Observation of Anderson localization in disordered nanophotonic structures

Deep-subwavelength engineering of stealthy hyperuniformity

Light behaviours in disordered materials have been of research interest primarily at length scales beyond or comparable to the wavelength of light, because order and disorder are often believed to be almost indistinguishable in the subwavelength regime according to effective medium theory (EMT). However, it was demonstrated that the breakdown of EMT occurs even at deep-subwavelength scales when interface phenomena, such as the Goos-Hänchen effect, dominate light flows. Here we develop the engineering of disordered multilayers at deep-subwavelength scales to achieve angle-selective manipulation of wave localization. To examine the disorder-dependent EMT breakdown, we classify the intermediate regime of microstructural phases between deep-subwavelength crystals and uncorrelated disorder through the concept of stealthy hyperuniformity (SHU). We devise material phase transitions from SHU to uncorrelated disorder for distinct angular responses of wave localization by tailoring the short-range and long-range order in SHU multilayers. The result paves the way to the realization of deep-subwavelength disordered metamaterials, bridging the fields of disordered photonics and metamaterials.

Time Refraction and Time Reflection above Critical Angle for Total Internal Reflection

We study the time reflection and time refraction of waves caused by a spatial interface with a medium undergoing a sudden temporal change in permittivity. We show that monochromatic waves are transformed into a pulse by the permittivity change, and that time reflection is enhanced at the vicinity of the critical angle for total internal reflection. In this regime, we find that the evanescent field is transformed into a propagating pulse by the sudden change in permittivity. These effects display enhancement of the time reflection and high sensitivity near the critical angle, paving the way to experiments on time reflection and photonic time crystals at optical frequencies.

Anderson Localization in the Subwavelength Regime

In this paper, we use recent breakthroughs in the study of coupled subwavelength resonator systems to reveal new insight into the mechanisms responsible for the fundamental features of Anderson localization. The occurrence of strong localization in random media has proved difficult to understand, particularly in physically derived multi-dimensional models and systems with long-range interactions. We show here that the scattering of time-harmonic waves by high-contrast resonators with randomly chosen material parameters reproduces the characteristic features of Anderson localization. In particular, we show that the hybridization of subwavelength resonant modes is responsible for both the repulsion of energy levels as well as the widely observed phase transition, at which point eigenmode symmetries swap and very strong localization is possible. We derive results from first principles, using asymptotic expansions in terms of the material contrast parameter and obtain a characterization of the localized modes in terms of generalized capacitance matrices. This model captures the long-range interactions of the wave-scattering system and provides a concise framework to explain the exotic phenomena that are observed.

Anomalous transmission and Anderson localization for alternating propagated and evanescent waves at the deep-subwavelength scale

Deep-subwavelength features have a minimal impact on wave transport in all dielectric systems; thus the homogenization approach was commonly adopted. Recently, the breakdown of effective medium theory (EMT) for the incident wave near the total reflection (TR) angle was demonstrated in a deep-subwavelength dielectric multilayer. Additionally, anomalous transmission was reported at angles exceeding the TR angle when introducing disorder and was attributed to Anderson localization. Here we firstly demonstrated that the alleged anomalous transmission also occurs in the disorder-free case, illustrating that attributing anomalous transmission to Anderson localization deserves a more in-depth study. To clarify the underlying physics of this asserted anomalous transmission, Anderson localization and broken EMT, the incident angle dependent reflectivity and modes for ordered and disordered deep-subwavelength multilayers were investigated systematically. Actually, the EMT is still convincing and the anomalous transmission is reasonable after a simple correction. However, the anomalous transmission is more accessible and the permittivity correction is more imperative in the disordered system due to the Anderson localization. These findings can be expanded to other wave systems such as acoustic waves and matter waves, providing insight into EMT and deepening our understanding of the intriguing transport phenomena in deep subwavelength systems.

