Showing papers on "Phase (waves) published in 1969"

Exact and Approximate Solutions for Multiple Scattering by Cloudy and Hazy Planetary Atmospheres

Abstract: Solutions are obtained for the problem of multiple scattering by a plane parallel atmosphere with anisotropic phase functions typical of cloud and haze particles. The resulting albedos, angular distributions of intensities, and planetary magnitudes are compared to solutions obtained with approximate analytic phase functions and, in the case of the cloud phase function, to the solution obtained with the forward diffraction peak omitted from the phase function. It is shown that the cloud phase function with the truncated peak yields results practically identical to those obtained with the complete cloud phase function, not only for albedos and magnitudes, but also for the angular distribution; the approximation introduces errors of several per cent in the angular distribution for direct backscattering (the region of the glory), for emergent angles near grazing regardless of the incident angle, and, of course, a larger error occurs for total scattering angles near 0°. However, the errors are unimpor...

LARGE NONLINEAR OPTICAL COEFFICIENT AND PHASE MATCHED SECOND HARMONIC GENERATION IN LiIO3

Abstract: The second harmonic of a Nd laser has been produced in LiIO3 in a phase matching direction of 30° to the c axis with high conversion efficiency. The nonlinear optical coefficient t31 is among the highest so far reported for phase matchable substances using λ = 1.06 μ. LiIO3 can be grown from water solutions with excellent optical quality.

PSK error performance with Gaussian noise and interference

Abstract: A single, constant amplitude, in-band, additive interference is included in the analysis of detecting phase shift keyed signals in gaussian noise. For coherent detection we give a method applicable to any M-phase system, and evaluate the symbol error probability for M = 2, 3, and 4. For differential detection we treat the important cases M = 2, 4, 8, and 16, offering comprehensive numerical results for each. The analysis in each case is based on a single sinusoid with random phase adding to the noisy phase shift keyed signal. The results are then interpreted to include an angle modulation impressed on the continuous wave interferer. The receiver consists of an ideal phase discriminator with a perfect slicer. The channel is also assumed ideal in that intersymbol interference is not considered.

Transverse Mode Locking.

Abstract: The possibility of phase locking the transverse modes of a laser is considered. It is shown that if a transverse mode set having a Poisson intensity distribution can be phase locked, a scanning laser beam can be produced.

Electron-Ion Interaction and the Fermi Surfaces of the Alkali Metals

Abstract: A method is proposed whereby the partial-wave phase shifts which characterize the scattering of plane waves by the ionic cores in a metallic lattice may be deduced from experimental Fermi-surface data. The method is applied to an analysis of currently available experimental data on the shapes of the Fermi surfaces of the alkali metals. Starting from the full many-body theory of conduction electrons in a metallic lattice, it is shown that the shape of the Fermi surface may be derived from a one-electron-like Schr\"odinger equation which involves a nonlocal effective potential. The augmented-plane-wave method is applied to solve the nonrelativistic Schr\"odinger equation for the shapes of the surfaces of constant energy in k space, in the approximation where the effective potential may be represented by an angular-momentum-dependent potential of muffin-tin form. The partial-wave phase shifts of the muffin-tin potential are adjusted to bring the area distortions of the computed surface into agreement with the experimental data. The phase shifts deduced in this way are shown to be largely independent of the radius of the muffin-tin sphere. It is found that the shapes of the Fermi surfaces of the alkali metals are systematically influenced by the position of each metal in the periodic table. Lithium shows a strong $p$ phase shift, which anticipates the onset of the $p$ resonance in the second row of the periodic table. The phase shifts in sodium are found to converge rapidly in angular momentum, presumably because the $p$-like component of the ionic potential is largely cancelled by the $p$-like core states, while the $d$-like component of the ionic potential is rather weak. Potassium, rubidium, and cesium show increasingly strong $d$ phase shifts, which are associated with the positions of these metals at the heads of the $3d$, $4d$, and $5d$ transition series. Only for potassium are the experimental data sufficiently accurate to show the influence of a small $f$ phase shift. The method of phase-shift analysis has several advantages as a technique by which the radial distortions of the Fermi surface of a metal may be deduced from experimental data on the anisotropy of its extremal cross-sectional area. These include rapid convergence of the series of phase shifts, the use of a model surface generated in a way closely related to a first-principles band-structure calculation, and the possibility of applying the technique both to nearly-free-electron metals and to metals of the transition series. The radial distortions of the Fermi surfaces of the alkali metals are computed, and the results are compared with those of earlier calculations. Finally, it is shown that our results impose criteria which must be satisfied by any effective potential of muffin-tin form that may be proposed to represent the effects of electron exchange and correlation in the alkali metals.

