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At least 217 records · Page 12

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗

Computed potential energy surfaces for chemical reactions

The minimum energy path for the addition of a hydrogen atom to N2 is characterized in CASSCF/CCI calculations using the (4s3p2d1f/3s2p1d) basis set, with additional single point calculations at the stationary points of the potential energy surface using the (5s4p3d2f/4s3p2d) basis set. These calculations represent the most extensive set of ab initio calculations completed to date, yielding a zero point corrected barrier for HN2 dissociation of approx. 8.5 kcal mol/1. The lifetime of the HN2 species is estimated from the calculated geometries and energetics using both conventional Transition State Theory and a method which utilizes an Eckart barrier to compute one dimensional quantum mechanical tunneling effects. It is concluded that the lifetime of the HN2 species is very short, greatly limiting its role in both termolecular recombination reactions and combustion processes.

Walch, Stephen P.↗

Performance Characterization of the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) CCD Cameras

The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) is a sounding rocket instrument currently being developed by NASA's Marshall Space Flight Center (MSFC), the National Astronomical Observatory of Japan (NAOJ), and other partners. The goal of this instrument is to observe and detect the Hanle effect in the scattered Lyman-Alpha UV (121.6nm) light emitted by the Sun's chromosphere. The polarized spectrum imaged by the CCD cameras will capture information about the local magnetic field, allowing for measurements of magnetic strength and structure. In order to make accurate measurements of this effect, the performance characteristics of the three on- board charge-coupled devices (CCDs) must meet certain requirements. These characteristics include: quantum efficiency, gain, dark current, read noise, and linearity. Each of these must meet predetermined requirements in order to achieve satisfactory performance for the mission. The cameras must be able to operate with a gain of 2.0+/- 0.5 e--/DN, a read noise level less than 25e-, a dark current level which is less than 10e-/pixel/s, and a residual non- linearity of less than 1%. Determining these characteristics involves performing a series of tests with each of the cameras in a high vacuum environment. Here we present the methods and results of each of these performance tests for the CLASP flight cameras.

solar↗

Paleomagnetic Analysis Using SQUID Microscopy

Superconducting quantum interference device (SQUID) microscopes are a new generation of instruments that map magnetic fields with unprecedented spatial resolution and moment sensitivity. Unlike standard rock magnetometers, SQUID microscopes map magnetic fields rather than measuring magnetic moments such that the sample magnetization pattern must be retrieved from source model fits to the measured field data. In this paper, we presented the first direct comparison between paleomagnetic analyses on natural samples using joint measurements from SQUID microscopy and moment magnetometry. We demonstrated that in combination with apriori geologic and petrographic data, SQUID microscopy can accurately characterize the magnetization of lunar glass spherules and Hawaiian basalt. The bulk moment magnitude and direction of these samples inferred from inversions of SQUID microscopy data match direct measurements on the same samples using moment magnetometry. In addition, these inversions provide unique constraints on the magnetization distribution within the sample. These measurements are among the most sensitive and highest resolution quantitative paleomagnetic studies of natural remanent magnetization to date. We expect that this technique will be able to extend many other standard paleomagnetic techniques to previously inaccessible microscale samples.

Weiss, Benjamin P.↗

Preliminary Modeling of CH3D From 4000 to 4550 cm (exp-1)

A new study of 12CH3D line positions and intensities was performed for the upper portion of the Enneadecad polyad between 4000 and 4550/cm. For this, FTIR spectra were recorded with D-enriched methane samples (at 80 K with a Bruker 125 IFS at 0.005/cm resolution and at 291 K with the McMath-Pierce FTS at 0.011/cm resolution, respectively). Line positions and intensities were retrieved by least square curve-fitting procedures and analyzed using the effective Hamiltonian and the effective dipole moment expressed in terms of irreducible tensor operators adapted to symmetric top molecules. Initially, only the cold spectrum was used to identify quantum assignments and predict 12CH3D relative intensities in this region. To assign higher quanta up to J equal 14, additional line positions and intensities were obtained from two room temperature spectra. In the final stage, measured intensities from both the cold and the room temperature data were normalized to corresponding values at 296 K and then averaged. Combining the two temperature datasets confirmed the assumed quantum assignments and also demonstrated the relative accuracies to be better than 70.0002/cm for line positions and at least +/-6% for intensities so that approx.1160 features were selected. Including additional assignments from the room temperature spectra alone permitted 1362 line intensities of 11 bands (involving 23 vibrational symmetry components) to be reproduced with an RMS of 9%. Over 4085 selected positions for 12 bands were modeled to 0.008/cm. Nevertheless a number of known assignments could not be modeled to within our experimental precisions. More work is needed to obtain a complete characterization of this complex polyad.

