Propagation Of Higher Order Modes Research Articles

Practical Aspects of Phase-Shifter and Driver Design for a Tactical Multifunction Phased-Array RADAR System

Three microwave garnet phase-shifter designs are used in the AEGIS weapons system. The microwave design is straight-forward except that the toroid assembly is potted with silicone rubber to increase its power-handling capability and the magnetizing wires are shielded with a spiral-wrapped wire to prevent the propagation of higher order modes. The driver circuit uses a new "flux-feedback" concept for improved accuracy and employs monolithic circuits, hybrid circuits, and discrete components. Mechanical and electrical design of the interfaces with mating components are important cost considerations and the chosen designs are described in detail. Several techniques for improving production yield are discussed and a table of production statistics is provided. Performance histograms and data averages as a function of time and operating frequency are also presented.

LSE/sub 20/-Mode Characteristics in Phase-Shifter Parametrization

The validity of considering the LSE/sub 20/-mode propagation threshold as the limiting factor in selecting rectangular-wave-guide ferrite-phase-shifter dimensions is examined theoretically and experimentally using a dielectric model. Depending on the effective dielectric constant of the loading material, it is shown that the LSE/sub 20/-mode cutoff may, in many cases, be exceeded without introducing spurious mode resonances. In addition, the effect of magnetization on the y-independent modal cutoffs is investigated. It is concluded that the dielectric model represents a worst case condition as far as higher order mode propagation is concerned.

An Experimental and Theoretical Investigation of Elastic Wave Propagation in a Cylinder

A high-speed computer was used to investigate the problem of wave propagation in an isotropic elastic cylinder. Dispersion curves corresponding to real, imaginary, and complex propagation constants for the symmetric and the first four antisymmetric modes of propagation are given. The radial distributions of axial and radial displacements and of shear and normal stresses are given for the symmetric mode. By using a finite number of modes of propagation, an approximate solution is found for the problem of the L(0,1) mode impinging on a traction-free interface. The reflection coefficient is determined in this way and the accompanying generation of higher order modes at the interface is shown to cause a high-amplitude end resonance. Experimental results obtained by using the resonance method in conjunction with a long rod are presented to substantiate the calculated reflection coefficient and the frequency of end resonance. Phase velocities, based on measurements of the wavelength of standing waves and resonance frequencies, were obtained for the symmetric and first two antisymmetric modes. These measurements extend into the frequency range of more than one propagating mode. The rms deviation between theoretical and experimental results is in general less than 0.2% with the exception of the dispersion curve for the L(0,2) mode which deviates by 0.7%.

Optical losses in "close-confinement" epitaxial p-n junction lasers - Theory and experiment

The optical losses of (single heterojunction) epitaxial injection lasers fabricated by liquid-phase epitaxy (LPE) have been described in terms of a simple waveguide model. Experimental and theoretical comparisons were made of LPE lasers with identical impurity profiles except for the addition of the Al x Ga 1-x As p+-p heterojunction ( \DeltaE_{g}\sim 0.1 eV) within 1-2 \mu of the p-n junction. This reduces the room-temperature absorption loss and hence the laser threshold-current density. The values of the internal laser loss α at 300°K range from 20 to 40 cm-1, while in the homojunction LPE lasers α is typically close to 100 cm-1. The laser gain coefficient β in the close-confinement lasers ranges from 3 to 6 \times 10^{-3} cm/A; values of \sim3 \times 10^{-3} cm/A. are estimated in similarly doped homojunction LPE lasers. However, β in diffused lasers is known to be substantially lower, \sim \leq 10^{-3} cm/A. We believe that substantial electron confinement exists in the homo-junction LPE laser because of the doping discontinuity at the p+p interface, which is absent in the diffused lasers. Thus, the β values are correspondingly lower in the diffused lasers. The addition of the (AlGa)As heterojunction does not, apparently, increase the electron confinement greatly as compared to homojunction LPE lasers when the active region width is about 2 μ (the optimum value for overall laser performance) for a given doping level. Values of the exterior differential quantum efficiency of 43 percent are obtained at 300°K in close-confinement lasers, which means that most of the light internally generated is emitted. Because of the reduced internal loss, the spontaneous exterior efficiency is also greatly increased by the addition of the heterojunction (a factor of 2-3). State-of-the-art values of the threshold current density of the optimum structures are 10 000 A/cm2for a cavity length of 20 mils, with values of 8000 A/cm2in exceptional units. A power conversion efficiency at 300°K of 10 percent has been measured, which agrees with the theoretically predicted value. It is noteworthy that the diode series resistance is unaffected by the addition of the heterojunction. The laser characteristics have been studied as a function of varying acceptor concentration, donor concentration, and bandgap energy discontinuity at the p+-p interface. Semiquantitative agreement for the laser loss between theory and experiment at 300°K and 77°K is obtained for an active region width of \sim 2 \mu , using reasonable values of the index of refraction differences between the various laser regions and free carrier losses. The major difference between simple waveguide theory and experiment is in the dependence on the width of the active region. Instead of a decrease in α with increasing width, the opposite occurs in the range investigated because the theory is not applicable when the width of the active region substanfially exceeds the minority carrier diffusion length. Furthermore, higher order mode propagation has been neglected. Such modes have been experimentally observed when d \cong 5 \mu . The addition of the heterojunction greatly reduces the laser loss due to light leakage from the active region into the p+ region. The contribution to the laser loss resulting from leakage into the n-type side of the junction is small. It is unaffected, of course, by the addition of the heterojunction. This loss could be further reduced by use of a double heterojunction structure. Based on the theoretical results and comparison with experiment in which the Zn concentration is changed,it is concluded that the dominant loss is due to free carrier absorption (holes mainly) in the active region of the close-confinement lasers. Thus, it is not expected that the laser-loss coefficient will substantially vary with the cavity length. However, in the homojunction LPE (or diffused) laser this may not be the case. There the refractive index difference \Deltan between the p+ and active p region is relatively small; hence, small variations in \Deltan due to increasing the laser photon energy by decreasing the cavity length may substantially reduce the optical waveguiding effect. Finally, we note that work in progress indicates that close-confinement lasers are capable of long-term operation (2000 hours) with power reductions of 20 percent or less when operating at a current density of 50 000 A/cm2(0.04 percent duty cycle). However, it is known that the laser life depends on the imperfection density in the active region. Hence, the metallurgy of the device is a key factor that must be carefully controlled in laser fabrication. In particular, dislocations can be introduced as a result of the slight lattice mismatch at the (AlGa)As-GaAs interface.

