40 research outputs found
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 . Depending on the sign of
, the medium is absorbing or amplifying. The transmitted intensity
decays exponentially as the waveguide length
, regardless of the sign of . The localization length
is computed as a function of the mean free path , the absorption or
amplification length , and the number of modes in the waveguide
. 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 and . An approximate
interpolation formula for all 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
Reflection of light from a disordered medium backed by a phase-conjugating mirror
This is a theoretical study of the interplay of optical phase-conjugation and
multiple scattering. We calculate the intensity of light reflected by a
phase-conjugating mirror when it is placed behind a disordered medium. We
compare the results of a fully phase-coherent theory with those from the theory
of radiative transfer. Both methods are equivalent if the dwell time
\tau_{dwell} of a photon in the disordered medium is much larger than the
inverse of the frequency shift 2\Delta\omega acquired at the phase-conjugating
mirror. When \tau_{dwell} \Delta\omega < 1, in contrast, phase coherence
drastically affects the reflected intensity. In particular, a minimum in the
dependence of the reflectance on the disorder strength disappears when
\Delta\omega is reduced below 1/\tau_{dwell}. The analogies and differences
with Andreev reflection of electrons at the interface between a normal metal
and a superconductor are discussed.Comment: 27 pages RevTeX with 11 figures included with psfi
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
Study of transmission and reflection from a disordered lasing medium
A numerical study of the statistics of transmission () and reflection
() of quasi-particles from a one-dimensional disordered lasing or amplifying
medium is presented. The amplification is introduced via a uniform imaginary
part in the site energies in the disordered segment of the single-band tight
binding model. It is shown that is a non-self-averaging quantity. The
cross-over length scale above which the amplification suppresses the
transmittance is studied as a function of amplification strength. A new
cross-over length scale is introduced in the regime of strong disorder and weak
amplification. The stationary distribution of the backscattered reflection
coefficient is shown to differ qualitatively from the earlier analytical
results obtained within the random phase approximation.Comment: 5 pages RevTex (twocolumn format), 5 EPS figures, considerably
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Berry phase and adiabaticity of a spin diffusing in a non-uniform magnetic field
An electron spin moving adiabatically in a strong, spatially non-uniform
magnetic field accumulates a geometric phase or Berry phase, which might be
observable as a conductance oscillation in a mesoscopic ring. Two contradicting
theories exist for how strong the magnetic field should be to ensure
adiabaticity if the motion is diffusive. To resolve this controversy, we study
the effect of a non-uniform magnetic field on the spin polarization and on the
weak-localization effect. The diffusion equation for the Cooperon is solved
exactly. Adiabaticity requires that the spin-precession time is short compared
to the elastic scattering time - it is not sufficient that it is short compared
to the diffusion time around the ring. This strong condition severely
complicates the experimental observation.Comment: 16 pages REVTEX, including 3 figure
Dynamic effect of phase conjugation on wave localization
We investigate what would happen to the time dependence of a pulse reflected
by a disordered single-mode waveguide, if it is closed at one end not by an
ordinary mirror but by a phase-conjugating mirror. We find that the waveguide
acts like a virtual cavity with resonance frequency equal to the working
frequency omega_0 of the phase-conjugating mirror. The decay in time of the
average power spectrum of the reflected pulse is delayed for frequencies near
omega_0. In the presence of localization the resonance width is
tau_s^{-1}exp(-L/l), with L the length of the waveguide, l the mean free path,
and tau_s the scattering time. Inside this frequency range the decay of the
average power spectrum is delayed up to times t simeq tau_s exp(L/l).Comment: 10 pages including 2 figure
Statistical Properties of the Reflectance and Transmittance of an Amplifying Random Media
Statistical properties of the transmittance () and reflectance () of an
amplifying layer with one-dimensional disorder are investigated analytically.
Whereas the transmittance at typical realizations decreases exponentially with
the layer thickness just as it does in absorbing media, the average
and \ are shown to
be infinite even for finite due to the contribution of low-probable
resonant realizations corresponding to the non-Gaussian tail of the
distribution of . This tail differs drastically from that in the case of
absorption. The physical meaning of typical and resonant realizations is
discussed.Comment: 5 pages (RevTeX