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Because of their massless nature, photons do not interact in linear optical media. However, light beam propagation in nonlinear media permits to break this paradigm, and makes it possible to observe photon-photon interactions. Based on this principle, a beam of light propagating in a nonlinear multimode optical system can be described as a gas of interacting particles. As a consequence, the spatio-temporal evolution of this photon gas is expressed in terms of macroscopic thermodynamic variables, e.g., temperature and chemical potential. Moreover, the gas evolution is subject to experiencing typical thermodynamic phenomena, such as thermalization. The meaning of thermodynamic variables associated with the photon gas must not be confused with their classical counterparts, e.g., the gas temperature cannot be measured by means of standard thermometers. Although the thermodynamic parameters of a multimode photon gas result from a rigorous mathematical derivation, their physical meaning is still unclear. In this work, we report on optical calorimetric measurements, which exploit nonlinear beam propagation in multimode optical fibers. Our results show that, indeed, heat only flows from a hot to a cold photon gas subsystem. This provides an unequivocal demonstration that nonlinear multimode wave propagation phenomena are governed by the second law of thermodynamics. In addition to be fundamental, our findings provide a new approach to light-by-light activated management of laser beams.

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 closer 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 overlocked 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 $M_s$ with $M_s=2,3,\ldots,M$, depending on the choice of input and output channels.

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

Standard exceptional points (EPs) are non-Hermitian degeneracies that occur in open systems. At an EP, the Taylor series expansion becomes singular and fails to converge -- a feature that was exploited for several applications. Here, we theoretically introduce and experimentally demonstrate a new class of parity-time symmetric systems [implemented using radio frequency (rf) circuits] that combine EPs with another type of mathematical singularity associated with the poles of complex functions. These nearly divergent exceptional points can exhibit an unprecedentedly large eigenvalue bifurcation beyond those obtained by standard EPs. Our results pave the way for building a new generation of telemetering and sensing devices with superior performance.

A comment has been recently posted on the arXiv (arXiv:1902.07504) that discuss our recent work on encircling multiple exceptional points in Nat. Commun. 9, 4808 (2018). In that comment, the authors claim that our approach is prone to errors. In discussing their findings, they also indicate that a method presented by their team in Phys. Rev. A 98, 023818 (2018) (presumed to give correct results in all situations) was published prior to our work. First, we would like to note that both their work and ours were posted on the arXiv within a week from each other. Second and more importantly, as we will show below, their analysis and conclusion concerning the validity of our approach as presented in the comment article (arXiv:1902.07504) are not correct. As we will demonstrate, a proper application of our method does indeed provide the correct results.

Blue-enhanced, broadband supercontinuum generation in a 50 um core fluorine-doped graded-index multimode fiber is demonstrated by pumping with a 1064 nm picosecond source. Multi-octave supercontinuum spectrum extending from ~400 nm to 2,400 nm is achieved in a relatively short fiber. The measured spectrum and multimode nonlinear properties are compared to those of a germanium-doped graded-index multimode fiber. It is shown that engineering the glass composition and thus its chromatic dispersion and absorption characteristics, provides a novel and effective approach to further controlling the nonlinear dynamics in highly multimoded parabolic-index fibers.

Exceptional points (EPs) are singularities that arise in non-Hermitian physics. Current research efforts focus only on systems supporting isolated EPs characterized by increased sensitivity to external perturbations, which makes them potential candidates for building next generation optical sensors. On the downside, this feature is also the Achilles heel of these devices: they are very sensitive to fabrication errors and experimental uncertainties. To overcome this problem, we introduce a new design concept for implementing photonic EPs that combine the robustness required for practical use together with their hallmark sensitivity. Particularly, our proposed structure exhibits a hypersurface of Jordan EPs (JEPs) embedded in a larger space, and having the following peculiar features: (1) A large class of undesired perturbations shift the operating point along the exceptional surface (ES), thus leaving the system at another EP which explains the robustness; (2) Perturbations due to back reflection/scattering force the operating point out of the ES, leading to enhanced sensitivity. Importantly, our proposed geometry is relatively easy to implement using standard photonics components and the design concept can be extended to other physical platforms such as microwave or acoustics.

