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In an earlier paper, on the same subject, a number of factors affecting communication with space vehicles were discussed. Among these were receiver signal-to-noise ratio as a function of temperature, cosmic noise, auroral displays, Faraday rotation of the plane of polarization, and gaseous refraction and absorption. The additional material in this paper treats in a semiquantitative manner and in greater detail the application of elevated heights for earth terminals of space communication systems. This expedient takes advantage of elevated heights to reduce the effects of water vapor and oxygen on limiting the spectrum for radio communication. It is possible to attain some isolation of circuits and extend the range of communication in selected portions of band of 10 to 60 kmc.

This paper supplements and assesses an optical measuring technique for the local determination of the cubic and uniaxial anisotropy fields K1/Ms and Ku/Ms in uniaxial magnetic films reported in a recent paper. Graphs for the quick evaluation of the Ku/Ms values are given. The accuracy of the method is assessed by comparison with FMR measurements. The origin of the nonuniformity in the domain pattern of a (111) LPE garnet film with the chemical composition Y2.5Gd0.5Fe4Ga1O12 grown on a GGG substrate is investigated by local optical measurements of the magnetic film parameters K1/Ms, Ku/Ms, compensation temperature, and magneto‐optic Faraday rotation. It is correlated with local structural parameters of the substrate as stress birefringence from ellipsometric measurements and inhomogeneity of the lattice constant measured by x‐ray topography.

This paper, which is the written version of the 1962 Guthrie Lecture, describes the physics underlying the radio astronomical researches at Jodrell Bank. The following topics are covered: (i) the physical theory of the scattering of radio waves from the ionized columns of meteor trails based on the classical expression for the scattering cross section of a free electron; the effects of resonance and polarization, the manifestation of the diffraction pattern, the measurement of velocities, and the application to the measurement of certain physical parameters in the high atmosphere; (ii) the possible alternative processes occurring in the scattering of radio waves from auroral formations; (iii) the lunar scattering of radio waves, the effects of libration which give rise to the short period fading and the Faraday rotation in the ionosphere which is responsible for the long period variations in signal strength; (iv) the origin of radio waves from the galaxy and their explanation in terms of synchrotron emission from relativistic electrons in the interstellar field, and thermal emission from ionized hydrogen clouds; (v) the problem of the energy requirements in the localized galactic supernova sources and in the radio sources which are extragalactic at great distances; (vi) the line emission from neutral hydrogen on 21 cm as it affects the work at Jodrell Bank, particularly the attempt to measure the interstellar field by observation of the Zeeman effect which has recently given a positive result. The paper ends by reference to the evolution by Hanbury Brown of the intensity interferometer at Jodrell Bank and to the problem of the scintillation of the radio stars.

In a previous paper, simple analytic expressions describing internal conical refraction were derived. That analysis is extended in this paper to describe the effects of optical activity or Faraday rotation on conical refraction. By use of a similar analysis, the generally elliptical-wave modes to which the incident wave bundle couples were determined and the Poynting vector associated with each mode was found. From the variation of the Poynting vector with wave position, the structure of the cone and the irradiance variation within it were determined. The calculations are compared with published experimental results. From this analysis, we infer a variation of the position of the dark spaces in polarized light with polarization, which is not indicated by previous work.

This paper reviews the ground-based and rocket techniques that are presently being used to determine electron density profiles in the ionospheric D region. Ground-based techniques include VLF, LF, and MF sounding; differential absorption and differential phase measurements using partial reflections; wave interaction; and incoherent scatter. Rocket techniques include differential absorption and Faraday rotation in association with high-resolution dc probes calibrated by means of the radio measurements. The characteristics of the aforementioned techniques are presented, including time and height resolution, accuracy estimates, preferred height ranges, and problems encountered. Electron density profiles obtained with these techniques are presented for comparable solar zenith angles and undisturbed solar and geophysical conditions.

