Yaakov Lumer

Photonic Floquet Topological Insulators

Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on their surfaces. In two dimensions, electrons on the surface of a topological insulator are not scattered despite defects and disorder, providing robustness akin to that of superconductors. Topological insulators are predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Substantial effort has been directed towards realizing topological insulators for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. But because magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatter-free edge states requires a fundamentally different mechanism—one that is free of magnetic fields. A number of proposals for photonic topological transport have been put forward recently. One suggested temporal modulation of a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, in which temporal variations in solid-state systems induce topological edge states. Here we propose and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport—a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrödinger equation where the propagation coordinate (z) acts as ‘time’. Thus the helicity of the waveguides breaks z-reversal symmetry as proposed for Floquet topological insulators. This structure results in one-way edge states that are topologically protected from scattering.

Efficient extracavity generation of radially and azimuthally polarized beams.

We demonstrate an efficient transformation of a linearly polarized Gaussian beam to a radially or an azimuthally polarized doughnut (0,1)* Laguerre-Gaussian beam of high purity. We use a spatially variable retardation plate, composed of eight sectors of a lambda/2 retardation plate, to transform a linear polarization distribution to radial/azimuthal distribution. We transformed an Nd:YAG Gaussian beam with M(2)=1.3 to a radially and azimuthally polarized (0,1)* Laguerre-Gaussian beams with M(2)=2.5 and degree of radial/azimuthal polarization of 96-98%.

Observation of a Topological Transition in the Bulk of a Non-Hermitian System.

Topological insulators are insulating in the bulk but feature conducting states on their surfaces. Standard methods for probing their topological properties largely involve probing the surface, even though topological invariants are defined via the bulk band structure. Here, we utilize non-hermiticy to experimentally demonstrate a topological transition in an optical system, using bulk behavior only, without recourse to surface properties. This concept is relevant for a wide range of systems beyond optics, where the surface physics is difficult to probe.

Topologically protected bound states in photonic parity–time-symmetric crystals

Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.

Observation of unconventional edge states in ‘photonic graphene’

Graphene, a two-dimensional honeycomb lattice of carbon atoms, has been attracting much interest in recent years. Electrons therein behave as massless relativistic particles, giving rise to strikingly unconventional phenomena. Graphene edge states are essential for understanding the electronic properties of this material. However, the coarse or impure nature of the graphene edges hampers the ability to directly probe the edge states. Perhaps the best example is given by the edge states on the bearded edge that have never been observed-because such an edge is unstable in graphene. Here, we use the optical equivalent of graphene-a photonic honeycomb lattice-to study the edge states and their properties. We directly image the edge states on both the zigzag and bearded edges of this photonic graphene, measure their dispersion properties, and most importantly, find a new type of edge state: one residing on the bearded edge that has never been predicted or observed. This edge state lies near the Van Hove singularity in the edge band structure and can be classified as a Tamm-like state lacking any surface defect. The mechanism underlying its formation may counterintuitively appear in other crystalline systems.

Birefringence-induced bifocusing for selection of radially or azimuthally polarized laser modes

We develop a round-trip matrix diagonalization method for quantitative description of selection of radially or azimuthally polarized beams by birefringence-induced bifocusing in a simple laser resonator. We employ different focusing between radially and tangentially polarized light in thermally stressed laser rods to obtain low-loss stable oscillation in a radially polarized Laguerre-Gaussian, LG(0,1)*, mode. We derive a free-space propagator for the radially and azimuthally polarized LG(0,1)* modes and explain basic principles of mode selection by use of a round-trip matrix diagonalization method. Within this method we calculate round-trip diffraction losses and intensity distributions for the lowest-loss transverse modes. We show that, for the considered laser configuration, the round-trip loss obtained for the radially polarized LG(0,1)* mode is significantly smaller than that of the azimuthally polarized mode. Our experimental results, obtained with a diode side-pumped Nd:YAG rod in a flat-convex resonator, confirm the theoretical predictions. We achieved a pure radially polarized LG(0,1)* beam with M(2)=2.5 and tens of watts of output power.

Causality effects on accelerating light pulses

We study accelerating and decelerating shape-preserving temporal Airy wave-packets propagating in dispersive media. We explore the effects of causality, and find that, whereas decelerating pulses can asymptotically reach zero group velocity, pulses that accelerate towards infinite group velocity inevitably break up, after a specific critical point. The trajectories and the features of causal pulses are analyzed, along with the requirements for the existence of the critical point and experimental schemes for its observation. Finally, we show that causality imposes similar effects on accelerating pulses in the presence of local Kerr-like nonlinearities.

2 kW, M2 < 10 radially polarized beams from aberration-compensated rod-based Nd:YAG lasers.

Radially polarized light in a 2.1 kW, good quality beam was obtained from a Nd:YAG rod-based master oscillator power amplifier. Several techniques were utilized: a pure radially polarized oscillator, efficient pump chambers, external compensation of lower-order aberrations, and higher-order aberration compensation by pairing of pump chambers.

Topological Optical Waveguiding in Silicon and the Transition between Topological and Trivial Defect States

One-dimensional models with topological band structures represent a simple and versatile platform to demonstrate novel topological concepts. Here we experimentally study topologically protected states in silicon at the interface between two dimer chains with different Zak phases. Furthermore, we propose and demonstrate that, in a system where topological and trivial defect modes coexist, we can probe them independently. Tuning the configuration of the interface, we observe the transition between a single topological defect and a compound trivial defect state. These results provide a new paradigm for topologically protected waveguiding in a complementary metal-oxide-semiconductor compatible platform and highlight the novel concept of isolating topological and trivial defect modes in the same system that can have important implications in topological physics.

Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories

Self-accelerating beams--shape-preserving bending beams--are attracting great interest, offering applications in many areas such as particle micromanipulation, microscopy, induction of plasma channels, surface plasmons, laser machining, nonlinear frequency conversion and electron beams. Most of these applications involve light-matter interactions, hence their propagation range is limited by absorption. We propose loss-proof accelerating beams that overcome linear and nonlinear losses. These beams, as analytic solutions of Maxwells equations with losses, propagate in absorbing media while maintaining their peak intensity. While the power such beams carry decays during propagation, the peak intensity and the structure of their main lobe region are maintained over large distances. We use these beams for manipulation of particles in fluids, steering the particles to steeper angles than ever demonstrated. Such beams offer many additional applications, such as loss-proof self-bending plasmons. In transparent media these beams show exponential intensity growth, which facilitates other novel applications in micromanipulation and ignition of nonlinear processes.