STUDY ON LIGHT LOCALIZATION OF ONE-DIMENSIONAL DISORDERED MULTILAYER

Antimonite and cryolite are used as the high and low refractive index coating materials to be evaporated alternately to the glass substrates. All cryolite layers have the same thickness d/4n_a, and the thickness of antimonite layers varies randomly around an average value d/4n_b, with d=650nm, n_a and n_b their refractive indices. Three kinds of multilayer are prepared, they possess the same degree of thickness disorder, but different total lengths, i.e., 10, 15 and 21 perioda. We measure the transmission and reflection spectrum after the light passing through these multilayers. The exponential intensity variation versus total length is experi-mentally demonstrated, and the light localization length is then obtained. Our experimental results can be fitted very well with the numerical simulation. Based on the measured and calculated localization length, the effects of phase coherent: Bragg reflection and Anderson localization are discussed.     

Quantum correlations in two-particle Anderson localization

We predict quantum correlations between noninteracting particles evolving simultaneously in a disordered medium. While the particle density follows the single-particle dynamics and exhibits Anderson localization, the two-particle correlation develops unique features that depend on the quantum statistics of the particles and their initial separation. On short time scales, the localization of one particle becomes dependent on whether or not the other particle is localized. On long time scales, the localized particles show oscillatory correlations within the localization length. These effects can be observed in Anderson localization of nonclassical light and ultracold atoms.     

The ballistic dimer resonance in the one-dimensional disordered photonic crystals

The propagation of electromagnetic waves in one-dimensional disordered dielectric layer stack is studied theoretically using the transfer matrix formalism. The presence of the dimer unit cells inside a host photonic crystal, as the intentionally short range disorder correlation, provides predicted dimer resonances, leading to the break down of the Anderson localization. However while suitably adjusting the intrinsic defect unit cell parameters (i.e. the defect dielectric constants), the light can be transmitted on larger localization length through a ballistic canal, opening up possibilities for performing better tailored ballistic optical filters. Moreover, by increasing the rate of disorder (i.e. the defects concentration and/or the length of the system) the quality of the transmission around the ballistic resonance can be improved with the smoother corresponding allowed mini bands.     

Anderson localization for radial tree-like random quantum graphs

We prove that certain random models associated with radial, tree-like, rooted quantum graphs exhibit Anderson localization at all energies. The two main examples are the random length model (RLM) and the random Kirchhoff model (RKM). In the RLM, the lengths of each generation of edges form a family of independent, identically distributed random variables (iid). For the RKM, the iid random variables are associated with each generation of vertices and moderate the current flow through the vertex. We consider extensions to various families of decorated graphs and prove stability of localization with respect to decoration. In particular, we prove Anderson localization for the random necklace model.     

Resonance elastic scattering of light by a quantum well with statistically uneven boundaries

A theory is formulated for the elastic scattering of light through quasi-two-dimensional exciton states in a quantum well with randomly uneven walls. The nonlocal exciton susceptibility is expressed in terms of random functions describing the shape of the quantum well boundaries up to and including linear terms in the unevenness height. The resonance elastic scattering cross sections in the presence of arbitrary statistical unevenness are calculated in the Born approximation for all channels in which the initial and final states are represented by an electromagnetic TM or TE mode. The spectral and angular dependences of the scattering probability are calculated with the unevenness characterized by Gaussian correlation functions. It follows from numerical estimates that elastic scattering in quantum wells should be observed for unevenness having an rms height of the order of the thickness of an atomic monolayer. Fiz. Tverd. Tela (St. Petersburg) 41, 330–336 (February 1999)     

A tunable terahertz-band oscillator based on a two-well nanostructure with a coherent electron subsystem

A theory of coherent resonance tunneling of electrons in a two-well nanostructure (TWNS) in the presence of a strong electromagnetic field is developed. The TWNS consists of two identical tunnel-coupled quantum wells to which a dc electric field is applied. Radiative transitions occur between two levels that arise due to the interwell interference and the dc electric field. The wavefunctions and polarization currents in the TWNS are found in the case of a strong electromagnetic field, and the oscillation power is determined as a function of the coherent pumping current and the parameters of the structure. It is shown that oscillations are possible in the relevant terahertz band, with fine frequency tuning by a dc field. It is found that the interference of electrons between quantum wells plays a crucial role. This interference significantly suppresses the effect of the electromagnetic field on the resonance tunneling and enhances the oscillation up to the highest possible level. It is proved that there exists an optimal regime of strong-field oscillations without inverse population and saturation, which are inherent in conventional lasers.     

