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In recent years the idea of coupling between incoherent beams has attracted a great deal of attention. A number of photorefractive conjugators and oscillators have been proposed1,2 with the doublephase-conjugate mirror (DPCM)3 and its modified version, the double-colour-pumped-oscillator (DCPO)4, as one of the most popular ones. In both of these configurations, two new beams are simultaneously self-generated due to the interaction of the two mutually incoherent input beams.

Magneto-inductive waveguides are linear periodic structures consisting of regular arrangements of L-C resonators coupled together by mutual inductances M. Magneto-inductive cable is a low-loss flexible variant, based on overlapping inductors and parallel plate capacitors formed by double-sided patterning of copper-clad polyimide. The properties of cable arrays formed from a set of parallel magneto-inductive lines are investigated. Numerical solutions are provided for typical arrangements. Analytic methods are introduced for estimating the coupling between elements in neighboring cables and the frequency dependence of cross-talk. Theoretical confirmation is provided by experimental results for cables operating at ≈100 MHz. Strategies for reducing cross-talk using alternative element designs that achieve low mutual inductance by cancellation of induced currents are explored.

Ten children in the age range of 3 to 17 years with moderate to severe aortic valve stenosis (gradients of 55 to 109 mm Hg) underwent cardiac operations. At the time of the operation, during bypass, balloon dilation of the stenotic valve was performed and the results were visually assessed by the surgeon. Of the 10 consecutive cases, only three showed dilation results that were comparable to what seems optimal from a surgical point of view. The adverse effects in the remaining seven patients and the corrective measures taken were as follows: (1) too extensive a rupture requiring stabilizing sutures in one patient; (2) too short a rupture, requiring additional commissurotomy in three patients; (3) rupture into the valve leaflet, requiring valve suture and corrective comissurotomy in another three patients. This last, rather serious complication occurred in patients having functionally bicuspid valves with slightly thickened free valve edges, whereas valves with severely thickened edges ruptured in the commissure line but often to an insufficient degree. Because of the high incidence of suboptimal separation of the stenotic aortic valves with balloon dilation, we recommend that further evaluation of long-term results and identification of unsuitable cases should precede widespread use of the technique.

The dispersion characteristics of space charge waves propagating in a photoconducting material are derived. It is shown that both forward and backward waves can propagate depending on the materials parameters. Special cases include the low attenuation space charge waves used in the past for interaction with acoustic waves. The interaction with optical waves is investigated when the photoconductor is also an electro-optic (i.e., photorefractive) material. It is shown that power can be transferred from the optical waves to the space charge waves and vice versa. Experiments conducted in the past on two-beam interactions are reinterpreted in terms of new types of interactions that involve space charge waves. New experiments for the excitation and detection of space charge waves are proposed.

Energy transfer between waves in photorefractive media occurs generally in one direction only, with a coupling dependent on the imaginary part of the modulated space charge field. Ringhofer and Solymar1 have described a mechanism in which energy is transferred inward from two pump beams and in which the coupling is partially dependent on the real part of the space charge field. This talk explores qualitative features of this mechanism such as the symmetry between the internal companion orders and the two pump beams and the required frequency detuning among the four beams. Experimental studies in which one pump beam was frequency shifted off a moving mirror allowed experimental verification of this mechanism in ring and linear resonators.

It has been shown experimentally1 that a subharmonic beam may appear spontaneously between two pump beams without detuning either of the beams when a field varying sinusoidally or in the form of a square wave is applied across the crystal. That work has now been extended to cover the rise of the subharmonics as a function of time and their dependence under stationary conditions on the ratio between the pump intensities. The experiments were done on photorefractive bismuth silicate crystals. A simple theory is found to describe well the repetition frequency at which the subharmonics appear.

