Quadratic Solitons Research Articles

Quadratic-soliton-enhanced mid-IR molecular sensing

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 CO2 using cavity simultons around 4 μm and achieve an enhancement of 6000. Additionally, we demonstrate large sensitivity at high concentrations of CO2, 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.

Broadband frequency comb generation through cascaded quadratic nonlinearity in thin-film lithium niobate microresonators.

Broadband frequency comb generation through cascaded quadratic nonlinearity remains experimentally untapped in free-space cavities with bulk χ(2) materials mainly due to the high threshold power and restricted ability of dispersion engineering. Thin-film lithium niobate (LN) is a good platform for nonlinear optics due to the tight mode confinement in a nano-dimensional waveguide, the ease of dispersion engineering, large quadratic nonlinearities, and flexible phase matching via periodic poling. Here we demonstrate broadband frequency comb generation through dispersion engineering in a thin-film LN microresonator. Bandwidths of 150 nm (80 nm) and 25 nm (12 nm) for center wavelengths at 1560 and 780 nm are achieved, respectively, in a cavity-enhanced second-harmonic generation (doubly resonant optical parametric oscillator). Our demonstration paves the way for pure quadratic soliton generation, which is a great complement to dissipative Kerr soliton frequency combs for extended interesting nonlinear applications.

Routing to mid-infrared microcomb via near-infrared direct pump.

Mid-infrared (MIR) microcomb provides a new way into the "molecular fingerprint" region. However, it remains rather a challenge to realize the broadband mode-locked soliton microcomb, which is often limited by the performance of available MIR pump sources and coupling devices. Here, we propose an effective approach towards broadband MIR soliton microcombs generation via a direct pump in the near-infrared (NIR) region, through full utilization of the second- and third-order nonlinearities in a thin-film lithium niobate microresonator. The optical parametric oscillation process contributes to conversion from the pump at 1550 nm to the signal around 3100 nm, and the four-wave mixing effect promotes spectrum expansion and mode-locking process. While the second-harmonic and sum-frequency generation effects facilitate simultaneous emission of the NIR comb teeth. Both the continuous wave and pulse pump sources with relatively low power can support a MIR soliton with a bandwidth over 600 nm and a concomitant NIR microcomb with a bandwidth of 100 nm. This work can provide a promising solution for broadband MIR microcombs by breaking through the limitation of available MIR pump sources, and can deepen the understanding of the physical mechanism of the quadratic soliton assisted by the Kerr effect.

Robust Pulse-Pumped Quadratic Soliton Assisted by Third-Order Nonlinearity

The generation of a quadratic soliton in a pulse-pumped microresonator has attracted significant interest in recent years. The strong second-order nonlinearity and high peak power of pumps offer a straightforward way to increase efficiency. In this case, the influence of the third-order nonlinearity effect becomes significant and cannot be ignored. In this paper, we study the quadratic soliton in a degenerate optical parametric oscillator driven synchronously by the pulse pump with third-order nonlinearity. Our simulations verify that the robustness of quadratic soliton generation is enhanced when the system experiences a perturbation from pump power, cavity detuning, and pump pulse width. These results represent a new way of manipulating frequency comb in resonant microphotonic structures.

High‐Power Mid‐IR Few‐Cycle Frequency Comb from Quadratic Solitons in an Optical Parametric Oscillator

AbstractPowerful 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, the generation of an intrinsically locked frequency comb source centered at 4.18 µm from an optical parametric oscillator (OPO) operating in the simulton regime is reported, in which formation of purely quadratic solitons leads to enhanced performance. Advantages of operation in the simulton regime in direct experimental comparisons to the conventional regime are shown, which are also supported by simulation and theory. 565 mW of average power, 900 nm of instantaneous 3 dB bandwidth, 350% slope efficiency, and 44% conversion efficiency are achieved, a performance that is superior to previous OPO demonstrations and other sources in this wavelength range. Here, a new avenue toward MIR frequency comb generation with high power and efficiency is opened, and the great potential of soliton generation based on quadratic nonlinearity in the MIR spectral region is suggested.

Temporal walk-off induced dissipative quadratic solitons

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.

Fundamental and vortex dissipative quadratic solitons supported by spatially localized gain

We consider settings providing the existence of stable two-dimensional (2D) dissipative solitons with zero and nonzero vorticity in optical media with the quadratic ($\chi^{(2)}$) nonlinearity. To compensate the spatially uniform loss in both the fundamental-frequency (FF) and second-harmonic (SH) components of the system, a strongly localized amplifying region ("hot spot",HS), carrying the linear gain, is included, acting onto either the FF component or SH one. In both cases, the Gaussian radial gain profile supports stable fundamental dissipative solitons pinned to the HS. The structure of existence and stability domains for the 2D solitons is rather complex. They demonstrate noteworthy features, such as bistability and spontaneous symmetry breaking. A ring-shaped gain profile acting onto the FF component supports stable vortex solitons, with the winding number up to 5, and multipoles. Nontrivial transformation of vortex-soliton profiles upon either growth of the gain value or stretching the gain profile is observed.