This paper is concerned with magneto-optical properties of EuO single crystals, doped with up to 5-at.% Gd. The optical absorption and the Faraday rotation have been measured above and below the magnetic-ordering temperatures and in various magnetic fields. In addition the reflectivity between 13 eV and 250 \ensuremath{\mu}m has been observed and the Curie temperature has been determined. The measurements permit the evaluation of the magnetic short-and long-range order. The exchange interaction between free electrons and $4f$ spins can be determined and is found to decrease with increasing doping. The analysis of the optical data permits the derivation of the carrier concentration, their mobility, and temperature dependence. The carrier concentration shows an exchange-induced ionization near ${T}_{C}$ for nondegenerate samples and the mobility has a sharp minimum at ${T}_{C}$. The transport parameters also reflect the fact that the electron-$4f$-spin interaction decreases with increasing Gd concentration, probably owing to electrostatic-shielding effects.

The paper describes the polarization characteristics of decametric type III solar radio bursts at two closely spaced frequencies, 34.993 and 34.997 MHz. From the simultaneous orientation angle measurements at these two frequencies, it is concluded that the total Faraday rotation suffered by type III bursts could be of the order of 103 rad. Polarization characteristics of a few bursts displaying fine structure (4 kHz) in frequency similar to type IIIb bursts have also been described.

A comprehensive treatment of the subject is given, with a large number of computed results of cut-off points and phase constants for the case of a guide containing a concentric ferrite rod of arbitrary radius. The wave equation for the ferrite is derived in cylindrical co-ordinates, and solved. The wave equation for the isotropic medium surrounding the ferrite is also solved. The boundary conditions are then applied and the characteristic equations obtained for the case of the filled guide, the partly filled guide, and the guide filled with dielectric. By putting the phase constant s equal to 0 in the characteristic equation, it has been possible to solve for the ratio of ferrite radius to guide radius at cut-off. By plotting cut-off curves, a study of the normal mode spectrum can be made. This paves the way for an attack upon the characteristic equation proper, and curves of phase constant against radius ratio are obtained for various values of the properties of the ferrite and the geometry of the system. Faraday rotation, power flow, and losses are next discussed. The paper ends with an account of checking methods and accuracy of the computed results.

The Faraday rotation has been measured in calcite parallel to the optic axis for the wavelengths λ 5893, λ 5780, λ 5461, λ 4358 and λ 4047 A. A dispersion formula for the magnetic rotation has been fitted up using the same absorption frequencies that are used in refractive dispersion. It is shown that the magneto-optic anomaly factors for the various absorption frequencies are different and the value of the anomaly factor for the absorption wavelength λ 1535, is very much lower than that for the other absorption wavelengths. (γ1535 = 0·20, γ1000 = γ500 = 0·825.) This paper also reports the values of the Verdet constant of NaClO3 for a few wavelengths from λ 5780 to λ 3650 A. A numerical error in the earlier measurements has been noticed and rectified here. In this case also a dispersion formula for magnetic rotation has been proposed and it is found that for this crystal γ1850 = 0·46 while γ900 = 0·74.

1. Introduction .—If plane polarised light be transmitted through a medium under the influence of a magnetic field parallel to the direction of propagation, the plane of polarisation is in general rotated. This circumstance is known as the Faraday effect, after its discoverer. For light of a given wave-length, the magnitude of the rotation per unit distance is found to be proportional to the magnetisation. The direction of rotation varies with different substances, being termed diamagnetic, or positive, if in the direction of the current producing the field, and paramagnetic, or negative, if in the opposite sense. The sign of the effect does not depend upon whether the substance is dia- or paramagnetic; negative diamagnetics are, however, infrequent. Thin films of ferromagnetics exhibit an enormous negative rotation, proportional to the magnetisation, and in the following we shall attempt to explain the origin of this by using a very simple model for the substance. We shall consider a single crystal of the metal, and, following Heisenberg, we shall choose the Heitler-London model, where each electron is considered as being attached to an atom, as a first approximation. The interaction of the electrons gives rise to the well-known exchange forces. In a ferromagnetic these exchange forces are of vital importance, and it is therefore necessary to consider states and transitions of the crystal as a whole. Further, it is well known that in a ferromagnetic the average orbital angular momentum is zero. In view of this fact, and in the interest of simplicity, we shall consider a model where each atom possesses one electron in an s -state, outside a closed shell. This, of course, does not correspond to the facts, but any other model would be very much more difficult to handle. Having chosen a model with bound electrons, we shall have no conduction (without including polar states), and shall therefore not have the typical metallic absorption of light, such as is associated with “free” electrons. With the extremely rough model used, it is obvious that we can only expect to obtain the order of magnitude of the rotation, and some idea of its variation with the intensity of magnetisation.