Mapping complex profiles of light intensity with interferometric lithography

Solving Maxwell's equations numerically to map electromagnetic fields in the vicinity of nanostructured metal surfaces can be a daunting task when studying non-periodic, extended patterns. However, for many nanophotonic applications such as sensing or photovoltaics it is often important to have an accurate description of the actual, experimental spatial field distributions near device surfaces. In this article, we show that the complex light intensity patterns formed by closely-spaced multiple apertures in a metal film can be faithfully mapped with sub-wavelength resolution, from near-field to far-field, in the form of a 3D solid replica of isointensity surfaces. The permittivity of the metal film plays a role in shaping of the isointensity surfaces, over the entire examined spatial range, which is captured by simulations and confirmed experimentally.

Control of localization and optical properties with deep-subwavelength engineered disorder

The effect of deep subwavelength disorder in one-dimensional dichromic multilayer films on the optical transmission, localization length, and Goos-Hänchen shift around the critical angle is analyzed using sets of disordered multilayer films with different degrees of order metric τ. For each Gaussian-perturbed multilayer film designed by a Metropolis algorithm targeting the predetermined order metric τ, the numerically obtained localization length and transmission show excellent agreement with the recent theoretical analysis developed for disordered multilayer films, further revealing τ-dependence of the Goos-Hänchen shift across the critical angle. Emphasizing the role of deep subwavelength structures in disorder-induced transmission enhancement, our result thus paves the way toward the inverse design of a deep subwavelength disordered structural landscape for the targeted order metric τ or abnormal optical responses - including the Goos-Hänchen shift.

Observation of Anderson localization beyond the spectrum of the disorder

Anderson localization predicts that transport in one-dimensional uncorrelated disordered systems comes to a complete halt, experiencing no transport whatsoever. However, in reality, a disordered physical system is always correlated because it must have a finite spectrum. Common wisdom in the field states that localization is dominant only for wave packets whose spectral extent resides within the region of the wave number span of the disorder. Here, we show experimentally that Anderson localization can occur and even be dominant for wave packets residing entirely outside the spectral extent of the disorder. We study the evolution of wave packets in synthetic photonic lattices containing bandwidth-limited (correlated) disorder and observe strong localization for wave packets centered at twice the mean wave number of the disorder spectral extent and at low wave numbers, both far beyond the spectrum of the disorder. Our results shed light on fundamental aspects of disordered systems and offer avenues for using spectrally shaped disorder for controlling transport.

Universal Behavior of the Scattering Matrix Near Thresholds in Photonics

Scattering thresholds and their associated spectral square root branch points are ubiquitous in photonics. In this Letter, we show that the scattering matrix has a simple universal behavior near scattering thresholds. We use unitarity, reciprocity, and time-reversal symmetry to construct a two-parameter model for a two-port scattering matrix near a threshold. We demonstrate this universal behavior in three different optical systems, namely, a photonic crystal slab, a planar dielectric interface, and a junction between metallic waveguides of different widths.

Generation of Non-Rayleigh Nondiffracting Speckles

Optical speckle fields with both non-Rayleigh statistics and nondiffracting characteristics in propagation are an important light source for many applications. However, tailoring either non-Rayleigh statistical speckles or nondiffracting speckles are only investigated independently in previous studies. Here, we report the first observation of optical speckles that remain diffraction-free over a long axial distance while keeping non-Rayleigh statistics simultaneously. We further show the enhancement of Anderson localization of light with the non-Rayleigh nondiffracting speckles. The work presented here provides a versatile framework for customizing optical fields with desired speckle patterns for applications in the fields of solid-state physics, cold atoms, and optical imaging.

Spatial coherence of light inside three-dimensional media

Speckle is maybe the most fundamental interference effect of light in disordered media, giving rise to fascinating physical phenomena and cutting edge applications. While speckle formed outside a sample is easily measured and analysed, true bulk speckle, as formed inside random media, is difficult to investigate directly due to the obvious issue of physical access. Furthermore, its proper theoretical description poses enormous challenges. Here we report on the first direct measurements of spatially resolved intensity correlations of light inside a disordered medium, using embedded DNA strings decorated with emitters separated by a controlled nanometric distance. Our method provides in situ access to fundamental properties of bulk speckles as their size and polarization degrees of freedom, both of which are found to deviate significantly from theoretical predictions. The deviations are explained, by comparison with rigorous numerical calculations, in terms of correlations among polarization components and non-universal near-field contributions at the nanoscale.

