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Driven nonlinear resonators provide a fertile ground for phenomena related to phase transitions far from equilibrium, which can open opportunities unattainable in their linear counterparts. Here, we show that optical parametric oscillators (OPOs) can undergo second-order phase transitions in the spectral domain between degenerate and non-degenerate regimes. This abrupt change in the spectral response follows a square-root dependence around the critical point, exhibiting high sensitivity to parameter variation akin to systems around an exceptional point. We experimentally demonstrate such a phase transition in a quadratic OPO. We show that the divergent susceptibility of the critical point is accompanied by spontaneous symmetry breaking and distinct phase noise properties in the two regimes, indicating the importance of a beyond nonlinear bifurcation interpretation. We also predict the occurrence of first-order spectral phase transitions in coupled OPOs. Our results on non-equilibrium spectral behaviors can be utilized for enhanced sensing, advanced computing, and quantum information processing. Non-equilibrium and collective behaviors such as phase transitions in optical systems can lead to interesting applications in photonics. Here the authors demonstrate spectral phase transition in a ubiquitous nonlinear driven-dissipative system, the optical parametric oscillator.

A plethora of applications have recently motivated extensive efforts regarding the generation of Kerr solitons and coherent frequency combs. However, the Kerr (cubic) nonlinearity is inherently weak. By contrast, strong quadratic nonlinearity in optical resonators is expected to provide a promising alternative means for soliton formation. Here we demonstrate dissipative quadratic soliton formation via non-stationary optical parametric amplification in the presence of pronounced temporal walk-off between pump and signal, leading to half-harmonic generation accompanied by a substantial pulse compression (exceeding a factor of 40) supported at low pump pulse energies (~4 pJ). The quadratic soliton forms in a low-finesse cavity in both normal and anomalous dispersion regimes. We present a route to considerably improve the performance of the demonstrated quadratic soliton when extended to an integrated platform to realize highly efficient extreme pulse compression, leading to the formation of few-cycle soliton pulses starting from ultra-low-energy picosecond-scale pump pulses.The formation of ultra-short dissipative quadratic solitons is realized using optical parametric amplification at low pump energies and in the presence of substantial temporal walk-off between the pump and signal.

Optical frequency comb is an enabling technology for a multitude of applications from metrology to ranging and communications. The tremendous progress in sources of optical frequency combs has mostly been centered around the near-infrared spectral region, while many applications demand sources in the visible and mid-infrared, which have so far been challenging to achieve, especially in nanophotonics. Here, we report widely tunable frequency comb generation using optical parametric oscillators in lithium niobate nanophotonics. We demonstrate sub-picosecond frequency combs tunable beyond an octave extending from 1.5 up to 3.3 μm with femtojoule-level thresholds on a single chip. We utilize the up-conversion of the infrared combs to generate visible frequency combs reaching 620 nm on the same chip. The ultra-broadband tunability and visible-to-mid-infrared spectral coverage of our source highlight a practical and universal path for the realization of efficient frequency comb sources in nanophotonics, overcoming their spectral sparsity. Here the authors provide the experimental demonstration of a widely tunable integrated frequency comb source unlocking the spectrum from the visible to the mid-infrared in a thin-film lithium niobate platform.

Dual-comb spectroscopy has been proven beneficial in molecular characterization but remains challenging in the mid-infrared region due to difficulties in sources and efficient photodetection. Here we introduce cross-comb spectroscopy, in which a mid-infrared comb is upconverted via sum-frequency generation with a near-infrared comb of a shifted repetition rate and then interfered with a spectral extension of the near-infrared comb. We measure CO 2 absorption around 4.25 µm with a 1-µm photodetector, exhibiting a 233-cm −1 instantaneous bandwidth, 28000 comb lines, a single-shot signal-to-noise ratio of 167 and a figure of merit of 2.4 × 10 6 Hz 1/2 . We show that cross-comb spectroscopy can have superior signal-to-noise ratio, sensitivity, dynamic range, and detection efficiency compared to other dual-comb-based methods and mitigate the limits of the excitation background and detector saturation. This approach offers an adaptable and powerful spectroscopic method outside the well-developed near-IR region and opens new avenues to high-performance frequency-comb-based sensing with wavelength flexibility. The authors introduce and demonstrate cross-comb spectroscopy in the mid-infrared as a variant of dual-comb spectroscopy. It provides enhanced performance and allows mid-infrared spectral information to be obtained by near-infrared detection.

Optical solitons have long been of interest both from a fundamental perspective and because of their application potential. Both cubic (Kerr) and quadratic nonlinearities can lead to soliton formation, but quadratic solitons can practically benefit from stronger nonlinearity and achieve substantial wavelength conversion. However, despite their rich physics, quadratic cavity solitons have been used only for broadband frequency comb generation, especially in the mid-infrared. Here, we show that the formation dynamics of mid-infrared quadratic cavity solitons, specifically temporal simultons in optical parametric oscillators, can be effectively leveraged to enhance molecular sensing. We demonstrate significant sensitivity enhancement while circumventing constraints of traditional cavity enhancement mechanisms. We perform experiments sensing CO 2 using cavity simultons around 4 μm and achieve an enhancement of 6000. Additionally, we demonstrate large sensitivity at high concentrations of CO 2 , beyond what can be achieved using an equivalent high-finesse linear cavity by orders of magnitude. Our results highlight a path for utilizing quadratic cavity nonlinear dynamics and solitons for molecular sensing beyond what can be achieved using linear methods. Optical molecular sensors benefit many applications from fundamental science to industry. In this work, the authors leverage the formation dynamics of cavity solitons to achieve molecular sensing in the mid-infrared spectral region.