Influence of cubic nonlinearity effect on quadratic solitons in boundary-constrained self-focusing oscillatory response function system

In this paper, we theoretically study the influence of cubic nonlinearity effect on quadratic solitons in the boundary-constrained self-focusing oscillatory response function system. Based on the Newton iteration approach, we numerically solve the nonlinear coupled-wave equations with both quadratic and cubic nonlinearity. Moreover, a family of quadratic solitons is obtained. By comparing the quadratic solitons with both quadratic and cubic nonlinearity with those with only quadratic nonlinearity, we find that the cubic nonlinearity changes the transverse distribution of the soliton profiles only slightly. However, because of the existence of the cubic nonlinearity, quadratic solitons can be found only in the strongly nonlocal case and general nonlocal case, and they cannot be found in the weakly nonlocal case, in which the quadratic solitons with only quadratic nonlinearity can be found. In addition, the existence of cubic nonlinearity reduces the number of extended half-periods of the quadratic solitons. Through the linear stability analysis of the obtained soliton solutions, it is found that the stability intervals of solitons are also shrunk due to the existence of the cubic nonlinearity. The results of the linear stability analysis are verified by the numerical simulations of soliton propagations through using the split-step Fourier method.

Floquet Edge Multicolor Solitons

AbstractTopological insulators are unique physical structures that are insulators in their bulk, but support currents at their edges which can be unidirectional and topologically protected from scattering on disorder and inhomogeneities. Photonic topological insulators can be crafted in materials that exhibit a strong nonlinear response, thus opening the door to the exploration of the interplay between nonlinearity and topological effects. Among the fascinating new phenomena arising from this interplay is the formation of topological edge solitons—hybrid asymmetric states localized across and along the interface due to different physical mechanisms. Such solitons have so far been studied only in materials with Kerr‐type, or cubic, nonlinearity. Here, the first example of the topological edge soliton supported by parametric interactions in nonlinear media is presented. Such solitons exist in Floquet topological insulators realized in arrays of helical waveguides made of a phase‐matchable material. Floquet edge solitons bifurcate from topological edge states in the spectrum of the fundamental frequency wave and remain localized over propagation distances drastically exceeding the helix period, while travelling along the edge of the structure. A theory of such states is developed. It is shown that multicolor solitons in a Floquet system exists in the vicinity of (formally infinite) set of linear resonances determined by the Floquet phase matching conditions. Away from resonance, soliton envelopes can be described by a period‐averaged single nonlinear Schrödinger equation with an effective cubic nonlinear coefficient whose magnitude and sign depend on the overall phase‐mismatch between the fundamental frequency and second harmonic waves. Such total phase‐mismatch includes the intrinsic mismatch and the geometrically‐induced mismatch introduced by the array, and its value reveals one of the genuine effects exhibited by the Floquet quadratic solitons. The results open fundamental new prospects for the exploration of a range of parametric frequency‐mixing phenomena in photonic Floquet quadratic nonlinear media.

Quadratic Solitons in Singly Resonant Degenerate Optical Parametric Oscillators

By identifying the similarities between the coupled-wave equations and the parametrically driven nonlinear Schr\odinger equation, we show the existence conditions of quadratic solitons in continuous-wave pumped singly resonant degenerate optical parametric oscillators (SRDOPOs). Compared to the previously explored doubly resonant DOPOs, quadratic solitons in SRDOPOs are advantageous in their robustness against perturbations induced by dispersion of the effective third-order nonlinearity and temporal walk-off between the signal and the pump. Terahertz comb bandwidth and femtosecond pulse duration are attainable in an example periodically poled Lithium niobate waveguide resonator in the short-wave infrared. The working principle can be extended to other material platforms, making it a competitive ultrashort pulse and broadband comb source architecture at the mid-infrared spectral range.

Quadratic soliton mode-locked degenerate optical parametric oscillator.

We examine the existence condition of the quadratic soliton mode-locked degenerate optical parametric oscillator in the previously unexplored parameter space. We study the nature of the quadratic solitons and divide their dynamics into two distinctive branches, depending on the system parameters. Origin of the quadratic soliton perturbation is identified, and strategy to mitigate its detrimental effect is developed. Frequency comb with terahertz bandwidth and femtosecond pulse duration are attainable in an example periodically poled lithium niobate waveguide resonator. Design rules of the quadratic soliton mode-locking are summarized. The principle can be further extended to other material platforms, making it a competitive ultrashort pulse and broadband comb source architecture at the mid-infrared.

Quadratic Soliton Combs in Doubly Resonant Dispersive Optical Parametric Oscillators

We present temporal quadratic solitons in doubly resonant temporal dispersive optical parametric oscillators without a walk-off in numerical simulations. In frequency domain, these cavity solitons correspond to coherent dual-combs with smooth envelopes in half-harmonic and pump fields. We also investigate the soliton existence region, and the soliton behavior with parameters in this cavity system. We believe our work offers valuable insights into the practical generation of quadratic soliton combs in optical parametric oscillators.

