Contains research objectives, summary of research and reports on one research project.National Aeronautics and Space Administration (Grant NGR 22-009-526)Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DAAB07-71-C-030

Owens, D. Kingston

Weiss, Rainer

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VII. GRAVITATION RESEARCHAcademic and Research StaffProf. R. WeissDr. D. J. MuehlnerR. L. BenfordGraduate StudentsMargaret A. Frerking N. A. PierreD. K. Owens M. RosenbluhRESEARCH OBJECTIVES AND SUMMARY OF RESEARCHThe research in this group is in the field broadly labeled experimental relativity.Our objective is an experimental investigation of the gravitational interaction and themeasurement of cosmological observables.Specific Projects1. Astronomy in the Region 1-0. 1 mmOur present knowledge concerning the sky in the region between 1 mm and 0. 1 mmis still very limited. This region of the electromagnetic spectrum includes the cosmicisotropic background radiation, thermal radiation by interstellar dust, and most likelydiscrete sources that are not visible in other regions of the spectrum, in particular, dis-tant sources that may give information concerning the early history of the universe.Our major effort in this area for the last few years has been to obtain a set of mea-surements of the spectrum of the isotropic background radiation in the region 3-0.5 mm(3-20 cm-l), using a liquid-helium-cooled balloon-borne radiometer. In a series ofmeasurements from September 1969 to September 1971 (reported in Quarterly ProgressReport No. 105, pp. 17 -53) we established that the isotropic background radiation fol-lows a Planck distribution appropriate to a blackbody at approximately 2. 7K inthe 3-12 cm - 1 region. The blackbody peak occurs at 6 cm - . In the region beyond12 cm - 1 , atmospheric radiation, primarily from ozone and water, dominates the spec-trum even at 40 km altitude.-1In an effort to measure the spectrum in the region above 12 cm-1 we made a flightin October 1972 at 44 km altitude with a new complement of filters. One of thesefilters extends the measurement of the isotropic radiation to 16 cm- 1. Two other fil-ters were included to measure the column densities of ozone and water separately. Theresults of this flight are still being analyzed, but indications are that the isotropic spec-trum is a Planck distribution up to 16 cm -l and that it is indeed the atmosphere thatproduces an excess flux for frequencies greater than 16 cm-1Further measurements of the spectrum from balloon platforms with present infra-red technology do not appear to be promising unless we can achieve altitudes of 60 kmThis work is supported by the National Aeronautics and Space Administration(Grant NGR 22-009 -526) and by the Joint Services Electronics Programs (U. S. Army,U. S. Navy, U. S. Air Force) under Contract DAAB07 -71-C-0300.QPR No. 108(VII. GRAVITATION RESEARCH)or higher. These experiments seem to be good candidates for space-shuttle flights.Our major new effort in far infrared astronomy is a balloon-borne experiment tomeasure the isotropy of the background radiation in the spectral region 3-10 cm-1which includes almost all of the energy of the cosmic background radiation and a minimalamount of atmospheric radiation. In principle, with a balloon-borne differential radiom-eter using existing technology, it should be possible to measure .01% anisotropies of thebackground radiation in a balloon flight of 2 hours.The symmetry properties of the expansion of the universe can be determined bymeasuring the moments of the intensity distribution of the background radiation. It isbelieved that there should be a first moment in the distribution caused by the Earth'smotion relative to the average rest frame of the universe - the co -moving referenceframe. This anisotropy can be characterized by a temperature that is dependent onthe direction of observationT (1-p2)1/2T(P, 6) = 1 - p cos ewhere p = v/c, v is the velocity of the Earth relative to the frame in which the radi-ation is isotropic and of temperature T , 6 is the angle between the direction ofobservation and the velocity v.The bandpass from 3-10 cm - 1 includes almost all of the energy of a 2.7 0 K black-body so that the intensity is given by the Stefan-Boltzmann law: I(T) cc T 4The variation in intensity as a function of direction of observation is then of orderI 4p cos 0.