Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections

Compact photonic crystal spectrometer with resolution beyond the fabrication precision

We present a compact silicon photonic crystal spectrometer with a footprint of 740 × 9 µm2 and excellent wavelength resolution (∼0.01 nm at single and <0.03 nm at multiple wavelength operation) across a telecom bandwidth of 10 nm. Although our design targets a wavelength resolution of 1.6 nm, within the current state-of-the-art fabrication precision of 2 nm, we achieve a resolution that exceeds these limits. This enhanced resolution is made possible by leveraging the random localization of light within the device.

Asymmetric comb waveguide for strong interactions between atoms and light

Coupling quantum emitters and nanostructures, in particular cold atoms and optical waveguides, has recently raised a large interest due to unprecedented possibilities of engineering light-matter interactions. In this work, we propose a new type of periodic dielectric waveguide that provides strong interactions between atoms and guided photons with an unusual dispersion. We design an asymmetric comb waveguide that supports a slow mode with a quartic (instead of quadratic) dispersion and an electric field that extends far into the air cladding for an optimal interaction with atoms. We compute the optical trapping potential formed with two guided modes at frequencies detuned from the atomic transition. We show that cold Rubidium atoms can be trapped as close as 100 nm from the structure in a 1.3-mK-deep potential well. For atoms trapped at this position, the emission into guided photons is largely favored, with a beta factor as high as 0.88 and a radiative decay rate into the slow mode 10 times larger than the free-space decay rate. These figures of merit are obtained at a moderately low group velocity of c/50.

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.

Quantifying the Robustness of Topological Slow Light

The backscattering mean free path ξ, the average ballistic propagation length along a waveguide, quantifies the resistance of slow light against unwanted imperfections in the critical dimensions of the nanostructure. This figure of merit determines the crossover between acceptable slow-light transmission affected by minimal scattering losses and a strong backscattering-induced destructive interference when the waveguide length L exceeds ξ. Here, we calculate the backscattering mean free path for a topological photonic waveguide for a specific and determined amount of disorder and, equally relevant, for a fixed value of the group index n_{g} which is the slowdown factor of the group velocity with respect to the speed of light in vacuum. These two figures of merit, ξ and n_{g}, should be taken into account when quantifying the robustness of topological and conventional (nontopological) slow-light transport at the nanoscale. Otherwise, any claim on a better performance of topological guided light over a conventional one is not justified.

Dimensional ensemble and (topological) fracton thermodynamics: the slow route to equilibrium

The use of the dimensional-ensemble becomes compulsory when spatial dimensions are not well defined. Consequently, apart from temperature, thermodynamic equilibrium requires an additional configurational parameter. Two representative cases are considered in detail: oscillators with undefined spatial dimension and topological fractons. Spatial dimension and energy are determined as a function of temperature in both cases. At low temperatures, specific heat behaves exponentially, meaning it creates a slow route to equilibrium. In accordance with experiments, calculations suggest that the spatial dimension diminishes when temperature decreases. Parameter values are computed using data obtained from almost two-dimensional graphene and porous compounds.

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.

Adaptive Control of Necklace States in a Photonic Crystal Waveguide

Resonant cavities with high quality factor and small mode volume provide crucial enhancement of light-matter interactions in nanophotonic devices that transport and process classical and quantum information. The production of functional circuits containing many such cavities remains a major challenge, as inevitable imperfections in the fabrication detune the cavities, which strongly affects functionality such as transmission. In photonic crystal waveguides, intrinsic disorder gives rise to high-Q localized resonances through Anderson localization; however their location and resonance frequencies are completely random, which hampers functionality. We present an adaptive holographic method to gain reversible control on these randomly localized modes by locally modifying the refractive index. We show that our method can dynamically form or break highly transmitting necklace states, which is an essential step toward photonic-crystal-based quantum networks and signal processing circuits, as well as slow light applications and fundamental physics.

Level spacing statistics for light in two-dimensional disordered photonic crystals

We study the distribution of eigenfrequency spacings (the so-called level spacing statistics) for light in a two-dimensional (2D) disordered photonic crystal composed of circular dielectric (silicon) rods in air. Disorder introduces localized transverse-magnetic (TM) modes into the band gap of the ideal crystal. The level spacing statistics is found to approach the Poisson distribution for these modes. In contrast, for TM modes outside the band gap and for transverse-electric (TE) modes at all frequencies, the level spacing statistics follows the Wigner-Dyson distribution.

