Anderson-localized Modes Research Articles

Tunable Anderson localization in disorder graphene sheet arrays.

We study the electromagnetic wave propagating in coupled monolayer graphene waveguide arrays (CMGWAs). It is found that Anderson localization exists when the disorder in the coupling strength between adjacent waveguides is introduced. We find that changing the statistical parameters of the disorder coupling strength between waveguides can be used to tailor the properties of the Anderson localization modes in the strong coupling region which is beyond the coupled-mode theory. Benefiting from the electric tunable surface conductivity, we further demonstrate via the full vectorial simulation that the localization strength of the Anderson localized mode can be manipulated by changing the applied gate voltage on the CMGWAs. Our results might facilitate the manipulation of electromagnetic wave propagation in the coupled waveguide array system.

Spatial and temporal localization of light in two dimensions

Quasi-resonant scattering of light in two dimensions can be described either as a scalar or as a vectorial electromagnetic wave. Performing a scaling analysis we observe in both cases long lived modes, yet only the scalar case exhibits Anderson localized modes together with extremely long mode lifetimes. We show that the localization length of these modes is influenced only by their position, and not their lifetime. Investigating the reasons for the absence of localization, it appears that both the coupling of several polarizations and the presence of near-field terms are able to prevent long lifetimes and Anderson localization.

Perfect absorption in nanotextured thin films via Anderson-localized photon modes

Researchers use Anderson localization in nanotextured amorphous silicon and demonstrate enhanced absorption of light. The enhancement of light absorption in absorber layers is crucial in a number of applications, including photovoltaics1 and thermoelectrics. The efficient use of natural resources and physical constraints such as limited charge extraction in photovoltaic devices require thin but efficient absorbers. Among the many different strategies used2,3,4,5,6,7, light diffraction8 and light localization9,10 at randomly nanotextured interfaces have been proposed to improve absorption. Although already exploited in commercial devices, the enhancement mechanism for devices with nanotextured interfaces is still subject to debate. Using coherent two-dimensional nanoscopy and coherent light scattering, we demonstrate the existence of localized photonic states in nanotextured amorphous silicon layers as used in commercial thin-film solar cells. Resonant absorption in these states accounts for the enhanced absorption in the long-wavelength cutoff region. Our observations establish that Anderson localization—that is, strong localization—is a highly efficient resonant absorption enhancement mechanism offering interesting opportunities for the design of efficient future absorber layers.

Linear and nonlinear Rabi oscillations of a two-level system resonantly coupled to an Anderson-localized mode

We use time-domain numerical simulations of a two-dimensional (2D) scattering system to study the interaction of a collection of emitters resonantly coupled to an Anderson-localized mode. For a small electric field intensity, we observe the strong coupling between the emitters and the mode, which is characterized by linear Rabi oscillations. Remarkably, a larger intensity induces non-linear interaction between the emitters and the mode, referred to as the dynamical Stark effect, resulting in non-linear Rabi oscillations. The transition between both regimes is observed and an analytical model is proposed which accurately describes our numerical observations.

Statistical measurements of quantum emitters coupled to Anderson-localized modes in disordered photonic-crystal waveguides.

We present a statistical study of the Purcell enhancement of the light emission from quantum dots coupled to Anderson-localized cavities formed in disordered photonic-crystal waveguides. We measure the time-resolved light emission from both single quantum emitters coupled to Anderson-localized cavities and directly from the cavities that are fed by multiple quantum dots. Strongly inhibited and enhanced decay rates are observed relative to the rate of spontaneous emission in a homogeneous medium. From a statistical analysis, we report an average Purcell factor of 4.5 ± 0.4 without applying any spectral tuning. By spectrally tuning individual quantum dots into resonance with Anderson-localized modes, a maximum Purcell factor of 23.8 ± 1.5 is recorded, which is at the onset of the strong-coupling regime. Our data quantify the potential of Anderson-localized cavities for controlling and enhancing the light-matter interaction strength in a photonic-crystal waveguide, which is of relevance for cavity quantum-electrodynamics experiments, efficient energy harvesting and random lasing.

The single-channel regime of transport through random media.