-3The largest known contribution to p comes from the rotation of the galaxy, P ~ 10 -which gives a .04% anisotropy. The proper motion of our local group of galaxies isunknown, and may be measured in this experiment.2. Far Infrared DetectionWe are engaged in an experiment to detect far infrared radiation by parametric up-conversion in CdS pumped by the 5145 A line of the argon ion laser (see Quarterly Prog-ress Report No. 100, pp. 54-58).We are also making a study of "hot" electron effects in InSb; specifically, the radi-ation by hot electrons and the modulation of the far infrared properties of InSb by varyingthe electron temperature.3. Gravitational Antenna to Search for Gravitational Radiationfrom Collapsing Stars and PulsarsThe gravitational antenna is a set of virtually free masses mounted on low-frequencysuspensions that are arranged to form a Michelson interferometer. Gravitational radi-ation modulates the separation of the masses. The separation is measured with a nullservomechanism system that maintains the interferometer on a single fringe. A-2110-m version of the antenna has a theoretical sensitivity of 10 strain per square rootof detection bandwidth between 30 Hz and 10 kHz. The principal technological develop-ments accompanying the construction of the antenna are the development of a high-powerargon laser with an amplitude noise approaching the Poisson noise limit and thedesign and construction of horizontal suspensions with extremely low mode-modeQPR No. 108(VII. GRAVITATION RESEARCH)coupling. Principal optical components of the antenna are multipass delay linesincluding two spherical mirrors, or a corner reflector with a spherical mirror.4. Geomagnetic PulsesAn experiment is in progress to search for coincident geomagnetic field fluctuations-3over a 100-km baseline which have amplitudes of the order of 10-3 G and rise times less-1than 101 s. Events of this nature could be the cause of the signals that J. Weber, atthe University of Maryland, attributes to gravitational radiation. The instrumentationis extremely simple. Two 1-m2 induction coils, each with buffer storage, are usedto record the amplitude and rise time of geomagnetic fluctuations that exceed the thresh-old amplitude of 10 - 4 G in 10 - 1 s or less.R. WeissA. MEASUREMENT OF INTRINSIC LASER PHASE NOISEJoint Services Electronics Programs (Contract DAAB07-71-C-0300)D. K. OwensWe report a measurement of the phase fluctuations in the oscillation of a gas lasercaused by spontaneous emission. The phase fluctuations in the signal resulting from theheterodyne of two independent modes in the laser were measured with the instrumentshown in Fig. VII-1.The gas laser is a He-Ne laser operating at 1.153 im. The discharge tube is placedin an axial magnetic field and, because of the Zeeman effect in neon, the laser oscillates1-4at two closely spaced frequencies with opposite circular polarizations. An etalon andan iris in the laser cavity limit oscillation to only one longitudinal and one radial modefor each polarization. Furthermore, the etalon can be rotated to equalize the cavitylosses for the two circular polarizations. One of the cavity mirrors is mounted on apiezoelectric transducer in order to adjust the cavity resonance so that both polarizationmodes oscillate with the same intensity. Under these conditions, and for a sufficientlystrong magnetic field, the difference (beat) frequency between the two oscillating modesis linearly proportional to the axial magnetic field strength.The laser is incorporated in a servo system that locks the beat signal 900 out ofphase to an external oscillator by controlling the magnetic field on the discharge tube.The servo removes low-frequency, large-amplitude fluctuations in the beat frequencyand permits convenient access through the servo error signal to the laser phase fluc-tuations.The laser beam passes through a linear polarizer that converts the two circularlypolarized waves into a linearly polarized wave