Nikitin, A. V.↗

Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 − S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

infrared radiation↗

Testing and characterization of an IR CBIRD FPA

High performance IR cameras are in great demand for a variety of applications, including defense (e.g. night vision, missile detection) and space (e.g. imaging at IR wavelengths). IR focal plane arrays (FPAs) are an essential component of IR cameras. An FPA is a collection of detectors at the focal plane of an imaging device, where each detector can be thought of a pixel in the image it is detecting. The FPA in this study is based on Complimentary Barrier Infrared Detectors (CBIRDs). The CBIRD FPA was tested by imaging flat black body targets at three different temperatures, 20ºC, 25ºC, and 30ºC, with images captured using SEIR software. The important figures of merit for an IR FPA, Noise Equivalent Difference Temperature (NEDT), Noise Equivalent Irradiance (NEI), detectivity (D*), responsivity, and quantum Efficiency (QE), were extracted from the image data for each individual detector using a MATLAB program, as was the array Modulation Transfer Function MTF. The test results show a mean NEDT of 16.98mK and an MTF of about 0.34 at the Nyquist frequency. Overall, the array performs well in the MWIR range and takes quality IR images.

Das, Tanya↗

Scattering and Diffraction of Electromagnetic Radiation: An Effective Probe to Material Structure

Scattered electromagnetic waves from material bodies of different forms contain, in an intricate way, precise information on the intrinsic, geometrical and physical properties of the objects. Scattering theories, ever deepening, aim to provide dependable interpretation and prediction to the complicated interaction of electromagnetic radiation with matter. There are well-established multiple-scattering formulations based on classical electromagnetic theories. An example is the Generalized Multi-particle Mie-solution (GMM), which has recently been extended to a special version ̶ the GMM-PA approach, applicable to finite periodic arrays consisting of a huge number (e.g., >>106) of identical scattering centers [1]. The framework of the GMM-PA is nearly complete. When the size of the constituent unit scatterers becomes considerably small in comparison with incident wavelength, an appropriate array of such small element volumes may well be a satisfactory representation of a material entity having an arbitrary structure. X-ray diffraction is a powerful characterization tool used in a variety of scientific and technical fields, including material science. A diffraction pattern is nothing more than the spatial distribution of scattered intensity, determined by the distribution of scattering matter by way of its Fourier transform [1]. Since all linear dimensions entered into Maxwell's equations are normalized by wavelength, an analogy exists between optical and X-ray diffraction patterns. A large set of optical diffraction patterns experimentally obtained can be found in the literature [e.g., 2,3]. Theoretical results from the GMM-PA have been scrutinized using a large collection of publically accessible, experimentally obtained Fraunhofer diffraction patterns. As far as characteristic structures of the patterns are concerned, theoretical and experimental results are in uniform agreement; no exception has been found so far. Closely connected with the spatial distribution of scattered intensities are cross sections, such as for extinction, scattering, absorption, and radiation pressure, as a critical type of key quantity addressed in most theoretical and experimental studies of radiative scattering. Cross sections predicted from different scattering theories are supposed to be in general agreement. For objects of irregular shape, the GMM-PA solutions can be compared with the highly flexible Discrete Dipole Approximation (DDA) [4,5] when dividing a target to no more than ~106 unit cells. Also, there are different ways to calculate the cross sections in the GMM-PA, providing an additional means to examine the accuracy of the numerical solutions and to unveil potential issues concerning the theoretical formulations and numerical aspects. To solve multiple scattering by an assembly of material volumes through classical theories such as the GMM-PA, the radiative properties of the component scatterers, the complex refractive index in particular, must be provided as input parameters. When using a PA to characterize a material body, this involves the use of an adequate theoretical tool, an effective medium theory, to connect Maxwell's phenomenogical theory with the atomistic theory of matter. In the atomic theory, one regards matter as composed of interacting particles (atoms and molecules) embedded in the vacuum [6]. However, the radiative properties of atomic-scaled particles are known to be substantially different from bulk materials. Intensive research efforts in the fields of cluster science and nanoscience attempt to bridge the gap between bulk and atom and to understand the transition from classical to quantum physics. The GMM-PA calculations, which place virtually no restriction on the component-particle size, might help to gain certain insight into the transition.

