physical application. In the context of a general treatment of the problem, this article presents such a solution. The optimum decision scheme obtained consists in comparing, with a predetermined threshold k, a quadratic form (of function space) in the received waveform x(t), namely, ${\eqlignno{\rm choose} \quad r_{0}(s, t) \quad if \int\int x(s)h(s, t)x(t) \quad ds dt \quad \lt; k, \cr {\rm choose} \quad r_{1}(st) \quad if \int\int x(s)h(s, t)x(t) \quad ds dt \geqq k},$ where r 0 (s, t) and r 1 (s, t) are the covariance functions while h(s, t) is given as a solution of the integral equation, $\int\int r_{0}(s, u)h(u, v)r_{1}(v, t) du dv = r_{1}(s, t) - r_{0}(s, t).$ This may be regarded as a generalization of the “correlation detection” in the case of binary sure signals in noise. Section I defines the problem, reviews the literature, and, together with certain pertinent remarks, summarizes principal results. A detailed mathematical treatment follows in Section II and the Appendices.
TL;DR: The basic program structure of the no. 1 ESS must perform switching functions reliably and promptly, its design must be economical of memory and execution time, and must accommodate office growth easily.
Abstract: The stored program of the no. 1 ESS must perform switching functions reliably and promptly. Its design must be economical of memory and execution time, and must accommodate office growth easily. The program is organized so that an interrupt system initiates the input-output programs that must be performed to accurate timing tolerances. The data collected by these input-output programs are passed to the call processing programs which decide what course of action the calls shall follow. The program also assigns an appropriate share of central control time for maintenance and administrative functions. The program is generic in the sense that specific quantities which change from office to office are looked up in tables and are not embedded in the program itself. This article describes the basic program structure and illustrates it with some typical programs.
TL;DR: In this article, a combination of spectrum analysis and frequency detection is described which has some of the theoretical advantages of both, and the spectrum analysis circuit forms are compared with demodulators using frequency detectors, with and without FM feedback, in regard to theoretical noise sensitivities.
Abstract: Some theoretical aspects of the demodulation of wideband, low-power FM signals are discussed. It is assumed that a band-limited, continuous, analog signal is supplied to the modulator and is recovered to a fidelity suitable for television, telephone, or carrier telephone. Much of the paper assumes that the baseband signal is sampled and clamped before it is applied to the frequency modulator. The combination has been called PAM-FM and is characterized by a piecewise constant transmitted frequency. PAM-FM can be demodulated by spectrum analysis means not suitable for continuously varying frequencies. It is shown that a spectrum generator can be derived from the techniques of radar pulse compression, and is equivalent to an infinite set of correlators or matched filters plus means for scanning their terminals. The spectrum analysis circuit forms are compared with demodulators using frequency detectors, with and without FM feedback, in regard to theoretical noise sensitivities. The theoretical sensitivities are quite similar for spectrum analysis and FMFB under conditions assumed. The comparisons disclose that frequency detectors (followed by filters) enjoy a disguised but efficient use of a differential phase coherence which is a characteristic of FM signals. A combination of spectrum analysis and frequency detection is described which has some of the theoretical advantages of both.
TL;DR: In this article, a broad class of nonlinear control systems containing a single memoryless nonlinear element is studied, and conditions under which there exists a unique periodic response, with a given period, to an arbitrary periodic input with the same period, and an upper bound on the mean square error incurred by applying the describing-function technique.
Abstract: In this paper we study a broad class of nonlinear control systems containing a single memoryless nonlinear element. We present conditions under which there exists a unique periodic response, with a given period, to an arbitrary periodic input with the same period, and we derive an upper bound on the mean-square error incurred by applying the describing-function technique. The expression for the error reflects the intuitive engineering arguments that are often employed to justify the use of the describing-function method. Conditions are also presented under which subharmonic response components and self-sustained oscillations cannot occur.
TL;DR: In this paper, the authors describe an example of another class of gas lenses, which utilizes the difference of specific refractive index between different gases to achieve focusing in a region where there is a variation in relative concentration of different gases.
Abstract: Because of the current interest in gas lenses for possibe use in longdistance laser beam transmission, it seems worthwhile to report on the successful operation of an example of another class of gas lenses. This class of lenses utilizes the difference of specific refractive index of different gases to achieve focusing in a region where there is a variation in relative concentration of different gases. In the device to be described, two gases flow together continuously from opposing tubes into a mixing chamber. The chamber is designed so that t he effective interface where the gases meet is an axially symmetric curved surface, which acts as a lens for light passing down the axis of t he opposing tubes.
TL;DR: The ALPAK system has been programmed within the BE-SYS-4 monitor system on the IBM 7090 computer, but the language and concepts are machine-independent, and several practical applications are described.
Abstract: This is the second in a series of papers describing the ALPAK system for nonnumerical algebra on a digital computer. The first paper, Ref. 1, is concerned with polynomials in several variables and truncated power series with polynomial coefficients. This paper is concerned with rational functions of several variables and truncated power series with rational-function coefficients. A third paper, Ref. 3, will discuss systems of linear equations with rational-function coefficients. The ALPAK system has been programmed within the BE-SYS-4 monitor system on the IBM 7090 computer, but the language and concepts are machine-independent. Several practical applications are described in Ref. 1. This paper is divided into five sections. The first deals with basic concepts, the second defines canonical forms, and the third describes ALPAK's greatest common divisor algorithm. These three sections do not presuppose any knowledge of computers or computer programming. Section IV describes the use and the implementation of the algebraic operations relating to rational functions of several variables and truncated power series with rational-function coefficients. The reader of this section is assumed to be familiar with the basic concepts of computer programming and with Ref. 1. Finally, Section V discusses very briefly some of our plans and hopes for the future.
TL;DR: In this paper, the authors present a simple matching formulae for dcoherent laser light that takes full account of the laws that govern optical mides, and describe a matching experiment for illustration.
Abstract: In experiments with dcoherent laser light it is frequently necessary to transform a given Gaussian beam1,2 into a Gaussian beam with certain desired parameters. It is required, for example, to transform the light beam emerging from a laser oscillating in a fundamental mode in order to provide for optimum injection into a light transmission line2,3 (consisting of a sequence of lenses), or for optimum coupling into a spherical mirror interferometer.4 In these cases one has to “mathc” the incoming beam to the natural mode of the system in question. Lenses inserted in the beam perform the matching transformation. The design of a matching configuration has to take full account of the laws1,2,3 that govern optical mides. This leads to a somewhat complex analysis.5 The results, however, are quite simple matching formulae which are presented in this brief. A matching experiment is described for illustration.