Nonlinear Arrays Research Articles

Near- and far-field beam forming using a linear array in deep and shallow water

Underwater sources are typically characterized in terms of a source level based on measurements made in the free-field. Measurements made in a harbor environment, where multiple reflections, high background noise and short propagation paths are typical, violates these conditions. The subject of this paper is estimation of source location and source level from such measurements. Data from a test conducted at the US Navy Acoustic Research Detachment in Bayview, Idaho during the summers of 2010 and 2011 are analyzed. A line array of omnidirectional hydrophones was deployed from a barge in both deep and shallow water using calibrated acoustic sources to evaluate the effectiveness of post-processing techniques, as well as line array beamforming, in minimizing reflected path contributions and improving signal-to-noise ratio. A method of estimating the location of the sources while taking into account a real, non-linear array based on these measurements is presented. [Work supported by the Applied Research Laboratory under an Eric Walker Scholarship.]

Identifiability Analysis for Array Shape Self-Calibration Based on Hybrid Cramér-Rao Bound

In array shape self-calibration where the sensor position errors and source locations are both unknown, the identifiability of the unknowns is a fundamental problem. Previously, using an approximate hybrid Cramer-Rao bound (HCRB), it was found that under the assumption of small random errors, a nominally linear array is impossible to self-calibrate, but a nominally non-linear array is possible to self-calibrate with three noncollinear far-field sources. In this letter, both small and large random errors are considered, thus the crucial small-error approximation has to be dropped. An accurate HCRB is then derived using fully the prior information about the errors. The accurate HCRB proves that if it is tight, a perturbed nominally linear array is possible to self-calibrate. The larger the sensor position errors, the easier the self-calibration. This is important because of the wide application of linear array. Moreover, two noncollinear far-field sources are sufficient to self-calibrate an array of arbitrary nominal shape.

Bifurcation topology transfer in nonlinear nanocantilever arrays subject to parametric and internal resonances

The collective nonlinear dynamics of a coupled array of nanocantilevers is investigated while tak- ing into account the main sources of nonlinearities. The amplitude and phase equations of this device, subject to parametric and internal resonances, are analytically derived by means of a multi-modal Galerkin discretiza- tion coupled with a multiscale analysis. Based on the steady-state solutions of these equations, the frequency responses are numerically computed for a two-beam array. The effects of different parameters are investigated and several dynamical aspects are confirmed by numerical simulations. Particularly, we have demonstrated that the bifurcation topology transfer is imposed by the first nanocantilever and it can be general to the collective nonlinear dynamics of the NEMS array.

Minimizing sidelobe levels and facilitating null placements of nonlinear antenna arrays using an improved particle swarm optimization method

Purpose – The aim of this paper is to explore the potential of particle swarm optimization (PSO) methods for minimizing the sidelobe levels (SLL) and placing null at arbitrary angles of a nonlinear antenna array. Design/methodology/approach – An improved PSO algorithm is designed. Findings – The improved PSO method is an efficient and robust global optimizer for minimizing the SLL and placing null at arbitrary angles of a nonlinear antenna array. Originality/value – Some improvements, such as the design of some new formulae for both position and velocity updating, the introduction of an age variable, and the devise of an intensification searches using the cross entropy method, are proposed.

Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices

We study numerically time evolution in classical lattices with weak or moderate nonlinearity which leads to interactions between linear modes. Our results show that in a certain strength range a moderate nonlinearity generates a dynamical thermalization process which drives the system to the quantum Gibbs distribution of probabilities, or average oscillation amplitudes. The effective dynamical temperature of the lattice varies from large positive to large negative values depending on the energy of the initially excited modes. This quantum Gibbs distribution is drastically different from the usually expected energy equipartition over linear modes corresponding to a regime of classical thermalization. Possible experimental observations of this dynamical thermalization are discussed for cold atoms in optical lattices, nonlinear photonic lattices and optical fiber arrays.

