Experimental study of intrinsic localized mode mobility in a cyclic, balanced, 1D nonlinear transmission line.

Mobile intrinsic localized modes (ILMs) in balanced nonlinear capacitive-inductive cyclic transmission lines are studied by experiment, using a spatiotemporal driver under damped steady-state conditions. Without nonlinear balance, the experimentally observed resonance between the traveling ILM and normal modes of the nonlinear transmission line generates lattice drag via the production of a lattice backwave. In our experimental study of a balanced running ILM in a steady state, it is observed that the fundamental resonance can be removed over extended, well-defined driving frequency intervals and strongly suppressed over the complete ILM driving frequency range. Because both of these nonlinear capacitive and inductive elements display hysteresis our observation demonstrates that the experimental system, which is only partially self-dual, is surprisingly tolerant, regarding the precision necessary to eliminate the ILM backwave. It appears that simply balancing the cell dual nonlinearities makes the ILM envelope shape essentially the same at the two locations in the cell, so that the effective lattice discreteness seen by the ILM nearly vanishes.

Experimental investigation of supertransmission for an intrinsic localized mode in a cyclic nonlinear transmission line.

In this experimental study of the nonlinear loss mechanism between traveling localized excitation and the underlying extended normal mode spectrum for a 1D lattice, three types of cyclic, electric, nonlinear transmission lines (NLTLs) are used. They are nonlinear capacitive, inductive, and capacitive+inductive NLTLs. To maintain a robust, steady-state traveling intrinsic localized mode (ILM), a traveling wave driver is used. The ILM loses energy because of a resonance between it and the extended NLTL modes. A wake field excitation is detected directly from ILM velocity experiments by the decrease in ILM speed and by the observation of the wake. Its properties are quantified via a two-dimensional Fourier map in the frequency-wavenumber domain, determined from the measured spatial-time voltage pattern. Simulations support and extend these experimental findings. We find for the capacitive+inductive NLTL configuration, when the two nonlinear terms are theoretically balanced, the wake excitation is calculated to become very small, giving rise to supertransmission over an extended driving frequency range.

Supertransmission channel for an intrinsic localized mode in a one-dimensional nonlinear physical lattice.

It is well known that a moving intrinsic localized mode (ILM) in a nonlinear physical lattice looses energy because of the resonance between it and the underlying small amplitude plane wave spectrum. By exploring the Fourier transform (FT) properties of the nonlinear force of a running ILM in a driven and damped 1D nonlinear lattice, as described by a 2D wavenumber and frequency map, we quantify the magnitude of the resonance where the small amplitude normal mode dispersion curve and the FT amplitude components of the ILM intersect. We show that for a traveling ILM characterized by a specific frequency and wavenumber, either inside or outside the plane wave spectrum, and for situations where both onsite and intersite nonlinearity occur, either of the hard or soft type, the strength of this resonance depends on the specific mix of the two nonlinearities. Examples are presented demonstrating that by engineering this mix the resonance can be greatly reduced. The end result is a supertransmission channel for either a driven or undriven ILM in a nonintegrable, nonlinear yet physical lattice.

Dynamics of impurity attraction and repulsion of an intrinsic localized mode in a driven 1-D cantilever array.

Both low frequency and high frequency impurity modes have been produced in a SiN micromechanical cantilever array by illumination with either an infrared or visible laser. When such laser-induced impurities are placed near a driven intrinsic localized mode (ILM), it is either repelled or attracted. By measuring the linear response spectrum for these two cases, it was found that vibrational hopping of the ILM takes place when the natural frequency of the ILM and an intrinsic even symmetry linear local mode are symmetrically located about the driven ILM frequency so that parametric excitation of these two linear modes is enhanced, amplifying the lateral motion of the ILM. Numerical simulations are consistent with these signature findings. It is also demonstrated that the correct sign of the observed interaction can be found with a harmonic lattice-impurity model but the magnitude of the effect is enhanced in a nonlinear lattice.

