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

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

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

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 figur

Effect of amplification on conductance distribution of a disordered waveguide

Introduction of optical gain to a disordered system results in enhanced fluctuations [$F_{(2)}=var(\tilde{g})/^2$] of dimensionless conductance $\tilde{g}$, similar to the effect of Anderson localization in passive medium. Using numerical simulations we demonstrate that despite of such qualitative similarity, the whole distribution of conductance of amplifying random media is drastically different from that of passive system with the same value of $F_{(2)}$.Comment: 4 pages, 4 figure