Light scattering on random dielectric layers

Scattering of light by a random stack of dielectric layers represents a one-dimensional scattering problem, where the scattered field is a three-dimensional vector field. We investigate the dependence of the scattering properties (band gaps and Anderson localization) on the wavelength, strength of randomness and relative angle of the incident wave. There is a characteristic angular dependence of Anderson localization for wavelengths close to the thickness of the layers. In particular, the localization length varies non-monotonously with the angle. In contrast to Anderson localization, absorptive layers do not have this characteristic angular dependence.     

Periodic oscillations in transmission decay of anderson localized one-dimensional dielectric systems

It is well recognized that the transmittance of Anderson localized systems decays exponentially on average with sample size, showing large fluctuations brought up by extremely rare occurrences of necklaces of resonantly coupled states, possessing almost unity transmission. We show here that in a one-dimensional (1D) random photonic system with resonant layers these fluctuations appear to be very regular and have a period defined by the localization length xi of the system. We stress that necklace states are the origin of these well-defined oscillations. We predict that in such a random system efficient transmission channels form regularly each time the increasing sample length fits so-called optimal-order necklaces and demonstrate the phenomenon through numerical experiments. Our results provide new insight into the physics of Anderson localization in random systems with resonant units.     

Chromaticity-tunable white light emission from organic multiple-quantum-well structure

Organic multiple quantum wells (MQWs) white light emitting devices are fabricated in which blue fluorescent dye, a trimer of N-anylbenzimidazole (TPBI) and orange fluorescent rubrene doped tris (8-hydroxyquinoline) Aluminum act as quantum-well light emitting layers between triphenyldiamine derivative (TPD) potential barrier layers, and aluminium complex (Alq) act as an electron transporter and green emitter. The injected carriers are confined in different quantum wells and Alq layer. The white light emission comes from a combination of photons generated in different light emitting layers. The Commission Internationale de l' Eclairage (CIE) coordinates of the emitted light are tuned by increasing the number of TPBI wells due to its low fluorescent efficiency compared with rubrene.     

Mobility edge in the three dimensional Anderson model

The localization length as a function of energy and disorder of a three dimensional disordered system described by the Anderson Hamiltonian is determined. The phase diagram for localization is discussed with particular emphasis on the mechanisms which are important for localization (quantum interference and tunneling).     

Quantum Hall effect-insulator transition in the InAs/GaAs system with quantum dots

The InAs/GaAs structures consisting of quantum-dot layers with electronic properties typical of two-dimensional systems are investigated. It is found that, at a low concentration of charge carriers, the variable-range-hopping conductivity is observed at low temperatures. The localization length corresponds to characteristic quantum-dot cluster sizes determined using atomic-force microscopy (AFM). The quantum Hall effect-insulator transition induced by a magnetic field occurs in InAs/GaAs quantum-dot layers with metallic conductivity. The resistivities at the transition point exceed the resistivities characteristic of electrons in heterostructures and quantum wells. This can be explained by the large-scale fluctuations of the potential and, hence, the electron density.     

Bands of Localized Electromagnetic Waves in 3D Random Media

Anderson localization of electromagnetic waves in three-dimensional disordered dielectric structures is studied using a simple yet realistic theoretical model. An effective approach based on analysis of probability distributions, not averages, is developed. The disordered dielectric medium is modeled by a system of randomly distributed electric dipoles. Spectra of certain random matrices are investigated and the possibility of appearance of the continuous band of localized waves emerging in the limit of an infinite medium is indicated. It is shown that localization could be achieved without tuning the frequency of monochromatic electromagnetic waves to match the internal (Mie-type) resonances of individual scatterers. A possible explanation for the lack of experimental evidence for strong localization in 3D as well as suggestions how to make localization experimentally feasible are also given. Rather peculiar requirements for setting in localization in 3D as compared to 2D are indicated.     

Enhanced resonant backscattering of excitons in disordered quantum wells

A clear signature of enhanced backscattering of excitons is observed in the directional resonant Rayleigh scattering of light from localized two-dimensional excitons in disordered quantum wells. Its spectral dependence and time dynamics are measured and theoretically predicted in a quantitative way. The intensity enhancement has a large momentum span extending beyond the external light emission cone. This is a consequence of the small localization length of the exciton as a massive particle probed close to the band bottom. The localization length can be controlled by the photon kinetic energy. This constitutes a qualitative difference to backscattering phenomena in other branches of physics.     

