Nonlinear Arrays Research Articles

On the structure of ZnI2

A new structure for ${\rm ZnI_2}$ is proposed which it exists in tetragonal state. In this structure the ${\rm ZnI_2}$ molecule exists in a nonlinear array and forms the basis of the tetragonal unit cell with one basis per unit cell. The structural analysis based on the reflections listed in ASTM 30-1479 shows that the proposed structure is correct.

Excitation of strongly confined scalar and vector self-trapped beams in one-dimensional arrays of Kerr-nonlinear channel waveguides

The excitation and propagation of both scalar and vector optical waves in one-dimensional nonlinear arrays of channel waveguides was investigated both theoretically and experimentally. In this arrangement vector discrete solitons are also possible through the coexistence of two orthogonally polarized fields. At high input power levels a rapid collapse of the power back to the incidence channel occurred over a small power range for both scalar and vector inputs.

Simultaneous beam steering and null formation with coupled, nonlinear oscillator arrays

The ability of coupled, nonlinear oscillator arrays to produce simultaneous beam steering and null generation is presented. This technique, which extends the capabilities of such arrays to include interference suppression, is realized through a generalization of Steyskal's method of pattern nulling by phase perturbation. An illustrative example is provided.

Biologically inspired structural diagnostics through beamforming with phased transducer arrays

This paper discusses research in the use of biologically inspired spatial phased transducer arrays for the nondestructive evaluation of homogeneous and heterogeneous structural components. It is shown that beamforming, which is used by orb web spiders to locate their prey in a network of web fibers, can be achieved by applying weights and time delays to the tapped signals from a transducer array in a narrow frequency band to obtain desired directional sensitivities and optimal array gains. The resulting spatio-temporal filters are then used to detect, locate and quantify structural damage. The theory of beamsteering and beamforming for processing propagating wave data in damaged elastic media is discussed. Experimental results for homogeneous and heterogeneous plates are given to verify the theoretical discussions. Design considerations for the phased arrays are examined as are the benefits of nonlinear array geometries for better spatial coverage. The advantage of using adaptive over conventional beamforming is demonstrated with a Frost Constraint adaptive technique.

Breathers and thermal relaxation as a temporal process: A possible way to detect breathers in experimental situations

Breather stability and longevity in thermally relaxing nonlinear arrays is investigated under the scrutiny of the analysis and tools employed for time series and state reconstruction of a dynamical system. We briefly review the methods used in the analysis and characterize a breather in terms of the results obtained with such methods. Our present work focuses on spontaneously appearing breathers in thermal Fermi-Pasta-Ulam arrays but we believe that the conclusions are general enough to describe many other related situations; the particular case described in detail is presented as another example of systems where three incommensurable frequencies dominate their chaotic dynamics (reminiscent of the Ruelle-Takens scenario for the appearance of chaotic behavior in nonlinear systems). This characterization may also be of great help for the discovery of breathers in experimental situations where the temporal evolution of a local variable (like the site energy) is the only available/measured data.

A subspace method for space time adaptive processing

The problem of space-time adaptive processing (STAP) using a nonlinear array is considered. A key part of STAP is the estimation of the space-time covariance matrix of the received data. The conventional method of doing this causes significant performance degradation at short ranges because of the nonstationarity of the data. We present an alternative algorithm which circumvents this problem by projecting the data on the subspace orthogonal to the clutter and jammer subspaces. The clutter subspace is computed from the known array manifold, while the jammer subspace is estimated from clutter-free measurements. Numerical examples illustrate the performance improvement achieved at short ranges.

Gap Solitons Coexisting with Bright Soliton in Nonlinear Fiber Arrays

Gap Solitons Coexisting with Bright Soliton in Nonlinear Fiber Arrays

H-2 Evaluation of closed cracks by nonlinear ultrasonic phased array(Measurement techniques, Imaging, Nondestructive testing, Acousto-optics)

H-2 Evaluation of closed cracks by nonlinear ultrasonic phased array(Measurement techniques, Imaging, Nondestructive testing, Acousto-optics)

Globally coupled noisy oscillators with inhomogeneous periodic forcing

We study the collective properties of an array of nonlinear noisy oscillators driven by nonidentical periodic signals. We consider the case of a globally coupled array of harmonically forced, weakly nonlinear oscillators where there is a constant difference between the phases of the forcing signals applied to adjacent oscillators. This system is a prototypical model of a nonlinear phased array receiver. We derive analytical results for the array output in the limit of a large number of oscillators for the noise-free and noisy cases. Numerical simulations show good agreement with the theoretical analysis.