Laser‐Verstärker und Phasenunschärfe

Abstract: Extending recent calculations of GLASSGOLD and HOLLIDAY [3] the amplification process by means of a laser amplifier is treated theoretically in case of an arbitrary quantum mechanical state of the incident electromagnetic field. An explicit expression for GLAUBER's P-function representing the state of the field after amplification, is found. Interpreting this function as a classical distribution function for the complex amplitude of the field, a distribution function W(φ; t) for the phase is obtained by averaging over the real amplitude. With the help of W(φ; t) the phase uncertainty (δφ)2 for the amplified field is calculated. The result approximately agrees with the expression for(δφ)2 following from the phase operator originally introduced by HEITLER if applying it to the incident field. Thus a connection between the phase operator and an experimental arrangement is established.

Acoustic surface waves on silicon

Abstract: Acoustic surface wave phase velocities have been measured on (001), (110), and (111) surfaces of single‐crystal silicon using the wedge method. Good agreement between the theoretical and experimental results was obtained.

An optical homodyne technique for measurement of amplitude and phase of subangstrom ultrasonic vibrations

Abstract: An optical homodyne technique is utilized to measure sub-angstrom dynamic mechanical deformations. For measurement in the frequency domain, where synchronous detection is used both the amplitude and phase of the mechanical signal can be measured with a high sensitivity; displacements less than 10-2A were measured with normal environment acoustic noise. Measurement in the time domain is also feasible with reduced sensitivity.

Phase-matching for optical up-conversion with maximum angular aperture — theory and practice

Abstract: An equation of quadratic form is derived relating the phase mismatchΔk=¦ksum −kpump −kslgnl ¦ in an optical sum-frequency generation process to the angle ψ between the pump and signal wave vectors. For a special value ofkpump a solution ofΔk=0 exists having degenerate roots and consequently a single value of ψ. Because of this it is possible to choose a non-collinear phasematching situation for an optical up-converter which tolerates a much larger signal beam divergence than if a collinear-beam interaction were chosen. The case of up-conversion of 10.6μm radiation to the visible, using ruby-laser pumped proustite was chosen as an example for experimental study. Under tangential phase-matching conditions an angular acceptance angle of the infra-red beam of 300 mrad was achieved for a crystal 0.45 cm long.

Stabilized mode-locked laser arrangement

Abstract: It has been observed that the pulse-train output of a modelocked Nd:YA1G laser exhibits a 180* phase instability. As a result it is not possible to achieve long term stable operation of such a laser by abstracting from the output pulse train a signal whose frequency corresponds to the axial-mode fundamental beat frequency. However, the phase of the second harmonic of this fundamental beat frequency which may be abstracted from the output pulse train does not exhibit such a 180* phase instability. Accordingly this second harmonic signal can be utilized as a discriminant from which a fundamental signal may be derived. In turn this derived fundamental signal is applied to drive an intracavity phase modulator. In this way the laser is stabilized in its mode-locked state by feedback techniques despite the aforementioned phase-instability characteristic.

Apparatus for controlling a beam of coherent electro-magnetic waves

Abstract: Focusing means in the path of a beam of coherent electromagnetic waves focus the beam on a focal plane. The beam intensity varies across the diameter. First transparent refractive means in the path of the more intense portion of the beam transmits the waveforms but retards their phase. Second transparent refractive means in the path of the less intense portion of the beam transmits the less intense waveforms but retards their phase an amount different from that of the first refractive means. Interference at the focal plane between the phase changed waveforms alters the original intensity profile of the waveforms. By controlling the relative phase changes the intensity pattern can be altered to be substantially uniform across the beam with only small loss of energy.

