Phase mapping of ultrashort pulses in bimodal photonic structures: A window on local group velocity dispersion

The amplitude and phase evolution of ultrashort pulses in a bimodal waveguide structure has been studied with a time-resolved photon scanning tunneling microscope (PSTM). When waveguide modes overlap in time intriguing phase patterns are observed. Phase singularities, arising from interference between different modes, are normally expected at equidistant intervals determined by the difference in effective index for the two modes. However, in the pulsed experiments the distance between individual singularities is found to change not only within one measurement frame, but even depends strongly on the reference time. To understand this observation it is necessary to take into account that the actual pulses generating the interference signal change shape upon propagation through a dispersive medium. This implies that the spatial distribution of phase singularities contains direct information on local dispersion characteristics. At the same time also the mode profiles, wave vectors, pulse lengths, and group velocities of all excited modes in the waveguide are directly measured. The combination of these parameters with an analytical model for the time-resolved PSTM measurements shows that the unique spatial phase information indeed gives a direct measure for the group velocity dispersion of individual modes. As a result interesting and useful effects, such as pulse compression, pulse spreading, and pulse reshaping become accessible in a local measuremen

Full field inversion in photoacoustic tomography with variable sound speed

Recently, a novel measurement setup has been introduced to photoacoustic tomography, that collects data in the form of projections of the full 3D acoustic pressure distribution at a certain time instant. Existing imaging algorithms for this kind of data assume a constant speed of sound. This assumption is not always met in practice and thus leads to erroneous reconstructions. In this paper, we present a two-step reconstruction method for full field detection photoacoustic tomography that takes variable speed of sound into account. In the first step, by applying the inverse Radon transform, the pressure distribution at the measurement time is reconstructed point-wise from the projection data. In the second step, one solves a final time wave inversion problem where the initial pressure distribution is recovered from the known pressure distribution at the measurement time. For the latter problem, we derive an iterative solution approach, compute the required adjoint operator, and show its uniqueness and stability

Search for astro-gravity correlations

A new approach in the gravitational wave experiment is considered. In addition to the old method of searching for coincident reactions of two separated gravitational antennae it was proposed to seek perturbations of the gravitational detector noise background correlated with astrophysical events such as neutrino and gamma ray bursts which can be relaibly registered by correspondent sensors. A general algorithm for this approach is developed. Its efficiency is demonstrated in reanalysis of the old data concerning the phenomenon of neutrino-gravity correlation registered during of SN1987A explosion.Comment: 29 pages (LaTeX), 4 figures (EPS

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809