Transport of charge-density waves in the presence of disorder: classical pinning versus quantum localization

We consider the interplay of the elastic pinning and the Anderson localization in the transport properties of a charge-density wave in one dimension, within the framework of the Luttinger model in the limit of strong repulsion. We address a conceptually important issue of which of the two disorder-induced phenomena limits the mobility more effectively. We argue that the interplay of the classical and quantum effects in transport of a very rigid charge-density wave is quite nontrivial: the quantum localization sets in at a temperature much smaller than the pinning temperature, whereas the quantum localization length is much smaller than the pinning length.     

Magnetic field effects on the localization of electromagnetic waves in random 1D systems which are almost periodic

The effects of an externally applied magnetic field on the Anderson localization of electromagnetic waves in an alternating layered system of vacuum and semiconducting slabs are studied. Specifically, a waveguide formed from perfectly conducting parallel plates which contain between them an array of vacuum and n-type semiconductor slabs is examined in the presence of an external static magnetic field applied parallel to both the plates and the slab surfaces. The widths of the slabs in the array are random but with a randomness such that the array of slabs is almost periodic, and we study only electromagnetic modes which propagate perpendicular to the slab surfaces. The localization length is obtained by studying the reflection and transmission properties of a finite array of slabs in the limit that it becomes semi-infinite. Two types of system are treated: (i) a reciprocal system which exhibits a localization length that does not depend on the sign of the applied magnetic field, and (ii) a non-reciprocal system which exhibits a localization length that depends on the sign of the applied magnetic field.     

Localization of cold atoms in state-dependent optical lattices via a Rabi Pulse

We propose a novel realization of Anderson localization in nonequilibrium states of ultracold atoms in an optical lattice. A Rabi pulse transfers part of the population to a different internal state with infinite effective mass. These frozen atoms create a quantum superposition of different disorder potentials, localizing the mobile atoms. For weakly interacting mobile atoms, Anderson localization is obtained. The localization length increases with increasing disorder and decreasing interaction strength, contrary to the expectation for equilibrium localization.     

Giant exciton resonance reflectance in Bragg MQW structures

We have studied the reflectivity from heterostructures with a finite number of equidistant quantum wells. A giant amplification of the reflectance has been observed in the multiple quantum wells satisfying the Bragg condition kd=π, where k is the light wavevector in the exciton resonance region and d is the period of the structure. No difference in the photoluminescence intensity and decay time has been found on the Bragg and "anti-Bragg" (kd=π/2) structures.     

Longitudinal Optical Fields in Light Scattering from Dielectric Spheres and Anderson Localization of Light

Recent research has shown that coupling between point scatterers in a disordered medium by longitudinal electromagnetic fields is harmful for Anderson localization of light. However, it has been unclear if this feature is generic or specific for point scatterers. The present work demonstrates that the intensity of longitudinal field outside a spherical dielectric scatterer illuminated by monochromatic light exhibits a complicated, nonmonotonous dependence on the scatterer size. Moreover, the intensity is reduced for a hollow sphere, whereas one can adjust the parameters of a coated sphere to obtain a relatively low longitudinal field together with a strong resonant scattering efficiency. Therefore, random arrangements of structured (hollow or coated) spheres may be promising three‐dimensional disordered materials for reaching Anderson localization of light.     

Disorder in quantum vacuum: Casimir-induced localization of matter waves

Disordered geometrical boundaries such as rough surfaces induce important modifications to the mode spectrum of the electromagnetic quantum vacuum. In analogy to Anderson localization of waves induced by a random potential, here we show that the Casimir-Polder interaction between a cold atomic sample and a rough surface also produces localization phenomena. These effects, that represent a macroscopic manifestation of disorder in quantum vacuum, should be observable with Bose-Einstein condensates expanding in proximity of rough surfaces.     

Magnetic field effects on the localization of electromagnetic waves in random 1D systems which are almost periodic

Abstract

The effects of an externally applied magnetic field on the Anderson localization of electromagnetic waves in an alternating layered system of vacuum and semiconducting slabs are studied. Specifically, a waveguide formed from perfectly conducting parallel plates which contain between them an array of vacuum and n-type semiconductor slabs is examined in the presence of an external static magnetic field applied parallel to both the plates and the slab surfaces. The widths of the slabs in the array are random but with a randomness such that the array of slabs is almost periodic, and we study only electromagnetic modes which propagate perpendicular to the slab surfaces. The localization length is obtained by studying the reflection and transmission properties of a finite array of slabs in the limit that it becomes semi-infinite. Two types of system are treated: (i) a reciprocal system which exhibits a localization length that does not depend on the sign of the applied magnetic field, and (ii) a non-reciprocal system which exhibits a localization length that depends on the sign of the applied magnetic field.