This paper describes experimental observations of electron beam‐plasma interaction in low‐pressure mercury‐vapor discharges. Comprehensive data have been obtained of rf growth, phase velocity, axial and radial electric field profiles in the interaction region, and Faraday rotation, for the case of transverse modulation, i.e., for growth in the first azimuthally‐varying mode (m = 1). The work complements previous parallel studies of the axisymmetric mode (m = 0) made with axial modulation. The results are compared with cold‐ and warm‐plasma theories of the interaction. It is concluded that the warm‐plasma theory gives a satisfactory approximation to the experimental results, and that the remaining discrepancies are due to lack of sharpness of the experimental beam edge.

This paper reports methods of obtaining the components of Faraday rotation tenser in anisotropic crystals, using longitudinal and transverse Faraday rotation along the optic axis. It is found that in crystals belonging to triclinic, monoclinic and orthorhombic symmetry, one can get 6 out of 9, 3 or 4 out of 5, and 2 out of 3 components respectively. In the case of uniaxial crystals only 1 component can be obtained. By measuring Faraday rotation in a randomly oriented polycrystal one more component in all the above classes can be obtained.

The complete experimental set-up of an accurate photoelectric polarimeter with an ultraviolet sensitive photomultiplier, a tuned amplifier followed by a cathode-ray oscillograph has been described in this paper. This has been used for the measurement of Faraday rotation in a perfect fused quartz specimen showing no residual birefringence. Measurements have been made for number of wavelengths λ 5780 to λ 2848 A. The following dispersion formula for magneto-optic rotation which fits the experimental data to 1/2% has been proposed using the same absorption frequencies that are responsible for refractive dispersion, $$V = {e \over {2mc^2 }}{1 \over n} \times 0 \cdot 793\left[ {{{0 \cdot 001915 \lambda ^2 } \over {(\lambda ^2 - (0 \cdot 0600)^2 )^2 }} + {{0 \cdot 004664 \lambda ^2 } \over {(\lambda ^2 - (0 \cdot 1060)^2 )^2 }} + {{0 \cdot 002223 \lambda ^2 } \over {(\lambda ^2 - (0 \cdot 1190)^2 )^2 }}} \right]$$ where V is in radians and λ in microns. The magneto-optic anomaly factor is 0·793 for all the absorption frequencies. The available data on crystalline quartz has also been analysed and the values of the Verdet constant, the magneto-optic anomaly factor and the magnetic rotativity of the two substances have been compared and found to be significantly different.

At the Electronics Laboratory of the Military Research and Development Center, Bangkok, Thailand (13.7°N latitude, 100.1°E longitude), Faraday rotation observations of the 54-MHz signal from the Transit 4-A (1961 Omicron 1) satellite were made during 10 months of a sunspot minimum period (1964). The satellite has an essentially circular orbit with an inclination of 67° and a spin-stabilized linear-polarized antenna. In this paper, two methods of analysis, involving rotation rate and total number of rotations, are applied to the Bangkok observations. The rotation-rate method is used to determine the electron content when the angle between the ray path and the geomagnetic field is 90° (transverse position). The total-rotations method is used to determine the latitudinal variations of the electron content for five selected satellite passes from a joint analysis of observations at three stations, Singapore, Bangkok, and Hong Kong. A comparison of the calculated critical frequency with observed ionosonde critical frequencies at Singapore, Bangkok, and Macao shows some evidence that the equivalent slab thickness may be considered independent of latitude near the magnetic equator.

