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Statistical mechanics demands that the temperature of a system is positive provided that its internal energy has no upper bound. Yet if this condition is not met, it is possible to attain negative temperatures for which higher-order energy states are thermodynamically favored. Although negative temperatures have been reported in spin and Bose-Hubbard settings as well as in quantum fluids, the observation of thermodynamic processes in this regime has thus far remained elusive. Here, we demonstrate isentropic expansion-compression and Joule expansion for negative optical temperatures, enabled by purely nonlinear photon-photon interactions in a thermodynamic microcanonical photonic system. Our photonic approach provides a platform for exploring new all-optical thermal engines and could have ramifications in other bosonic systems beyond optics, such as cold atoms and optomechanics.

We develop a linear theory for non-Hermitian optical systems having exceptional points. In contrast to previous studies, our analysis results in an exact expression for the resolvent operator without the need to use perturbation expansions.

Shaping the light emission characteristics of laser systems is of great importance in various areas of science and technology. In a typical lasing arrangement, the spatial profile of the mode tends to remain self-similar throughout the cavity. Here, we introduce a paradigm shift where a spatially evolving mode is faithfully settled into a pair of bi-orthogonal states at the two facets of a laser cavity. This is achieved by deliberately eliminating non-adiabatic jumps in a purposely designed structure that features a dynamic encirclement of a non-Hermitian exceptional point. The resulting state transfer reflects the unique topology of the associated Riemann surfaces. Our approach provides a route to develop versatile mode selective active, Comment: A supplemental file is available on the Journal's website

Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogonality of their eigenmodes, and the presence of exceptional points (EPs). Here, we derive a closed form series expansion of the resolvent associated with an arbitrary non-Hermitian system in terms of the ordinary and generalized eigenfunctions of the underlying Hamiltonian. This in turn reveals an interesting and previously overlooked feature of non-Hermitian systems, namely that their lineshape scaling is dictated by how the input (excitation) and output (collection) profiles are chosen. In particular, we demonstrate that a configuration with an EP of order M can exhibit a Lorentzian response or a super-Lorentzian response of order M

We demonstrate both theoretically and experimentally that coupled metallic nanolasers can be used to emulate spin-Hamiltonians. Depending on the geometry of the array, we observe ferromagnetic and antiferromagnetic behaviors, as well as geometric frustration.

The synthesis of ultrathin photonic structures in order to effectively redirect and mold optical wave fronts into arbitrary shapes is of crucial importance in modern beam steering, imaging, and sensing technologies. To this end, planar subwavelength systems such as optical metasurfaces have been intensely investigated in recent years. Such arrangements rely on abrupt, yet controllable, phase shifts imparted on the incident beam, by means of judiciously designed anisotropic nanoantennas. Here, we propose and demonstrate an altogether different methodology in order to manipulate the flow of light, by adopting a diatomic parity-time ($\mathcal{P}\mathcal{T}$)-symmetric Bravais-lattice topology, the unit cell of which involves only a transparent and a lossy optical component. In this respect, a honeycomblike configuration is employed, the principal symmetries of which are progressively broken through specific geometric transformations. The complex near-field coupling interactions between neighboring diffractive elements give rise to a discerning enhancement or attenuation along specific directions in the far field, over a broad range of wavelengths in the visible domain. In this work, we report the realization of an all-passive $\mathcal{P}\mathcal{T}$-symmetric optical metasurface on a flexible polyimide substrate, capable of demonstrating selective directional scattering. Our study draws a clear connection between surface topology and radiation directivity, which can be systematically utilized toward observing unconventional transport effects in flat- and curved-space $\mathcal{P}\mathcal{T}$ lattices.

Applied Physics Letters journal paper entitled "Experimental observation of a photonic hook".

A new scheme for ultrasensitive micro-ring laser gyroscopes based on the physics of exceptional points is proposed. In such systems, the sensitivity to low rotation rates can be enhanced by several orders of magnitude.

We show that an Aharonov-Bohm like suppression of optical tunneling can take place in linear and nonlinear twisted multicore optical fiber structures. The energy exchange is analyzed under nonlinear conditions and a viable setting to observe these effects is suggested.

