Atomtronic circuits of diodes and transistors.

We illustrate that open quantum systems composed of neutral, ultracold atoms in one-dimensional optical lattices can exhibit behavior analogous to semiconductor electronic circuits. A correspondence is demonstrated for bosonic atoms, and the experimental requirements to realize these devices are established. The analysis follows from a derivation of a quantum master equation for this general class of open quantum systems.

Photorefractive BaTiO(3) spheres and spherical disks.

We have produced single-crystal spheres and spherical disks of photorefractive barium titanate (BaTiO(3)) . The spheres and disks allow direct fiber-to-fiber two-beam coupling without additional optical elements. We also investigate the spontaneous oscillation of triangles and other whispering-gallery modes in these spherical structures.

Two-beam Coupling Modules for Photorefractive Optical Circuits.

Modules that perform photorefractive two-beam coupling operations have been built, characterized, and tested. These portable modules, interconnected by fiber optics, dispense with the need for repeated alignment and greatly facilitate the prototyping of complex signal- or image-processing photorefractive circuits. To evaluate the performance of the modules in a photorefractive circuit, we interconnected them in the feature extractor configuration: a ring configuration composed of two modules that selects the strongest signal within the signals presented on its input. With two signals at the input, an output contrast ratio of 45.4 dB is obtained for an input contrast ratio of 5 dB.

Waveguide atom beam splitter for laser-cooled neutral atoms.

A laser-cooled neutral-atom beam from a low-velocity intense source is split into two beams while it is guided by a magnetic-field potential. We generate our multimode beam-splitter potential with two current-carrying wires upon a glass substrate combined with an external transverse bias field. The atoms are guided around curves and a beam-splitter region within a 10-cm guide length. We achieve a maximum integrated flux of 1.5x10(5)atoms/s with a current density of 5x10(4)amp/cm (2) in the 100-microm -diameter wires. The initial beam can be split into two beams with a 50/50 splitting ratio.

Stabilization of the speckle pattern of a multimode fiber undergoing bending.

The propagation of light in a multimode optical fiber waveguide results in speckle, a complicated mapping of the input field onto the output field. The speckle pattern changes as the fiber undergoes twists and bends. We show theoretically and demonstrate experimentally that changes in the mapping caused by bends in one region of the fiber can be compensated with bends applied along a fixed region of the fiber. In this way the output speckle pattern of the fiber can be stabilized. In this method it is supposed that the modes evolve adiabatically without intermixing and that the analytical dependence of perturbed propagation eigenvalues of the modes follows R(-2) behavior, where R is the local value of bend radius.

Nonstationary self-focusing in photorefractive media.

We consider nonstationary self-focusing of an optical beam propagating in a photorefractive medium in the framework of a two-dimensional model.

Collapse of a transverse-mode continuum in a self-imaging photorefractively pumped ring resonator.

We demonstrate the collapse of a continuum of transverse modes in a self-imaging ring resonator that is photorefractively pumped. The resulting localized mode has an arbitrary transverse location. The mode collapse results from placing saturable photorefractive gain and loss media in spatially conjugate resonator planes. The transverse position of the localized mode is unstable under small cavity misalignments, and it drifts across the transverse aperture while retaining its spatial form.

Acoustic signal recognition with a photorefractive time-delay neural network.

We present a photorefractive processor for audio-acoustic signal recognition based on the time-delay neural network model of Hopfield and Tank [in Neural Models of Plasticity, J. H. Byrne, ed. (Academic, New York, 1989), p. 363-377]. We demonstrate the recognition of three words by programming the interconnection weights of the time-delay network.

Self-organized learning of purely temporal information in a photorefractive optical resonator.

A photorefractive resonator containing an optical delay line is shown to learn temporal information through a self-organization process. We present experiments in which a resonator mode selectively learns the mostfrequently presented signals at the input. We also demonstrate the self-organized association of two different analog signals with two different resonator modes.

A life-sized physical model of the human cochlea with optical holographic readout.

A life-sized physical model of the human cochlea is demonstrated. The model consists of two fluid-filled chambers separated by a polymer membrane and connected through a small hole that serves the same functional purpose as the helicotrema. The dimensions of the two chambers were made identical to those of scala vestibuli and scala tympani in the real cochlea. The membrane's width and length are the same as the values measured for the biological basilar membranes, and its thickness is chosen to give it appropriate rigidity. A piezoelectric transducer drives the system via an elastic window (acting as the oval window) on one side of the scala vestibuli. The resulting vibration pattern on the basilar membrane is investigated with an optical novelty filter, with detection sensitivity of 0.3 A at 2 kHz with a 1-Hz bandwidth. The overall response of this model is found to be a good extrapolation of Bekesy's low-frequency data. However, the tuning curves of this model are not as sharp as those found by Rhode, Johnstone, and others from the in vivo measurements. Possible implications of these results are discussed.

Photorefractive delay line for the visualization and processing of time-dependent signals.

We present an optical time-delay line based on photorefractive beam coupling in a rotating crystal. The delay line can be tapped continuously or at selected positions.We demonstrate a 64-channel device with a BaTiO(3) crystal rotating at 1.5 rpm, which gives approximately a 167-Hz bandwidth and 0.5 s of time delay for each channel.

Fiber-optic acoustic Fourier transducer for audio sound processing.