The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media. Here we demonstrate that in deeply localized quasi-1D systems, the single dominant transmission eigenchannel is formed by an individual Anderson-localized mode or by a ‘necklace state’. In this single-channel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings. Using statistical criteria of the single-channel regime and pulsed excitations of the disordered samples allows us to identify long-lived localized modes and short-lived necklace states at long and short time delays, respectively.

Flat band states: Disorder and nonlinearity

We study the critical behaviour of Anderson localized modes near intersecting flat and dispersive bands in the quasi-one-dimensional diamond ladder with weak diagonal disorder $W$. The localization length $\xi$ of the flat band states scales with disorder as $\xi \sim W^{-\gamma}$, with $\gamma \approx 1.3$, in contrast to the dispersive bands with $\gamma =2$. A small fraction of dispersive modes mixed with the flat band states is responsible for the unusual scaling. Anderson localization is therefore controlled by two different length scales. Nonlinearity can produce qualitatively different wave spreading regimes, from enhanced expansion to resonant tunneling and self-trapping.

Strong Coupling to Two-Dimensional Anderson Localized Modes

We use a scattering formalism to derive a condition of strong coupling between a resonant scatterer and an Anderson localized mode for electromagnetic waves in two dimensions. The strong coupling regime is demonstrated based on exact numerical simulations, in perfect agreement with theory. The strong coupling threshold can be expressed in terms of the Thouless conductance and the Purcell factor. This connects key concepts in transport theory and cavity quantum electrodynamics, and provides a practical tool for the design or analysis of experiments.

Quantifying the intrinsic amount of fabrication disorder in photonic-crystal waveguides from optical far-field intensity measurements

Residual disorder due to fabrication imperfections has important impact in nanophotonics where it may degrade device performance by increasing radiation loss or spontaneously trap light by Anderson localization. We propose and demonstrate experimentally a method of quantifying the intrinsic amount of disorder in state-of-the-art photonic-crystal waveguides from far-field measurements of the Anderson-localized modes. This is achieved by comparing the spectral range where Anderson localization is observed to numerical simulations, and the method offers sensitivity down to ≃1 nm.

Disorder-limited photon propagation and Anderson-localization in photonic crystal waveguides

We investigate the disorder-limited propagation of photons in photonic crystal waveguides in the slow-light regime. We use analysis of Fabry-Perot resonances to map the mode dispersion and extract the photon localization length. Propagation lengths are deduced to be limited to less than 20 μm for group index >50. Anderson-localized modes are observed at high group indices, when the localization lengths are shorter than the waveguide lengths, consistent with the Fabry-Perot analysis. The results have consequences for integrated quantum-dot single-photon circuits which rely on slow-light effects to enhance emission rates.

Statistical Theory of a Quantum Emitter Strongly Coupled to Anderson-Localized Modes

A statistical theory of the coupling between a quantum emitter and Anderson-localized cavity modes is presented based on a dyadic Green's function formalism. The probability of achieving the strong light-matter coupling regime is extracted for an experimentally realistic system composed of InAs quantum dots embedded in a disordered photonic crystal waveguide. We demonstrate that by engineering the relevant parameters that define the quality of light confinement, i.e., the light localization length and the loss length, strong coupling between a single quantum dot and an Anderson-localized cavity is within experimental reach. As a consequence, confining light by disorder provides a novel platform for quantum electrodynamics experiments.

Probing the statistical properties of Anderson localization with quantum emitters

Wave propagation in disordered media can be strongly modified by multiple scattering and wave interference. Ultimately, the so-called Anderson-localized regime is reached when the waves become strongly confined in space. So far, Anderson localization of light has been probed in transmission experiments by measuring the intensity of an external light source after propagation through a disordered medium. However, discriminating between Anderson localization and losses in these experiments remains a major challenge. In this paper, we present an alternative approach where we use quantum emitters embedded in disordered photonic crystal waveguides as light sources. Anderson-localized modes are efficiently excited and the analysis of the photoluminescence spectra allows us to explore their statistical properties, for example the localization length and average loss length. With increasing the amount of disorder induced in the photonic crystal, we observe a pronounced increase in the localization length that is attributed to changes in the local density of states, a behavior that is in stark contrast to entirely random systems. The analysis may pave the way for accurate models and the control of Anderson localization in disordered photonic crystals.