Xu, Yu-Lin↗

Materials, structures, and devices for high-speed electronics

Advances in materials, devices, and instrumentation made under this grant began with ex-situ null ellipsometric measurements of simple dielectric films on bulk substrates. Today highly automated and rapid spectroscopic ellipsometers are used for ex-situ characterization of very complex multilayer epitaxial structures. Even more impressive is the in-situ capability, not only for characterization but also for the actual control of the growth and etching of epitaxial layers. Spectroscopic ellipsometry has expanded from the research lab to become an integral part of the production of materials and structures for state of the art high speed devices. Along the way, it has contributed much to our understanding of the growth characteristics and material properties. The following areas of research are summarized: Si3N4 on GaAs, null ellipsometry; diamondlike carbon films; variable angle spectroscopic ellipsometry (VASE) development; GaAs-AlGaAs heterostructures; Ta-Cu diffusion barrier films on GaAs; GaAs-AlGaAs superlattices and multiple quantum wells; superconductivity; in situ elevated temperature measurements of III-V's; optical constants of thermodynamically stable InGaAs; doping dependence of optical constants of GaAs; in situ ellipsometric studies of III-V epitaxial growth; photothermal spectroscopy; microellipsometry; and Si passivation and Si/SiGe strained-layer superlattices.

Woollam, John A.↗

Deep Space Network, Cryogenic HEMT LNAs

Exploration of the Solar System with automated spacecraft that are more than ten astronomical units (1 AU = 149,597,870.691 km) from earth requires very large antennae employing extremely sensitive receivers. A key figure of merit in the specification of the spacecraft-to-earth telecommunications link is the ratio of the antenna gain to operatio nal noise temperature (G/Top) of the system. The Deep Space Network (DSN) receivers are cryogenic, low-noise amplifiers (LNAs) which addres s the need to maintain Top as low as technology permits. Historicall y, the extra-ordinarily sensitive receive systems operated by the DSN have required ctyogenically cooled, ruby masers, operating at a physi cal temperature near the boiling point of helium, as the LNA. Althoug h masers continue to be used today, they are hand crafted at JPL and expensive to manufacture and maintain. Recent advances in the developm ent of indium phosphide (InP) based high electron mobility transistor s (HEMTs) combined with cryogenic cooling near the boiling point of h ydrogen have made this alternate technology comparable with and a fraction of the cost of maser technology. InP HEMT LNA modules are demons trating noise temperatures less than ten times the quantum noise limi t (10hf/k) from 1 to 100 GHz. To date, the lowest noise LNA modules developed for the DSN have demonstrated noise temperatures of 3.5 K and 8.5 K at 8.5 K at 32 GHz, respectively. Front-end receiver packages employing these modules have demonstrated operating system noise temperatures of 17 K at 8.4 GHz (on a 70m antenna at zenith) and 39 K at 3 2 GHz (on a 34m antenna at zenith). The development and demonstration of cryogenic, InP HEMT based front-end amplifiers for the DSN requir es accurate component and module characterization, and modeling from 1 to 100 GHz at physical temperatures down to 12 K. The characterizati on and modeling begins with the HEMT chip, proceeds to the multi-stag e HEMT LNA module, and culminates with the complete front-end cryogenic receiver package for the antenna. This presentation will provide a n overview of this development process. Examples will be shown for de vices, LNA modules, front-end receiver packages, antennae employing these packages and the improvements to the down-link capacity.

low-noise amplifiers (LNAs)↗

How to characterize the nonlinear amplifier?

The conception of the amplification of the coherent field is formulated. The definition of the coefficient of the amplification as the relation between the mean value of the field at the output to the value at the input and the definition of the noise as the difference between the number of photons in the output mode and square of the modulus of the mean value of the output amplitude are considered. Using a simple example it is shown that by these definitions the noise of the nonlinear amplifier may be less than the noise of the ideal linear amplifier of the same amplification coefficient. Proposals to search another definition of basic parameters of the nonlinear amplifiers are discussed. This definition should enable us to formulate the universal fundamental lower limit of the noise which should be valid for linear quantum amplifiers as for nonlinear ones.