that is amplitude-modulated at the beatfrequency. The radiation is detected by a germanium avalanche photodiode cooled toQPR No. 108(VII. GRAVITATION RESEARCH)200'K. The photodiode output is amplified by a low-noise, broadband preamplifier,squared by a Schmitt trigger and then applied to a phase detector and a frequency dis-criminator. The output of the phase detector (point ® in Fig. VII-1) is proportionalMAGNET COIL FOR LINEARIR IS FARADAY EFFECT POLARIZER7 -DETECTORSOLENOID MAGNET IC 20DISCHARGE TUBE PIEZOELECTRICTRANSDUCER Fig. VII-1.OSC LLATORCALIBRATION Servo system and He-Ne laser.IFREOENCY The length of the laser cavityFREQUENCYI DISCRIMINATOR is 107 cm, and the discharge isPOWER SCHMITT 58 cm long. The mirrors haveAMEL F FER PREAMPLI F ERAMPLFER FLTER TRIGGER PREAMPLFER a 120-cm radius of curvature.AND PHASESERVO DETECTORCOMPENSATIONLOCK N LOCALRECORDER AMPLIFIER OS CILLA ORTUNED TO w,to the phase difference between the beat signal and the local oscillator. The phase detec-tor output is the servo error signal that controls the current in the solenoid coil aroundthe discharge tube. The frequency discriminator facilitates the phase lock and ceases tobe part of the servo system when the phase lock has been attained.The power spectrum of the voltage fluctuations measured at is obtained by usinga lock-in amplifier as a narrow bandpass filter. From these measurements it is possibleto infer the spectrum of the laser phase fluctuations that would be present if the servowere not used. To do so it is only necessary to note that with respect to phase fluctua-tions, the servo system is linear and hence can be analyzed in the frequency domain.Then, at any specific frequency in the closed-loop configuration, the amplitude of thevoltage at ( is proportional to the amplitude of the open-loop laser phase fluctuation.The constant of proportionality is frequency-dependent and is obtained by applying asinusoidally varying magnetic field to the etalon. Because of the Faraday effect in theetalon glass, the magnetic field produces a time-variant difference in the refractive indexfor left and right circularly polarized light. In effect, the cold cavity optical path lengthsfor the two polarizations are differentially modulated so that the beat frequency becomesmodulated at the frequency of the time-variant field. At ( this appears as a signal atthe modulation frequency. The constant of proportionality is the ratio of the amplitude ofthis signal to the amplitude of the open-loop modulation of the beat frequency. The open-loop beat-frequency modulation can be measured by varying the magnetic field on theetalon at a frequency outside the bandwidth of the servo. The signal at 0 is then inde-pendent of the servo and depends only on the gain of the phase detector and strength ofQPR No. 108(VII. GRAVITATION RESEARCH)the magnetic field on the etalon. These quantities can be measured and the ratio of thechange in beat frequency to magnetic field strength calculated. This ratio is frequency-independent and serves to calibrate the instrument at all modulation frequencies. Withthis information, we can also determine the Verdet constant of the etalon glass.Figure VII-Z shows the power spectrum 5 of the frequency fluctuations in the beatsignal for output mirror transmittances of 4. 3% and 1. 6%. In all of these experimentsthe beat frequency was 150 kHz, the discharge current was 20 mA, and the laser outputpower was kept constant at 6. 4 +. 3 iW per polarization by adjusting the etalon and cavitymirrors.8I Fig. VII- 2.Power spectra of the laser frequency fluctuationsfor S = 1.65 X 107 photons per mode (1. 6% case)o + 6oRT and S = 6. 2 X 10 photons per mode (4. 3% case).THEORETICALMINiMUM T=4.3% The theoretical minimum of the power spectrum,8 (determined from Eq. 1) is indicated for each case.o ++ I +++. System noise, which is primarily amplitude noiseI-.S converted into phase noise in the Schmitt trigger, isTHEORETICAL determined by measuring the noise at the mixerMINIMUM output when the photodiode is illuminated by infra-- SYSTEM NOISE /  red radiation from an LED amplitude-modulated/ at the beat frequency. The photo signals from theJ/ LED and laser are equal.102 103  104 105v (Hz)The cavity Q for each case was measured by using an auxiliary 1. 