Switching of discrete optical solitons in engineered waveguide arrays.

We demonstrate a simple concept for controlling nonlinear switching of discrete solitons in arrays of weakly coupled optical waveguides, for both cubic and quadratic nonlinear response. Based on the effective discrete nonlinear equations describing light propagation in the waveguide arrays in the tight-binding approximation, we demonstrate the key ideas of the array engineering by means of a steplike variation of the waveguide coupling. We demonstrate the digitized switching of a narrow input beam for up to 11 neighboring waveguides, in the case of the cubic nonlinearity, and up to 10 waveguides, in the case of the quadratic nonlinearity. We discuss our predictions in terms of the physics of the engineered Peierls-Nabarro (PN) potential experienced by strongly localized nonlinear modes in a lattice, and calculate the PN potential for the quadratic nonlinear array for the first time.

Beam Steering of Nonlinear Oscillator Arrays Through Manipulation of Coupling Phases

This paper describes three phase-shifterless beam steering techniques which exploit the synchronization properties of coupled nonlinear oscillator arrays. In each, the control parameters are the coupling phases of the local interactions between elements. The one-dimensional oscillator arrays under consideration are described by Phase Model-type equations, implying the assumption that the amplitude dynamics have achieved a steady state. Linear stability analyzes for each technique are provided which reveal significant differences in attainable scan angles.

Nonlinear-absorbing fiber array for large-dynamic-range optical limiting application against intense short laser pulses

A complete quantitative description of a nonlinear fiber array for optical limiting application against laser pulses in the picosecond–nanosecond regime is presented. We discuss the dynamics of the molecular photonic processes accompanying the propagation of a laser pulse through the fiber core made of materials that possess reverse saturable absorption, two-photon absorption (TPA), and excited-state absorption (ESA), and we detail the optical limiting effectiveness and limitations of these nonlinear absorption processes individually and in concert. In particular, we demonstrate the importance of excited-state population recycling in extending the dynamic range of the limiting action. Experimental results obtained from a particular fiber core material that possesses TPA and ESA show good agreement with theoretical expectations and demonstrate the optical limiting capability of such a nonlinear fiber array.

Acoustic pressure-vector sensor array

Pressure-vector sensors measure both scalar and vector components of the acoustic field. December 2003 measurements at the NUWC Seneca Lake test facility verify previous observations that acoustic ambient noise spectrum levels measured by acoustic intensity sensors are reduced relative to either acoustic pressure or acoustic vector sensor spectrum levels. The Seneca measurements indicate a reduction by as much as 15 dB at the upper measurement frequency of 2500 Hz. A nonlinear array synthesis theory for pressure-vector sensors will be introduced that allows smaller apertures to achieve narrow beams. The significantly reduced ambient noise of individual pressure-vector elements observed in the ocean by others, and now at Seneca Lake, should allow a nonlinearly combined array to detect significantly lower levels than has been observed in previous multiplicative processing of pressure sensors alone. Nonlinear array synthesis of pressure-vector sensors differs from conventional super-directive algorithms that linearly combine pressure elements with positive and negative weights, thereby reducing the sensitivity of conventional super-directive arrays. The much smaller aperture of acoustic pressure-vector sensor arrays will be attractive for acoustic systems on underwater vehicles, as well as for other applications that require narrow beam acoustic receivers. [The authors gratefully acknowledge the support of ONR and NUWC.]

Experimental observation of discrete modulational instability.

We report the first experimental observation of modulation instability in a discrete optical nonlinear array.

