Optical carrier wave shocking: detection and dispersion

Carrier wave shocking is studied using the Pseudo-Spectral Spatial Domain (PSSD) technique. We describe the shock detection diagnostics necessary for this numerical study, and verify them against theoretical shocking predictions for the dispersionless case. These predictions show Carrier Envelope Phase (CEP) and pulse bandwidth sensitivity in the single-cycle regime. The flexible dispersion management offered by PSSD enables us to independently control the linear and nonlinear dispersion. Customized dispersion profiles allow us to analyze the development of both carrier self-steepening and shocks. The results exhibit a marked asymmetry between normal and anomalous dispersion, both in the limits of the shocking regime and in the (near) shocked pulse waveforms. Combining these insights, we offer some suggestions on how carrier shocking (or at least extreme self-steepening) might be realised experimentally.Comment: 9 page

Status of the Fermilab Muon (g-2) Experiment

The New Muon $(g-2)$ Collaboration at Fermilab has proposed to measure the anomalous magnetic moment of the muon, $a_\mu$, a factor of four better than was done in E821 at the Brookhaven AGS, which obtained $a_\mu = [116 592 089 (63)] \times 10^{-11}$ $\pm 0.54$ ppm. The last digit of $a_{\mu}$ is changed from the published value owing to a new value of the ratio of the muon-to-proton magnetic moment that has become available. At present there appears to be a difference between the Standard-Model value and the measured value, at the $\simeq 3$ standard deviation level when electron-positron annihilation data are used to determine the lowest-order hadronic piece of the Standard Model contribution. The improved experiment, along with further advances in the determination of the hadronic contribution, should clarify this difference. Because of its ability to constrain the interpretation of discoveries made at the LHC, the improved measurement will be of significant value, whatever discoveries may come from the LHC.Comment: Proceedings of the PhiPsi09, Oct. 13-16, 2009, Beijing, China, 4 pages 2 figures. Version 2 includes Fermilab report number, minor corrections and one additional referenc

Carrier-wave steepened pulses and gradient-gated high-order harmonic generation using linear ramp waveforms

We show how to optimize the process of high-harmonic generation (HHG) by gating the interaction using the field gradient of a driving pulse with a linear ramp waveform. Since maximized field gradients are efficiently generated by self-steepening processes, we first present a generalized theory of optical carrier-wave self-steepened (CSS) pulses. This goes beyond existing treatments, which only consider third-order nonlinearity, and has the advantage of describing pulses whose wave forms have a range of symmetry properties. Although a fertile field for theoretical work, CSS pulses are difficult to realize experimentally because of the deleterious effect of dispersion. We therefore consider synthesizing CSS-like profiles using a suitably phased sub-set of the harmonics present in a true CSS wave form. Using standard theoretical models of HHG, we show that the presence of gradient-maximized regions on the wave forms can raise the spectral cut-off and so yield shorter attosecond pulses. We study how the quality of the attosecond bursts created by spectral filtering depends on the number of harmonics included in the driving pulse.Comment: 8 pages, 10 figures; with appendix not present in published versio

Computational Relativistic Astrophysics With Adaptive Mesh Refinement: Testbeds

We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS binary inspiral and coalescence carried out on a workstation having an accuracy equivalent to that of a $1025^3$ regular unigrid simulation, which is, to the best of our knowledge, larger than all previous simulations of similar NS systems on supercomputers. We believe the capability opens new possibilities in general relativistic simulations.Comment: 7 pages, 16 figure

Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators

Correlation functions $C(t) \sim$ in ohmically damped systems such as coupled harmonic oscillators or optical resonators can be expressed as a single sum over modes $j$ (which are not power-orthogonal), with each term multiplied by the Petermann factor (PF) $C_j$, leading to "excess noise" when $|C_j| > 1$. It is shown that $|C_j| > 1$ is common rather than exceptional, that $|C_j|$ can be large even for weak damping, and that the PF appears in other processes as well: for example, a time-independent perturbation \sim\ep leads to a frequency shift \sim \ep C_j. The coalescence of $J$ ($>1$) eigenvectors gives rise to a critical point, which exhibits "giant excess noise" ($C_j \to \infty$). At critical points, the divergent parts of $J$ contributions to $C(t)$ cancel, while time-independent perturbations lead to non-analytic shifts \sim \ep^{1/J}.Comment: REVTeX4, 14 pages, 4 figures. v2: final, 20 single-col. pages, 2 figures. Streamlined with emphasis on physics over formalism; rewrote Section V E so that it refers to time-dependent (instead of non-equilibrium) effect

Three-dimensional adaptive evolution of gravitational waves in numerical relativity

Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the sources. We have carried out an important step toward this goal, the evolution of weak gravitational waves using adaptive mesh refinement in the Einstein equations. The 2-level adaptive simulation is compared with unigrid runs at coarse and fine resolution, and is shown to track closely the features of the fine grid run.Comment: REVTeX, 7 pages, including three figures; submitted to Physical Review