153 jm He-Nelaser to determine the linewidth of the Fabry-Perot resonances of the laser cavity. TheQ was measured as (9. 9 1) X 10 7 for the 1.6% transmittance case, and (9.7 ±) X 107for the 4. 3% transmittance case. Since the power, Q, and discharge conditions areessentially the same for both cases, the only difference is in the radiation density storedin the laser cavity.Above 1 kHz, the spectrum appears flat and clearly shows that the frequency fluc-tuations increase with decreasing radiation density in the cavity. For the 1. 6% transmit-tance case, the number of stored photons per mode is 1.65 X 107 and the power spectrumis f (v) = (9.6 ± 2) X 10 - 2 Hz /Hz; for the 4.3% transmittance case the number of6 2 -1 2stored photons per mode is 6. 2 X 106 and f (v) = (2. 7 ± .3) X 10 Hz /Hz. Below 1 kHz,the spectrum is dominated by extrinsic sources such as acoustic and ground vibrations.The data strongly suggest that the frequency fluctuations above 1 kHz are due to spon-taneous emission.QPR No. 108(VII. GRAVITATION RESEARCH)The spectrum of the intrinsic frequency fluctuations of a single-mode laser is givenbyf2 (v) = D (1)where D is the intrinsic laser linewidth. 6' 7 A lower limit can be placed on D by usingthe formula derived by Scully and Lamb 81 vD - 2 SQ'where v is the laser oscillation frequency, S the number of photons stored in the mode,and Q the quality factor of the laser cavity. The spectrum of the beat-frequency fluc-tuations is twice that of (1), provided that the two modes are independent. With previ-ously given values of S and Q, we calculate the power spectra to beT = 4.3% fB(v) = 1. 4 X 10 - 1 Hz2/HzT = 1. 6% f (v) = 5. 1 X 10 - Hz /Hz.The measurements are consistent with theoretically predicted values.It is possible to measure extremely small Verdet constants with modest fields byusing the technique described in this report. For example, the etalon glass was foundto have a Verdet constant of 12. 5 X 10 - 3 min/G-cm, where a field of 1.7 G gave a largesignal-to-noise ratio. The intrinsic laser phase fluctuations limit our ability to mea-sure differences of refractive index in transparent materials for right and left circu-larly polarized light off (v ) LlasernR - n L  Z LfT s amplewhere T is the integration time.This technique may find application in the measurement of electron densities intenuous plasmas, and holds some promise for making a measurement of the refractiveindex of strong electric or magnetic fields as predicted by quantum electrodynamics. 9' 10References and Footnotes1. P. T. Bolwijn, in P. L. Kelley, B. Lax, and P. E. Tannenwald (Eds.), Proc.International Conference on the Physics of Quantum Electronics, Puerto Rico,1965 (McGraw-Hill Book Company, Inc., New York, 1966), p. 620.2. M. Sargent III, W. E. Lamb, Jr., and R. L. Fork, Phys. Rev. 164, 436 (1967).QPR No. 108(VII. GRAVITATION RESEARCH)3. M. Sargent III, W. E. Lamb, Jr., and R. L. Fork, Phys. Rev. 164, 450 (1967).4. R. Paananen, C. L. Tang, and H. Statz, Proc. IEEE 51, 63 (1963).5. In the frequency domain, phase fluctuations and frequency fluctuations are equiva-lent. The respective power spectra are related by v2 (v) = f 2(v).6. A. Maitland and M. H. Dunn, Laser Physics (North-Holland Publishing Co., Amster-dam, 1969), p. 288.7. W. E. Lamb, Jr., in C. DeWitt, A. Blanding, and C. Cohen-Tannoudja (Eds.),Quantum Optics and Electronics; Lectures Delivered at Les Houches during the1964 Session of the Summer School of Theoretical Physics, University of Grenoble(Gordon and Breach Publishers, Inc., New York, 1965), p. 377. The power spec-trum, f2(v), can be derived from results presented in references 6 and 7.8. M. O. Scully and W. E. Lamb, Jr., Phys. Rev. 159, 208 (1967).9. T. Erber, in B. Lax, F. Bitter and R. Mills (Eds.), International Conference onHigh Magnetic Fields, Cambridge, Massachusetts, 1961 (The M. I. T. Press, Cam-bridge, Mass., and John Wiley and Sons, Inc., New York, 1962), p. 706.10. R. Baier and P. Brertenlohner, Nuovo Cimento 47B, 117 (1967).QPR No. 108

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