Pulse propagation in chains with nonlinear interactions

Pulse propagation in nonlinear arrays continues to be of interest because it provides a possible mechanism for energy transfer with little dispersion. Here we show that common measures of pulse dispersion might be misleading; in strongly anharmonic systems they tend to reflect a succession of extremely narrow pulses traveling at decreasing velocities rather than the actual width of a single pulse. We present analytic estimates for the fraction of the initial energy that travels in the leading pulses. We also provide analytic predictions for the leading pulse velocity in a Fermi-Pasta-Ulam beta chain.

PDE-BASED HISTOGRAM MODIFICATION WITH EMBEDDED MORPHOLOGICAL PROCESSING OF THE LEVEL-SETS

This paper describes parallel histogram modification techniques with embedded morphological preprocessing methods within the CNN-UM framework. The procedure is formulated in terms of nonlinear partial differential equations (PDE) and approximated through finite differences in space, resulting in coupled nonlinear ordinary differential equations (ODE). The I/O mapping of the system (containing both local and global couplings) can be calculated by a complex analogic (analog and logic) algorithm executed on a stored program nonlinear array processor, called the cellular nonlinear network universal machine (CNN-UM3). We describe and illustrate how the implementation of the algorithm results in an adaptive multi-thresholding scheme when histogram modification is combined with embedded morphological processing at a finite (low) number of gray-scale levels. This has obvious advantages if the further processing steps are segmentation and/or recognition. Experimental results processing real-life and echocardiography images are measured on different hardware/software platforms, including a 64 × 64 CNN-UM chip (ACE4k6,17).

Collective and Individual Molecular Nonlinear Photonics of Liquid Crystals

This review will examine the origins of nonlinear light scattering processes in nematic liquid crystals, and explore various nonlinear photonic processes associated with optically induced director axis reorientation effects. Our theoretical prediction shows that the upper limit of nematic liquid crystal reorientation nonlinearity can be as high as 1000 cm2/W. The supra-nonlinear responses of nematic liquid crystals enable various self-action or electro-optical guiding, mixing, switching and modulation of light with unprecedented low power thresholds. Owing to the broadband birefringence of NLC, we expect to realize optical elements/devices capable of similar multi-functional operations throughout the visible — infrared regime. We also discuss the optical limiting action of isotropic-phase liquid crystal filled nonlinear fiber arrays.

Breathers and thermal relaxation in Fermi-Pasta-Ulam arrays.

Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review numerical results for the relaxation of breathers in Fermi-Pasta-Ulam arrays, with a specific focus on the different relaxation channels and their dependence on the interparticle interactions, dimensionality, initial condition, and system parameters.

Multiple speech signal enhancement using a microphone array

The ability to extract and enhance a primary speech signal from an environment with multiple speakers is an important issue. While methods exist for a variety of beamforming techniques [M. Brandstein and D. Ward, Microphone Arrays: Signal Processing Techniques and Applications (Springer, New York, 2001)] as well as for multi-source filtering in stationary noise [H. Saruwatari et al., ‘‘Speech Enhancement Using Nonlinear Microphone Array With Noise Adaptive Complementary Beamforming,’’ Proc. of IEEE ICASSP, pp. 1049–1052 (2000)], the theory has yet to be developed for integrating spatial filtering with additional enhancement methods to deal with non-stationary interference from interfering talkers. This paper presents a novel method for incorporating multiple parallel beamformers with traditional speech enhancement algorithms, particularly the Wiener filter and spectral subtraction. By iteratively improving the spectral magnitude estimates of each speech source, substantial improvement in overall signal separation can be obtained. The performance of the algorithm is illustrated using a simulated multiple speaker environment with resulting SNR and sSNR plots. [Work supported by the GAANN Fellowship.]

Non-Lipschitzian Control Algorithm for Nanoscale

We present a robust feedback control algorithm and apply it to the nonlinear oscillator array (Frenkel-Kontorova) model of nanoscale friction. The new control approach is based on the concepts of non-Lipschitzian dynamics and global targeting. We show that average quantities of the controlled system can be driven - exactly or approximately - towards desired targets which become additional, linearly stable attractors for the system's dynamics. Extensive numerical simulations show that the basins of attraction of these targets are reached in very short times and the control exhibits very strong robustness. We investigate the efficiency of the control in terms of various parameters (e.g., system size, non-Lipschitzian exponent).