arXiv subjects

Mikael C. Rechtsman

Publications and source records attributed to Mikael C. Rechtsman.

At least 37 records · Page 2Linked to original sources

arXiv2022

Reentrant delocalization transition in one-dimensional photonic quasicrystals

Waves propagating in certain one-dimensional quasiperiodic lattices are known to exhibit a sharp localization transition. We theoretically predict and experimentally observe that the localization of light in one-dimensional photonic quasicrystals may be followed by a second delocalization transition for some states on increasing quasiperiodic modulation strength - an example of a reentrant transition. We further propose that this phenomenon can be qualitatively captured by a dimerized tight-binding model with long-range couplings.

physics.optics↗

arXiv2022

Period-doubled Floquet Solitons

We propose and experimentally demonstrate a family of Floquet solitons in the bulk of a photonic topological insulator that have double the period of the drive. Our experimental system consists of a periodically-modulated honeycomb lattice of optical waveguides fabricated by femtosecond laser writing. We employ a Kerr nonlinearity in which self-focusing gives rise to spatial lattice solitons. Our photonic system constitutes a powerful platform where the interplay of time-periodic driving, topology and nonlinearity can be probed in a highly tunable way.

physics.optics↗

arXiv2022

Higher-order topological pumping and its observation in photonic lattices

The discovery of the quantization of particle transport in adiabatic pumping cycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linked the Chern number, a topological invariant characterizing the quantum Hall effect in two-dimensional electron gases, with the topology of dynamical periodic systems in one dimension. Here, we demonstrate its counterpart for higher-order topology. Specifically, we show that adiabatic cycles in two-dimensional crystals with vanishing dipole moments (and therefore zero overall particle transport) can nevertheless be topologically nontrivial. These cycles are associated with higher-order topology and can be diagnosed by their ability to produce corner-to-corner transport in certain metamaterial platforms. We experimentally verify the corner to corner transport associated with this topological pump by using an array of photonic waveguides adiabatically modulated in their separations and refractive indices. By mapping the dynamical phenomenon demonstrated here from two spatial and one temporal dimensions to three spatial dimensions, our observations are equivalent to the observation of chiral hinge states in a three-dimensional second-order topological insulator.

cond-mat.mes-hall↗

arXiv2022

Quantized Fractional Thouless Pumping of Solitons

In many contexts, the interaction between particles gives rise to emergent and perhaps unanticipated physical phenomena. An example is the fractional quantum Hall effect, where interaction between electrons gives rise to fractionally quantized Hall conductance. In photonic systems, the nonlinear response of an ambient medium acts to mediate interaction between photons; in the mean-field limit these dynamics are described by the nonlinear Schrödinger (also called Gross-Pitaevskii) equation. Recently, it was shown that at weak nonlinearity, soliton motion in nonlinear Thouless pumps (a dimensionally reduced implementation of a Chern insulator) could be quantized to the Chern number of the band from which the soliton bifurcates. Here, we show theoretically and experimentally using arrays of coupled optical waveguides that sufficiently strong nonlinearity acts to fractionally quantize the motion of solitons. Specifically, we find that the soliton returns to itself after multiple cycles of the Thouless pump - but displaced by an integer number of unit cells - leading to a rich fractional plateaux structure describing soliton motion. Our results demonstrate a perhaps surprising example of the behavior of non-trivial topological systems in the presence of interactions.

physics.optics↗

arXiv2022

Observation of bound states in the continuum embedded in symmetry bandgaps

In the last decade, symmetry-protected bound states in the continuum (BICs) have proven to be an important design principle for creating and enhancing devices reliant upon states with high quality (Q) factors, such as sensors, lasers, and those for harmonic generation. However, as we show, current implementations of symmetry-protected BICs in photonic crystal slabs can only be found at the center of the Brillouin zone and below the Bragg-diffraction limit, which fundamentally restricts their use to single-frequency applications. By 3D-micro printing a photonic crystal structure using two-photon polymerization, we demonstrate that this limitation can be overcome by altering the radiative environment surrounding the slab to be a three-dimensional photonic crystal. This allows for the protection of a line of BICs by embedding it in a symmetry bandgap of the crystal. Moreover, we experimentally verify that just a single layer of this photonic crystal environment is sufficient. This concept significantly expands the design freedom available for developing next-generation devices with high-Q states.

physics.optics↗

arXiv2021

The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps

Nonlinear Thouless pumps for bosons exhibit quantized pumping via soliton motion, despite the lack of a meaningful notion of filled bands. However, the theoretical underpinning of this quantization, as well as its relationship to the Chern number, has thus far been lacking. Here we show that for low power solitons, transport is dictated by the Chern number of the band from which the soliton bifurcates. We do this by expanding the discrete nonlinear Schrödinger equation (equivalently, the Gross-Pitaevskii equation) in the basis of Wannier states, showing that the soliton's position is dictated by that of the Wannier state throughout the pump cycle. Furthermore, we describe soliton pumping in two dimensions.