A unified SVM framework for signal estimation

This paper presents a review in the form of a unified framework for tackling estimation problems in Digital Signal Processing (DSP) using Support Vector Machines (SVMs). The paper formalizes our developments in the area of DSP with SVM principles. The use of SVMs for DSP is already mature, and has gained popularity in recent years due to its advantages over other methods: SVMs are flexible non-linear methods that are intrinsically regularized and work well in low-sample-sized and high-dimensional problems. SVMs can be designed to take into account different noise sources in the formulation and to fuse heterogeneous information sources. Nevertheless, the use of SVMs in estimation problems has been traditionally limited to its mere use as a black-box model. Noting such limitations in the literature, we take advantage of several properties of Mercerʼs kernels and functional analysis to develop a family of SVM methods for estimation in DSP. Three types of signal model equations are analyzed. First, when a specific time-signal structure is assumed to model the underlying system that generated the data, the linear signal model (so-called Primal Signal Model formulation) is first stated and analyzed. Then, non-linear versions of the signal structure can be readily developed by following two different approaches. On the one hand, the signal model equation is written in Reproducing Kernel Hilbert Spaces (RKHS) using the well-known RKHS Signal Model formulation, and Mercerʼs kernels are readily used in SVM non-linear algorithms. On the other hand, in the alternative and not so common Dual Signal Model formulation, a signal expansion is made by using an auxiliary signal model equation given by a non-linear regression of each time instant in the observed time series. These building blocks can be used to generate different novel SVM-based methods for problems of signal estimation, and we deal with several of the most important ones in DSP. We illustrate the usefulness of this methodology by defining SVM algorithms for linear and non-linear system identification, spectral analysis, non-uniform interpolation, sparse deconvolution, and array processing. The performance of the developed SVM methods is compared to standard approaches in all these settings. The experimental results illustrate the generality, simplicity, and capabilities of the proposed SVM framework for DSP.

Mid-mantle heterogeneities associated with Izanagi plate: Implications for regional mantle viscosity

We employed S-to-P converted waveforms to detect mid-mantle scattering beneath northeastern China and the adjacent Japan Sea. Broadband and short-period waveforms recorded by seismic arrays for eight moderate-sized deep earthquakes were analyzed using a non-linear array stacking technique, and mid-mantle scatterers within the depth range 930–1120 km were clearly revealed. The heterogeneities have an overall lateral extent of ∼800 km, and mostly occur within a region with a high velocity anomaly. The accumulation of MORB-like slab materials at mid-mantle depths might cause a different chemical composition than that of the surrounding peridotitic mantle. The spatial isolation of the heterogeneities from the stagnant Pacific slab suggests an origin related to the subduction of ancient Izanagi plate. In combination with the reconstruction history of plate motions, we estimate the viscosity of the topmost lower mantle to vary from 1.0×1022 to 1.6×1023 Pas, which can be used as an independent constraint on the rheology of the lower mantle on a regional scale.

Interlayer Magnetoresistance due to Chiral Soliton Lattice Formation in Hexagonal Chiral MagnetCrNb3S6

We investigate the interlayer magnetoresistance (MR) along the chiral crystallographic axis in the hexagonal chiral magnet CrNb3S6. In a region below the incommensurate-commensurate phase transition between the chiral soliton lattice and the forced ferromagnetic state, a negative MR is obtained in a wide range of temperature, while a small positive MR is found very close to the Curie temperature. Normalized data of the negative MR almost falls into a single curve and is well fitted by a theoretical equation of the soliton density, meaning that the origin of the MR is ascribed to the magnetic scattering of conduction electrons by a nonlinear, periodic, and countable array of magnetic soliton kinks.

Evaluations on underdetermined blind source separation in adverse environments using time-frequency masking

The successful implementation of speech processing systems in the real world depends on its ability to handle adverse acoustic conditions with undesirable factors such as room reverberation and background noise. In this study, an extension to the established multiple sensors degenerate unmixing estimation technique (MENUET) algorithm for blind source separation is proposed based on the fuzzy c-means clustering to yield improvements in separation ability for underdetermined situations using a nonlinear microphone array. However, rather than test the blind source separation ability solely on reverberant conditions, this paper extends this to include a variety of simulated and real-world noisy environments. Results reported encouraging separation ability and improved perceptual quality of the separated sources for such adverse conditions. Not only does this establish this proposed methodology as a credible improvement to the system, but also implies further applicability in areas such as noise suppression in adverse acoustic environments.

Double-discrete solitons in fishnet arrays of optical fibers

We demonstrate that crossed arrays of optical fibers support the double-discrete linear and nonlinear propagation of light beams, in which not only the transverse coordinate (the fiber's number) is discrete, but also the longitudinal (propagation) coordinate, i.e., the number of the fiber-crossing site, is effectively discrete too. In the linear limit, this transmission regime features double-discrete self-collimation. The nonlinear fishnet arrays with both focusing and defocusing nonlinearities give rise to double-discrete spatial solitons. Solitons bifurcating from two different branches of the linear dispersion relation feature strong interactions and form composite states. In the continuum limit, the model of the nonlinear fishnet reduces to a system of coupled-mode equations similar to those describing Bragg gratings, but without the cross-phase-modulation terms.