Switching of phase-locked states in the intracavity phase-modulated He-Ne laser

Abstract: It is known that there exist two solutions for the He-Ne laser phase locked by synchronous internal phase modulation. One corresponds to a phase difference between adjacent modes of even integers of π (even state) and the other to odd integers of π (odd state). Although their frequency power spectra in general look similar, they appear in the time response as two different sets of pulse trains 180° out of phase with respect to each other. Of the two, for a given set of conditions, it has not yet been possible to predict which state will oscillate. In our observations we find that, if the modulation frequency is fixed slightly higher than the average axial-mode spacing near the line center, the two states can be controlled by varying the amplitude of the modulation signal, resulting in a switching action between the two states. Furthermore, we find that in a narrow region of "detuning" and in a small range of modulation amplitudes, both states oscillate simultaneously. The above results were analyzed by considering the asymmetry in the frequency characteristics of the gain medium due to the presence of the isotope Ne22in the He-Ne mixture. Based on this fact and the concept of "supermode" competition, we give a physical explanation for the observed behaviors. This is supported by the absence of amplitude-dependent switching in a He-Ne tube containing only pure isotope Ne20. We observe also in a He-Ne tube containing 75% Ne20and 25% Ne22the dominance of one state over the other; this result is consistent with the qualitative theory given.

Continuity of Phase Shift at Continuum Bound State

Abstract: When a separable potential has a bound state in the continuum, there are two possible definitions of the phase shift. It is shown that if the phase shift is chosen to be the boundary value of the phase of an analytic function, then it has a jump discontinuity of magnitude $\ensuremath{\pi}$ at each continuum bound state. Some advantages of this definition, as opposed to one giving a continuous phase shift, are presented.

Phase-responsive circuits

Abstract: This invention relates to a circuit which provides an indication, on a display, of phase changes in signals from a variable phase signal source. The phase of these signals may vary in dependence upon displacement of, for example, a machine slide. The number of clock pulses generated by a clock pulse source between the occurrence of the leading edge of a reference signal and the occurrence of the next leading edge of the variable phase signal gives a measure of the phase relationship between the two signals. Changes in phase between successive cycles of the variable phase signal are detected by a comparator and a detector which cause a number of counting pulses, equal to the difference between the clock pulse counts of the two successive cycles, to be fed to a reversible counter, together with a ''''Count Up'''' or a ''''Count Down'''' instruction. The number in the counter and in the display gives a measure of the resultant phase shift relative to the phase at the time of setting the counter. The number of clock pulses generated per cycle of the reference signal may be chosen so that the number displayed gives the machine slide displacement directly in inches or metric units.

Variable frequency phase matching distance measuring and positioning device

Abstract: The invention is a laser driven distance measuring device, the output of which can be used to precisely control the distance between objects. Interrogating signals, modulated by a control signal, are beamed towards an object and the phase of reflected portions of these signals compared with that of the modulating control signal. The frequency of the transmitted signals is varied until a desired phase match between the transmitted and received signals is achieved. The distance to an object is determined mathematically from the value of two adjacent frequencies at which the designated phase relationship is observed to occur. By measuring the change in frequency of the modulating control signal necessary to effect the desired phase match with a reference frequency, a control signal is generated which can be utilized to adjust the distance measured.

Realization of an all-pass transfer function

Abstract: A simple circuit, using a grounded inverting operational amplifier, is described for realizing an adjustable phase shift from -π to +π of an incoming signal without a change in amplitude with respect to phase. This circuit is seen as an alternative to that of Genin.

Phase Effects in the Nonlinear Interaction of “Negative”-Energy Waves

Abstract: Nonlinear interaction of “negative”-energy waves is studied assuming well-defined phases and perfect matching conditions. The results are compared with those of the random-phase approach, and significant differences in the dynamics due to phase effects are pointed out.

Diffraction Images of Coherently Illuminated Objects in the Presence of Aberrations

Abstract: Diffraction images of coherently illuminated objects in the presence of aberrations are studied; in particular the images of edges, discs and bars are obtained for both amplitude and phase objects. Representative numerical calculations are included.

The π N partial waves at low energies and in the unphysical region

Abstract: The real parts of theπN partial wave amplitudesfl±(−) have been calculated from fixed-t dispersion relations, using phase shifts up to 2 GeV and the reggeizedp-exchange model at higher energies. The comparison with Refl±(−) as calculated directly from phase shifts shows to what extent the input is consistent with the fixed-t relation. The result is also of interest for the test of simple models, in particular for the comparison with predictions from current algebra. — A new evaluation of the partial wave dispersion relation forf0+(−) is presented. Combined with the first method it shows that the determination of thep-coupling parameter is based on an assumption which is difficult to justify.