cond-mat.mes-hall↗

arXiv2021

Observation of Quadratic (Charge-2) Weyl Point Splitting in Near-Infrared Photonic Crystals

Weyl points are point degeneracies that occur in momentum space of periodic materials, and are associated with a quantized topological charge. We experimentally observe in a 3D micro-printed photonic crystal that a charge-2 Weyl point can be split into two charge-1 Weyl points as the protecting symmetry of the original charge-2 Weyl point is broken. Moreover, we use a theoretical analysis to confirm where the charge-1 Weyl points move within the Brillouin zone as the strength of the symmetry breaking increases, and confirm it in experiments using Fourier-transform infrared spectrometry. This micro-scale observation and control of Weyl points is important for realizing robust topological devices in the near-infrared.

physics.optics↗

arXiv2021

Quantized Nonlinear Thouless Pumping

The sharply quantized transport observed in the integer quantum Hall effect can be explained via a simple one-dimensional model with a time-periodic, adiabatically varying potential in which electronic charge is pumped from one side of the system to the other. This so-called `Thouless pump' captures the topological physics of the quantum Hall effect using the notion of dimensional reduction: The time-varying potential mathematically maps onto a momentum coordinate in a conceptual second dimension. Importantly, this assumes an electronic system in equilibrium and in its ground state, that is, with uniformly filled bands below a Fermi energy. Here, we theoretically propose and experimentally demonstrate quantized nonlinear Thouless pumping of photons with a band that is decidedly not uniformly occupied. In our system, nonlinearity acts to quantize transport via soliton formation and spontaneous symmetry breaking bifurcations. Quantization follows from the fact that the instantaneous soliton solutions centered upon a given unit cell are identical after each pump cycle, up to translation invariance; this is an entirely different mechanism from traditional Thouless pumping of fermions in equilibrium. Our result shows that nonlinearity and interparticle interactions can induce quantized transport and topological behavior even where the linear limit does not.

physics.optics↗

arXiv2021

Point-Defect-Localized Bound States in the Continuum in Photonic Crystals and Structured Fibers

We show that point defects in two-dimensional photonic crystals can support bound states in the continuum (BICs). The mechanism of confinement is a symmetry mismatch between the defect mode and the Bloch modes of the photonic crystal. These BICs occur in the absence of bandgaps and therefore provide an alternative mechanism to confine light. Furthermore, we show that such BICs can propagate in a fiber geometry and exhibit arbitrarily small group velocity which could serve as a platform for enhancing non-linear effects and light-matter interactions in structured fibers.

physics.optics↗

arXiv2021

Photonic Topological Anderson Insulators

The hallmark property of two-dimensional topological materials is the incredible robustness of the quantized Hall conductivity to disorder. That robustness arises from the fact that in the topological band gap, transport can occur only along the edges modes, which are immune to scattering. However, for sufficiently strong disorder, the band gap closes and the system becomes topologically trivial as all states become localized, such that all transport vanishes -- in accordance with Anderson localization. It therefore came as a surprise when it was suggested that, for a two-dimensional quantum spin-Hall topological system, the opposite could occur. In so-called topological Anderson insulators, the emergence of protected edge states and quantized transport is caused by the introduction of disorder. However, to date, the observation of the topological Anderson insulator phase has been elusive. In this article, we report the first experimental demonstration of a topological Anderson insulator. We do that in a photonic implementation: an array of helical, evanescently-coupled waveguides in a detuned honeycomb geometry. Under proper conditions, adding on-site disorder, in the form of random variations in the refractive index contrast defining the waveguides, drives the system from a trivial phase into a topological state.

cond-mat.mes-hall↗

arXiv2020

Observation of unidirectional soliton-like edge states in nonlinear Floquet topological insulators

A salient feature of solid-state topological materials in two dimensions is the presence of conducting electronic edge states that are insensitive to scattering by disorder. Such unidirectional edge states have been explored in many experimental settings beyond solid-state electronic systems, including in photonic devices, mechanical and acoustic structures, and others. It is of great interest to understand how topological states behave in the presence of inter-particle interactions and nonlinearity. Here we experimentally demonstrate unidirectional soliton-like nonlinear states on the edge of photonic topological insulators consisting of laser-written waveguides. As a result of the optical Kerr nonlinearity of the ambient glass, the soliton-like wavepacket forms a non-diffracting coherent structure that slowly radiates power because of the intrinsic gaplessness of the system. The realization of soliton-like edge states paves the way to an understanding of topological phenomena in nonlinear systems and those with inter-particle interactions.