Propagating intrinsic localized mode in a cyclic, dissipative, self-dual one-dimensional nonlinear transmission line.

A well-known feature of a propagating localized excitation in a discrete lattice is the generation of a backwave in the extended normal mode spectrum. To quantify the parameter-dependent amplitude of such a backwave, the properties of a running intrinsic localized mode (ILM) in electric, cyclic, dissipative, nonlinear 1D transmission lines, containing balanced nonlinear capacitive and inductive terms, are studied via simulations. Both balanced and unbalanced damping and driving conditions are treated. The introduction of a unit cell duplex driver, with a voltage source driving the nonlinear capacitor and a synchronized current source, the nonlinear inductor, provides an opportunity to design a cyclic, dissipative self-dual nonlinear transmission line. When the self-dual conditions are satisfied, the dynamical voltage and current equations of motion within a cell become the same, the strength of the fundamental, resonant coupling between the ILM and the lattice modes collapses, and the associated fundamental backwave is no longer observed.

Generation of localized modes in an electrical lattice using subharmonic driving.

We show experimentally and numerically that an intrinsic localized mode (ILM) can be stably produced (and experimentally observed) via subharmonic, spatially homogeneous driving in the context of a nonlinear electrical lattice. The precise nonlinear spatial response of the system has been seen to depend on the relative location in frequency between the driver frequency, ω(d), and the bottom of the linear dispersion curve, ω(0). If ω(d)/2 lies just below ω(0), then a single ILM can be generated in a 32-node lattice, whereas, when ω(d)/2 lies within the dispersion band, a spatially extended waveform resembling a train of ILMs results. To our knowledge, and despite its apparently broad relevance, such an experimental observation of subharmonically driven ILMs has not been previously reported.

Far-infrared absorption of PbSe nanorods.

Measurements of the far-infrared absorption spectra of PbSe nanocrystals and nanorods are presented. As the aspect ratio of the nanorods increases, the Fröhlich sphere resonance splits into two peaks. We analyze this splitting with a classical electrostatic model, which is based on the dielectric function of bulk PbSe but without any free-carrier contribution. Good agreement between the measured and calculated spectra indicates that resonances in the local field factors underlie the measured spectra.

Experimental observation of the bifurcation dynamics of an intrinsic localized mode in a driven 1D nonlinear lattice.

Linear response spectra of a driven intrinsic localized mode in a micromechanical array are measured as it approaches two fundamentally different kinds of bifurcation points. A linear phase mode associated with this autoresonant state softens in frequency and its amplitude grows as the upper frequency bifurcation point is approached, similar to the soft-mode kinetic transition for a single driven Duffing resonator. A lower frequency bifurcation point occurs when the four-wave-mixing partner of this same phase mode intercepts the top of the extended wave branch, initiating a second kinetic transition process.

Holographic Fourier transform spectrometer for terahertz region.

Because of the development of detector arrays stationary interferometric spectrometers now have many applications in the visible and IR; however, these same array sizes make it impractical to design a single Fourier optics system with the necessary large field angles required for the terahertz region. By dividing the Fourier optics into independent components in each arm of an interferometer we show that the aberrations are dramatically reduced, while the same theoretical throughput as in the scanning Michelson interferometer is maintained.

Direct observation of the discrete character of intrinsic localized modes in an antiferromagnet.

In a strongly nonlinear discrete system, the spatial size of an excitation can become comparable to, and influenced by, the lattice spacing. Such intrinsic localized modes (ILMs)--also called 'discrete breathers' or 'lattice solitons'--are responsible for energy localization in the dynamics of discrete nonlinear lattices. Their energy profiles resemble those of localized modes of defects in a harmonic lattice but, like solitons, they can move (although, unlike solitons, some energy is exchanged during collisions between them). The manipulation of these localized energy 'hotspots' has been achieved in systems as diverse as annular arrays of coupled Josephson junctions, optical waveguide arrays, two-dimensional nonlinear photonic crystals and micromechanical cantilever arrays. There is also some evidence for the existence of localized excitations in atomic lattices, although individual ILMs have yet to be identified. Here we report the observation of countable localized excitations in an antiferromagnetic spin lattice by means of a nonlinear spectroscopic technique. This detection capability permits the properties of individual ILMs to be probed; the disappearance of each ILM registers as a step in the time-dependent signal, with the surprising result that the energy staircase of ILM excitations is uniquely defined.

Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line.

The experimental properties of intrinsic localized modes (ILMs) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest-neighbor intersite potentials. Here it is shown for a one-dimensional lumped electrical transmission line that a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis, the nonlinear inductive current equations are transformed to flux transmission line equations with analog onsite hard potential nonlinearities. Approximate analytic results compare favorably with those obtained from a driven damped lattice model and with eigenvalue simulations. For this mono-element lattice, ILMs above the top of the plane wave spectrum are the result. We find that the current ILM is spatially compressed relative to the corresponding flux ILM. Finally, this study makes the connection between the dynamics of mass and force constant defects in the harmonic lattice and ILMs in a strongly anharmonic lattice.

Switching dynamics and linear response spectra of a driven one-dimensional nonlinear lattice containing an intrinsic localized mode.

An intrinsic localized mode (ILM) represents a localized vibrational excitation in a nonlinear lattice. Such a mode will stay in resonance as the driver frequency is changed adiabatically until a bifurcation point is reached, at which point the ILM switches and disappears. The dynamics behind switching in such a many body system is examined here through experimental measurements and numerical simulations. Linear response spectra of a driven micromechanical array containing an ILM were measured in the frequency region between two fundamentally different kinds of bifurcation points that separate the large amplitude ILM state from the two low amplitude vibrational states. Just as a natural frequency can be associated with a driven harmonic oscillator, a similar natural frequency has been found for a driven ILM via the beat frequency between it and a weak, tunable probe. This finding has been confirmed using numerical simulations. The behavior of this nonlinear natural frequency plays important but different roles as the two bifurcation points are approached. At the upper transition its frequency coalesces with the driver and the resulting bifurcation is very similar to the saddle-node bifurcation of a single driven Duffing oscillator, which is treated in an Appendix. The lower transition occurs when the four-wave mixing partner of the natural frequency of the ILM intersects the topmost extended band mode of the same symmetry. The properties of linear local modes associated with the driven ILM are also identified experimentally for the first time and numerically but play no role in these transitions.

Symmetry-breaking dynamical pattern and localization observed in the equilibrium vibrational spectrum of NaI.

Intrinsic localized modes (ILMs) - also known as discrete breathers - are localized excitations that form without structural defects in discrete nonlinear lattices. For crystals in thermal equilibrium ILMs were proposed to form randomly, an idea used to interpret temperature activated signatures of ILMs in α-U and NaI. Here, however, we report neutron scattering measurements of lattice vibrations in NaI that provide evidence of an underlying organization: (i) with small temperature changes ILMs move as a unit back-and-forth between [111] and [011] orientations, and (ii) when [011] ILMs lock in at 636 K the transverse optic (TO) mode splits into three modes with symmetry-breaking dynamical structure resembling that of a superlattice, but there are no superlattice Bragg reflections and the pattern itself has crystal momentum. We conclude that this dynamical pattern is not derived from the rearrangement of atoms but from a coherent arrangement of ILMs decorating the crystal lattice in equilibrium.

Traveling and stationary intrinsic localized modes and their spatial control in electrical lattices.

This work focuses on the production of both stationary and traveling intrinsic localized modes (ILMs), also known as discrete breathers, in two closely related electrical lattices; we demonstrate experimentally that the interplay between these two ILM types can be utilized for the purpose of spatial control. We describe a novel mechanism that is responsible for the motion of driven ILMs in this system, and quantify this effect by modeling in some detail the electrical components comprising the lattice.

