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Arrays of nonlinear resonators offer a fertile ground for a wide range of complex phenomena and opportunities for advanced photonic sensing and computing. Recently, significant attention has focused on studying coupled resonators in special-purpose configurations either on chips or in table-top experiments. However, a path to realizing a large-scale programmable network of nonlinear photonic resonators remains elusive because of the challenges associated with simultaneously achieving strong nonlinearity, independent operation of the resonators, and programmability of the couplings. In this work, we break these barriers by realizing large-scale, time-multiplexed optical parametric oscillators (OPOs) on a single lithium niobate nanophotonic chip. We show independent operation of 70 identical OPOs in an ultrafast nanophotonic circuit. The OPOs exhibit an ultra-low threshold of a few picojoules, substantially surpassing the strength of nonlinearity of other platforms. Using our ultrafast nanophotonic circuit, a network of N OPOs with programmable all-to-all couplings requires only a few additional components. The time-multiplexed nanophotonic OPOs can enable myriad applications, including ultrafast classical and quantum information processing., Comment: 19 pages, 5 figures

Traditional absorption spectroscopy has fundamental difficulty in resolving small absorbance from strong background due to the instability of laser sources. Existing background-free methods in broadband vibrational spectroscopy help to alleviate this problem but face challenges in realizing either low extinction ratios or time-resolved field measurements. Here, we introduce optical-parametric-amplification-enhanced background-free spectroscopy, in which the excitation background is first suppressed by an interferometer and then the free-induction decay that carries molecular signatures is selectively amplified. We show that this method can further improve the limit of detection in linear interferometry by order(s) of magnitude without requiring lower extinction ratios or time-resolved measurement, which can benefit sensing applications in detecting trace species., Comment: 11 pages, 5 figures

Mode-locked lasers (MLLs) have enabled ultrafast sciences and technologies by generating ultrashort pulses with peak powers substantially exceeding their average powers. Recently, tremendous efforts have been focused on realizing integrated MLLs not only to address the challenges associated with their size and power demand, but also to enable transforming the ultrafast technologies into nanophotonic chips, and ultimately to unlock their potential for a plethora of applications. However, till now the prospect of integrated MLLs driving ultrafast nanophotonic circuits has remained elusive because of their typically low peak powers, lack of controllability, and challenges with integration with appropriate nanophotonic platforms. Here, we overcome these limitations by demonstrating an electrically-pumped actively MLL in nanophotonic lithium niobate based on its hybrid integration with a III-V semiconductor optical amplifier. Our MLL generates $\sim$4.8 ps optical pulses around 1065 nm at a repetition rate of $\sim$10 GHz, with pulse energy exceeding 2.6 pJ and a high peak power beyond 0.5 W. We show that both the repetition rate and the carrier-envelope-offset of the resulting frequency comb can be flexibly controlled in a wide range using the RF driving frequency and the pump current, paving the way for fully-stabilized on-chip frequency combs in nanophotonics. Our work marks an important step toward fully-integrated nonlinear and ultrafast photonic systems in nanophotonic lithium niobate.

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-IR. Here, we show that the formation dynamics of mid-IR quadratic cavity solitons 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 quadratic cavity solitons around 4 $\mu$m and achieve an equivalent path length 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., Comment: 22 pages, 4 figures

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 frequency combs tunable from visible to mid-infrared on a single chip based on ultra-widely tunable optical parametric oscillators in lithium niobate nanophotonics. Using picosecond-long pump pulses around 1 $\mu$m and tuning of the quasi-phase matching, we show sub-picosecond frequency combs tunable beyond an octave extending from 1.5 $\mu$m up to 3.3 $\mu$m with femtojoule-level thresholds. 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 nanophotonic source can be combined with an on-chip picosecond source as its pump, as well as pulse shortening and spectral broadening mechanisms at its output, all of which are readily available in lithium niobate nanophotonics. Our results highlight a practical and universal path for the realization of efficient frequency comb sources in nanophotonics overcoming their spectral sparsity.