physics.optics↗

arXiv2020

Observation of a charge-2 photonic Weyl point in the infrared

Weyl points are robust point degeneracies in the band structure of a periodic material, which act as monopoles of Berry curvature. They have been at the forefront of research in three-dimensional topological materials (whether photonic, electronic or otherwise) as they are associated with novel behavior both in the bulk and on the surface. Here, we present the experimental observation of a charge-2 photonic Weyl point in a low-index-contrast photonic crystal fabricated by two-photon polymerization. The reflection spectrum obtained via Fourier Transform Infrared (FTIR) spectroscopy closely matches simulations and shows two bands with quadratic dispersion around a point degeneracy. This work provides a launching point towards all-dielectric, low-contrast three-dimensional photonic topological devices.

physics.optics↗

arXiv2020

Observation of a higher-order topological bound state in the continuum

Higher-order topological insulators are a recently discovered class of materials that can possess zero-dimensional localized states regardless of the dimension of the lattice. Here, we experimentally demonstrate that the topological corner-localized modes of higher-order topological insulators can be symmetry protected bound states in the continuum; these states do not hybridize with the surrounding bulk states of the lattice even in the absence of a bulk bandgap. As such, this class of structures has potential applications in confining and controlling light in systems that do not support a complete photonic bandgap.

physics.optics↗

arXiv2019

Observation of Topological Band Gap Solitons

Topological materials exhibit properties dictated by quantised invariants that make them robust against perturbations. This topological protection is a universal wave phenomenon that applies not only in the context of electrons in solid-state materials but also to photonic systems, ultracold atoms, mechanical systems, circuits, exciton-polaritons and beyond. However, the vast majority of research in these systems has focused on the linear domain, i.e., where inter-particle interactions do not play a role. Here, we experimentally observe solitons -- waves that propagate without changing shape as a result of nonlinearity -- in the bulk of a photonic Floquet topological insulator. These solitons exhibit fundamentally different behaviour than solitons in ordinary band gaps in that they execute cyclotron-like orbits that are associated with the topology of the lattice. Specifically, we employ a laser-written waveguide array with periodic variations along the waveguide axis that give rise to non-zero Floquet winding number, where the nonlinearity arises from the optical Kerr effect of the ambient glass. The effect described here is applicable to a range of bosonic systems due to its description by the focusing nonlinear Schrödinger equation, i.e., the Gross-Pitaevskii equation with attractive interactions.

physics.optics↗

arXiv2019

Braiding photonic topological zero modes

A remarkable property of quantum mechanics in two-dimensional (2D) space is its ability to support "anyons," particles that are neither fermions nor bosons. Theory predicts that these exotic excitations can be realized as bound states confined near topological defects, like Majorana zero modes trapped in vortices in topological superconductors. Intriguingly, in the simplest cases the nontrivial phase that arises when such defects are "braided" around one another is not intrinsically quantum mechanical; rather, it can be viewed as a manifestation of the geometric (Pancharatnam-Berry) phase in wave mechanics, enabling the simulation of such phenomena in classical systems. Here we report the first experimental measurement in any system, quantum or classical, of the geometric phase due to such a braiding process. These measurements are obtained using an interferometer constructed from highly tunable 2D arrays of photonic waveguides. Our results introduce photonic lattices as a versatile playground for the experimental study of topological defects and their braiding, complementing ongoing efforts in solid-state systems and cold atomic gases.

physics.optics↗

arXiv2019

Fractal waveguide arrays induce maximal localization

The ability to transmit light through an array of closely packed waveguides while minimizing interwaveguide coupling has important implications for fields such as discrete imaging and telecommunications. Proposals for achieving these effects have leveraged phenomena ranging from Floquet-induced flat bands to Anderson localization. Here we demonstrate that, for strongly detuned waveguides, optimal localization is achieved not by disorder but by fractal potentials. We further show that, in both 1D and 2D, these structures possess a localization-delocalization phase transition.

physics.optics↗

arXiv2019

Bound states in the continuum through environmental design

We propose a new paradigm for realizing bound states in the continuum (BICs) by engineering the environment of a system to control the number of available radiation channels. Using this method, we demonstrate that a photonic crystal slab embedded in a photonic crystal environment can exhibit both isolated points and lines of BICs in different regions of its Brillouin zone. Finally, we demonstrate that the intersection between a line of BICs and line of leaky resonance can yield exceptional points connected by a bulk Fermi arc. The ability to design the environment of a system opens up a broad range of experimental possibilities for realizing BICs in three-dimensional geometries, such as in 3D-printed structures and the planar grain boundaries of self-assembled systems.

physics.optics↗

arXiv2019

Broadband topological slow light through higher momentum-space winding

Slow-light waveguides can strongly enhance light-matter interaction, but suffer from narrow bandwidth, increased backscattering, and Anderson localization. Edge states in photonic topological insulators resist backscattering and localization, but typically cross the bandgap over a single Brillouin zone, meaning that slow group velocity implies narrow-band operation. Here we show theoretically that this can be circumvented via an edge termination that causes the edge state to wind many times around the Brillouin zone, making it both slow and broadband.

physics.optics↗