skip to main content

Title: Nonlinear interactions between vibration modes with vastly different eigenfrequencies

Nonlinear interactions between modes with eigenfrequencies that differ by orders of magnitude are ubiquitous in various fields of physics, ranging from cavity optomechanics to aeroelastic systems. Simplifying their description to a minimal model and grasping the essential physics is typically a system-specific challenge. We show that the complex dynamics of these interactions can be distilled into a single generic form, namely, the Stuart-Landau oscillator. With our model, we study the injection locking and frequency pulling of a low-frequency mode interacting with a blue-detuned high-frequency mode, which generate frequency combs. Such combs are tunable around both the high and low carrier frequencies. By discussing the analogy with a simple mechanical system model, we offer a minimalistic conceptual view of these complex interactions originating the frequency combs, together with showcasing their frequency tunability.

more » « less
Author(s) / Creator(s):
Publisher / Repository:
Nature Publishing Group
Date Published:
Journal Name:
Communications Physics
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Mid-infrared (MIR) spectrometers are invaluable tools for molecular fingerprinting and hyper-spectral imaging. Among the available spectroscopic approaches, GHz MIR dual-comb absorption spectrometers have the potential to simultaneously combine the high-speed, high spectral resolution, and broad optical bandwidth needed to accurately study complex, transient events in chemistry, combustion, and microscopy. However, such a spectrometer has not yet been demonstrated due to the lack of GHz MIR frequency combs with broad and full spectral coverage. Here, we introduce the first broadband MIR frequency comb laser platform at 1 GHz repetition rate that achieves spectral coverage from 3 to 13 µm. This frequency comb is based on a commercially available 1.56 µm mode-locked laser, robust all-fiber Er amplifiers and intra-pulse difference frequency generation (IP-DFG) of few-cycle pulses inχ(2)nonlinear crystals. When used in a dual comb spectroscopy (DCS) configuration, this source will simultaneously enable measurements with μs time resolution, 1 GHz (0.03 cm−1) spectral point spacing and a full bandwidth of >5 THz (>166 cm−1) anywhere within the MIR atmospheric windows. This represents a unique spectroscopic resource for characterizing fast and non-repetitive events that are currently inaccessible with other sources.

    more » « less
  2. Abstract

    Dissipative Kerr solitons in resonant frequency combs offer a promising route for ultrafast mode-locking, precision spectroscopy and time-frequency standards. The dynamics for the dissipative soliton generation, however, are intrinsically intertwined with thermal nonlinearities, limiting the soliton generation parameter map and statistical success probabilities of the solitary state. Here, via use of an auxiliary laser heating approach to suppress thermal dragging dynamics in dissipative soliton comb formation, we demonstrate stable Kerr soliton singlet formation and soliton bursts. First, we access a new soliton existence range with an inverse-sloped Kerr soliton evolution—diminishing soliton energy with increasing pump detuning. Second, we achieve deterministic transitions from Turing-like comb patterns directly into the dissipative Kerr soliton singlet pulse bypassing the chaotic states. This is achieved by avoiding subcomb overlaps at lower pump power, with near-identical singlet soliton comb generation over twenty instances. Third, with the red-detuned pump entrance route enabled, we uncover unique spontaneous soliton bursts in the direct formation of low-noise optical frequency combs from continuum background noise. The burst dynamics are due to the rapid entry and mutual attraction of the pump laser into the cavity mode, aided by the auxiliary laser and matching well with our numerical simulations. Enabled by the auxiliary-assisted frequency comb dynamics, we demonstrate an application of automatic soliton comb recovery and long-term stabilization against strong external perturbations. Our findings hold potential to expand the parameter space for ultrafast nonlinear dynamics and precision optical frequency comb stabilization.

