Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity

We consider solutions to the second-harmonic generation equations in two-and three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stability of the solutions to be predicted. Then, we directly simulate the two-dimensional case, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that spatiotemporal solitons indeed exist and are stable. Furthermore, they are not, in the general case, equivalent to the previously known cylindrical spatial solitons. Direct simulations generate solitons with some internal oscillations. However, these oscillations neither grow nor do they exhibit any significant radiative damping. Numerical solutions of the stationary version of the equations produce the same solitons in their unperturbed form, i.e., without internal oscillations. Strictly stable solitons exist only if the system has anomalous dispersion at both the fundamental harmonic and second harmonic (SH), including the case of zero dispersion at SH. Quasistationary solitons, decaying extremely slowly into radiation, are found in the presence of weak normal dispersion at the second-harmonic frequency.

Light guiding light: Nonlinear refraction in rubidium vapor

Recently there has been experimental and theoretical interest in cross-dispersion effects in rubidium vapor, which allows one beam of light to be guided by another. We present theoretical results which account for the complications created by the D line hyperfine structure of rubidium as well as the presence of the two major isotopes of rubidium. This allows the complex frequency dependence of the effects observed in our experiments to be understood and lays the foundation for future studies of nonlinear propagation.

Complete modulational-instability gain spectrum of nonlinear quasi-phase-matching gratings

We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phase-matching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher-order gain bands. (C) 2004 Optical Society of America.

Coherent molecular solitons in Bose-Einstein condensates

We analyze the coherent formation of molecular Bose-Einstein condensate (BEC) from an atomic BEG, using a parametric field theory approach. We point out the transition between a quantum soliton regime, where atoms couple in a local way to a classical soliton domain, where a stable coupled-condensate soliton can form in three dimensions. This gives the possibility of an intense, stable atom-laser output. [S0031-9007(98)07283-4].

Demonstration of the spatial separation of the entangled quantum sidebands of an optical field

Quantum optics experiments on bright beams are based on the spectral analysis of field fluctuations and typically probe correlations between radio-frequency sideband modes. However, the extra degree of freedom represented by this dual-mode picture is generally ignored. We demonstrate the experimental operation of a device which can be used to separate the quantum sidebands of an optical field. We use this device to explicitly demonstrate the quantum entanglement between the sidebands of a squeezed beam.

Canonical Bose gas simulations with stochastic gauges

A technique to simulate the grand canonical ensembles of interacting Bose gases is presented. Results are generated for many temperatures by averaging over energy-weighted stochastic paths, each corresponding to a solution of coupled Gross-Pitaevskii equations with phase noise. The stochastic gauge method used relies on an off-diagonal coherent-state expansion, thus taking into account all quantum correlations. As an example, the second-order spatial correlation function and momentum distribution for an interacting 1D Bose gas are calculated.

Spatial, temporal, and human dimensions of air pollution in Brisbane

Arriving in Brisbane some six years ago, I could not help being impressed by what may be prosaically described as its atmospheric amenity resources. Perhaps this in part was due to my recent experiences in major urban centres in North America, but since that time, that sparkling quality and the blue skies seem to have progressively diminished. Unfortunately, there is also objective evidence available to suggest that this apparent deterioration is not merely the result of habituation of the senses. Air pollution data for the city show trends of increasing concentrations of those very substances that have destroyed the attractiveness of major population centres elsewhere, with climates initially as salubrious. Indeed, present figures indicate that photochemical smog in unacceptably high concentrations is rapidly becoming endemic also over Brisbane. These regrettable developments should come as no surprise. The society at large has not been inclined to respond purposefully to warnings of impending environmental problems, despite the experiences and publicity from overseas and even from other cities within Australia. Nor, up to the present, have certain politicians and government officials displayed stances beyond those necessary for the maintenance of a decorum of concern. At this stage, there still exists the possibility for meaningful government action without the embarrassment of losing political favour with the electorate. To the contrary, there is every chance that such action may be turned to advantage with increased public enlightenment. It would be more than a pity to miss perhaps the final remaining opportunity: Queensland is one of the few remaining places in the world with sufficient resources to permit both rational development and high environmental quality. The choice appears to be one of making a relatively minor investment now for a large financial and social gain the near future, or, permitting Brisbane to degenerate gradually into just another stagnated Los Angeles or Sydney. The present monograph attempts to introduce the problem by reviewing the available research on air quality in the Brisbane area. It also tries to elucidate some seemingly obvious, but so far unapplied management approaches. By necessity, such a broad treatment needs to make inroads into extensive ranges of subject areas, including political and legal practices to public perceptions, scientific measurement and statistical analysis to dynamics of air flow. Clearly, it does not pretend to be definitive in any of these fields, but it does try to emphasize those adjustable facets of the human use system of natural resources, too often neglected in favour of air pollution control technology. The crossing of disciplinary boundaries, however, needs no apology: air quality problems are ubiquitous, touching upon space, time and human interaction.