We present an electrically pumped parity-time-symmetric coupled microring laser. Using the interplay between gain and loss, single mode operation is demonstrated with no penalty in terms of output power or threshold pump intensity.

We demonstrate the possibility of observing the signatures of parity-time symmetry in ultralong cavities where the structural parameters are prone to statistical variations. We present a model for an alyzing such arrangements, a nd p redict an d d emonstrate t he o ccurrence of p hase transition in a PT-symmetric cavity.

The PT-symmetry breaking for topological defect-states are studied in SSH micro-resonator laser arrays. For defect modes, the PT-symmetry breaking threshold reduces when the coupling strength between closely paired elements is increased. Such topological defect-modes are demonstrated in a 16-ring SSH PT-laser arrangement.

In recent years, the concept of parity-time (PT) symmetry has received considerable attention in the field of optics and photonics. In PT-symmetric arrangements, the interaction between gain/loss-contrast and coupling leads to the formation of exceptional points in parameter space. At these junctures, not only the eigenvalues but also the eigenvectors tend to merge, resulting in a sudden reduction of the dimensionality of the eigen-space. Consequently, in the vicinity of such points, the eigenfrequencies are strongly affected by external perturbationsas the system regains its original dimensionality. This unique behavior can be utilized to fundamentally enhance the sensitivity of micro-resonators. Here, we experimentally investigate this effect in integrated semiconductor PT-symmetric microring lasers that are biased at exceptional points. Using this arrangement, we demonstrate >10- fold enhancement in sensitivity. Our results also show that unlike standard microcavities, the parity-time symmetric system responds to the square-root of the perturbation. Our work provides a new avenue for enhancing the sensitivity of optical integrated sensors.

We predict and experimentally demonstrate that the lasing threshold can be lowered by virtue of PT-symmetry, and for the first time observe PT-symmetry-breaking in a long fiber cavity despite the presence of random phase fluctuations.

We predict and experimentally observe that TT-Symmetry breaking occurs in long (> 10 m) fiber cavities, despite the fact that the free-spectral range (FSR) is infinitesimally small (λ fsr

We introduce a family of non-Hermitian optical potentials that are given in terms of double-exponential periodic functions. The center of $\mathcal{PT}$ symmetry is not around zero and the potential satisfies a shifted $\mathcal{PT}\text{-symmetry}$ relation at two distinct locations. Motivated by wave transmission through thin phase screens and gratings, we examine these refractive index modulations from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics, abrupt phase transitions in the eigenvalue spectrum, and exceptional points in the band structure are examined in detail. In addition, the nonlinear properties of wave propagation in Kerr nonlinearity media are studied. In particular, coherent structures such as lattice solitons are numerically identified by applying the spectral renormalization method. The spatial symmetries of such lattice solitons follow the shifted $\mathcal{PT}\text{-symmetric}$ relations. Furthermore, such lattice solitons have a power threshold and their linear and nonlinear stabilities are critically dependent on their spatial symmetry point.

We demonstrate that many features of PT-symmetric lasing, such as the lower predicted lasing threshold and PT-symmetric phase transition, are sufficiently robust to be observed in a long fiber cavity (>1 km) despite random phase fluctuations.

In quantum theory, any Hamiltonian describing a physical system is mathematically represented by a self-adjoint linear operator to ensure the reality of the associated observables. In an attempt to extend quantum mechanics into the complex domain, it was realized few years ago that certain non-Hermitian parity-time (PT) symmetric Hamiltonians can exhibit an entirely real spectrum. Much of the reported progress has been remained theoretical, and therefore hasn't led to a viable experimental proposal for which non Hermitian quantum effects could be observed in laboratory experiments. Quite recently however, it was suggested that the concept of PT-symmetry could be physically realized within the framework of classical optics. This proposal has, in turn, stimulated extensive investigations and research studies related to PT-symmetric Optics and paved the way for the first experimental observation of PT-symmetry breaking in any physical system. In this paper, we present recent results regarding PT-symmetric Optics.