Topological insulators possess protected boundary states which are robust against disorders and have immense implications in both fermionic and bosonic systems. Harnessing these topological effects in nonequilibrium scenarios is highly desirable and has led to the development of topological lasers. The topologically protected boundary states usually lie within the bulk bandgap, and selectively exciting them without inducing instability in the bulk modes of bosonic systems is challenging. Here, we consider topological parametrically driven nonlinear resonator arrays that possess complex eigenvalues only in the edge modes in spite of the uniform pumping. We show parametric oscillation occurs in the topological boundary modes of one and two dimensional systems as well as in the corner modes of a higher order topological insulator system. Furthermore, we demonstrate squeezing dynamics below the oscillation threshold, where the quantum properties of the topological edge modes are robust against certain disorders. Our work sheds light on the dynamics of weakly nonlinear topological systems driven out-of-equilibrium and reveals their intriguing behavior in the quantum regime.

Coupled systems with multiple interacting degrees of freedom provide a fertile ground for emergent dynamics, which is otherwise inaccessible in their solitary counterparts. Here we show that coupled nonlinear optical resonators can undergo self-organization in their spectrum leading to a first-order phase transition. We experimentally demonstrate such a spectral phase transition in time-multiplexed coupled optical parametric oscillators. We switch the nature of mutual coupling from dispersive to dissipative and access distinct spectral regimes of the parametric oscillator dimer. We observe abrupt spectral discontinuity at the first-order transition point. Furthermore, we show how non-equilibrium phase transitions can lead to enhanced sensing, where the applied perturbation is not resolvable by the underlying linear system. Our approach could be exploited for sensing applications that use nonlinear driven-dissipative systems, leading to performance enhancements without sacrificing sensitivity.Dispersive coupling between two optical parametric oscillators induces a first-order phase transition in the system at a critical detuning. This manifests as a discontinuity in the dimer’s spectrum, which may be useful for enhanced sensing.

Optical nonlinear functions are crucial for various applications in integrated photonics, including all-optical information processing1, photonic neural networks2,3 and on-chip ultrafast light sources4,5. However, the weak native nonlinearity of most nanophotonic platforms has imposed barriers for such functions by necessitating large driving energies, high-Q cavities or integration with other materials with stronger nonlinearity. Here we effectively utilize the strong and instantaneous quadratic nonlinearity of lithium niobate nanowaveguides for the realization of cavity-free all-optical switching. By simultaneous engineering of the dispersion and quasi-phase matching, we design and demonstrate a nonlinear splitter that can achieve ultralow switching energies down to 80 fJ, featuring a fastest switching time of ~46 fs and a lowest energy–time product of 3.7 × 10−27 J s in integrated photonics. Our results can enable on-chip ultrafast and energy-efficient all-optical information processing, computing systems and light sources.Researchers exploit the quadratic nonlinearity of lithium niobate nanowaveguides and demonstrate cavity-free all-optical switching. Switching energies down to 80 fJ, switching times down to ~46 fs and energy–time products of 3.7 × 10−27 J s are shown.

New physics and novel applications in various fields ranging from biology, and spectroscopy, to manipulation of quantum systems are driven by the availability of coherent light sources including frequency combs in the visible and mid-infrared spectral regimes. Nonlinear optical systems, that are parametrically driven by technologically mature near-infrared lasers, are leveraged in this regard to access challenging wavelengths where conventional lasers may be unavailable. It is of paramount importance to miniaturize these systems and replace the traditional bulky setups thereby paving the way for a plethora of applications. Optical parametric oscillators are among the most prominent examples of such nonlinear systems and beyond their indispensable usage as light sources (both classical and quantum) their unique non-equilibrium dynamics can endow a wealth of functionalities absent in their linear counterparts. These properties can be engineered and utilized for realizing highly sensitive sensors as well as special-purpose computing hardware that may outperform conventional digital computers. A network of these coupled parametric oscillators can be made to interact leading to emergent behaviors that are not expected from the individual constituents.In this work, we experimentally and theoretically study the dynamics of individual and coupled optical parametric oscillators towards sensing and computing applications. We explore a previously avoided regime of operation for generating ultra-short pulses from these parametrically driven nonlinear resonators that lead to extreme pulse compression. We engineer the nonlinear dynamics of these systems to realize all-optical spectral phase transitions (both first-order and second-order) that behave as highly-sensitive sensors. We show how these critical phenomena can be utilized to enhance the solution accuracy of physics-based solvers in finding optimum solutions to combinatorial optimization problems in the context of coherent Ising machines. We also realize optical parametric oscillators in integrated lithium-niobate nanophotonic platform and demonstrate a mid-infrared frequency comb source that is widely tunable over an octave accompanied by visible frequency comb generation. We develop a comprehensive description to investigate the noise properties of optical parametric oscillators that provide new insights into the phase noise behavior of optical parametric oscillators in their various operating regimes. Finally, we propose a system of parametrically driven resonators as a synthetic medium with highly reconfigurable interactions that can host a plethora of emergent phenomena ranging from topological behaviors to non-Hermitian dynamics. These networks of nonlinear resonators display intriguing dynamical properties in contrast to their static counterparts in condensed-matter physics with implications in quantum sensing and robust device functionality.