Light in disordered materials generates rich interference patterns called speckle, whose properties are known only on the outside of a sample. Here, the authors provide direct measurements and understanding of speckle generated inside a material, retrieving fundamental information that remained inaccessible up to now.

Controlling wave fronts with tunable disordered non-Hermitian multilayers

Unique and flexible properties of non-Hermitian photonic systems attract ever-increasing attention via delivering a whole bunch of novel optical effects and allowing for efficient tuning light-matter interactions on nano- and microscales. Together with an increasing demand for the fast and spatially compact methods of light governing, this peculiar approach paves a broad avenue to novel optical applications. Here, unifying the approaches of disordered metamaterials and non-Hermitian photonics, we propose a conceptually new and simple architecture driven by disordered loss-gain multilayers and, therefore, providing a powerful tool to control both the passage time and the wave-front shape of incident light with different switching times. For the first time we show the possibility to switch on and off kink formation by changing the level of disorder in the case of adiabatically raising wave fronts. At the same time, we deliver flexible tuning of the output intensity by using the nonlinear effect of loss and gain saturation. Since the disorder strength in our system can be conveniently controlled with the power of the external pump, our approach can be considered as a basis for different active photonic devices.

Details of the topological state transition induced by gradually increased disorder in photonic Chern insulators

Using two well-defined empirical parameters, we numerically investigate the details of the disorder-induced topological state transition (TST) in photonic Chern insulators composed of two-dimensional magnetic photonic crystals (MPCs). The TST undergoes a gradual process, accompanied with some interesting phenomena as the disorder of rod positions in MPCs increases gradually. This kind of TST is determined by the competition among the topologically protected edge state, disorder-induced wave localizations and bulk states in the system. More interestingly, the disorder-induced wave localizations almost have no influence on the one-way propagation of the original photonic topological states (PTSs), and the unidirectional nature of the PTSs at the edge area can survive even when the bulk states arise at stronger disorders. Our results provide detailed demonstrations for the deep understanding of fundamental physics underlying topology and disorder and are also of practical significance in device fabrication with PTSs.

Partially disordered nano-porous metallic oxide engineering: surface morphology controllability and multiple scattering properties

Random multiple light scattering in disordered photonics leads to interesting and unexpected physical phenomena. Here, we demonstrate two types of partially disordered nano-porous metallic oxide materials: disordered grating nano-pores and two-dimensional disordered nano-tubes, which are produced just with one-step anodic oxidation. The relations among the processing parameters, morphology properties and multiple scattering characteristics are investigated. The surface morphology controllability can be achieved by simply changing the processing direct voltages, leading to different scattering properties. The probabilistic model of partially disordered nano-porous metallic oxide is constructed according to the nano-structure characteristics of oxide, and the rigorous coupled wave analysis is utilized for optical field simulation to exhibit the theoretical multiple scattering properties. Futhermore, the experimental scattering fields are measured and are analysed by statistical method. The research focuses on the disorder caused by one-step oxidation, which is distinct from previous studies that introducing disorder into periodic materials, and would open up new prospects for sensing, bionics and structural color.

Machine learning identifies scale-free properties in disordered materials

The vast amount of design freedom in disordered systems expands the parameter space for signal processing. However, this large degree of freedom has hindered the deterministic design of disordered systems for target functionalities. Here, we employ a machine learning approach for predicting and designing wave-matter interactions in disordered structures, thereby identifying scale-free properties for waves. To abstract and map the features of wave behaviors and disordered structures, we develop disorder-to-localization and localization-to-disorder convolutional neural networks, each of which enables the instantaneous prediction of wave localization in disordered structures and the instantaneous generation of disordered structures from given localizations. We demonstrate that the structural properties of the network architectures lead to the identification of scale-free disordered structures having heavy-tailed distributions, thus achieving multiple orders of magnitude improvement in robustness to accidental defects. Our results verify the critical role of neural network structures in determining machine-learning-generated real-space structures and their defect immunity.

