115 research outputs found
On applicability of inhomogeneous diffusion approach to localized transport through disordered waveguides
In this work we show analytically and numerically that wave transport through
random waveguides can be modeled as a diffusion with an inhomogeneous diffusion
coefficient (IDC). In localized regime, IDC retains the memory of the source
position. In an absorbing random medium, IDC becomes independent of the source.Comment: 5 pages, 3 figure
Photonic band structure of ZnO photonic crystal slab laser
We recently reported on the first realization of ultraviolet photonic crystal
laser based on zinc oxide [Appl. Phys. Lett. {\bf 85}, 3657 (2004)]. Here we
present the details of structural design and its optimization. We develop a
computational super-cell technique, that allows a straightforward calculation
of the photonic band structure of ZnO photonic crystal slab on sapphire
substrate. We find that despite of small index contrast between the substrate
and the photonic layer, the low order eigenmodes have predominantly
transverse-electric (TE) or transverse-magnetic (TM) polarization. Because
emission from ZnO thin film shows strong TE preference, we are able to limit
our consideration to TE bands, spectrum of which can possess a complete
photonic band gap with an appropriate choice of structure parameters. We
demonstrate that the geometry of the system may be optimized so that a sizable
band gap is achieved.Comment: 8 pages, 7 figure
Polariton Local States in Periodic Bragg Multiple Quantum Well Structures
We analytically study optical properties of several types of defects in Bragg
multiple quantum well structures. We show that a single defect leads to two
local polariton modes in the photonic band gap. These modes lead to
peculiarities in reflection and transmission spectra. Detailed recommendations
for experimental observation of the studied effects are given.Comment: 3 pages, 1 figure, RevTex, Submitted to Opt. Let
Inverse Design of Perfectly Transmitting Eigenchannels in Scattering Media
Light-matter interactions inside turbid medium can be controlled by tailoring
the spatial distribution of energy density throughout the system. Wavefront
shaping allows selective coupling of incident light to different transmission
eigenchannels, producing dramatically different spatial intensity profiles. In
contrast to the density of transmission eigenvalues that is dictated by the
universal bimodal distribution, the spatial structures of the eigenchannels are
not universal and depend on the confinement geometry of the system. Here, we
develop and verify a model for the transmission eigenchannel with the
corresponding eigenvalue close to unity. By projecting the original problem of
two-dimensional diffusion in a homogeneous scattering medium onto a
one-dimensional inhomogeneous diffusion, we obtain an analytical expression
relating the intensity profile to the shape of the confining waveguide.
Inverting this relationship enables the inverse design of the waveguide shape
to achieve the desired energy distribution for the perfectly transmitting
eigenchannel. Our approach also allows to predict the intensity profile of such
channel in a disordered slab with open boundaries, pointing to the possibility
of controllable delivery of light to different depths with local illumination.Comment: 9 pages, 6 figure
Local polariton modes and resonant tunneling of electromagnetic waves through periodic Bragg multiple quantum well structures
We study analytically defect polariton states in Bragg multiple-quantum-well
structures and defect induced changes in transmission and reflection spectra.
Defect layers can differ from the host layers in three ways: exciton-light
coupling strength, exciton resonance frequency, and inter-well spacing. We show
that a single defect leads to two local polariton modes in the photonic
bandgap. These modes cause peculiarities in reflection and transmission
spectra. Each type of defect can be reproduced experimentally, and we show that
each of these plays a distinct role in the optical properties of the system.
For some defects, we predict a narrow transmission window in the forbidden gap
at the frequency set by parameters of the defect. We obtain analytical
expressions for corresponding local frequencies as well as for reflection and
transmission coefficients. We show that the presence of the defects leads to
resonant tunneling of the electromagnetic waves via local polariton modes
accompanied by resonant enhancement of the field inside the sample, even when a
realistic absorption is taken into account. On the basis of the results
obtained, we make recommendations regarding the experimental observation of the
effects studied in readily available samples.Comment: 17 pages, 10 figures, RevTex, Submitted to PR
Concept of local polaritons and optical properties of mixed polar crystals
The concept of local polaritons is used to describe optical properties of
mixed crystals in the frequency region of their {\it restrahlen} band. It is
shown that this concept allows for a physically transparent explanation of the
presence of weak features in the spectra of so called one-mode crystals, and
for one-two mode behavior. The previous models were able to explain these
features only with the use of many fitting parameters. We show that under
certain conditions new impurity-induced polariton modes may arise within the
{\it restrahlen} of the host crystals, and study their dispersion laws and
density of states. Particularly, we find that the group velocity of these
excitations is proportional to the concentration of the impurities and can be
thousands of times smaller then the speed of light in vacuum.Comment: 21 pages, 5 figures, RevTex, Phys. Rev. B, 62, 6301 (2000
Shape-dependence of transmission, reflection and absorption eigenvalue densities in disordered waveguides with dissipation
The universal bimodal distribution of transmission eigenvalues in lossless
diffusive systems un- derpins such celebrated phenomena as universal
conductance fluctuations, quantum shot noise in condensed matter physics and
enhanced transmission in optics and acoustics. Here, we show that in the
presence of absorption, density of the transmission eigenvalues depends on the
confinement geometry of scattering media. Furthermore, in an asymmetric
waveguide, densities of the reflection and absorption eigenvalues also depend
of the side from which the waves are incident. With increas- ing absorpotion,
the density of absorption eigenvalues transforms from single-peak to
double-peak function. Our findings open a new avenue for coherent control of
wave transmission, reflection and absorption in random media.Comment: 9 pages 8 figure
Lie point symmetries of differential--difference equations
We present an algorithm for determining the Lie point symmetries of
differential equations on fixed non transforming lattices, i.e. equations
involving both continuous and discrete independent variables. The symmetries of
a specific integrable discretization of the Krichever-Novikov equation, the
Toda lattice and Toda field theory are presented as examples of the general
method.Comment: 17 pages, 1 figur
Critical States Embedded in the Continuum
We introduce a class of critical states which are embedded in the continuum
(CSC) of one-dimensional optical waveguide array with one non-Hermitian defect.
These states are at the verge of being fractal and have real propagation
constant. They emerge at a phase transition which is driven by the imaginary
refractive index of the defect waveguide and it is accompanied by a mode
segregation which reveals analogies with the Dicke super -radiance. Below this
point the states are extended while above they evolve to exponentially
localized modes. An addition of a background gain or loss can turn these
localized states to bound states in the continuum.Comment: 4.5 pages, 3 figures, 1 page of supplementary material including one
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