Phase transitions and the associated symmetry breaking are at the heart of many physical phenomena. Coupled systems with multiple interacting degrees of freedom provide a fertile ground for emergent dynamics that 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 which can pave the way for the realization of novel transition-edge sensors. 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 results can pave the way for sensing using nonlinear driven-dissipative systems leading to performance enhancements without sacrificing sensitivity.

Powerful and efficient optical frequency combs in the mid-infrared (MIR) spectral region are highly desirable for a broad range of applications. Despite extensive efforts utilizing various techniques, MIR frequency comb sources are still lacking power, efficiency, or bandwidth for many applications. Here, we report the generation of an intrinsically locked frequency comb source centered at 4.18 {\mu}m from an optical parametric oscillator (OPO) operating in the simulton regime, in which formation of purely quadratic solitons lead to enhanced performance. We show advantages of operation in the simulton regime in direct experimental comparisons to the conventional regime, which are also supported by simulation and theory. We achieve 565 mW of average power, 900 nm of instantaneous 3-dB bandwidth, 350% of slope efficiency, and 44% of conversion efficiency; a performance that is superior to previous OPO demonstrations and other sources in this wavelength range. This work opens a new avenue toward MIR frequency comb generation with high power and efficiency and suggests the great potential of soliton generation based on quadratic nonlinearity in the MIR spectral region., Comment: 12 pages, 6 figures (main text); 3 pages, 0 figure (supplementary materials)

Widely-tunable coherent sources are desirable in nanophotonics for a multitude of applications ranging from communications to sensing. The mid-infrared spectral region (wavelengths beyond 2 $\mu$m) is particularly important for applications relying on molecular spectroscopy. Among tunable sources, optical parametric oscillators typically offer some of the broadest tuning ranges; however, their implementations in nanophotonics have been limited to narrow tuning ranges and only at visible and near-infrared wavelengths. Here, we surpass these limits in dispersion-engineered periodically-poled lithium niobate nanophotonics and demonstrate ultra-widely tunable optical parametric oscillators. With a pump wavelength near 1 $\mu$m, we generate output wavelengths tunable from 1.53 $\mu$m to 3.25 $\mu$m in a single chip with output powers as high as tens of milliwatts. Our results represent the first octave-spanning tunable source in nanophotonics extending into the mid-infrared which can be useful for numerous integrated photonic applications.

One of the most fundamental quantum states of light is squeezed vacuum, in which noise in one of the quadratures is less than the standard quantum noise limit. Significant progress has been made in the generation of optical squeezed vacuum and its utilization for numerous applications. However, it remains challenging to generate, manipulate, and measure such quantum states in nanophotonics with performances required for a wide range of scalable quantum information systems. Here, we overcome this challenge in lithium niobate nanophotonics by utilizing ultrashort-pulse phase-sensitive amplifiers for both generation and all-optical measurement of squeezed states on the same chip. We generate a squeezed state spanning over more than 25 THz of bandwidth supporting only a few optical cycles, and measure a maximum of 4.9 dB of squeezing ($\sim$11 dB inferred). This level of squeezing surpasses the requirements for a wide range of quantum information systems. Our results on generation and measurement of few-optical-cycle squeezed states in nanophotonics enable a practical path towards scalable quantum information systems with THz clock rates and open opportunities for studying non-classical nature of light in the sub-cycle regime., Comment: 8 pages, 4 figures

A plethora of applications have recently motivated extensive efforts on the generation of low noise Kerr solitons and coherent frequency combs in various platforms ranging from fiber to whispering gallery and integrated microscale resonators. However, the Kerr (cubic) nonlinearity is inherently weak, and in contrast, strong quadratic nonlinearity in optical resonators is expected to provide an alternative means for soliton formation with promising potential. Here, we demonstrate the formation of a dissipative quadratic soliton via non-stationary optical parametric amplification in the presence of significant temporal walk-off between pump and signal leading to half-harmonic generation accompanied by a substantial pulse compression (exceeding a factor of 40) at low pump pulse energies ($\sim$ 4 picojoules). The bright quadratic soliton forms in a low-finesse cavity in both normal and anomalous dispersion regimes, which is in stark contrast with bright Kerr solitons. We present a route to significantly improve the performance of the demonstrated quadratic soliton when extended to an integrated nonlinear 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 that are widely tunable from ultra-violet to mid-infrared spectral regimes.