Improving quality cost performance with qualimetrical methods: a case from a high-speed packaging process

Quality costing has become a key pillar for monitoring process efficiency while documenting product integrity. A robust technique for profiling economically complex industrial processes is proposed in this work. The presentation is focused on the performance evaluation of a single product response where data is collected by group and subgroup replication in order to account for uncertainty that may intrude in any phase of production. Data transformed by Taguchi’s original quality loss functions are subjected to non-parametric analysis customized to handle highly dense non-linear orthogonal arrays. The economic design outlined in this article is capacitated by the data collection efficiency of popular fractional factorial designs and the data compression capabilities of rank sums for repetitive non-regular sampling schemes. The master rank ordering concept is introduced to actuate the non-parametric analysis of the converted quality loss cost data. The distribution-free character of the developments facilitates screening for prominent effects where perplexing issues such as compliance to normality and sparsity assumptions are waived. The overall approach is shown to be easy to implement and convenient to use. The technique is illustrated on a real study where four controlling factors are adjusted through an L9(34) orthogonal array in order to rectify the packaging check-weighing operation of a pharmaceutical enterprise. Our proposed economic data mining diagnosticated that the input weight, the feed rate and the internal conversion rate were significant at a level of 0.10 with a three-way composite P statistic of 2,203. The input weight was found to be the preponderant effect at a significance level of 0.10 accumulating a sum of squared rank sums of 797. The optimal operating settings were found to be 50 g, 30 m/s and 19 counts/s for the input weight, feed rate and the internal conversion rate, respectively.

A bootstrapping-based statistical procedure for multivariate calibration of sensor arrays

One of the major challenges of calibrating a sensor array lies in the typically large samples required to estimate a high-quality multivariate calibration (MC) model, which functionally relates the array responses to the target analyte concentrations. For the efficient calibration of sensor arrays, this work develops a multi-stage procedure to guide the sampling in a sequential manner: Preliminary experiments are performed in the initial stage to collect some data; in each subsequent stage, information is derived from all the data collected from the previous stages and is employed to obtain the optimal design of the current-stage experiments. The design optimization at each stage seeks to optimize the quality of the MC model with a given sample size, and is performed based on the new statistical inference method, which quantifies the dependence of the MC model quality (the uncertainty/variability of the model estimates) upon the design of experiments. The proposed statistical inference takes advantages of both forward and inverse calibration modeling in the literature, is able to accommodate nonlinear sensor arrays, and utilizes the bootstrapping resampling method to handle the statistical inference issues that cannot be adequately addressed by existing methods. Substantial simulation studies have been performed to demonstrate the efficiency of the multi-stage procedure over the traditional once-and-for-all sampling.

Repulsively induced photon superbunching in driven resonator arrays

We analyze the non-equilibrium behaviour of driven nonlinear photonic resonator arrays under the selective excitation of specific photonic many-body modes. Targeting the unit-filled ground state, we find a counter-intuitive `super bunching' in the emitted photon statistics in spite of relatively strong onsite repulsive interaction. We consider resonator arrays with Kerr nonlinearities described by the Bose Hubbard model, but also show that an analogous effect is observable in near-future experiments coupling resonators to two-level systems as described by the Jaynes Cummings Hubbard Hamiltonian. For the experimentally accessible case of a pair of coupled resonators forming a photonic molecule, we provide an analytical explanation for the nature of the effect.

Intrinsic Localized Modes of Harmonic Oscillations in Nonlinear Oscillator Arrays

Intrinsic localized modes (ILMs) are investigated in an array with N Duffing oscillators that are weakly coupled with each other when each oscillator is subjected to sinusoidal excitation. The purpose of this study is to investigate the behavior of ILMs in nonlinear multi-degree-of-freedom (MDOF) systems. In the theoretical analysis, van der Pol's method is employed to determine the expressions for the frequency response curves for fundamental harmonic oscillations. In the numerical calculations, the frequency response curves are shown for N = 2 and 3 and compared with the results of the numerical simulations. Basins of attraction are shown for a two-oscillator array with hard-type nonlinearities to examine the possibility of appearance of ILMs when an oscillator is disturbed. The influences of the connecting springs for both hard- and soft-type nonlinearities on the appearance of the ILMs are examined. Increasing the values of the connecting spring constants may cause Hopf bifurcation followed by amplitude modulated motion (AMM) including chaotic vibrations. The influence of the imperfection of an oscillator is also investigated. Bifurcation sets are calculated to show the influence of the system parameters on the excitation frequency range of ILMs. Furthermore, time histories are shown for the case of N = 10, and many patterns of ILMs may appear depending on the initial conditions.