Longitudinal Section Mode Analysis of Dielectrically Loaded Rectangular Waveguides with Application to Phase Shifter Design

The structure consisting of an E-plane dielectric slab partially filling a rectangular waveguide is examined with attention on those higher order mode propagation characteristics that are relevant to the design of nonreciprocal remanence ferrite phase shifters. The validity of the model is established by introducing experimental comparison in the form of VSWR measurements for both pure dielectric loading and an actual composite ferrite phase shifter. Emphasis is placed on the consideration of possible mechanisms for the elimination of LSE/sub 11/, LSM/sub 11/, and LSE/sub 12/ modes, since certainly the first, most probably the second, and quite possibly the third will propagate in a practical device. Experimental verification of theoretical predictions is established and phaser design guidelines are drawn. Some additional topics, such as slabcorner chamfering and the effect of the switching wire, are included for completeness.

Higher-Order Cylindrical Surface-Wave Modes

A general theory of the propagation of higher-order modes on cylindrical surface-wave structures is examined and applied to the dielectric-clad rod. A theory is developed in which the boundary conditions at the guide are specified by an impedance dyadic. The characteristic equation for the structure is then obtained in terms of the elements of the dyadic. The equation is solved and yields a set of conditions which are satisfied by the values of the dyadic elements at the cutoff points for each of the higher-order modes. A mode without a cutoff frequency is shown to exist on the structure used. The relationship between the guide wavelength and frequency has been verified experimentally.

Theoretical Study of Symmetric Wave Propagation in a Semi-Infinite Elastic Isotropic Cylinder

The boundary conditions at the traction-free interface of a semi-infinite elastic cylinder can, with one exception, be satisfied exactly only if an infinite number of modes of propagation is considered. For the low-frequency range (diameter<wavelength), there exists only a single mode of propagation with a real propagation constant [the L(0,1) mode]; however, there is also an infinite number of modes of propagation with complex propagation constants. All of these modes are required to satisfy the boundary conditions. An approximate solution is found for the problem of the L(0,1) mode impinging on a traction-free interface by using only a finite number of modes of propagation. The reflection coefficient for the L(0,1) mode is given. The accompanying generation of higher-order modes with complex propagation constants is shown to cause high-amplitude end resonances at isolated frequencies. Results are given for approximations with 3, 5, 7, and 9 modes.

Acoustical Propagation of Higher Order Modes in the Region of Cutoff

Experimental data on the amplitude of transverse particle velocity associated with the (1,0) mode of rectangular tube for frequencies in the region of cutoff are presented. The distance decay from the source is exponential for frequencies investigated in the range f/fc⩽0.998 where f is the frequency of excitation and fc is the mode cutoff frequency. At cutoff, the amplitude drops to the fraction 1/e of its value at the source over a distance interval equal to about 8 times the tube width. For frequencies above f/fc = 1.01 the progressive wave pattern appears fully developed. Comparison data between theoretical and measured values of attenuation for frequencies below cutoff are also presented.