Verbs as Spatial Deixis markers in Jingulu

Contrary to the common pattern of spatial terms being metaphorically extended to location in time, the Australian language Jingulu shows an unusual extension of temporal markers to indicate location in space. Light verbs, which typically encode tense, aspect, mood and associated motion, are occasionally found on nouns to indicate the relative location of the referent with respect to the speaker. It is hypothesised that this pattern resulted from the reduction of verbal clauses used as relative modifiers to the nouns in question.

Spatial Technologies: What use are they to managers of environmental lands?

This paper reviews the potential use of three types of spatial technology to land managers, namely satellite imagery, satellite positioning systems and supporting computer software. Developments in remote sensing and the relative advantages of multispectral and hyperspectral images are discussed. The main challenge to the wider use of remote sensing as a land management tool is seen as uncertainty whether apparent relationships between biophysical variables and spectral reflectance are direct and causal, or artefacts of particular images. Developments in satellite positioning systems are presented in the context of land managers’ need for position estimates in situations where absolute precision may or may not be required. The role of computer software in supporting developments in spatial technology is described. Spatial technologies are seen as having matured beyond empirical applications to the stage where they are useful and reliable land management tools. In addition, computer software has become more user-friendly and this has facilitated data collection and manipulation by semi-expert as well as specialist staff.

Short-term spatial diffusion in sigma o+ o- optical molasses

We have measured the spatial diffusion of atoms in a three-dimensional sigma(+)-sigma(-) optical molasses over twenty milliseconds timescale, starting from the initial interaction of the atoms with the molasses. We find that the diffusion constants agree well with a linear model for these short time scales and also compare favourably to other studies of diffusion made over longer time scales. These measurements enable us to quantify the detection method known as freezing molasses. We discuss this method, for detecting and measuring the momentum distribution of cold atoms, which relies on the slow diffusion of atoms in optical molasses to produce a freeze-frame of the spatial distribution of the atoms. This method enables a longer interrogation interval, providing a greatly increased signal-to-noise ratio. (C) 1998 Elsevier Science B.V.

Data partitioning for parallel spatial join processing

The cost of spatial join processing can be very high because of the large sizes of spatial objects and the computation-intensive spatial operations. While parallel processing seems a natural solution to this problem, it is not clear how spatial data can be partitioned for this purpose. Various spatial data partitioning methods are examined in this paper. A framework combining the data-partitioning techniques used by most parallel join algorithms in relational databases and the filter-and-refine strategy for spatial operation processing is proposed for parallel spatial join processing. Object duplication caused by multi-assignment in spatial data partitioning can result in extra CPU cost as well as extra communication cost. We find that the key to overcome this problem is to preserve spatial locality in task decomposition. We show in this paper that a near-optimal speedup can be achieved for parallel spatial join processing using our new algorithms.

Three-dimensional quantum solitons with parametric coupling

We consider the quantum field theory of two bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium, this corresponds to the process of second-harmonic generation (via chi((2)) nonlinearity) modified by the chi((3)) nonlinearity. The quantum solitons or energy eigenstates (bound-state solutions) are obtained exactly in the simplest case of two-particle binding, in one, two, and three space dimensions. We also investigate three-particle binding in one space dimension. The results indicate that the exact quantum solitons of this field theory have a singular, pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. To estimate the physically accessible radii and binding energies of the bound states, we impose a momentum cutoff on the nonlinear couplings. In the case of nonlinear optical interactions, the resulting radii and binding energies of these photonic particlelike excitations in highly nonlinear parametric media appear to be close to physically observable values.

Multidimensional parametric quantum solitons

We consider the parametric quantum field theory involving cubic and quartic couplings of two bosonic fields. This is exactly soluble for the two-particle energy eigenstates (or quantum solitons) in one, two, and three space dimensions. We estimate the binding energies and corresponding radii in the case of photonic fields in nonlinear optical materials, and Bose-Einstein condensates. [S1050-2947(98)51110-9].

Theory of multidimensional parametric band-gap simultons

Multidimensional spatiotemporal parametric simultons (simultaneous solitary waves) are possible in a nonlinear chi((2)) medium with a Bragg grating structure, where large effective dispersion occurs near two resonant band gaps for the carrier and second-harmonic field, respectively. The enhanced dispersion allows much reduced interaction lengths, as compared to bulk medium parametric simultons. The nonlinear parametric band-gap medium permits higher-dimensional stationary waves to form. In addition, solitons can occur with lower input powers than conventional nonlinear Schrodinger equation gap solitons. In this paper, the equations for electromagnetic propagation in a grating structure with a parametric nonlinearity are derived from Maxwell's equation using a coupled mode Hamiltonian analysis in one, two, and three spatial dimensions. Simultaneous solitary wave solutions are proved to exist by reducing the equations to the coupled equations describing a nonlinear parametric waveguide, using the effective-mass approximation (EMA). Exact one-dimensional numerical solutions in agreement with the EMA solutions are also given. Direct numerical simulations show that the solutions have similar types of stability properties to the bulk case, providing the carrier waves are tuned to the two Bragg resonances, and the pulses have a width in frequency space less than the band gap. In summary, these equations describe a physically accessible localized nonlinear wave that is stable in up to 3 + 1 dimensions. Possible applications include photonic logic and switching devices. [S1063-651X(98)06109-1].