Localization in a Disordered Multi-Mode Waveguide with Absorption or Amplification

An analytical and numerical study is presented of transmission of radiation through a multi-mode waveguide containing a random medium with a complex dielectric constant $\epsilon= \epsilon'+i\epsilon''$. Depending on the sign of $\epsilon''$, the medium is absorbing or amplifying. The transmitted intensity decays exponentially $\propto\exp(-L/\xi)$ as the waveguide length $L\to\infty$, regardless of the sign of $\epsilon''$. The localization length $\xi$ is computed as a function of the mean free path $l$, the absorption or amplification length $|\sigma|^{-1}$, and the number of modes in the waveguide $N$. The method used is an extension of the Fokker-Planck approach of Dorokhov, Mello, Pereyra, and Kumar to non-unitary scattering matrices. Asymptotically exact results are obtained for $N\gg1$ and $|\sigma|\gg1/N^2l$. An approximate interpolation formula for all $\sigma$ agrees reasonably well with numerical simulations.Comment: 13 pages, RevTeX, 1 postscript figur

Probability of Reflection by a Random Laser

A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre ensemble of random-matrix theory. The statistical fluctuations of the albedo (the ratio of reflected and incident power) are computed for arbitrary ratio of sample thickness, mean free path, and absorption or amplification length. On approaching the laser threshold all moments of the distribution of the albedo diverge. Its modal value remains finite, however, and acquires an anomalous dependence on the illuminated surface area.Comment: 8 pages (revtex), 3 figures, to appear in Phys.Rev.Let

Brightness of a phase-conjugating mirror behind a random medium

A random-matrix theory is presented for the reflection of light by a disordered medium backed by a phase-conjugating mirror. Two regimes are distinguished, depending on the relative magnitude of the inverse dwell time of a photon in the disordered medium and the frequency shift acquired at the mirror. The qualitatively different dependence of the reflectance on the degree of disorder in the two regimes suggests a distinctive experimental test for cancellation of phase shifts in a random medium.Comment: 4 pages LaTeX. 2 Postscript figures include

Field and intensity correlations in amplifying random media

We study local and nonlocal correlations of light transmitted through active random media. The conventional approach results in divergence of ensemble averaged correlation functions due to existence of lasing realizations. We introduce conditional average for correlation functions by omitting the divergent realizations. Our numerical simulation reveals that amplification does not affect local spatial correlation. The nonlocal intensity correlations are strongly magnified due to selective enhancement of the contributions from long propagation paths. We also show that by increasing gain, the average mode linewidth can be made smaller than the average mode spacing. This implies that light transport through a diffusive random system with gain could exhibit some similarities to that through a localized passive system, owing to dominant influence of the resonant modes with narrow width.Comment: 5 pages, 4 figure

Probability of reflection by a random laser

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The Friendly Settlement of Human Rights Abuses in the Americas

We present a new method for estimation of seismic coda shape. It falls into the same class of methods as non-parametric shape reconstruction with the use of neural network techniques where data are split into a training and validation data sets. We particularly pursue the well-known problem of image reconstruction formulated in this case as shape isolation in the presence of a broadly defined noise. This combined approach is enabled by the intrinsic feature of seismogram which can be divided objectively into a pre-signal seismic noise with lack of the target shape, and the remainder that contains scattered waveforms compounding the coda shape. In short, we separately apply shape restoration procedure to pre-signal seismic noise and the event record, which provides successful delineation of the coda shape in the form of a smooth almost non-oscillating function of time. The new algorithm uses a recently developed generalization of classical computational-geometry tool of alpha-shape. The generalization essentially yields robust shape estimation by ignoring locally a number of points treated as extreme values, noise or non-relevant data. Our algorithm is conceptually simple and enables the desired or pre-determined level of shape detail, constrainable by an arbitrary data fit criteria. The proposed tool for coda shape delineation provides an alternative to moving averaging and/or other smoothing techniques frequently used for this purpose. The new algorithm is illustrated with an application to the problem of estimating the coda duration after a local event. The obtained relation coefficient between coda duration and epicentral distance is consistent with the earlier findings in the region of interest

Comment on "Direction of optical energy flow in a transverse magnetic field

Quantum Matter and Optic

Amplification or Reduction of Backscattering in a Coherently Amplifying or Absorbing Disordered Chain

We study localization properties of a one-dimensional disordered system characterized by a random non-hermitean hamiltonian where both the randomness and the non-hermiticity arises in the local site-potential; its real part being random, and a constant imaginary part implying the presence of either a coherent absorption or amplification at each site. While the two-probe transport properties behave seemingly very differently for the amplifying and the absorbing chains, the logarithmic resistance $u$ = ln$(1+R_4)$ where $R_4$ is the 4-probe resistance gives a unified description of both the cases. It is found that the ensemble-averaged $$ increases linearly with length indicating exponential growth of resistance. While in contrast to the case of Anderson localization (random hermitean matrix), the variance of $u$ could be orders of magnitude smaller in the non-hermitean case, the distribution of $u$ still remains non-Gaussian even in the large length limit.Comment: 11 LaTeX pages plus 14 EPS figure

Single parameter scaling in 1-D localized absorbing systems

Numerical study of the scaling of transmission fluctuations in the 1-D localization problem in the presence of absorption is carried out. Violations of single parameter scaling for lossy systems are found and explained on the basis of a new criterion for different types of scaling behavior derived by Deych et al [Phys. Rev. Lett., {\bf 84}, 2678 (2000)].Comment: 7 pages, 6 figures, RevTex, submitted to Phys. Rev.