Temporal quadratic solitons and their interaction with dispersive waves in lithium niobate nanowaveguides

Optical solitons are self-stabilizing structures in which nonlinear effects counteract dispersion or diffraction. The dynamics of optical Kerr solitons, and in particular their interactions with low-amplitude radiation, have previously been shown to be crucial in understanding super continuum generation in optical fibers. Here the authors present a theory of interaction of quadratic solitons with radiation, and demonstrate that such phenomena can be observed in newly emerging Lithium Niobate nano-waveguides.

A simple approach to study the boundary-induced trajectory evolution of spatial nonlocal quadratic solitons: Based on the Green’s function method

Based on the Green’s function method, we propose a simple and time saving approach to study the boundary-induced trajectory of the bell-like bright quadratic solitons. The results obtained from the proposed approach approximate well to those obtained from the direct numerical simulation of the full model equations, which are precise but suffer from time consuming. Based on the proposed approach, it is revealed that the boundary-induced zigzag trajectory of the soliton is affected by several aspects, including the degree of nonlocality, the sample width, the initial displacement of the soliton from the boundary, and the oblique degree of the incident field.

Quadratic soliton combs in doubly resonant second-harmonic generation.

We report a theoretical investigation of quadratic frequency combs in a dispersive second-harmonic generation cavity system. We identify different dynamical regimes and demonstrate that the same system can exhibit both bright and dark localized cavity solitons in the absence of a temporal walk-off.

Boundary enhanced effects on the existence of quadratic solitons

We investigate, both analytically and numerically, the boundary enhanced effects exerted on the quadratic solitons consisting of fundamental waves and oscillatory second harmonics in the presence of boundary conditions. The nonlocal analogy predicts that the soliton for fundamental wave is supported by the balance between equivalent nonlinear confinement and diffraction (or dispersion). Under Snyder and Mitchell’s strongly nonlocal approximation, we obtain the analytical soliton solutions both with and without the boundary conditions to show the impact of boundary conditions. We can distinguish explicitly the nonlinear confinement between the second harmonic mutual interaction and the enhanced effects caused by remote boundaries. Those boundary enhanced effects on the existence of solitons can be positive or negative, which depend on both sample size and nonlocal parameter. The piecewise existence regime of solitons can be explained analytically. The analytical soliton solutions are verified by the numerical ones and the discrepancy between them is also discussed.

Dark-bright quadratic solitons with a focusing effective Kerr nonlinearity

Dark-bright quadratic solitons with a focusing effective Kerr nonlinearity

Bright nonlocal quadratic solitons induced by boundary confinement

Under the Dirichlet boundary conditions, a family of bright quadratic solitons exists in the regime where the second harmonic can be regarded as the refractive index of the fundamental wave with an oscillatory nonlocal response. By simplifying the governing equations into the Snyder-Mitchell mode, the approximate analytical solutions are obtained. Taking them as the initial guess and using a numerical code, we found two branches of bright solitons, of which the beam width increases (branch I) and decreases (branch II) with the increase of the sample size, respectively. If the nonlocality is fixed and the sample size is varied, the soliton width varies piecewise and approximately periodically. In each period, solitons only exist in a small range of sample size. Single-hump fundamental wave solitons with the same beam width in narrower samples can be, if the second harmonics are connected smoothly, jointed to be a multihump soliton in a wider sample whose size is the sum of those for the narrower ones. The dynamical simulation shows that the found solitons are unstable.

Femtosecond mode locking based on adiabatic excitation of quadratic solitons

We demonstrate a new approach for pulse formation in mode-locked lasers, based on exciting intracavity solitons in a two-dimensionally patterned quasi-phase-matching (QPM) grating. Through an adiabatic following process enabled by an apodized QPM crystal, we transiently excite multicolor nonlinear states within the crystal, utilize their advantageous properties for pulse formation and stabilization, and then convert the energy back to the resonating laser pulse before the end of the crystal in order to suppress losses. This idea gives access to large nonlinearities that would otherwise be too lossy for use intracavity. In our case, the states accessed are self-defocusing Kerr-like nonlinearities based on phase-mismatched second-harmonic generation. The QPM device has an additional transverse gradient, for tuning the nonlinearity and to aid in laser self-starting. We demonstrate the technique in a semiconductor saturable absorber mirror mode-locked laser with Yb:CALGO as the gain medium, producing 100 fs pulses at 540 MHz repetition rate, with 760 mW of average output power. We present comprehensive theoretical and numerical modeling of the laser to understand the new mode-locking regime. Our approach offers a flexible and compact route to managing nonlinearities inside laser cavities while suppressing the losses that could otherwise prevent or deteriorate mode-locked operation, and is particularly interesting for highly compact bulk, fiber, and waveguide lasers with gigahertz repetition rates and operating wavelengths from the near- to mid-infrared spectral regions.

Stable quadratic solitons consisting of fundamental waves and oscillatory second harmonics subject to boundary confinement

We investigate quadratic solitons consisting of fundamental waves and oscillatory second harmonics, which can be stable when subject to boundary confinement. A family of quadratic solitons whose fundamental waves can be monopole, dipole, or even multipole are found numerically. The existence of solitons, depending on the sample size and degree of nonlocality, are given for strongly, generally, and weakly nonlocal cases, respectively.