Symmetry Breaking in Photonic Crystals: On-Demand Dispersion from Flatband to Dirac Cones

We demonstrate that symmetry breaking opens a new degree of freedom to tailor energy-momentum dispersion in photonic crystals. Using a general theoretical framework in two illustrative practical structures, we show that breaking symmetry enables an on-demand tuning of the local density of states of the same photonic band from zero (Dirac cone dispersion) to infinity (flatband dispersion), as well as any constant density over an adjustable spectral range. As a proof of concept, we demonstrate experimentally the transformation of the very same photonic band from a conventional quadratic shape to a Dirac dispersion, a flatband dispersion, and a multivalley one. This transition is achieved by finely tuning the vertical symmetry breaking of the photonic structures. Our results provide an unprecedented degree of freedom for optical dispersion engineering in planar integrated photonic devices.

Observation of Anderson localization in disordered nanophotonic structures

Anderson localization is an interference effect crucial to the understanding of waves in disordered media. However, localization is expected to become negligible when the features of the disordered structure are much smaller than the wavelength. Here we experimentally demonstrate the localization of light in a disordered dielectric multilayer with an average layer thickness of 15 nanometers, deep into the subwavelength regime. We observe strong disorder-induced reflections that show that the interplay of localization and evanescence can lead to a substantial decrease in transmission, or the opposite feature of enhanced transmission. This deep-subwavelength Anderson localization exhibits extreme sensitivity: Varying the thickness of a single layer by 2 nanometers changes the reflection appreciably. This sensitivity, approaching the atomic scale, holds the promise of extreme subwavelength sensing.

Anderson localization in synthetic photonic lattices

Synthetic photonic lattices provide unique capabilities to realize theoretical concepts emerging in different fields of wave physics via the utilization of powerful photonic technologies. Here we observe experimentally Anderson localization for optical pulses in time domain, using a photonic mesh lattice composed of coupled fiber loops. We introduce a random potential through programmed electro-optic pulse phase modulation, and identify the localization features associated with varying degree of disorder. Furthermore, we present a practical approach to control the band-gap width in photonic lattices by varying the coupling between the fiber loops, and reveal that the strongest degree of localization is limited and increases in lattices with wider band-gaps. Importantly, this opens a possibility to enhance or reduce the effect of disorder and associated localization of optical pulses.

Soliton Pulse Propagation in the Presence of Disorder-Induced Multiple Scattering in Photonic Crystal Waveguides

We introduce a new coupled mode theory to model nonlinear Schrödinger equations for counterpropagating Bloch modes that include disorder-induced multiple scattering effects on nonlinear soliton propagation in photonic crystal waveguides. We also derive subunit-cell coupling coefficients and use these to introduce a generalized length scale associated with each coupling effect. In particular, we define a multiple-scattering length scale that quantifies the spatial extent of a disorder-induced cavity mode. Our numerical simulations of nonlinear pulse propagation are in excellent qualitative agreement with recent experiments and provide insight into how structural disorder inhibits soliton propagation and other nonlinear propagation effects in photonic crystal waveguides.

Direct imaging of isofrequency contours in photonic structures

The isofrequency contours of a photonic crystal are important for predicting and understanding exotic optical phenomena that are not apparent from high-symmetry band structure visualizations. We demonstrate a method to directly visualize the isofrequency contours of high-quality photonic crystal slabs that show quantitatively good agreement with numerical results throughout the visible spectrum. Our technique relies on resonance-enhanced photon scattering from generic fabrication disorder and surface roughness, so it can be applied to general photonic and plasmonic crystals or even quasi-crystals. We also present an analytical model of the scattering process, which explains the observation of isofrequency contours in our technique. Furthermore, the isofrequency contours provide information about the characteristics of the disorder and therefore serve as a feedback tool to improve fabrication processes.

Measurement of the profiles of disorder-induced localized resonances in photonic crystal waveguides by local tuning

Near the band edge of photonic crystal waveguides, localized modes appear due to disorder. We demonstrate a new method to elucidate spatial profile of the localized modes in such systems using precise local tuning. Using deconvolution with the known thermal profile, the spatial profile of a localized mode with quality factor (Q) > 10⁵ is successfully reconstructed with a resolution of 2.5 μm.