Observation of photon-photon thermodynamic processes under negative optical temperature conditions.

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.

Linear response theory of open systems with exceptional points.

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 Ms with Ms = 2, 3, …, M, depending on the choice of input and output channels.

Topological modes in a laser cavity through exceptional state transfer.

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 transverse spatial profile of a laser mode tends to remain self-similar throughout the entire cavity. Going beyond this paradigm, we demonstrate here how to shape a spatially evolving mode such that it faithfully settles into a pair of bi-orthogonal states at the two opposing facets of a laser cavity. This was achieved by purposely designing a structure that allows the lasing mode to encircle a non-Hermitian exceptional point while deliberately avoiding non-adiabatic jumps. The resulting state transfer reflects the unique topology of the associated Riemann surfaces associated with this singularity. Our approach provides a route to developing versatile mode-selective active devices and sheds light on the interesting topological features of exceptional points.

Airy light-sheet Raman imaging.

Light-sheet fluorescence microscopy has greatly improved the speed and overall photostability of optically sectioning cellular and multi-cellular specimens. Similar gains have also been conferred by light-sheet Raman imaging; these schemes, however, rely on diffraction limited Gaussian beams that hinder the uniformity and size of the imaging field-of-view, and, as such, the resulting throughput rates. Here, we demonstrate that a digitally scanned Airy beam increases the Raman imaging throughput rates by more than an order of magnitude than conventional diffraction-limited beams. Overall, this, spectrometer-less, approach enabled 3D imaging of microparticles with high contrast and 1 µm axial resolution at 300 msec integration times per plane and orders of magnitude lower irradiation density than coherent Raman imaging schemes. We detail the apparatus and its performance, as well as its compatibility with fluorescence light-sheet and quantitative-phase imaging towards rapid and low phototoxicity multimodal imaging.

Nonlinear scattering by non-Hermitian multilayers with saturation effects.

We theoretically investigate the optical properties of a one-dimensional non-Hermitian dispersive layered system with saturable gain and loss. We solve the nonhomogeneous Helmholtz equation perturbatively by applying the modified transfer matrix method and we obtain closed-form expressions for the reflection or transmission coefficients for TM incident waves. The nonreciprocity of the scattering process can be directly inferred from the analysis of the obtained expressions. It is shown that by tuning the parameters of the layers we can effectively control the impact of nonlinearity on the scattering characteristics of the non-Hermitian layered structure. In particular, we investigate the asymmetric and nonreciprocal characteristics of the reflectance and transmittance of multilayered parity-time (PT)-symmetric slab. We demonstrate that incident electromagnetic wave may effectively tunnel through the PT-symmetric multilayered structures with zero reflection. The effect of nonlinearity to the scattering matrix eigenvalues is systematically examined.

Integrative quantitative-phase and airy light-sheet imaging.

Light-sheet microscopy enables considerable speed and phototoxicity gains, while quantitative-phase imaging confers label-free recognition of cells and organelles, and quantifies their number-density that, thermodynamically, is more representative of metabolism than size. Here, we report the fusion of these two imaging modalities onto a standard inverted microscope that retains compatibility with microfluidics and open-source software for image acquisition and processing. An accelerating Airy-beam light-sheet critically enabled imaging areas that were greater by more than one order of magnitude than a Gaussian beam illumination and matched exactly those of quantitative-phase imaging. Using this integrative imaging system, we performed a demonstrative multivariate investigation of live-cells in microfluidics that unmasked that cellular noise can affect the compartmental localization of metabolic reactions. We detail the design, assembly, and performance of the integrative imaging system, and discuss potential applications in biotechnology and evolutionary biology.

Experimental Observation of PT Symmetry Breaking near Divergent Exceptional Points.

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.

Sensing with Exceptional Surfaces in Order to Combine Sensitivity with Robustness.

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 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 or backscattering 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.

Accelerated nonlinear interactions in graded-index multimode fibers.

Multimode optical fibers have recently reemerged as a viable platform for addressing a number of long-standing issues associated with information bandwidth requirements and power-handling capabilities. As shown in recent studies, the complex nature of such heavily multimoded systems can be effectively exploited to observe altogether novel physical effects arising from spatiotemporal and intermodal linear and nonlinear processes. Here, we study for the first time, accelerated nonlinear intermodal interactions in core-diameter decreasing multimode fibers. We demonstrate that in the anomalous dispersion region, this spatiotemporal acceleration can lead to relatively blue-shifted multimode solitons and blue-drifting dispersive wave combs, while in the normal domain, to a notably flat and uniform supercontinuum, extending over 2.5 octaves. Our results pave the way towards a deeper understanding of the physics and complexity of nonlinear, heavily multimoded optical systems, and could lead to highly tunable optical sources with very high spectral densities.

Instant and efficient second-harmonic generation and downconversion in unprepared graded-index multimode fibers.

We show that germanium-doped graded-index multimode silica fibers can exhibit relatively high conversion efficiencies (∼6.5%) for second-harmonic generation when excited at 1064 nm. This frequency-doubling behavior is also found to be accompanied by an effective downconversion. As opposed to previous experiments carried out in single- and few-mode fibers where hours of preparation were required, in our system, these χ(2) related processes occur almost instantaneously. The efficiencies observed in our experiments are, to the best of our knowledge, among the highest ever reported in unprepared fibers.

Robustness and mode selectivity in parity-time (PT) symmetric lasers.