Anderson localization of near-visible light in two dimensions

We report on the observation of Anderson localization of near-visible light in two-dimensional systems. Our structures consist of planar waveguides in which disorder is introduced by randomly placing pores with controlled diameter and density. We show how to design structures in which localization can be observed and describe both the realization of the materials and the actual observation of Anderson localized modes by near-field scanning microscopy.

Cavity Quantum Electrodynamics with Anderson-Localized Modes

A major challenge in quantum optics and quantum information technology is to enhance the interaction between single photons and single quantum emitters. This requires highly engineered optical cavities that are inherently sensitive to fabrication imperfections. We have demonstrated a fundamentally different approach in which disorder is used as a resource rather than a nuisance. We generated strongly confined Anderson-localized cavity modes by deliberately adding disorder to photonic crystal waveguides. The emission rate of a semiconductor quantum dot embedded in the waveguide was enhanced by a factor of 15 on resonance with the Anderson-localized mode, and 94% of the emitted single photons coupled to the mode. Disordered photonic media thus provide an efficient platform for quantum electrodynamics, offering an approach to inherently disorder-robust quantum information devices.

Harmonic vibrational excitations in graded elastic networks: Transition from phonons to gradons

We have identified a different type of transition from extended to localized vibrational states in one-dimensional graded elastic chains of coupled harmonic oscillators, in which the vibrating masses or nearest-coupling force constants vary linearly along the chain. We found that the delocalization transition occurs at the maximum frequency of the corresponding homogeneous chain, which is in a continuous single band. Although each state in the localized phase, called gradon, can be regarded as an impurity localized mode, the localization profile is clearly distinct from usual impurity modes or the Anderson localized modes. We also argue how gradons may affect the macroscopic properties of graded systems. Our results can provide insights into many analogous systems with graded characters.

Vibrational spectroscopy of an amorphous∕crystalline sandwich structure for silicon: Numerical results

We study the lattice dynamics of an amorphous∕crystalline∕silicon sandwich model using the environment-dependent interatomic potential (EDIP). We establish a base line by computing the vibrational properties of the component bulk crystal and bulk amorphous structures, which show reasonable agreement with experiment and with Stillinger-Weber (SW) potential results. We study the confinement of the modes in the different structural regions (crystal, amorphous, and interface). Low-frequency modes have disproportionate weight in the amorphous structure because of its lower shear elastic constants, and there are some narrow frequency bands with confinement of modes to the crystal. We examine the localization properties of modes at different frequencies by computing the inverse participation ratio. We find Anderson-localized modes in the amorphous structure with a mobility edge at a frequency below the maximum crystal vibration frequency. This frequency relation leads to modes that are extended in the crystal but localized or evanescent in the amorphous. We also find evidence for disorder-inducded quasilocalized modes in the crystal near the amorphous∕crystal interface. Resonance modes, which appear in the bulk amorphous structure, are not present in the EDIP results for the sandwich structure, although they do exist in the SW results. We discuss the lowest- (nonzero-) frequency modes, which arise from transverse-acoustic vibrations propagating perpendicular to the amorphous∕crystal interface.

Anderson-localized ballooning modes in general toroidal plasmas

Ballooning instabilities are investigated in three-dimensional magnetic toroidal plasma confinement systems with low global magnetic shear. The lack of any continuous symmetry in the plasma equilibrium can lead to these modes being localized along the field lines by a process similar to Anderson localization. This produces a multibranched local eigenvalue dependence, where each branch corresponds to a different unit cell of the extended covering space in which the eigenfunction peak resides. These phenomena are illustrated numerically for the three-field-period heliac H-1 [S. M. Hamberger et al., Fusion Technol. 17, 123 (1990)], and contrasted with an axisymmetric s-α tokamak model. The localization allows a perturbative expansion about zero shear, enabling the effects of shear to be investigated.

Phononic band structure in a mass chain

The vibrational properties of a finite one-dimensional string-mass chain are studied experimentally and theoretically. In the experiment both normal mode analysis and pulse analysis are used to obtain the eigenfrequencies of the string-mass chain. The theoretical predictions are made based upon the numerical solution to the wave equation. The phononic band structure for a periodically massed string as well as Anderson localized gap modes for a disordered system are found. The theoretical and experimental results match satisfactorily well.