    more » « less
  3. Computationally efficient modeling of gas turbine combustion is challenging due to the chaotic multi-scale physics and the complex non-linear interactions between acoustic, hydrodynamic, and chemical processes. A large-eddy simulation (LES) is conducted for the model combustor of Meier et al. (1) using an unstructured mesh finite volume method with turbulent combustion effects modeled using a flamelet-based method. The flow field is validated via comparison to averaged and unsteady high-frequency particle image velocimetry (PIV) fields. A high degree of correlation is noted with the experiment in terms of flow field snapshots and via modal analysis. The dynamics of the precessing vortex core (PVC) is quantitatively characterized using dynamic mode decomposition. The validated FOM dataset is used to construct projection-based ROMs, which aim to reduce the system dimension by projecting the state onto a reduced dimensional linear manifold. The use of a structure-preserving least squares formulation (SP-LSVT) guarantees stability of the ROM, compared to traditional model reduction techniques. The SP-LSVT ROM provides accurate reconstruction of the combustion dynamics within the training region, but faces a significant challenge in future state predictions. This limitation is mainly due to the increased projection error, which in turn is a direct consequence of the highly chaotic nature of the flow field, involving a wide range of disperse coherent structures. Formal projection-based ROMs have not been applied to a problem of this scale and complexity, and achieving accurate and efficient ROMs is a grand challenge problem. Further advances in non-linear manifold projections or adaptive basis projections have the potential to improve the predictive capability of this class of ROMs. 
    more » « less
  4. Abstract

    Femtosecond mode-locked laser frequency combs have served as the cornerstone in precision spectroscopy, all-optical atomic clocks, and measurements of ultrafast dynamics. Recently frequency microcombs based on nonlinear microresonators have been examined, exhibiting remarkable precision approaching that of laser frequency combs, on a solid-state chip-scale platform and from a fundamentally different physical origin. Despite recent successes, to date, the real-time dynamical origins and high-power stabilities of such frequency microcombs have not been fully addressed. Here, we unravel the transitional dynamics of frequency microcombs from chaotic background routes to femtosecond mode-locking in real time, enabled by our ultrafast temporal magnifier metrology and improved stability of dispersion-managed dissipative solitons. Through our dispersion-managed oscillator, we further report a stability zone that is more than an order-of-magnitude larger than its prior static homogeneous counterparts, providing a novel platform for understanding ultrafast dissipative dynamics and offering a new path towards high-power frequency microcombs.

    more » « less

    Observations of historical tsunami earthquakes reveal that ruptures of these earthquakes propagate slowly at shallow depth with longer duration, depletion in high-frequency radiation and larger discrepancy of Mw–Ms than ordinary megathrust earthquakes. They can effectively generate tsunami and lead to huge damage to regional populated areas near the coast. In this study, we use a recently developed dynamic earthquake simulator to explore tsunami earthquake generation from a physics-based modelling point of view. We build a shallow-dipping subduction zone model in which locally locked, unstable patches (asperities) are distributed on a conditionally stable subduction interface at shallow depth. The dynamic earthquake simulator captures both quasi-static and dynamic processes of earthquake cycles. We find that earthquakes can nucleate on these asperities and propagate into the surrounding conditionally stable zone at slow speeds, generating tsunami earthquakes. A high normal stress asperity, representing a subducted seamount, can act as an asperity in some events but as a barrier in other events over multiple earthquake cycles. Low normal stress asperities typically act as asperities in tsunami earthquakes. The degree of velocity-weakening in the conditionally stable zone, which may sustain rupture at different speeds or stop rupture, is critical for tsunami earthquake generation and affects its recurrence interval. Distributed asperities may rupture in isolated events separated by tens of years, or in a sequence of events separated by hours to days, or in one large event in a cascade fashion, demonstrating complex interactions among them. The recurrence interval on a high normal stress asperity is much larger than that on low normal stress asperities. These modelling results shed lights on the observations from historical tsunami earthquakes, including the 1994 and 2006 Java tsunami earthquakes and 2010 Mentawai tsunami earthquake.

    more » « less