This paper presents an analytical investigation of the dependence of Faraday rotation and ellipticity on the heating dc electric field in III‐V semiconductors at low temperatures (k0T ℏωl), and the elastic scattering by ionized impurities and acoustic phonons in the passive region (e

The paper reviews some of the research and development projects which led to the designs for a ferrite directional coupler, a ferrite microwave switch and ferrite-loaded cavity filters. Directional coupling is accomplished at microwave frequencies by extending a ferrite cylinder through the common wall of two rectangular waveguides joined at the broad face. Experimental data for coupling and directivity are given for two ferrite materials as a function of frequency, biasing field and diameter of the Ferrite post. A microwave circulator utilizing ferrite elements can be converted into a fast-acting microwave switch by placing the ferrite in a pulsed magnetic field. The design of a switch based on the Faraday rotation phenomenon and techniques for the reduction of the short-circuited-turn effect of the waveguide are discussed. Large ferrite samples are placed in microwave cavities with the object of achieving tunable microwave filters. Experimental data at X-band frequencies on variation of cavity resonant frequency, bandwidth, loss, cavity and window coupling are given as a function of applied magnetic field. Of particular interest are the results obtained with a circularly polarized cavity designed to produce a reflectionless filter which couples nearly 100% of the energy from the main waveguide at the cavity resonant frequency.

The general formalism of the variational theory of the Faraday effect established in the first part of this paper is now applied to the actual computation of the Verdet constant of the hydrogen molecule, of water and of some saturated hydrocarbons. The numerical results have a correct order of magnitude and even, for hydrogen, are rather close to the experimental value.

This paper describes the effects on Faraday rotation and optical absorption of substituting bismuth into various single crystal iron garnets. The large negative contribution to the Faraday rotation produced by the presence of bismuth is of the diamagnetic form and is associated with an optical transition around 415 nm. The magnitude of the bismuth contribution depends on the concentrations of bismuth and tetrahedrally coordinated Fe3+ions, suggesting that both these ions are involved in the transition responsible for the additional rotation. The absorption arising from the bismuth increases with decreasing wavelengths. However, the increase in magnitude of the rotation is such that the figure of merit is increased above that of YIG, peaking at 560 nm with a value of 5.2 deg/dB. The Faraday rotation and figure of merit of low magnetization garnets, suitable for magnetooptic devices, are also increased in the visible by the presence of bismuth.

The resonant Faraday effect occurs for radiation at frequencies close to the absorption lines of a magneto-active material. In the paper we present a theory for isolated absorption lines with Voigt profiles. The background source is also assumed to have a Voigt profile. The theory shows how the resonant Faraday effect can be used to determine relative transition probabilities, as well as the magnitude of the Lorentzian component of the line profiles.Experimental results for an argon plasma are presented and show that the relative transition probabilities of atomic transitions with a common lower level can be measured to an accuracy of ± 1%. For strong absorption lines, the Voigt "a" parameter can also be determined to an accuracy of 10%, even when the Doppler width is 14 times larger than the Lorentzian width.

The paper describes a simple and accurate method for computing ionospheric and tropospheric bending. The only assumptions made are that the refractive gradient is radial and that the refractive index profile can be approximated by a finite number of linear segments whose thickness is small compared with the earth's radius. These assumptions are readily justifiable in all practical cases. Since there are no limitations on the angle of elevation and the shape of the refractive index profile, the method has a wide application and it is extended to cover other refractive effects such as retardation, Doppler error and Faraday Rotation.

In photoviscoelasticity, the difference in principal stresses at a point depends not only on the history of isochromatic-fringe order, but also on the history of isoclinic angle. Thus, meaningful interpretation of the isochromatic data in terms of stress cannot be made without knowledge of the isoclinic history. When the isoclinic angle is changing rapidly, the traditional method of rotating the polarizer-analyzer pair in a plane polariscope by mechanical means is limited by practical rotation rates. Magnetic rotation of the polarization, using the Faraday effect, is possible, but suffers from the problem that the isoclinic patterns are viewed sequentially. This limitation is also inherent in the slower mechanical-rotation method. This paper describes a new method of viewing several full-field isoclinic patterns simultaneously. Thus, the recording system has more time to make each record, and requirements on film speed and framing rates may be relaxed by an order of magnitude.

The paper describes some results of a theoretical and experimental investigation of the propagation behavior of circular cylindrical wave guides containing longitudinally magnetized ferrite rods. As long as no concentration of the RF-magnetic field in the ferrite occurs, theoretical expressions for the propagation constants can be given by applying first-order perturbation method. Faraday rotation measurements have been made between 5000 and 7600-mcs using commercially available ferrites. Reasonable agreement between theoretical and experimental results has been found for a thin axial ferrite rod in an air-filled guide in both cases of saturated and nonsaturated ferrites. Energy concentration in the ferrite determines the propagation behavior in the partially filled waveguide. This effect can be enhanced by surrounding the ferrite rod with a dielectric tube. For a given rod diameter and permittivity of the tube there is an optimum outer diameter of the tube for which the Faraday rotation becomes maximum.