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 non-equilibrium 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.

Optical nonlinear functions are crucial for various applications in integrated photonics, such as all-optical information processing, photonic neural networks and on-chip ultrafast light sources. Due to the weak nonlinearities in most integrated photonic platforms, realizing optical nonlinear functions typically requires large driving energies in the picojoules level or beyond, thus imposing a barrier for most applications. Here, we tackle this challenge and demonstrate an integrated nonlinear splitter device in lithium niobate nano-waveguides by simultaneous engineering of the dispersion and quasi-phase matching. We achieve non-resonant all-optical switching with ultra-low energies down to tens of femtojoules, a near instantaneous switching time of 18 fs, and a large extinction ratio of more than 5 dB. Our nonlinear splitter simultaneously realizes switch-on and -off operations and features a state-of-the-art switching energy-time product as low as $1.4 \times10^{-27}$ J$\cdot$s. We also show a path toward attojoule level all-optical switching by further optimizing the device geometry. Our results can enable on-chip ultrafast and energy-efficient all-optical information processing, computing systems, and light sources.

Dual-comb spectroscopy has been proven a powerful tool in molecular characterization, which remains challenging to implement in the mid-infrared region due to difficulties in the realization of two mutually locked comb sources and efficient photodetection. Moreover, the detection capability of dual-comb spectroscopy is fundamentally limited by the strong excitation background and detector saturation. Here we introduce a variant of dual-comb spectroscopy called 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 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 avoid the limits of the background excitation and detector saturation. We experimentally demonstrate a proof-of-concept measurement of atmospheric CO2 around 4.25 $\mu$m, with a 233-$cm^{-1}$ instantaneous bandwidth, 28000 comb lines, a single-shot SNR of 167, and a figure of merit of $2.4\times10^{6} Hz^{1/2}$. Cross-comb spectroscopy can be realized using up- or down-conversion and offers an adaptable and powerful spectroscopic method outside the well-developed near-IR region. This approach opens new avenues to high-performance molecular sensing with wavelength flexibility, which can impact a wide swath of applications., Comment: 12 pages, 5 figures (main text); 34 pages, 14 figures (supplementary materials)

High-index dielectrics can confine light into nano-scale leading to enhanced nonlinear response. However, increased momentum in these media can deteriorate the overlap between different harmonics which hinders efficient nonlinear interaction in wavelength-scale resonators in the absence of momentum matching. Here, we propose an alternative approach for light confinement in anisotropic particles. The extra degree of freedom in anisotropic media allows us to control the evanescent waves near the center and the radial momentum away from the center, independently. This can lead to a strong light confinement as well as an excellent field overlap between different harmonics which is ideal for nonlinear wavelength conversion. Controlling the evanescent fields can also help to surpass the constrains on the radiation bandwidth of isotropic dielectric antennas. This can improve the light coupling into these particles, which is crucial for nano-scale nonlinear optics. We estimate the second-harmonic generation efficiency as well as optical parametric oscillation threshold in these particles to show the strong nonlinear response in these particles even away from the center of resonances. Our approach is promising to be realized experimentally and can be used for many applications, such as large-scale parallel sensing and computing.