A quadratic two-photon photocurrent is measured in a novel multiple-quantum well GaAs laser waveguide at 1550nm. We show that this device is ideal for nonlinear detection and signal processing applications due to its large efficiency and high sensitivity. In particular, we measure the autocorrelation trace of a 100 fs pulse using sub-watt peak power levels.

The polarization structure of nonparaxial spatial solitons in a transparent medium with the electronic mechanism of Kerr nonlinearity is studied theoretically. It is demonstrated analytically in the weak nonparaxiality approximation that the regime of polarization locking, in which all the field components have the same propagation constant, is the only stable regime. Estimates of the rate of transition of the initial metastable regime of rotation of the polarization ellipse to the regime of polarization locking are presented. Based on a numerical solution of the nonlinear Maxwell equations, the presence of the nonparaxial regime of polarization locking is confirmed and the main characteristics of the corresponding spatial solitons are obtained.

We experimentally demonstrate the generation of an array of optical bottle beams by employing multiple self-accelerating Airy beams. This kind of optical bottle array is created by superimposing eight Airy beams along a circle, all with inward acceleration directed towards the center. In addition, we demonstrate stable trapping of multiple absorbing glassy carbon particles using the proposedoptical bottle array.

We show that Fano resonances created by two 𝒫𝒯 -symmetric nonlinear micro-resonators coupled to a waveguide, have line-shape and resonance position that depends on the direction of the incident light. We utilize these features in order to induce asymmetric transport, up to 47 dBs, in the optical C-window. Our theoretical proposal requires low input power and does not compromise the power or frequency characteristics of the output signal.

We experimentally realize the generation of high-order photon encoded W-states involving up to 16 optical modes. Furthermore, we exploit the inherent probabilistic properties of these multipartite entangled W-states for generating genuine random numbers.

Optical spatial solitons are self-trapped optical beams that exist by virtue of the balance between diffraction and nonlinearity. They propagate and interact with one another while displaying properties that are normally associated with real particles. Solitons, in general, manifest themselves in a large variety of wave/particle systems in nature: practically in any system that possesses both dispersion (in time or space) and nonlinearity. Solitons have been identified in optics, plasmas, fluids, condensed matter, particle physics, and astrophysics. Yet over the past decade, the forefront of soliton research has shifted to optics. In the paper, we describe the historical evolution of spatial solitons from speculative creatures to one of the most fascinating features optics has to offer.

We demonstrate optical interactions between stable self-trapped optical beams in soft-matter systems with pre-engineered saturable self-focusing optical nonlinearities. Our experiments, carried out in dilute suspensions of particles with negative polarizabilities, show that optical beam interactions can vary from attractive to repulsive, or can display an energy exchange depending on the initial relative phases. The corresponding observations are in good agreement with theoretical predictions.

We introduce the notion of Parity-Time Symmetry (PTS) and present its implications in wave transport. Using photonics and electronics frameworks we propose designs that support asymmetric transport due to the interplay of PTS and nonlinearity.

We experimentally observe anomalous wavepacket evolution in a realization of a one-dimensional finite binary Anderson model in the presence of short-range correlations. To this end, we employ weakly-coupled optical waveguides with propagation constants epsilon1 and epsilon2. The correlations enforce the creation of dimers, i.e. two adjacent waveguides with the same epsilon, randomly placed along the lattice. A transition from a ballistic to a superdiffusive wavepacket expansion and, eventually, to localization is observed as the contrast between the two propagation constants increases.

The evolution of spatially extended, entangled, anti-correlated two photon states in photonic waveguide arrays that induce classical transverse Anderson localization is theoretically and experimentally investigated.

We study a class of three-waveguide axially varying structures whose dynamics are described by the su(3) algebra. Their analytic propagator can be found based on the corresponding Lie group generators. In particular, we show that the field propagator corresponding to three-waveguide structures that have arbitrarily varying coupling coefficients and identical refractive indices is associated with the orbital angular momentum algebra. The conditions necessary to achieve perfect transmission from the first to the last waveguide element are obtained and particular cases are elucidated analytically., Comment: 5 pages, 4 figures

We experimentally demonstrate super-diffusion and the delocalization-localization phase transition in a random dimer structure. The system is implemented using weakly-coupled optical waveguides.