We demonstrate a fiber-optic acoustic transducer operating in the audio-frequency regime. The device is made of an array of 120 multimode optical fibers and a photorefractive novelty filter. Each fiber in the array acts as a cantilevered mechanical resonator. The resonant frequencies of the fibers logarithmically sample the acoustic spectrum from approximately 100 Hz to 5 kHz. Laser light is injected into all fibers simultaneously and is reflected from the end of each fiber. An optical novelty filter extracts the acoustic information from the reflected light. The output of the novelty filter is essentially a Fourier transform of the acoustic signal. The background intensity in the transducer output corresponds to a driving amplitude of approximately 50 A. We describe holographic storage of complex sound patterns that use a LiNbO(3) crystal and an acoustic transducer.

Photorefractive flip-flop.

We demonstrate an optical flip-flop that consists of two unidirectional ring resonators that are coupled competitively through two-beam interactions in a photorefractive BaTiO(3) crystal. This crystal provides an active loss for each ring that depends on the oscillation intensity of the other. The coupled rings exhibit flip-flop bistability when the net gain, given by the product of the passive cavity losses and the gain, is greater than unity but is less than the small-signal active loss. The state of the system can be switched with an injected signal.

Mode multiplexing and holographic demultiplexing communication channels on a multimode fiber.

Spatial mode multiplexing is used to transmit several communication channels on a single multimode optical fiber. Each channel is encoded by an orthogonal pattern produced by a spatial light modulator. A photorefractive medium holographically decodes the output speckle pattern at a receiver station. We demonstrate ring and star architectures for interconnection networks. Typical cross-talk-to-signal ratios, for fully interconnected three-processor networks, are -24 and -26 dB for the ring and star, respectively.

Model for second-harmonic generation in glass optical fibers based on asymmetric photoelectron emission from defect sites.

We present a self-consistent calculation of anomalous second-harmonic generation in glass optical fibers. Quantum interference between multiphoton absorption processes leads to asymmetric photoelectric emission from defects, creating a spatially periodic space-charge electric field. The second harmonic is found to grow exponentially along the fiber, then saturate to a maximum value proportional to the square of the fundamental intensity. The predicted conversion efficiency is in reasonable agreement with experiments.

Self-organizing photorefractive frequency demultiplexer.

We demonstrate a self-organizing photorefractive circuit that demultiplexes a beam that has two signals imposed on separate optical carrier frequencies into two beams, each containing one of the signals on its carrier. Unlike conventional demultiplexing techniques, this method requires little a priori knowledge about the carrier frequencies. The signal channels must be spatially uncorrelated, and their frequency separation must be more than the photorefractive response bandwidth (hertz to kilohertz). The optical circuit uses no local oscillator, and the photorefractive response bandwidth places no upper bound on the channel bandwidth. Experimental results for demultiplexing a beam that has two signals, with a BaTiO(3) circuit, show contrast ratios of better than 40:1 at the outputs.

Stabilization of laser beam alignment to an optical resonator by heterodyne detection of off-axis modes.

We demonstrate a method for real time alignment of a Gaussian beam to an optical resonator. While thefrequency of a source laser is stabilized to a fundamental cavity mode resonance, phase modulation sidebands are applied at the off-axis mode frequencies. Asymmetrical transmission of the sideband at the frequency of each off-axis mode produces amplitude modulated optical signals and indicates the extent of the misalignments. Phase sensitive detection of these optical signals provides the error signals which are minimized by a control system that steers the input beam. In this way, optimum coupling of an injected source beam can be maintained to the fundamental mode of the resonator. This active alignment technique has demonstrated a sensitivity to tilts of 0.1 nrad/ radicalHz and to lateral beam displacements of 0.08 nm/ radicalHz in the ~1-Hz-1-kHz frequency range. These values correspond to 2 parts in 10(7) radicalHz for both the far-field divergence angle and the beam waist size. Such performance is within a factor of 2 of the shot noise limitation of the error signal measurement for a detected power of 160 microW.

Bistable ring resonator utilizing saturable photorefractive gain and loss.

We demonstrate the bistable behavior of a unidirectional ring resonator that employs photorefractive loss as well as photorefractive gain. The gain and loss are established by two-beam coupling in two separate photorefractive BaTiO(3) crystals. Two-beam coupling loss plays the role of a programmable saturable absorber. Irreversible bistability occurs when the maximum net gain exceeds unity, while reversable bistability is obtained when the maximum net gain is less than one.

Optical tracking novelty filter.

We demonstrate an optical filter that displays the time-dependent features of a scene. The heart of the device is an interferometer that is sensitive not to the difference between two optical paths lengths but to changes in the path-length difference. The interferometer arms share a phase-conjugating mirror. The phase conjugator ensures that, at steady state, the output of the interferometer is dark. The response of the interferometer to a step differential change in the optical lengths is a decaying exponential having a time constant governed by the time response of the phase conjugator. The interferometer may be used to monitor time- and space-dependent optical phase changes that are due, for example, to transparent fluid motion. With a modified liquid-crystal television used as a spatial light phase modulator in the interferometer, we detect time-dependent features of an image viewed by a video camera.

Dynamic optical interconnects: volume holograms as optical two-port operators.

We view a real-time volume holographic medium as a programmable two-port device that operates on an optical electric field. A photorefractive two-port operator can be used to establish the interconnects required by neural network models. The index grating that forms in the medium serves to fully interconnect two layers of processing units and at the same time sums the input signals to the output layer. The dynamics of grating formation in photorefractive media are used to indicate the time evolution of the two-port operator when the diffraction efficiency of the medium is small. We experimentally demonstrate a projection operator whereby we store and recall, in iron-doped lithium niobate, seven 1-D images. The image storage is done without the usual angle or spatial encoding of reference beams. A projection operator is used to recognize what features of an input belong to a space defined by a set of stored vectors. The two-port operator can also be used to perform the complementary function: to recognize what features of an input do not belong to this space.