We present a theoretical model that predicts the color of images in a color hologram recorded by three laser lights and replayed in white light. Effects of bandwidth and replay scatter noise are included in the model. The model is used to generate spectral power distributions, which are transformed into points on the 1976 Commission Internationale de l'Eclairage (CIE) diagram. Eight color-display holograms were recorded1 at the following combinations of wavelengths: 458, 488 nm (blue), 514,529 nm (green), 633,647 nm (red). The object used was an array of Munsell color chips, including the eight recommended by the CIE.2 The holograms were reconstructed with a standard white-light source and were measured with a telespectrophotometer. Measured spectral power distributions of each Munsell-chip image were used to calculate points on the CIE diagram.

In 1988, Mallick et al.[1] found self-generated subharmonics in Bi12SiO20 (BSO). They used two coherent almost linear pump beams (wave vectors k→ p and k→ p ′ , see Fig. 1) with grating vector K→ and frequency detuning Ω, impinging on a 1 cm thick BSO crystal. For a certain frequency detuning, they observed a third beam in the middle between the two pump beams with intensity as high as 40% of the pump beam intensity. The length of the grating vector for the grating written by one of the pump beams and the third beam was approximately K/2 and therefore they called the new beam a K/2-subharmonic.

When a Bi12SiO20 crystal is used for two-wave photorefractive amplification and a constant voltage is applied to the crystal, the gain may be considerably enhanced by detuning one of the incident beams to produce a moving grating. Simple theory shows that the gain versus detuning curve has a single maximum that depends on the total incident intensity. When crystals with lengths greater than a few millimeters are used, one must take into account the effects of optical activity and absorption, the anisotropic nature of the photorefractive effect in Bi12SiO20 causes alternating regions of high and low coupling constants as the plane of polarization of the two beams rotates through the crystal under the influence of optical activity. In the particular example where the crystal length is such that there are two regions of high coupling constant at the beginning and the end of the crystal, the average intensities within the two regions will be different because of absorption, and the optimum detuning frequencies for the two regions will also be different. This results in a double maximum in the detuning curve. Theoretical predictions of multiple peaks have been experimentally confirmed.

Two-wave mixing in photorefractive media has been studied theoretically and experimentally by a number of researchers, and a wide range of prospective applications of the effect have been demonstrated or proposed. Recently, Hamel de Montchenault et al., have demonstrated the amplification of high frequency amplitude modulated signals via two-wave mixing in BSO.1,2 In this paper we develop a theoretical framework for the analysis of two-wave mixing with an amplitude modulated signal beam. Preliminary experimental confirmation of the theory is provided.

Diffraction efficiencies of ∼ 70% have been reported for planar gratings in silver halide emulsion. The main obstacle in increasing the efficiency is the granular structure of the recording material which causes scattering of the input light both at recording and at reconstruction. This study concentrates on the effect of noise gratings recorded when the incident beam interferes with its own scattered radiation. The experimental evaluation is divided into two parts. Firstly, one single beam is used for recording a holographic plate, and the transmitted intensity of the reconstructing beam illuminating the developed hologram is measured as a function of incident angle and wavelength. Dips in the measured intensity are associated with the reconstruction of a strong scattered beam. Secondly, a main grating is recorded by two incident beams, which also interfere with the field scattered by the grains and give rise to noise gratings. When a beam is incident upon the developed hologram at the same angle and wavelength as one of the recording beams then besides the desired beam the scattered radiation is also reconstructed. This may reduce the otherwise available efficiency by several percent.

An iterative method is used to find the solution for all the field amplitudes and for the detuning of oscillations arising in a linear passive phase conjugate mirror (PPCM). The effect of crystal absorption is included and both transmission and reflection gratings are investigated. In particular, it is shown that a PPCM can be realized with the aid of a BSO crystal in the presence of an applied electric field. >

It is shown that the concept of equivalent circuits can be extended to the case when the frequency of one of the interacting beams is slightly detuned. The total impedance (analogous to the space charge field) is plotted in several examples as the setuning, the spatial frequency and one of the circuit parameters varies.

Based on a previous formulation by Benlarbi et al. (1980) the diffraction properties of a thick, unslanted phase grating are investigated and compared, in specific examples, with the predictions of Kogenlik's (1969) two-wave theory. The agreement between the two theories is shown to depend on the amplitude of a dimensionless parameter.