The complex rotatory power of several rare-earth ions in the Ca${\mathrm{F}}_{2}$ lattice has been observed. Measurements on anomalous rotatory dispersion and concomitant circular dichroism about some spectral lines in Ca${\mathrm{F}}_{2}$:${\mathrm{Nd}}^{3+}$ and Ca${\mathrm{F}}_{2}$:${\mathrm{Er}}^{3+}$ crystals agree well with the theory of the preceding paper. The rotatory power of ${\mathrm{Gd}}^{3+}$ in Ca${\mathrm{F}}_{2}$ in the visible range is very small. By contrast, the rotation in (${\mathrm{Eu}}^{2+}$, ${\mathrm{Eu}}^{3+}$) doped Ca${\mathrm{F}}_{2}$ crystals is very large and stems from the ${\mathrm{Eu}}^{2+}$ ions. The rotatory dispersion measurements show that the strong absorption lines and bands of ${\mathrm{Eu}}^{2+}$ in the visible region are responsible for the large optical rotatory power of ${\mathrm{Eu}}^{2+}$. ${\mathrm{Gd}}^{3+}$ and ${\mathrm{Eu}}^{2+}$ are isoelectronic in structure, but the difference in their optical spectra gives rise to a significant difference in their optical rotatory power. This assertion is supported by experimental observations.

A technique has been developed for using a bimodal cavity to measure Faraday rotation at microwave frequencies with high sensitivity. Such measurements yield information about the off-diagonal elements of either the susceptibility or conductivity tensor of the sample being investigated. This paper presents a qualitative discussion of the behavior and use of this cavity. Previously presented analysis of the cavity operation is outlined and the measurements made to date, using the cavity, are indicated.

Measurement of Faraday rotation has for many years been used as a technique for evaluating the product of magnetic field and electron density in a plasma. This paper determines the equivalent rotation for the case when the probing radiation is within the emission profile of one of the plasma lines.

A combination of phase-path length difference and Faraday rotation angle data obtained from geostationary satellite transmissions is used to determine the integration constant necessary to convert phase-path length difference information into absolute values of total slant columnar electron content. The total content thus determined, which is the sum of the ionospheric and protonospheric contents, is measured with uncertainties about one order of magnitude smaller than the value of the protonospheric content. It is thus, in principle, possible to determine the latter by subtracting from the measurement the so-called 'Faraday content.' This idea, proposed by several authors in the past, is critically examined in the present paper. It is impossible to totally eliminate the ionospheric contribution to the measurements; however, it is shown that the degree of elimination depends on the type of distribution of the longitudinal component of the geomagnetic field along the path of observation. Satisfactory minimization of the ionospheric contribution can be accomplished only under certain geometries of observation.

At frequencies approaching the electron-lattice collision frequency, the weak field Faraday effect can be used to study details of scattering mechanisms that are manifested in the complex Hall terms of the permittivity tensor. Plane wave theories that may apply to experiments using infrared or visible light do not apply rigorously to the guided wave experiments that have been performed in this frequency range. This paper describes a guided wave theory relating the real and imaginary parts of the weak field Hall terms to microwave measurements performed on a degenerate TE mode waveguide containing a longitudinally magnetized cubic semiconductor. The theory assumes only that the magnetic field is small and takes losses and reflections into consideration exactly.

Linear ferrite devices for microwave applications include phase shifters, switches, isolators, circulators, and others whose operation is independent of the applied rf signal level. In this paper, propagation through an infinite ferrite medium is treated first, and points of operation for various ferrite devices are established on a normalized plot of effective permeability vs biasing field. Transfer matrix techniques are used to analyze slab configurations with transverse magnetization, such as those found in differential phase shifters for circulators, field‐displacement isolators, and certain latching phase shifters. These techniques permit computation of optimum geometry, field configurations, phase shift, and cutoff conditions. Suhl and Walker's analysis of the completely filled cylindrical waveguide is applied to the ferrite‐filled coaxial line and extended to study Faraday rotation, phase shift, and cutoff conditions in cylindrical rod geometries. Of particular interest is a simplified analysis of the Reggia‐Spencer phase shifter which predicts frequency dependence and critical geometry with good accuracy.