Kallistratova, Dmitri Kouznetsov↗

Resource constrained design of artificial neural networks using comparator neural network

We present a systematic design method executed under resource constraints for automating the design of artificial neural networks using the back error propagation algorithm. Our system aims at finding the best possible configuration for solving the given application with proper tradeoff between the training time and the network complexity. The design of such a system is hampered by three related problems. First, there are infinitely many possible network configurations, each may take an exceedingly long time to train; hence, it is impossible to enumerate and train all of them to completion within fixed time, space, and resource constraints. Second, expert knowledge on predicting good network configurations is heuristic in nature and is application dependent, rendering it difficult to characterize fully in the design process. A learning procedure that refines this knowledge based on examples on training neural networks for various applications is, therefore, essential. Third, the objective of the network to be designed is ill-defined, as it is based on a subjective tradeoff between the training time and the network cost. A design process that proposes alternate configurations under different cost-performance tradeoff is important. We have developed a Design System which schedules the available time, divided into quanta, for testing alternative network configurations. Its goal is to select/generate and test alternative network configurations in each quantum, and find the best network when time is expended. Since time is limited, a dynamic schedule that determines the network configuration to be tested in each quantum is developed. The schedule is based on relative comparison of predicted training times of alternative network configurations using comparator network paradigm. The comparator network has been trained to compare training times for a large variety of traces of TSSE-versus-time collected during back-propagation learning of various applications.

Wah, Benjamin W.↗

High-resolution near-infrared spectroscopy of water dimer

High-resolution near-infrared spectra are reported for all of the O-H stretch vibrational bands of the water dimer. The four O-H vibrations are characterized as essentially independent proton-donor or proton-acceptor motions. In addition to the rotational and vibrational information contained in these spectra, details are obtained concerning the internal tunneling dynamics in both the ground and excited vibrational states. These results show that, for tunneling motions which involve the interchange of the proton donor and acceptor molecules, the associated frequencies decrease substantially due to vibrational excitation. The predissociation lifetimes for the various states of the dimer are determined from linewidth measurements. These results clearly show that the predissociation dynamics is strongly dependent on the tunneling states, as well as the Ka quantum number, indicating that the internal tunneling dynamics plays an important role in determining the dissociation rate in this complex.

Huang, Z. S.↗

Line Coupling in Atmospheric Spectra

The theoretical modeling of atmospheric spectra is important for a number of different applications: for instance, in the determination of minor atmospheric constituents such as ozone, carbon dioxide, CFC's etc.; in monitoring the temperature profile for climate studies; and in measuring the incoming and outgoing radiation to input into global climate models. In order to accomplish the above mentioned goal, one needs to know the spectral parameters characterizing the individual spectral lines (frequency, width, strength, and shape) as well as the physical parameters of the atmosphere (temperature, abundances, and pressure). When all these parameters are known, it is usually assumed that the resultant spectra and concomitant absorption coefficient can then be calculated by a superposition of individual profiles of appropriate frequency, strength and shape. However, this is not true if the lines are 'coupled'. Line coupling is a subtle effect that takes place when lines of a particular molecule overlap in frequency. In this case when the initial states and the final states of two transitions are connected by collisions, there is a quantum interference resulting in perturbed shapes. In general, this results in the narrowing of Q-branches (those in which the rotational quantum number does not change), and vibration-rotational R- and P branches (those in which the rotational quantum number changes by +/- 1), and in the spectral region beyond band heads (regions where the spectral lines pile up due to centrifugal distortion). Because these features and spectral regions are often those of interest in the determination of the abundances and pressure-temperature profiles, one must take this effect into account in atmospheric models.

Tipping, R. H.↗

Coherent Mode Decomposition for Kolmogorov Optical Turbulence in a Finite Aperture

An analysis of the coherent mode decomposition of an optical field after propagation through atmospheric turbulence is presented. The coherent modes represent an ideal basis by which to decompose the field for design of mode-limited optical systems. Using the rotational symmetry of the Fredholm integral operator for Kolmogorov optical turbulence, it is shown that the coherent modes exhibit separable solutions classified by radial and azimuthal quantum numbers. The study of the coherent modes is then reduced that of the radial functions determined by the aperture-coherence diameter ratio and obscuration ratio. Analysis of the spectrum of eigenvalues yields sharp bounds on the efficiency of receivers using incoherent or coherent combining with mode-limited photonic devices in the presence of Kolmogorov turbulence. The effective number of modes needed to represent Kolmogorov optical turbulence is studied via the von Neumann entropy, purity, and largest eigenvalue, and the differences in the different definitions is discussed. The similarity of the coherent modes to linearly polarized (LP) fiber modes is quantified yielding a precise characterization of the maximum gain that can be achieved in mode-limited systems via mode shaping techniques. As a final application, a mode sorting technique is presented for optimally splitting power from atmospherically degraded light into a finite number of modes simultaneously maximizing total coupling efficiency and minimizing the average and instantaneous power ratio between channels.

free-space optical communication↗

A Highly Sensitive Multi-Element HgCdTe E-APD Detector for IPDA Lidar Applications