A set ofN + 2 coupled differential equations is derived for the amplitudes of the waves, and an analytic solution is presented for a simple case. The effect of the weak beams on the maximum conversion efficiency between the strong waves is discussed.

It is shown with the aid of analytical approximations and numerical calculations that the amplitudes of higher order modes in a volume phase hologram (thick phase grating) are only marginally affected by harmonics in the permittivity modulation.

The validity of 2-D coupled-wave theory is investigated for the case of Bragg diffraction of a Gaussian beam by a thick unslanted phase grating in transmission mode. Fourier plane wave decomposition theory, as presented in a companion article, is used to test 2-D coupled-wave theory under circumstances when its validity is in question, namely when the incident distribution is very narrow or fast-varying, or when the parametervo, due to Kogelnik (1969), which is proportional to the product of coupling rate and grating thickness, is very large. Numerical evaluations of the field patterns at output from the grating, obtained using plane-wave decomposition, are used to explore the effect of the gradual violation of the conditions (from the previous article) under which 2-D coupled-wave theory is valid.

The angular characteristics of transmission gratings are studied for the case when three parameters, namely the dielectric-constant modulation, the average dielectric constant and the grating vector vary with distance in the grating. The diffraction efficiency is worked out with the aid of a coupled-wave theory for linear and quadratic variation of the parameters. Gratings recorded in thick (≈ 60 µm) dichromated gelatin plates are measured. The spatial variations of the parameters are deduced by comparing the experimental and theoretical results.

The fidelity of reconstruction of 3-dimensional images by reflection and transmission holograms is investigated, concentrating on the measurement and theoretical modelling of large-scale geometric distortions in holograms illuminated by white or monochromatic light. Variable parameters include: recording and replay wavelengths; object position at recording; emulsion thickness and refractive index; replay light-source angle and distance; presence of a glass substrate, its thickness and refractive index. Holograms were recorded on Agfa 8E56HD photographic plates, and measurements made of image-point directions as a function of position on the hologram, revealing considerable image distortions even for modest changes in parameter values between recording and replay. The results are accurately modelled by the theory, which gives numerical values for point-by-point image positions, without any resort to paraxial approximations.

Thirty-seven children receiving chemotherapy including adriamycin were studied with echocardiography. Abnormal left ventricular function assessed by systolic time intervals (STI) and/or left ventricular shortening fraction (delta LVID) was present in 30%, and dilated left ventricle was in 45% of the case, often accompanied by thinning the left ventricular wall. Three patients developed congestive heart failure, one with fatal outcome. Two of these patients had received chest irradiation along with the chemotherapeutic treatment. These three patients with overt heart failure had gross abnormalities in several echocardiographic variables of which delta LVID seemed most specific.

A theoretical model for non-uniform volume gratings is described in which the refractive index modulation and grating vector are allowed to vary with depth. The predictions of the model are compared with the measured angular response of reflection gratings recorded in dichromated gelatin and the variations of the grating parameters with depth are deduced. Gratings produced by different processing techniques are analysed and the effects of processing on grating non-uniformities are discussed.

The current, velocity and fundamental kinetic power are calculated for an infinite electron beam subjected to sinusoidal velocity and current modulation. Space charge is taken into account rigorously and the solution is valid even when the a.c. quantities are comparable with the d.c. quantities. The validity of the solution breaks down, however, when electron overtaking occurs. It is shown in a number of examples that for sufficiently largo signals the accuracy of the small signal approximations deteriorates and small signal kinetic power is not conserved. It is also shown that some care must be exercised in assessing the amount of non-conservation because different definitions may lead to contradicting results.

The interaction of transverse acoustic waves with other excitations (cyclotron and helicon waves) is investigated and conditions for growing waves are discussed. The mathematical solution is obtained with the aid of the usual small signal assumptions and the dispersion equation derived is analysed in terms of the interactions of no more- than two waves.