Various methods for the determination of the ionospheric electron content are possible when satellite-borne signals can be used. The paper compares the results from Doppler shift, Faraday rotation, Doppler data combined with Faraday rotation data, and topside and bottomside soundings. The often neglected prerequisite for the application of Doppler and Faraday methods is radio propagation along the same ionospheric path for the different frequencies involved. Criteria for correct application are discussed. The comparison of inflection time moments is chosen for data selection. The usage of the Doppler slopes at the time of simultaneous inflection provides reliable data of the electron content. The diurnal variation is given. The Faraday rotation rate measurement has been made a continuous one by special equipment of G. Vogt. The simultaneous use of two Doppler slopes at different frequencies and of the Faraday rotation rate at one of these frequencies results in the measurement of the effective component of the geomagnetic field. Thus, a method free from any assumptions is on hand for the electron content. From the radio-frequency sounding of the topside-sounder satellites and from simultaneous bottomside soundings a complete ionospheric profile is obtained, the integration of which results in data for the total content. A comparison of the results of the different methods is permitted within the limitations brought about by the various theoretical and experimental assumptions made.

The paper outlines the method used at Ahmedabad for determining the total electron content in the ionosphere from differential Faraday rotations of plane polarised radio waves on 40.010 and 41.010 Mc./s. transmitted by NASA satellite 64-64A. The observations made during the period October 1964 to April 1965 are utilised to determine the diurnal variation of the total electron content up to the satellite height which was about 1,000 km. over Ahmedabad and Bombay latitudes. The curve of total electron content up to the satellite height shows similarity to the curve of maximum electron density at the F2 peak.

This paper contams the results of analysis of the total electron content (Is) measurements made from the recordings of Faraday rotation at Delhi of the 20- and 40-Mc/s transmissions of the satellite Explorer 22 (S

The "Magneto-optic Method of Chemical Analysis," discovered by Dr. Fred Allison 15 of the Alabama Polytechnic Insti tute at Auburn, Alabama, has been the subject of considerable controversy during the past several years. The great importance and almost unlimited possibilities of the method have warranted this discussion on the one hand while the failure of some experimenters to observe the effects and the lack of any feasible explanation of the phenomena account for the controversial nature of the discussions. The method depends upon the observance or non observance of a slight decrease in the intensity ( "min imum") of a beam of polarized light when acted on by a high frequency electro-magnetic field controlled by a motion of a sliding trolley. In February 1931 the author set up an apparatus roughly similar to that used by Dr. Allison and preliminary observations were begun in order to discover if possible the physical principles underlying the operation of the apparatus. Several not very serious at tempts to locate the sharp minima of light at t r ibuted by Beams and Allison 1,2 to a time lag in the Faraday Effect, failed. However minima of a broad type were observed and it was then deemed essential to work with a simpler set-up in order to determine if possible how the plane of polarization of the light is affected by the oscillatory discharge. The results of observations extending until September 1932 are given in a paper entitled "Magneto-optic Rotations by Condenser Discharge," 30 and more fully in a thesis presented in partial fulfillment of the requirements for the Degree of Master of Science at Vanderbilt University by W. M. Breazeale.

Since Hogan's* exposition of the extreme usefulness of the microwave Faraday effect numerous other laboratories have begun investigating propagation through ferrites and have made significant contributions to the art. In view of the tremendous interest which is being accorded this work this paper has been prepared to summarize some of the observations and developments to date. The plane wave theory is reviewed briefly with special attention being given to the mechanisms by which power is absorbed by the ferrite. The plane wave theory is then modified to describe various waveguide effects. Finally experimental procedures and results are presented to illustrate the theory and to provide general information regarding the design of devices employing these effects.