Engineered non-Hermitian systems featuring exceptional points can lead to a host of extraordinary phenomena in diverse fields ranging from photonics, acoustics, opto-mechanics, electronics, to atomic physics. Here we introduce and present non-Hermitian dynamics of coupled optical parametric oscillators (OPOs) arising from phase-sensitive amplification and de-amplification, and show their distinct advantages over conventional non-Hermitian systems relying on laser gain and loss. OPO-based non-Hermitian systems can benefit from the instantaneous nature of the parametric gain, noiseless phase-sensitive amplification, and rich quantum and classical nonlinear dynamics. We show that two coupled OPOs can exhibit spectral anti-PT symmetry and an exceptional point between its degenerate and non-degenerate operation regimes. To demonstrate the distinct potentials of the coupled OPO system compared to conventional non-Hermitian systems, we present higher-order exceptional points with two OPOs, tunable Floquet exceptional points in a reconfigurable dynamic non-Hermitian system, and generation of squeezed vacuum around exceptional points, all of which are not easy to realize in other non-Hermitian platforms. Our results show that coupled OPOs are an outstanding non-Hermitian setting with unprecedented opportunities in realizing nonlinear dynamical systems for enhanced sensing and quantum information processing.

Spectral behaviors of photonic resonators have been the basis for a range of fundamental studies, with applications in classical and quantum technologies. 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, map its dynamics to the universal Swift-Hohenberg equation, and extend it to Kerr OPOs. To emphasize the fundamental importance and consequences of this phase transition, 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.

Despite recent progress in nonlinear optics in wavelength-scale resonators, there are still open questions on the possibility of parametric oscillation in such resonators. We present a general approach to predict the behavior and estimate the oscillation threshold of multi-mode subwavelength and wavelength-scale optical parametric oscillators (OPOs). As an example, we propose an OPO based on Mie-type multipolar resonances, and we demonstrate that due to the low-Q nature of multipolar modes in wavelength-scale resonators, there is a nonlinear interaction between these modes. As a result, the OPO threshold, compared to the single-mode case, can be reduced by a factor that is significantly larger than the number of interacting modes. The multi-mode interaction can also lead to a phase transition manifested through a sudden change in the parametric gain as well as the oscillation threshold, which can be utilized for enhanced sensing. We establish an explicit connection between the second-harmonic generation efficiency and the OPO threshold. This allows us to estimate the OPO threshold based on measured or simulated second-harmonic generation in different classes of resonators, such as bound states in the continuum and inversely designed resonators. Our approach for analyzing and modeling miniaturized OPOs can open unprecedented opportunities for classical and quantum nonlinear photonics.

Continuous-wave pumped optical microresonators have been vastly exploited to generate frequency comb (FC) utilizing the Kerr nonlinearity. Most of the nonlinear materials used to build photonic platforms exhibit nonlinear losses such as multi-photon absorption, free-carrier absorption (FCA), and free-carrier dispersion (FCD) which can strongly affect the nonlinear characteristics of the devices made out of these materials. In this work, we model the Kerr FC based on modified Lugiato-Lefever Equation (LLE) along with the rate equation and develop analytical formulations to make quick estimations of the steady-state, modulation instability (MI) gain, bandwidth and the dynamics of Kerr Frequency-Comb (FC) in presence of nonlinear losses. Our analytical model is valid over a broad wavelength range of interest as it includes the effects of all nonlinear losses. Higher order (>3) characteristic polynomial of intra-cavity power describing the steady-state homogeneous solution of the modified LLE are discussed in detail. We derive the generalized analytical expressions for the threshold of normalized pump detuning to initiate the optical bistability which is a necessary condition for the FC generation. Free-carrier dispersion-led nonlinear cavity detuning is observed through the reverse Kerr-tilt of the resonant-peaks. We further deduce the expressions for the threshold pump intensity and the range of possible cavity detuning for the initiation of the MI when all the nonlinear losses are present. To corroborate our analytical findings, LLE along with the rate equations are solved numerically through split-step Fourier method. Our theoretical study can explain several experimental results which are previously reported and thereby is able to provide a better understanding of the comb dynamics.