Photonic-Crystal Scintillators: Molding the Flow of Light to Enhance X-Ray and γ-Ray Detection

Scintillators are central for detection of γ-ray, x-ray, and high energy particles in various applications, all seeking higher scintillation yield and rate. However, these are limited by the intrinsic isotropy of spontaneous emission of the scintillation light and its inefficient outcoupling. We propose a new design methodology for scintillators that exploits the Purcell effect to enhance their light emission. As examples, we show 1D photonic crystals from scintillator materials that achieve directional emission and fivefold enhancement in the number of detectable photons per excitation.

Probing nanoscale fluctuation of ferromagnetic meta-atoms with a stochastic photonic spin Hall effect

The photonic spin Hall effect, a deep subdiffraction-limited shift between the opposite spin components of light, emerges when light undergoes an evolution of polarization or trajectory that induces the geometric phase. Here, we study a stochastic photonic spin Hall effect arising from space-variant Berry-Zak phases, which are generated by disordered magneto-optical effects. This spin shift is observed from a spatially bounded lattice of ferromagnetic meta-atoms displaying nanoscale disorders. A random variation of the radii of the meta-atoms induces the nanoscale fluctuation. The standard deviation of the probability distribution of the spin shifts is proportional to the fluctuation of the meta-atoms. This enables us to detect a five-nanometre fluctuation by measuring the probability distribution of the spin shifts via weak measurements. Our approach may be used for sensing deep-subwavelength disorders by actively breaking the photonic spin symmetry and may enable investigations of fluctuation effects in magnetic nanosystems.

Effect of trapping geometry on the parametric resonances in a disordered Bose-Einstein condensate driven by an oscillating potential

We report parametric resonances (PRs) in a numerical investigation of a driven one-dimensional, interacting, and disordered Bose-Einstein condensate (BEC) confined in different traps. The BEC is excited by an oscillating Gaussian obstacle along a broad range of driving frequencies Ω. The PRs are detected via a quantity that is closely related to the time-average of the kinetic energy. The significant result of this work is that the trapping geometry plays a major role in defining the values of Ω at which PRs arise and controls their response to disorder. As such, it reveals the interplay of trapping geometry and disorder in these resonances. The dynamics of the modal coefficientC0(t) as well as that of the phase-mismatchδ(t) between theC0(t) andC1(t) are examined at and away from PR. At PR, |C0(t)| is generally found to be lower in magnitude than away from it, demonstrating that the atoms leave then= 0 ground state towards higher states. In the harmonic oscillator trap, the dynamic pattern ofδ(t) is found to be quite robust against changes in the disorder strength contrary to the box potential. This is because in the box the ratio of the random-potential and kinetic energies is higher than in the harmonic trap signaling that the influence of disorder is weaker in the latter.

Effects of deterministic disorder at deeply subwavelength scales in multilayered dielectric metamaterials

It is common understanding that multilayered dielectric metamaterials, in the regime of deeply subwavelength layers, are accurately described by simple effective-medium models based on mixing formulas that do not depend on the spatial arrangement. In the wake of recent studies that have shown counterintuitive examples of periodic and aperiodic (orderly or random) scenarios in which this premise breaks down, we study here the effects of deterministic disorder. With specific reference to a model based on Golay-Rudin-Shapiro sequences, we illustrate certain peculiar boundary effects that can occur in finite-size dielectric multilayers, leading to anomalous light-transport properties that are in stark contrast with the predictions from conventional effective-medium theory. Via parametric and comparative studies, we elucidate the underlying physical mechanisms, also highlighting similarities and differences with respect to previously studied geometries. Our outcomes may inspire potential applications to optical sensing, switching and lasing.

Manipulation of transmission by engineered disorder in one-dimensional photonic crystals

Uncovering how disorder affects light propagation is a key step to manipulating light transportation and localization utilizing engineered disorder in photonics. Herein, we study the disorder-induced localization, delocalization and inter-transition between them in the regions of photonic band gaps (PBGs) and their associated passbands of one-dimensional (1D) Photonic crystals (PhCs) under different types of disorder effect. We introduce two parameters to quantitatively evaluate how disorder effect can be exploited to tailor the localization and delocalization of light in 1D PhCs. Such parameters can clearly indicate the inter-transition between extended states and localized states. It is shown that both nontrivial and trivial disorder-induced transport scenarios exist depending on the types of disorder introduced to the otherwise periodic system. The disorder-induced band tailing, which is correlated with the disorder-induced redistribution of electric energy compared with periodic case, is crucial for observing these interesting disorder-induced light transportation scenarios. Our results might provide positive insight to the manipulation of light transmission in nanophotonics by engineered disorder.

