Simulation of ultrasonic imaging with linear arrays in causal absorptive media

Rigorous and efficient numerical methods are presented for simulation of acoustic propagation in a medium where the absorption is described by relaxation processes. It is shown how FFT-based algorithms can be used to simulate ultrasound images in pulse-echo mode. General expressions are obtained for the complex wavenumber in a relaxing medium. A fit to measurements in biological media shows the appropriateness of the model. The wavenumber is applied to three FFT-based extrapolation operators, which are implemented in a weak form to reduce spatial aliasing. The influence of the absorptive medium on the quality of images obtained with a linear array transducer is demonstrated. It is shown that, for moderately absorbing media, the absorption has a large influence on the images, whereas the dispersion has a negligible effect on the images.\ud \u

A Bayesian parameter estimation approach to pulsar time-of-arrival analysis

The increasing sensitivities of pulsar timing arrays to ultra-low frequency (nHz) gravitational waves promises to achieve direct gravitational wave detection within the next 5-10 years. While there are many parallel efforts being made in the improvement of telescope sensitivity, the detection of stable millisecond pulsars and the improvement of the timing software, there are reasons to believe that the methods used to accurately determine the time-of-arrival (TOA) of pulses from radio pulsars can be improved upon. More specifically, the determination of the uncertainties on these TOAs, which strongly affect the ability to detect GWs through pulsar timing, may be unreliable. We propose two Bayesian methods for the generation of pulsar TOAs starting from pulsar "search-mode" data and pre-folded data. These methods are applied to simulated toy-model examples and in this initial work we focus on the issue of uncertainties in the folding period. The final results of our analysis are expressed in the form of posterior probability distributions on the signal parameters (including the TOA) from a single observation.Comment: 16 pages, 4 figure

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page

High-Order-Mode Soliton Structures in Two-Dimensional Lattices with Defocusing Nonlinearity

While fundamental-mode discrete solitons have been demonstrated with both self-focusing and defocusing nonlinearity, high-order-mode localized states in waveguide lattices have been studied thus far only for the self-focusing case. In this paper, the existence and stability regimes of dipole, quadrupole and vortex soliton structures in two-dimensional lattices induced with a defocusing nonlinearity are examined by the theoretical and numerical analysis of a generic envelope nonlinear lattice model. In particular, we find that the stability of such high-order-mode solitons is quite different from that with self-focusing nonlinearity. As a simple example, a dipole (``twisted'') mode soliton which may be stable in the focusing case becomes unstable in the defocusing regime. Our results may be relevant to other two-dimensional defocusing periodic nonlinear systems such as Bose-Einstein condensates with a positive scattering length trapped in optical lattices.Comment: 14 pages, 10 figure

Exponential improvement in photon storage fidelities using subradiance and "selective radiance" in atomic arrays

A central goal within quantum optics is to realize efficient interactions between photons and atoms. A fundamental limit in nearly all applications based on such systems arises from spontaneous emission, in which photons are absorbed by atoms and then re-scattered into undesired channels. In typical treatments of atomic ensembles, it is assumed that this re-scattering occurs independently, and at a rate given by a single isolated atom, which in turn gives rise to standard limits of fidelity in applications such as quantum memories or quantum gates. However, this assumption can be violated. In particular, spontaneous emission of a collective atomic excitation can be significantly suppressed through strong interference in emission. Thus far the physics underlying the phenomenon of subradiance and techniques to exploit it have not been well-understood. In this work, we provide a comprehensive treatment of this problem. First, we show that in ordered atomic arrays in free space, subradiant states acquire an interpretation in terms of optical modes that are guided by the array, which only emit due to scattering from the ends of the finite chain. We also elucidate the properties of subradiant states in the many-excitation limit. Finally, we introduce the new concept of selective radiance. Whereas subradiant states experience a reduced coupling to all optical modes, selectively radiant states are tailored to simultaneously radiate efficiently into a desired channel while scattering into undesired channels is suppressed, thus enabling an enhanced atom-light interface. We show that these states naturally appear in chains of atoms coupled to nanophotonic structures, and we analyze the performance of photon storage exploiting such states. We find that selectively radiant states allow for a photon storage error that scales exponentially better with number of atoms than previously known bounds.Comment: Fixed minor typos, is now analogous to published versio