We experimentally demonstrate that hybrid ordered–disordered photonic lattices can generate faster than the ballistic growth of the second moment of a spreading wave packet for parametrically large time intervals.

We demonstrate quantum walks of a photon pair in a spatially extended Einstein-Podolsky-Rosen state coupled into an on-chip multiport photonic lattice. By varying the degree of entanglement we observe Anderson localization for pairs in a separable state and Anderson colocalization for pairs in an Einstein-Podolsky-Rosen entangled state. In the former case, each photon localizes independently, while in the latter neither photon localizes, but the pair colocalizes--revealing unexpected survival of the spatial correlations through strong disorder.

We demonstrate that light propagating in an appropriately designed lattice can exhibit dynamics akin to that expected from massless relativistic particles as governed by the one-dimensional Dirac equation. This is accomplished by employing a waveguide array with alternating positive and negative effective coupling coefficients, having a band structure with two intersecting minibands. Through this approach optical analogues of massless particle-antiparticle pairs are experimentally realized. One-dimensional conical diffraction is also observed for the first time in this work.

We study light propagation in disordered modulated Bloch arrays. For the specific system under consideration, our analysis predicts a 5 fold enhancement in light localization over that expected from a corresponding uniform lattice.

We observe superballistic transport in optical lattices where a finite disordered region embed- ded into a periodic structure acts as a light source of constant flux, boosting the spread of a wavepacket.

We show that only in a unique class of z-dependent lattices a true accelerating and diffractionless beam (different from Airy) can exist. Such beams are also possible under nonlinear conditions as exact traveling lattice solitons.

We study the light propagation in z-varying local parity-time symmetric coupled systems. We show that, unlike their conventional counterparts, our analysis predicts a peculiar unidirectional phase exchange.

We examine the unusual properties of multimoded PT-symmetric optical potentials. Multiple PT-thresholds, complex bifurcation mode organization, vortices in the transverse power flow, and phase singularities, are few of the exotic characteristics of multimode PT-Optics.

We report modal phase matched (MPM) second harmonic generation (SHG) in high-index contrast AlGaAs sub-micron ridge waveguides, by way of sub-mW continuous wave powers at telecommunication wavelengths. We achieve an experimental normalized conversion efficiency of ~14%/W/cm2, obtained through a careful sub-wavelength design supporting both the phase matching requirement and a significant overlap efficiency. Furthermore, the weak anomalous dispersion, robust fabrication technology and possible geometrical and thermal tuning of the device functionality enable a fully integrated multi-functional chip for several critical areas in telecommunications, including wavelength (time) division multiplexing and quantum entanglement.

When light waves propagate through disordered photonic lattices, they can eventually become localized due to multiple scattering effects. Here we show experimentally that while the evolution and localization of the photon density distribution is similar in the two cases of diagonal and off-diagonal disorder, the density-density correlation carries a distinct signature of the type of disorder. We show that these differences reflect a symmetry in the spectrum and eigenmodes that exists in off-diagonally disordered lattices but is absent in lattices with diagonal disorder., 4 pages, 3 figures, comments welcome

We show that parity-time symmetric Bragg grating structures, at the spontaneous PT-symmetry point, can act as unidirectional transparent media where the reflection from one side is suppressed while it is enhanced from the other.

We demonstrate symbiotic dynamics of light and nano-particles suspended in liquid. The light-force varies the local particle-density, modifies the fluid properties (surface-tension, viscosity), inducing flow in the fluid, causing synergetic nonlinear-dynamics of light and fluid.

Using modal phase matching, a continuous wave, wavelength tunable second harmonic source is experimentally demonstrated at telecommunication wavelengths. The sub-micron AlGaAs waveguide device offers a robust fabrication process making it ideal for integrated wavelength conversion.