Optical bistability in nonlinear subwavelength metal hole array involving Kerr materials

We investigate an optical bistability phenomenon in a structure consisting of a silver film with a hole array filling with Kerr medium with single wavelength. We explore the mechanism of optical bistability in our structures and find that the excitation condition of surface plasmon at this moment is related with that at last moment. The contrast of optical bistability can reach to the maximum at the wavelength of the transmission peak. Our structure can realize the function of the beam splitter.

ANALYSIS OF NOVEL FRACTAL OPTICAL ANTENNA ARRAYS - A CONCEPTUAL APPROACH

Fractal antennas have undergone dramatic changes since they were flrst considered for wireless systems. Numerous advancements are developed both in the area of fractal shaped elements and fractal antenna array technology for fractal electrodynamics. This paper makes an attempt of applying the concept of fractal antenna array technology in the RF regime to optical antenna array technology in the optical regime using nonlinear array concepts. The paper further discusses on the enhancement of nonlinear array characteristics of fractal optical antenna arrays using nonlinearities in coupled antennas and arrays in a conceptual manner.

ANALYSIS OF NONLINEAR FRACTAL OPTICAL ANTENNA ARRAYS - A CONCEPTUAL APPROACH

Fractal antennas have undergone dramatic changes since they were flrst considered for wireless systems. Numerous advancements are developed both in the area of fractal shaped elements and fractal antenna array technology for fractal electrodynamics. This paper makes an attempt of applying the concept of fractal antenna array technology in the RF regime to optical antenna array technology in the optical regime using nonlinear array concepts. The paper further discusses on the enhancement of nonlinear array characteristics of fractal optical antenna arrays using nonlinearities in coupled antennas and arrays in a conceptual manner.

Non-equilibrium many-body effects in driven nonlinear resonator arrays

We study the non-equilibrium behavior of optically driven dissipative coupled resonator arrays. Assuming each resonator is coupled with a two-level system via a Jaynes–Cummings interaction, we calculate the many-body steady state behavior of the system under coherent pumping and dissipation. We propose and analyze the many-body phases using experimentally accessible quantities such as the total excitation number, the emitted photon spectra and photon coherence functions for different parameter regimes. In parallel, we also compare and contrast the expected behavior of this system assuming the local nonlinearity in the cavities is generated by a generic Kerr effect as described by the Bose–Hubbard (BH) model rather than a Jaynes–Cummings interaction. We find that the behavior of the experimentally accessible observables produced by the two models differs for realistic regimes of interactions even when the corresponding nonlinearities are of similar strength. We analyze in detail the extra features available in the Jaynes–Cummings–Hubbard (JCH) model originating from the mixed nature of the excitations and investigate the regimes where the BH approximation would faithfully match the JCH physics. We find that the latter is true for values of the light–matter coupling and losses beyond the reach of current technology. Throughout the study we operate in the weak pumping, fully quantum mechanical regime where approaches such as mean field theory fail, and instead use a combination of quantum trajectories and the time evolving block decimation algorithm to compute the relevant steady state observables. In our study we have assumed small to medium size arrays (from 3 up to 16 sites) and values of the ratio of coupling to dissipation rate g/γ ∼ 20, which makes our results implementable with current designs in circuit QED and with near future photonic crystal set ups.

Coherent propagation and energy transfer in low-dimension nonlinear arrays

We present a theory of coherent propagation and energy or power transfer in a low-dimension array of coupled nonlinear waveguides. It is demonstrated that in the array with nonequal cores (e.g., with the central core) stable steady-state coherent multicore propagation is possible only in the nonlinear regime, with a power-controlled phase matching. The developed theory of energy or power transfer in nonlinear discrete systems is rather generic and has a range of potential applications including both high-power fiber lasers and ultrahigh-capacity optical communication systems.

Biphoton generation in quadratic waveguide arrays: a classical optical simulation.

Quantum entanglement became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demonstrated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. Spontaneous parametric down-conversion (SPDC) in nonlinear crystals provides an efficient source for entangled photon pairs, so-called biphotons. However, SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional arrays can be simulated through classical optical beam propagation in a two-dimensional photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-like inequality.