The behaviour of a thin sheet of electrons in a time-varying square wave magnetic field is investigated. It is shown that the growth of an initial disturbance which takes place in the first half of...

The paper is concerned with a theoretical study of photoconductive mixing phenomena. The output power at the difference frequency is obtained in terms of the applied optical input power, cavity shunt resistance and the physical properties of the semiconductor. The dependence on the length of the semiconductor is investigated and it is shown that a short length is preferable if ωτ≫ 1 (τ=recombination time, ω=difference frequency). If ωτ

Using previously derived formulae for the equivalent current (Warnocke and Guenard 1951) and for the electron motion (Solymar 1961 b) in a high frequency gap, the beam loading is calculated. The solution is valid both for large space charge and large modulations up to the point when electron overtaking occurs. The weak space charge and small signal theories are contained as limiting cases. The dependence of the admittance on space charge and modulation index is demonstrated in a. number of graphs.

The different mathematical approaches and physical explanations of acoustic amplications are briefly reviewed. It is concluded that in the case ωτ 1 two distinct gain mechanisms exist (one due to the properties of a special velocity class of electrons, the other depending on wave interaction effects) which have been considered separately in the past. A simple mathematical theory is presented which contains both gain mechanisms as limiting cases.

The propagation of the electromagnetic wave in a gradual transducer is discussed. It is shown that the incident mode and the geometry of the transducer determine the outgoing mode. Inverting this theorem, a method is suggested for the design of the transducer's surface for cases in which the desired modes in the uniform waveguides are given. The application of the method is illustrated in three examples.

The results of a detailed analysis of the propagation of circular electric modes, H0n, is extended, approximated and eventually adapted to the design of monotonic multi-section conical tapers. The formulae and graphs obtained are directly applicable to the calculation of mode conversion loss encountered when two colinear waveguides are connected together by means of a multi-section taper, and the conversion loss is related to the wavelength and the geometry of the structure. The design procedure is illustrated in detail by several numerical examples. It is thereby clearly demonstrated that, for a given mode conversion loss and bandwidth, a considerable reduction in the overall taper length is possible if a multi-section taper of suitable proportions is used in preference to a simple linear taper.

A rigorous analytic solution has been derived for the bunching of an in finite electron beam modulated by an infinitesimal gap. The solution is valid as long as no overtaking occurs. The amplitude of the nth harmonic (for n=1, 2, 4, 8)is plotted for different values of beam density and modulation coefficient and the points where overtaking first occurs are noted. The solution contains previously derived ballistic and space-charge theories as limiting cases.

A general analysis of the interaction of a slow wave with a drifting stream of carriers is presented, The slow wave has an associated electric field, and may be electromagnetic or acousto-electric in character. The effects of both collision and diffusion are included in the analysis. The vacuum travelling-wave tube and the acoustic semiconductor amplifier emerge as special cases. The results are used to evaluate the feasibility of obtaining net gain from the interaction of drifting carriers in a semiconductor with the electromagnetic wave guided by an external structure. The conditions which provide the best hope of success are identified. The required physical materials constants arc only partially known, but using the best available estimates the theory suggests that substantial gains should be attainable.

Some of the fundamental properties of multiple BWO's are examined in terms of a simple model. The starting conditions are found for both low and high space-charge conditions and particularly for the case in which there is a small difference between the velocities of the separate beams. The latter results are used to discuss the tolerances which must be met in multiple BWO's. Experiments carried out at X band provide some qualitative confirmation of the theory.

The interaction of two streams of change carriers with acoustic waves by means of the deformation potential is investigated. The mathematical description is in the form of double perturbation (streams perturbed by the acoustic waves, and acoustic waves perturbed by the streams) yielding a dispersion relationship which shows clearly the presence of mutual coupling between stream a, stream b and the lattice. A few special cases of the dispersion equation are investigated and it is shown that for certain acoustic waves in multi-valley semiconductors the two streams may be replaced by one stream void of space charge. A formula for the gain obtainable in the latter case is derived and it is shown that in the limit of ωτ→∞ the equations agree formally with those of Pierce(13) derived for travelling wave tubes. A consequences of this analogy is that the electron velocity for maximum gain agrees with the sound velocity. Experiments for observing the effect in n-type Germanium are proposed.

