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Register a new userStatistical properties of the laser beam propagating in a turbulent medium
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We examine statistical properties of a laser beam propagating in a turbulent medium. We prove that the intensity fluctuations at large propagation distances possess Gaussian probability density function and establish quantitative criteria for realizing the Gaussian statistics depending on the laser propagation distance, the laser beam waist, the laser frequency and the turbulence strength. We calculate explicitly the laser envelope pair correlation function and corrections to its higher order correlation functions breaking Gaussianity. We discuss also statistical properties of the brightest spots in the speckle pattern.
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The supernova-driven interstellar medium in star-forming galaxies has Reynolds numbers of the order of $10^{6}$ or even larger. We study, by means of adaptive mesh refinement hydro- and magnetohydrodynamical simulations that cover the full available range (from 10 kpc to sub-parsec) scales, the statistical properties of the turbulent interstellar gas and the dimension of the most dissipative structures. The scalings of the structure functions are consistent with a log-Poisson statistics of supersonic turbulence where energy is dissipated mainly through shocks.
This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for different types of the free energy probability distribution functions. In the second part of the review we discuss the problems which are still waiting for their solutions. Several mathematical appendices in the ending part of the review contain various technical details of the performed calculations.
We analyze theoretically and experimentally how nonlinear differential-transmission spectroscopy of a lambda-system medium can provide quantitative understanding of the optical dipole moments and transition energies. We focus on the situation where two optical fields spatially overlap and co-propagate to a single detector. Nonlinear interactions give cross-modulation between a modulated and non-modulated laser field, yielding differential transmission signals. Our analysis shows how this approach can be used to enhance the visibility of relatively weak transitions, and how particular choices in the experimental design minimize systematic errors and the sensitivity to changes in laser field intensities. Experimentally, we demonstrate the relevance of our analysis with spectroscopy on the donor-bound exciton system of silicon donors in GaAs, where the transitions from the two bound-electron spin states to a bound-exciton state form a lambda system. Our approach is, however, of generic value for many spectroscopy experiments on solid-state systems in small cryogenic measurement volumes where in-situ frequency or polarization filtering of control and signal fields is often challenging.
Using the replica method, we develop an analytical approach to compute the characteristic function for the probability $mathcal{P}_N(K,lambda)$ that a large $N times N$ adjacency matrix of sparse random graphs has $K$ eigenvalues below a threshold $lambda$. The method allows to determine, in principle, all moments of $mathcal{P}_N(K,lambda)$, from which the typical sample to sample fluctuations can be fully characterized. For random graph models with localized eigenvectors, we show that the index variance scales linearly with $N gg 1$ for $|lambda| > 0$, with a model-dependent prefactor that can be exactly calculated. Explicit results are discussed for Erdos-Renyi and regular random graphs, both exhibiting a prefactor with a non-monotonic behavior as a function of $lambda$. These results contrast with rotationally invariant random matrices, where the index variance scales only as $ln N$, with an universal prefactor that is independent of $lambda$. Numerical diagonalization results confirm the exactness of our approach and, in addition, strongly support the Gaussian nature of the index fluctuations.
Transforming a laser beam into a mass flow has been a challenge both scientifically and technologically. Here we report the discovery of a new optofluidics principle and demonstrate the generation of a steady-state water flow by a pulsed laser beam through a glass window. In order to generate a flow or stream in the same path as the refracted laser beam in pure water from an arbitrary spot on the window, we first fill a glass cuvette with an aqueous solution of Au nanoparticles. A flow will emerge from the focused laser spot on the window after the laser is turned on for a few to tens of minutes, the flow remains after the colloidal solution is completely replaced by pure water. Microscopically, this transformation is made possible by an underlying plasmonic nanoparticle-decorated cavity which is self-fabricated on the glass by nanoparticle-assisted laser etching and exhibits size and shape uniquely tailored to the incident beam profile. Hydrophone signals indicate that the flow is driven via acoustic streaming by a long-lasting ultrasound wave that is resonantly generated by the laser and the cavity through the photoacoustic effect. The principle of this light-driven flow via ultrasound, i.e. photoacoustic streaming by coupling photoacoustics to acoustic streaming, is general and can be applied to any liquids, opening up new research and applications in optofluidics as well as traditional photoacoustics and acoustic streaming.
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