Self-Induced Diffusion in Disordered Nonlinear Photonic Media

We find that waves propagating in a 1D medium that is homogeneous in its linear properties but spatially disordered in its nonlinear coefficients undergo diffusive transport, instead of being Anderson localized as always occurs for linear disordered media. Specifically, electromagnetic waves in a multilayer structure with random nonlinear coefficients exhibit diffusion with features fundamentally different from the traditional diffusion in linear noninteracting systems. This unique transport, which stems from the nonlinear interaction between the waves and the disordered medium, displays anomalous statistical behavior where the fields in multiple different realizations converge to the same intensity value as they penetrate deeper into the medium.

Different regimes of the Purcell effect in disordered photonic crystals

We demonstrate that disorder in photonic crystals could lead to pronounced modification of spontaneous emission rate in the frequency region corresponding to the photonic band gap (PBG). Depending on the amount of disorder, two different regimes of the Purcell effect occurs. We provide statistical analysis of Purcell coefficient on the frequency of the emitter and its position within the sample. For the moderate disorder, an enhancement of spontaneous emission occurs at the edge of PBG due to the modification of properties of the edge state. This effect is responsible for recently observed mirrorless lasing in photonic crystals at the edge of PBG. When the level of disorder increases, the spontaneous emission rate enhances within the PBG due to the appearance of the high quality factor states. This effect is likely responsible for a superlinear dependence of emissions on pumping observed in synthetic opals.

Wavefront shaping with disorder-engineered metasurfaces

Recently, wavefront shaping with disordered media has demonstrated optical manipulation capabilities beyond those of conventional optics, including extended volume, aberration-free focusing and subwavelength focusing. However, translating these capabilities to useful applications has remained challenging as the input-output characteristics of the disordered media (P variables) need to be exhaustively determined via O(P) measurements. Here, we propose a paradigm shift where the disorder is specifically designed so its exact input-output characteristics are known a priori and can be used with only a few alignment steps. We implement this concept with a disorder-engineered metasurface, which exhibits additional unique features for wavefront shaping such as a large optical memory effect range in combination with a wide angular scattering range, excellent stability, and a tailorable angular scattering profile. Using this designed metasurface with wavefront shaping, we demonstrate high numerical aperture (NA > 0.5) focusing and fluorescence imaging with an estimated ~2.2×108 addressable points in an ~8 mm field of view.

Disorder-induced optical transition from spin Hall to random Rashba effect

Disordered structures give rise to intriguing phenomena owing to the complex nature of their interaction with light. We report on photonic spin-symmetry breaking and unexpected spin-optical transport phenomena arising from subwavelength-scale disordered geometric phase structure. Weak disorder induces a photonic spin Hall effect, observed via quantum weak measurements, whereas strong disorder leads to spin-split modes in momentum space, a random optical Rashba effect. Study of the momentum space entropy reveals an optical transition upon reaching a critical point where the structure's anisotropy axis vanishes. Incorporation of singular topology into the disordered structure demonstrates repulsive vortex interaction depending on the disorder strength. The photonic disordered geometric phase can serve as a platform for the study of different phenomena emerging from complex media involving spin-orbit coupling.

Disorder-Induced Topological State Transition in Photonic Metamaterials

The topological state transition has been widely studied based on the quantized topological band invariant such as the Chern number for the system without intense randomness that may break the band structures. We numerically demonstrate the disorder-induced state transition in the photonic topological systems for the first time. Instead of applying the ill-defined topological band invariant in a disordered system, we utilize an empirical parameter to unambiguously illustrate the state transition of the topological metamaterials. Before the state transition, we observe a robust surface state with well-confined electromagnetic waves propagating unidirectionally, immune to the disorder from permittivity fluctuation up to 60% of the original value. During the transition, a hybrid state composed of a quasiunidirectional surface mode and intensively localized hot spots is established, a result of the competition between the topological protection and Anderson localization.