We investigate two important aspects of PT symmetric photonic molecule lasers, namely the robustness of their single longitudinal mode operation against instabilities triggered by spectral hole burning effects, and the possibility of more versatile mode selectivity. Our results, supported by numerically integrating the nonlinear rate equations and performing linear stability analysis, reveals the following: (1) In principle a second threshold exists after which single mode operation becomes unstable, signaling multimode oscillatory dynamics, (2) For a wide range of design parameters, single mode operation of PT lasers having relatively large free spectral range (FSR) can be robust even at higher gain values, (3) PT symmetric photonic molecule lasers are more robust than their counterpart structures made of single microresonators; and (4) Extending the concept of single longitudinal mode operation based on PT symmetry in millimeter long edge emitting lasers having smaller FSR can be challenging due to instabilities induced by nonlinear modal interactions. Finally we also present a possible strategy based on loss engineering to achieve more control over the mode selectivity by suppressing the mode that has the highest gain (i.e. lies under the peak of the gain spectrum curve) and switch the lasing action to another mode.

Self-structuring of stable dissipative breathing vortex solitons in a colloidal nanosuspension.

The self-structuring of laser light in an artificial optical medium composed of a colloidal suspension of nanoparticles is demonstrated using variational and numerical methods extended to dissipative systems. In such engineered materials, competing nonlinear susceptibilities are enhanced by the light induced migration of nanoparticles. The compensation of diffraction by competing focusing and defocusing nonlinearities, together with a balance between loss and gain, allow for self-organization of light and the formation of stable dissipative breathing vortex solitons. Due to their robustness, the breathers may be used for selective dynamic photonic tweezing of nanoparticles in colloidal nanosuspensions.

Versatile supercontinuum generation in parabolic multimode optical fibers.

We demonstrate that the pump's spatial input profile can provide additional degrees of freedom in tailoring at will the nonlinear dynamics and the ensuing spectral content of supercontinuum generation in highly multimoded optical fibers. Experiments and simulations carried out at 1550 nm indicate that the modal composition of the input beam can substantially alter the soliton fission process as well as the resulting Raman and dispersive wave generation that eventually lead to supercontinuum in such a multimode environment. Given the multitude of conceivable initial conditions, our results suggest that it is possible to pre-engineer the supercontinuum spectral content in a versatile manner.

Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope.

We propose a new scheme for ultrasensitive laser gyroscopes that utilizes the physics of exceptional points. By exploiting the properties of such non-Hermitian degeneracies, we show that the rotation-induced frequency splitting becomes proportional to the square root of the gyration speed (Ω), thus enhancing the sensitivity to low angular rotations by orders of magnitudes. In addition, at its maximum sensitivity limit, the measurable spectral splitting is independent of the radius of the rings involved. This Letter paves the way toward a new class of ultrasensitive miniature ring laser gyroscopes on chip.

Tailoring frequency generation in uniform and concatenated multimode fibers.

We demonstrate that frequency generation in multimode parabolic-index fibers can be precisely engineered through appropriate fiber design. This is accomplished by exploiting the onset of a geometric parametric instability that arises from resonant spatiotemporal compression. By launching the output of an amplified Q-switched microchip laser delivering 400 ps pulses at 1064 nm, we observe a series of intense frequency sidebands that strongly depend on the fiber core size. The nonlinear frequency generation is analyzed in three fiber samples with 50 µm, 60 µm, and 80 µm core diameters. We further demonstrate that by cascading fibers of different core sizes, a desired frequency band can be generated from the frequency lines parametrically produced in each section. The observed frequency shifts are in good agreement with analytical predictions and numerical simulations. Our results suggest that core scaling and fiber concatenation can provide a viable avenue in designing optical sources with tailored output frequencies.

Dark-state lasers: mode management using exceptional points.

By exploiting the inherent characteristics of dark-state resonators, we experimentally realize a single-frequency integrated microring laser system. This semiconductor laser can remain single-mode, even at high pump power levels, while allowing tunability over a wide spectral range. Our results demonstrate the potential of exceptional points as a versatile tool for mode selection in micro-cavity laser configurations.

Visible supercontinuum generation in a graded index multimode fiber pumped at 1064 nm.

We observe efficient supercontinuum generation that extends into the visible spectral range by pumping a low differential mode group delay graded index multimode fiber in the normal dispersion regime. For a 28.5 m long fiber, the generated spectrum spans more than two octaves, starting from below 450 nm and extending beyond 2400 nm. The main nonlinear mechanisms contributing to the visible spectrum generation are attributed to multipath four-wave mixing processes and periodic spatio-temporal breathing dynamics. Moreover, by exploiting the highly multimodal nature of this system, we demonstrate versatile generation of visible spectral peaks in shorter fiber spans by altering the launching conditions. A nonlinearly induced mode cleanup was also observed at the pump wavelength. Our results could pave the way for high brightness, high power, and compact, multi-octave continuum sources.

Optical revivals in nonuniform supersymmetric photonic arrays.

We investigate the problem of wavepacket revivals in coupled nonuniform linear optical structures. Starting from the photonic Bloch lattices and J(x) arrays, whose propagators are fully periodic, we use cascaded discrete supersymmetric transformations to generate a family of nonuniform isospectral lattices. These new structures exhibit perfect imaging for any initial condition despite the apparent lack of order in their physical parameters. We note, however. that the SUSY-induced disordered coefficients are not random but, rather, inherit some of the features associated with the original array.

Parity-time-symmetric coupled microring lasers operating around an exceptional point.

The behavior of a parity-time-symmetric coupled microring system is studied when operating in the vicinity of an exceptional point. Using the abrupt phase transition around this point, stable single-mode lasing is demonstrated in spectrally multimoded microring arrangements.

Constant-intensity waves and their modulation instability in non-Hermitian potentials.

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave's constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.