An HgCdTe electron avalanche photodiode (e-APD) detector has been developed for lidar receivers, one application of which is integrated path differential absorption lidar measurements of such atmospheric trace gases as CO2 and CH4. The HgCdTe APD has a wide, visible to mid-wave-infrared, spectral response, high dynamic range, substantially improved sensitivity, and an expected improvement in operational lifetime. A demonstration sensor-chip assembly consisting of a 4.3 lm cutoff HgCdTe 4 9 4 APD detector array with 80 micrometer pitch pixels and a custom complementary metal-oxide-semiconductor readout integrated circuit was developed. For one typical array the APD gain was 654 at 12 V with corresponding gain normalized dark currents ranging from 1.2 fA to 3.2 fA. The 4 9 4 detector system was characterized at 77 K with a 1.55 micrometer wavelength, 1 microsecond wide, laser pulse. The measured unit gain detector photon conversion efficiency was 91.1%. At 11 V bias the mean measured APD gain at 77 K was 307.8 with sigma/mean uniformity of 1.23%. The average, noise-bandwidth normalized, system noise-equivalent power (NEP) was 1.04 fW/Hz(exp 1/2) with a sigma/mean of 3.8%. The measured, electronics-limited, bandwidth of 6.8 MHz was more than adequate for 1 microsecond pulse detection. The system had an NEP (3 MHz) of 0.4 fW/Hz(exp 1/2) at 12 V APD bias and a linear dynamic range close to 1000. A gain-independent quantum-limited SNR of 80% of full theoretical was indicative of a gain-independent excess noise factor very close to 1.0 and the expected APD mode quantum efficiency.

NEP↗

Metriwave final report

The superconductor-insulator-superconductor (SIS) mixer is a device which is being used in the construction of very sensitive receivers in the millimeter and submillimeter wavelength regions. With its potential for conversion gain and quantum-limited performance, it is becoming a device of prime importance in radio astronomy as well as earth and planetary atmospheric research. Many of the parameters of the SIS mixer cannot be readily measured in the laboratory, however, since most commercially available test instruments use test signal powers large enough to saturate or destroy SIS junctions. Detailed here is the construction of a microwave network analyzer with extremely low test signal powers. The results of a development performed by Dynamics Technology, Inc., under a Phase 2 SBIR contract from NASA (NAS7-1025) are documented. The work resulted in a network analyzer to be delivered to workers at the Jet Propulsion Laboratory, which should be capable of SIS mixer characterization in support of their ongoing work in this area.

Williams, Wyman↗

Magnetometer Based on Optoelectronic Microwave Oscillator

proposed instrument, intended mainly for use as a magnetometer, would include an optoelectronic oscillator (OEO) stabilized by an atomic cell that could play the role of a magnetically tunable microwave filter. The microwave frequency would vary with the magnetic field in the cell, thereby providing an indication of the magnetic field. The proposed magnetometer would offer a combination of high accuracy and high sensitivity, characterized by flux densities of less than a picotesla. In comparison with prior magnetometers, the proposed magnetometer could, in principle, be constructed as a compact, lightweight instrument: It could fit into a package of about 10 by 10 by 10 cm and would have a mass <0.5 kg. As described in several prior NASA Tech Briefs articles, an OEO is a hybrid of photonic and electronic components that generates highly spectrally pure microwave radiation, and optical radiation modulated by the microwave radiation, through direct conversion between laser light and microwave radiation in an optoelectronic feedback loop. As used here, "atomic cell" signifies a cell containing a vapor, the constituent atoms of which can be made to undergo transitions between quantum states, denoted hyperfine levels, when excited by light in a suitable wavelength range. The laser light must be in this range. The energy difference between the hyperfine levels defines the microwave frequency. In the proposed instrument (see figure), light from a laser would be introduced into an electro-optical modulator (EOM). Amplitude-modulated light from the exit port of the EOM would pass through a fiber-optic splitter having two output branches. The light in one branch would be sent through an atomic cell to a photodiode. The light in the other branch would constitute the microwave-modulated optical output. Part of the light leaving the atomic cell could also be used to stabilize the laser at a frequency in the vicinity of the desired hyperfine or other quantum transition. The microwave signal from the output of the photodiode would be amplified (if necessary, as explained below) and fed back into the EOM. This system would oscillate if the amplification in the closed loop exceeded the linear absorption of the loop. The microwave amplifier may be unnecessary to sustain stable oscillations, depending on the power of the laser radiation at the photodetector and on particular features of the modulator and optical delay line.

Maleki, Lute↗