The gyromagnetic mechanism which controls the permeability of a ferrite at microwave frequencies is investigated theoretically in several simple cases, and the tensor form of the permeability in the general case is indicated. The theory is first applied to circular waveguides containing a ferrite magnetized along the axis. Experimental results are presented which confirm the expected presence of resonance absorption but also show low field losses. A possible explanation of these losses is suggested. Applications of the effects in the construction of isolators and circulators are described. These include resonance and reflection isolators for circularly polarized modes, and also devices which make use of Faraday rotation. The effects of transverse magnetization of the ferrite is then discussed. Applications in rectangular guide in the form of resonance isolators, non-reciprocal phase circulators and field displacement devices are described. Bi-refringent behaviour in circular guide is also described. The relative merits of the different types of isolator and circulator are compared at different frequencies in terms of ease of construction, and performance at one frequency and over a band. The characteristics of most of them can be theoretically calculated from the components of the permeability tensor, and the last part of the paper is devoted to methods for measuring these.

It is shown that the lack of linear polarization in the microwave radiation of solar bursts (reported in a earlier paper) may be explained by spatial dispersion of Faraday rotation. The maximum source diameter s without noticeable destruction of linear polarization is determined by the electron density and the magnetic field strength in the volume, where the linear polarization is generated. In the case where linear polarization is produced by the radiation source, s is smaller than only 20 km. In the other case where linear polarization is produced by mode coupling in a quasi-transverse magnetic field in the corona, the s-values are found to range from 10 to 6000 km, which is still much smaller than the generally adopted sizes of microwave burst sources. The second case has been investigated for several models of magnetic fields.

The most commonly used methods for the determination of the total electron content of the ionosphere from observations of orbiting satellite transmissions have been (a) single-frequency Faraday rotation, (b) differential Faraday rotation, and (c) differential Doppler. This paper compares these three methods and in particular the last two by obtaining continuous curves of electron content under a variety of conditions from analysis of Faraday rotation and differential Doppler data of signals from the Beacon Explorer satellites BE-B and BE-C. It is found that there may be 5–10% discrepancies in the absolute values of electron content derived by the differential Faraday and differential Doppler methods. However, content variations obtained by both methods are found to be consistent even during the passage of traveling disturbances.

The quantum theory of the complex dielectric tensor eij(ω, q), which has been developed in [6], is extended to the case of crossed electric and magnetic fields. The quasi-classical approximation is considered and the results are compared with earlier papers [6 to 9]. The expression for the complex conductivity tensor δij(ω, q) is used for studying the influence of the external uniform electric field on the intraband Faraday effect in semiconductors with simple band structure in two cases: the classical magnetic field and quantum limit. A brief discussion of the results is given. [Russian Text Ignored].

This paper reviews the work which has been carried out in these Laboratories during the past two years on single crystals of bismuth telluride and its alloys.The combination of experiments on Faraday rotation with those performed previously on galvanomagnetic effects has established that there are 3‐ and 6‐valley band structures associated with p‐ and n‐type Bi2Te3, respectively. However, observations of the anisotropy ratio for the electrical conductivity and of the galvanomagnetic coefficients for heavily doped n‐type material have shown that the shape of the equal‐energy surfaces is dependent on carrier concentration. Similar conclusions have been drawn from the behavior of the Seebeck coefficient at low temperatures.Measurements on Bi2Te3 at low temperatures and on alloys of Bi2Te3 have shown that the lattice thermal conductivity is particularly sensitive to the substitution of atoms of I, Se, or S for those of Te. It has also been shown that the anisotropy ratio for the lattice thermal conductivity i...

This paper presents a survey of the present position of the technology of optical communication systems. The gallium arsenide laser and gas lasers are compared as sources. The Pockel effect, acoustic and Faraday effect modulators are discussed. The advantages and disadvantages of various transmission systems are also discussed. Brief comments are made about various types of detectors. It is concluded that the information capacity is limited by the bandwidth of the source, modulator or detector. No satisfactory transmission system for long distance telecommunications use has yet been perfected, but guided systems of the type illustrated by a dielectric fibre guide, seem to offer the most promise. Despite the advances made in sources and modulators, many problems still remain before optical frequencies can be used for long distance telecommunication systems. Short range and outer space systems are feasible with the existing techniques.

The microwave mobility in a semiconductor can be obtained by mounting a sample in a bimodal cavity with an applied static magnetic field and then measuring the power transfer which is produced by the Faraday rotation in the sample. This paper gives an analysis of the effect based on the field distributions in the cavity and the wave propagation in the sample. The dependence of the power transfer on the static applied magnetic field, on the mobility and conductivity of the sample, and on an effective sample size is obtained.