Experimental and numerical exploration of intrinsic localized modes in an atomic lattice.

This review focuses attention on the experimental studies of intrinsic localized modes (ILMs) produced in driven atomic lattices. Production methods involve the application of modulational instability under carefully controlled conditions. One experimental approach is to drive the atomic lattice far from equilibrium to produce ILMs, the second is to apply a driver of only modest strength but nearby in frequency to a plane wave mode so that a slow transformation from large amplitude standing waves to ILMs takes place. Since, in either case, the number of ILMs produced is small, the experimental observation tool appropriate for this task is four-wave mixing. This nonlinear detection technique makes use of the nonlinearity associated with an ILM to enhance its signal over that produced by the more numerous, but linear, spin waves. The final topic deals with numerical simulations of a nonlinear nanoscale atomic lattice where the new feature is running ILMs.

Driven localized excitations in the acoustic spectrum of small nonlinear macroscopic and microscopic lattices.

Both bright and dark traveling, locked, intrinsic localized modes (ILMs) have been generated with a spatially uniform driver at a frequency in the acoustic spectrum of a nonlinear micromechanical cantilever array. Complementary numerical simulations show that a minimum density of modes, hence array size, is required for the formation of such locked smoothly running excitations. Additional simulations on a small 1D antiferromagnetic spin system are used to illustrate that such uniformly driven running ILMs should be a generic feature of a nanoscale atomic lattice.

Glasslike two-level systems in minimally disordered mixed crystals.

THz spectroscopy is used to identify a broad distribution of two-level systems, characteristic of glasses, in the substitutional monatomic mixed crystal systems, Ba(1-x)Ca(x)F(2) and Pb(1-x)Ca(x)F(2). In these minimally disordered systems, two-level behavior, which was not previously known to occur, begins at a specific CaF(2) concentration. The concentration dependence, successfully modeled using the statistics of the impurity distribution in the lattice, points to a collective dopant tunneling mechanism.

Controlled switching of intrinsic localized modes in a one-dimensional antiferromagnet.

Nearly-steady-state locked intrinsic localized modes (ILMs) in the quasi-1D antiferromagnet (C(2)H(5)NH(3))(2)CuCl(4) are detected via four-wave mixing emission or the uniform mode absorption. Exploiting the long-time stability of these locked ILMs, repeatable nonlinear switching is observed by varying the sample temperature, and localized modes with various amplitudes are created by modulation of the microwave driver power. This steady-state ILM locking technique could be used to produce energy localization in other atomic lattices.

Spectral selectivity of high-temperature solar absorbers.

Numerical calculations of the thermal emissivity (TH) and normal incidence solar absorptivity alpha(s) of model spectrally selective solar absorbers at high temperatures are reported. The model absorbers consist of Drude metal substrates coated with layers that are successively made better and better approximations to a selective solar absorber. We initially calculate the emissivity of the bare metal substrates (M)(TH) as a function of temperature. We then coat the metal substrate with a homogeneous dielectric layer of index n(L) and find that (TH) of the coated metal increases monotonically with n(L) from in(TH) at that temperature. The dielectric layer is then replaced by a selectively absorbing layer with the optimum physically realizable spectral absorptivity, and maximum values of alpha(s), and minimum values of (TH) are calculated as functions of operating temperature and layer thickness. Finally, we replace the homogeneous selective layer with one having a complex refractive index graded linearly through the thickness of the film. It is found that, compared with homogeneous films of the same thickness, the graded films typically have a higher alpha(s), and a lower (TH). For films thick enough to be useful absorber surfaces, however, the improvements in alpha(s), and (TH) are small.

A (3)he-cooled bolometer for the far infrared.

A germanium bolometer cooled to 0.37 K by liquid (3)He is described. This detector has a NEP of about 3 x 10(-14) W /Hz(1/2) which is more than three decades greater sensitivity than the Golay cell. The factors that determine the sensitivity of the detector are discussed.