In this letter, we report the first experimental observation of a photonic hook - a new type of near field curved light generated at the output of dielectric cuboid with broken symmetry having dimensions comparable to the electromagnetic wavelength. The radius of curvature associated with the generated photonic hook is smaller than the wavelength used while its minimum beam-waist is about 0.44 lamda. This represents the smallest radius of curvature ever recorded for any alectromagnetic beams., Comment: 5 pages, 3 figures

Monochromatic coherent light traversing a disordered photonic medium evolves into a random field whose statistics are dictated by the disorder level. Here we demonstrate experimentally that light statistics can be deterministically tuned in certain disordered lattices, even when the disorder level is held fixed, by controllably breaking the excitation symmetry of the lattice modes. We exploit a lattice endowed with disorder-immune chiral symmetry in which the eigenmodes come in skew-symmetric pairs. If a single lattice site is excited, a "photonic thermalization gap" emerges: the realm of sub-thermal light statistics is inaccessible regardless of the disorder level. However, by exciting two sites with a variable relative phase, as in a traditional two-path interferometer, the chiral symmetry is judiciously broken and interferometric control over the light statistics is exercised, spanning sub-thermal and super-thermal regimes. These results may help develop novel incoherent lighting sources from coherent lasers., Comment: 6 pages, 5 figures

We study transport properties of an array created by alternating $(a,b)$ layers with balanced loss/gain characterized by the key parameter $\gamma$. It is shown that for non-equal widths of $(a,b)$ layers, i.e., when the corresponding Hamiltonian is non-PT-symmetric, the system exhibits the scattering properties similar to those of truly PT-symmetric models provided that without loss/gain the structure presents the matched quarter stack. The inclusion of the loss/gain terms leads to an emergence of a finite number of spectral bands characterized by real values of the Bloch index. Each spectral band consists of a central region where the transmission coefficient $T_N \geq 1$, and two side regions with $T_N \leq 1$. At the borders between these regions the unidirectional reflectivity occurs. Also, the set of Fabry-Perrot resonances with $T_N=1$ are found in spite of the presence of loss/gain., Comment: 5 pages, 5 figures

We introduce a recursive bosonic quantization technique for generating classical PT photonic structures that possess hidden symmetries and higher order exceptional points. We study light transport in these geometries and we demonstrate that perfect state transfer is possible only for certain initial conditions. Moreover, we show that for the same propagation direction, left and right coherent transports are not symmetric with field amplitudes following two different trajectories. A general scheme for identifying the conservation laws in such PT-symmetric photonic networks is also presented.

We present a class of waveguide arrays that is the classical analog of a quantum harmonic oscillator where the mass and frequency depend on the propagation distance. In these photonic lattices refractive indices and second neighbor couplings define the mass and frequency of the analog quantum oscillator, while first neighbor couplings are a free parameter to adjust the model. The quantum model conserves the Ermakov-Lewis invariant, thus the photonic crystal also posses this symmetry., Comment: 8 pages, 3 figures

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 introduce a new type of Fano resonances, realized in a photonic circuit which consists of two nonlinear PT-symmetric micro-resonators side-coupled to a waveguide, which 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 set-up requires low input power and does not compromise the power and frequency characteristics of the output signal.

We investigate the properties of PT-symmetric tight-binding models by considering both bounded and unbounded models. For the bounded case, we obtain closed form expressions for the corresponding energy spectra and we analyze the structure of eigenstates as well as their dependence on the gain/loss contrast parameter. For unbounded PT-lattices, we explore their scattering properties through the development of analytical models. Based on our approach we identify a mechanism that is responsible to the emergence of localized states that are entirely due to the presence of gain and loss. The derived expressions for the transmission and reflection coefficients allow one to better understand the role of PT-symmetry in energy transport problems occurring in such PT-symmetric tight-binding settings. Our analytical results are further exemplified via pertinent examples., Comment: 28 pages, 13 figures

We show that complex PT-symmetric photonic lattices can lead to a new class of self-imaging Talbot effects. For this to occur, we find that the input field pattern, has to respect specific periodicities which are dictated by the symmetries of the system. While at the spontaneous PT-symmetry breaking point, the image revivals occur at Talbot lengths governed by the characteristics of the passive lattice, at the exact phase it depends on the gain and loss parameter thus allowing one to control the imaging process., Comment: 5 pages, 3 figures

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., Comment: 4 pages, 3 figures, comments welcome

We predict the quantum correlations between non-interacting particles evolving simultaneously in a disordered medium. While the particle density follows the single-particle dynamics and exhibits Anderson localization, the two-particle correlation develops unique features that depend on the quantum statistics of the particles and their initial separation. On short time scales, the localization of one particle becomes dependent on whether the other particle is localized or not. On long time scales, the localized particles show oscillatory correlations within the localization length. These effects can be observed in Anderson localization of non-classical light and ultra-cold atoms., Comment: 4 pages, 4 figures, comments welcome

We show analytically, numerically, and experimentally that a transversely stable one-dimensional [(1+1)D] bright Kerr soliton can exist in a 3D bulk medium. The transverse instability of the soliton is completely eliminated if it is made sufficiently incoherent along the transverse dimension. We derive a criterion for the threshold of transverse instability that links the nonlinearity to the largest transverse correlation distance for which the 1D soliton is stable, Comment: 14 pages, 2 figures