One of the methods currently being used to obtain total electron content data depends upon the accurate measurement of the total Faraday rotation of linearly polarized signals transmitted from geostationary satellites [Garriott et al., 1965; Yuen and Roelofs, 1966]. The amount of polarization rotation depends upon the values of electron concentration and magnetic field along the signal path, and since both quantities vary along the path, the calculation of content from rotation angle data can be difficult. The usual simplification used in the reduction of data is to assume that the ionosphere remains essentially constant in relative shape and height, and hence the value of the magnetic field can be set equal to a constant corresponding to the field at some point on the ray path. This value is chosen so that errors in content introduced by this simplifying assumption are equal and opposite above and below the chosen height. This paper considers the error introduced in the total content by changes in ionospheric layer height, and shows that if corrections are included, some of the smaller variations in electron content are apparent rather than real.

Reciprocal ensembles of coupled transmission lines have been studied for many years using matrix techniques. In this paper, the lossless multiconductor transmission line model is extended to permit a description of gyromagnetic coupling effects. The novel ingredient which allows such an extension is the incorporation of distributed gyrators into the elemental line-length prototype. These gyrators provide antireciprocal coupling between the ensemble conductors. The amount of coupling is expressed by a geometry-dependent factor which in effect measures a given structure relative to an ideal Faraday rotator in the same medium. The gyromagnetic coupling factor, in conjunction with the derived expressions for mode propagation factors and characteristic impedances, provides a means of interpolating between the known limits of no coupling and ideal Faraday rotation. General relations are derived for two-line systems and for symmetrical, quasi-TEM three-line systems.

At a result of new developments, the classical concepts of magnetic materials, characterized by hysteresis loss and eddy currents, are no longer adequate. Study of the ferrites has revealed new and important magnetic phenomena. These materials, because of their high resistivities and correspondingly low eddy currents, exhibit useful magnetic properties at frequencies well above those at which magnetic alloys are applicable. This paper reviews the new phenomena — domain wall motion and dimensional effects in the low megacycle region, and ferromagnetic resonance and the Faraday effect in the microwave region — and relates them to modern theory. Some possible microwave applications are discussed briefly.

This paper describes the results of a theoretical and experimental investigation of the tensor dielectric susceptibility of a plasma in which some of the participating atoms exhibit population inversion. The measurement of the real part of the tensor dielectric susceptibility in the vicinity of an optical resonance has previously been very difficult due to the large absorption near resonance; however, by examining a resonance for which the levels exhibit population inversion we have obtained a direct measure of the real part of the susceptibility by observing the "negative" Faraday rotation, i.e., "negative" circular birefringence associated with the resonance. We also observed for levels with inverted populations the complement of the inverse Zeeman effect, that is, we observed a Zeeman splitting of the gain curve in the amplifying medium. The high-gain $5d[\frac{3}{2}]_{1}^{}{}_{}{}^{0}\ensuremath{-}6p{[\frac{3}{2}]}_{1}$ transition of atomic xenon at 2.026 \ensuremath{\mu} in a helium-xenon mixture was used for these measurements. The observed results were consistent with the theory.

This paper presents the results of an experiment to measure the electron density above the ionosphere. The experiment utilized two coherent signals, one VHF and one UHF, transmitted from the Explorer VI satellite. The evidence of our data is that the electron concentration in the vicinity of the satellite, 18,000 km above the earth, was unusually high, of the order of 104 electrons/cm3. However, the results were influenced by unexpectedly high correction factors and possibly by an intense world-wide magnetic storm that occurred during the measurement period.

IN three very important and groundbreaking papers, Sofue, Fujimoto and Kawabata1, Kawabata et al.2, and Reinhardt and Thiel3 call attention to evidence which indicates that Faraday rotation is taking place in space outside our own Galaxy. Essentially they show that above low galactic latitudes, where material in the disk of our own Galaxy is known to produce Faraday rotation, extragalactic radio sources exhibit Faraday rotations which generally increase with the redshift of the source, and that these rotations behave similarly in certain regions of the sky.