Phase‐matched nonlinear interaction between circularly polarized waves

Abstract: This paper reports the first observation of phase‐matched nonlinear interaction between three circularly polarized waves.

Phase coherent and amplitude stable frequency shift oscillator apparatus

Abstract: A phase coherent and amplitude stable frequency shift oscillator apparatus comprising a negative impedance converter, biased into an unstable oscillatory condition, in combination with a pair of impedances respectively coupled to the input terminals thereof for determining the frequency of oscillation. One of the impedances includes a series resistive-reactive impedance circuit and the other includes a parallel resistive-reactive impedance circuit. Means are provided for changing the value of the resistive components of the impedances in order to alter the output frequency of the oscillator apparatus and a level limiting and buffering means is provided for stabilizing the oscillatory operation and buffering the output obtained from the apparatus.

Apparatus for digitally representing angular displacement

Abstract: A goniometer arrangement providing a digital representation of the angular position of the goniometer rotor includes a highfrequency source, a frequency divider formed by a first counter for deriving low-frequency pulses which are shaped to provide a sinusoidal voltage, and a second counter for counting the periods of the high frequency. The sinusoidal voltage is applied in phase quadrature to the fixed windings of the goniometer and the phase of the output from the second counter, which should correspond to the angular position of the goniometer rotor, is compared with a reference voltage derived from a further fixed winding in the goniometer. The phase of the first counter relative to the second counter is controlled in accordance with this comparison by varying the number of pulses supplied to one of the counters.

Dual harmonic frequency synthetic aperture radar

Abstract: A dual harmonic frequency synthetic aperture radar system in which synthetic aperture processing is used to achieve high angular resolution for two radars which operate at two or more harmonically related frequencies. These frequencies are related by the factor N. The processing is done so as to preserve the phase of the target return. After the synthetic aperture processing is completed, the phase angles are available at the two frequencies. The lower frequency phase angle is multiplied by N and compared with the phase angle at the upper frequency to obtain phase signature data on the target.

The focal properties of phase zone plates

Abstract: It is shown that the focal length of a phase zone plate is independent of the phase variation, but this does affect the intensity of the image.

Method and apparatus for stabilizing the phase of radiation

Abstract: Stabilization of the phase of the radiation utilized in a plural beam interferometric-type system is accomplished. Monitoring of the intensity of the interfering beams of radiation is performed so that a correction signal is generated. By applying the correction signal to control means, the speed of propagation of at least one of the radiation beams is altered to maintain a constant phase relationship.

Another realization of an all-pass transfer function using an operational amplifier

Abstract: A phase shift network is described which adjusts the phase from 0° to 360° of an incoming signal without change in amplitude with respect to phase.

I Multiple-Beam Interference and Natural Modes in Open Resonators

Abstract: Publisher Summary This chapter discusses multiple beam interference and natural modes in open resonators. Interferograms from multiple-beam interferometers with and without phase objects can always be expressed quantitatively as the superposition of several simultaneously excited modes of the interferometer system. The classical interference fringe and ring systems result from the superposition of the fields of many modes. The modes become prominent only when diffraction effects begin to play a major part. Application of the mode concept shows that the simple connection between object and interferogram predicted by the classical theory of multiple-beam interference holds a certain “resolution limit”. The relation is confirmed by measurements with centimeter waves and by experiments on resolution of small phase object structures in the optical region. The phase object in a wave field changes the emerging wave producing an exact phase image of the object. These effects are not noticed if only the Kirchhoff diffraction theory in the simple form is applied.

Digital data transmission system utilizing phase shift keying

Abstract: A digital data transmission system utilizing differential phase shift keying. In the transmitter serial data bits are grouped and the carrier wave is phase shifted by an angle determined from a comparison of successive data groups. In the receiver the successive phase shifts are detected by comparing the received signal in digital form with a digital reference, at a plurality of points in each cycle. When several matches are obtained for one phase, that phase is accepted as the phase of the received signal. The difference between the phases of successive portions of the received signal is utilized to reconstitute the transmitted data. Changes in polarity of the received signal are compared with the local reference signal to generate a control for the reference.

Holography of randomly moving objects

Abstract: It is shown that holograms of randomly moving objects can be taken if the reference wave is suitably phase‐modulated. By means of a mirror attached to the object, the modulation may be achieved automatically.