Rigorous analytical solution is derived for the quasi-linear partial differential equation system, governing the motion of the electrons in the buncher gap and in the adjoining drift space. The method closely follows that described by Solymar (1961 a) and so the validity of the solution breaks down after crossover. The nth harmonic of current (n =l, 2, 3, 4, 8) is plotted for a number of gap angles, space-charge coefficients (ω/ ωp) and modulation coefficients (α). It is shown that high harmonic currents can be obtained (as predicted by previous approximations) but beyond a certain critical density the approximations are no longer valid, and the harmonic content decreases drastically The solution contains the zero space-charge (ballistic) and infinitesimal gap theories as limiting cases.

This paper describes an optimum design of monotonic stepped transmission-line transformers when the reflection coefficient and the bandwidth ratio are prescribed. For the analysis, discontinuity capacitances and reflection interactions are neglected and the validity of the conclusions is therefore restricted to small steps. The analysis is applicable to a multistep transmission line of which the quarter-wave transformer is a special case. In particular, it is shown that if the number of steps is increased from three to five a larger bandwidth may be obtained, but it is not possible to reduce the over-all length in this manner. For a given bandwidth, the shortest taper is always a stepped transmission line and never a continuous one.

If the highest permitted harmonics of the distribution function (this is the quantity of interest in practical application) and the supergain ratio are given, what is the maximum attainable gain? In this paper this optimum problem is solved through the introduction of n dimensional vectors and tensors and the result is obtained in closed form. For the case of two harmonics, numerical results are given. It is concluded that a small improvement in the specific gain is accompanied by a large change in the supergain ratio. The examination of the maximum of the specific gain, without auxiliary condition, leads to the conclusion that the addition of every harmonic increases the value of specific gain, but that the improvement is negligibly small until the number of harmonics becomes greater than the size of the aperture in wavelength. Using the method developed in this paper it is possible for any finite number of harmonics to calculate the optimum distribution function, but the computations become very lengthy as the number of harmonics increases.

Experiments using a new photorefractive gain mechanism involving two pump beams are described. A ring resonator is used to provide a frequency‐shifted signal beam. The gain with two pumps of equal intensity is found to exceed that with a single pump by about a factor of 4.

The height of subharmonic steps is shown to depend strongly on the form of the current-phase difference relationship. The model used is that of Waldram et al. [1] in which an ideal Josephson junction (in parallel with a constant resistance) is driven by a constant current source.

Coupled partial differential equations are derived for the amplitude of the electric field in a general two‐dimensional volume hologram. Nonuniform amplitude distributions, nonplanar wave fronts, losses, and non‐Bragg incidence are considered both for dielectric and absorption gratings. The formulation is in holographic terminology but the equations are valid for weakly modulated Bragg devices in general.

The amplitudes of the spurious modes due to a small step in an over-moded circular waveguide are computed, assuming that one of the waveguides is fed by a pure H01 mode. It is shown that the amplitude of the H02 mode is the largest of the spurious modes. For the reduction of the conversion losses, a simple transducer is designed. Its radius is the geometrical mean of the radii of the two waveguides to be connected. Its length is one-half beat-wavelength of the H01 and H02 modes.

One hundred and forty school children, 75 boys and 65 girls, aged 7-18 years, underwent the following lung function tests: closing volume, slope of the alveolar plateau, maximal expiratory and inspiratory flows at 75, 50 and 25% of vital capacity, static and dynamic lung volumes. Lung volumes and maximal flows increase with height in an exponential way, the exponents varying between 2.6 and 3.1, while closing volume in per cent of vital capacity and the slope of the alveolar plateau decrease linearily with increasing height. Regression equations are given for each sex with height as determinant.