Temporal Dissipative Kerr Solitons Research Articles

Enhancing the long-term stability of dissipative Kerr soliton microcomb.

A temporal dissipative Kerr soliton (DKS) frequency comb can be generated in an optical micro-cavity relying on the rigid balance between cavity decay (dispersion) and parametric gain (nonlinear phase modulation) induced by an intense pump laser. In practice, to maintain such delicate double balances experienced by the intracavity soliton pulses, it requires precise control of the pump laser frequency and power, as well as the micro-cavity parameters. However, to date there still lacks experimental demonstration that simultaneously stabilizes all these key parameters to enhance the long-term DKS stability. Here, we demonstrate continuous working of a on-chip DKS microcomb for a record-breaking 14 days without showing any sign of breakdown. Such improved microcomb stability is enabled mainly by robust pump power coupling to the micro-cavity utilizing packaged planar-lightwave-circuit mode converters, and faithful locking of the pump frequency detuning via an auxiliary laser heating method. In addition to superior stability, the demonstrated DKS microcomb system also achieves favorable compactness, with all the accessory modules being assembled into a standard 4U case. We hope that our demonstration could prompt the practical utilization of Kerr microcombs in real-world applications.

Nonlinear filtering of an optical pulse train using dissipative Kerr solitons

The capability to store light for extended periods of time enables optical cavities to act as narrowband optical filters, whose linewidth corresponds to the cavity’s inverse energy storage time. Here, we report on nonlinear filtering of an optical pulse train based on temporal dissipative Kerr solitons in microresonators. Our experimental results in combination with analytical and numerical modeling show that soliton dynamics enables information storage about the system’s physical state longer than the cavity’s energy storage time, thereby giving rise to a filter width that can be more than an order of magnitude below the cavity’s intrinsic linewidth. Such nonlinear optical filtering can find immediate applications in optical metrology, and low-timing jitter ultrashort optical pulse generation and potentially opens new avenues for microwave photonics.

Thermally stable access to microresonator solitons via slow pump modulation.

Temporal dissipative Kerr solitons (DKSs) in microresonators provide ultra-short optical pulses and low-noise frequency combs with gigahertz to terahertz repetition rates. Owing to their unique properties, they have found application in fields, including optical communications, rapid laser ranging, and optical precision spectroscopy. However, due to the thermal instability encountered when entering the DKS regime, the stable generation of solitons remains challenging for many systems and usually requires rapid actuation of the pump laser detuning, pulsed driving, additional lasers, a particular mode structure and/or active feedback loops to stabilize the system. Here we show that slow pump modulation can remove the thermal instability and enable passively stable soliton states that can be readily accessed via arbitrarily slow laser tuning, thereby greatly reducing the technical complexity of stable DKS generation.

A microphotonic astrocomb

Earth-like planets, dark energy and variability of fundamental physical constants can be discovered by observing wavelength shifts in the optical spectra of astronomical objects1–5. These wavelength shifts are so tiny that exquisitely accurate and precise wavelength calibration of astronomical spectrometers is required. Laser frequency combs, broadband spectra of laser lines with absolutely known optical frequencies, are uniquely suited for this purpose6–13, provided their lines are resolved by the spectrometer. Generating such astronomical laser frequency combs (‘astrocombs’) remains challenging. Here, a microphotonic astrocomb is demonstrated via temporal dissipative Kerr solitons14–16 in photonic-chip-based silicon nitride microresonators17, directly providing a spurious-free spectrum of resolvable calibration lines. Sub-harmonically driven by temporally structured light18, the astrocomb is stabilized to a frequency standard, resulting in absolute calibration with a precision of 25 cm s–1 (radial velocity equivalent), relevant for Earth-like planet detection and cosmological research. The microphotonic technology can be extended in spectral span17,19–24, further boosting the calibration precision. A microphotonic astrocomb is demonstrated via temporal dissipative Kerr solitons in photonic-chip-based silicon nitride microresonators with a precision of 25 cm s–1 (radial velocity equivalent), useful for Earth-like planet detection and cosmological research.

From the Lugiato-Lefever equation to microresonator-based soliton Kerr frequency combs.

The model, that is usually called the Lugiato-Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and damped nonlinear Schroedinger equation, gives rise to dissipative spatial and temporal solitons. Recently, the rather idealized conditions, assumed in the LLE, have materialized in the form of continuous wave driven optical microresonators, with the discovery of temporal dissipative Kerr solitons (DKS). These experiments have revealed that the LLE is a perfect and exact description of Kerr frequency combs-first observed in 2007, i.e. 20 years after the original formulation of the LLE-and in particular describe soliton states. Observed to spontaneously form in Kerr frequency combs in crystalline microresonators in 2013, such DKS are preferred state of operation, offering coherent and broadband optical frequency combs, whose bandwidth can be extended exploiting soliton-induced broadening phenomena. Combined with the ability to miniaturize and integrate on-chip, microresonator-based soliton Kerr frequency combs have already found applications in self-referenced frequency combs, dual-comb spectroscopy, frequency synthesis, low noise microwave generation, laser frequency ranging, and astrophysical spectrometer calibration, and have the potential to make comb technology ubiquitous. As such, pattern formation in driven, dissipative nonlinear optical systems is becoming the central Physics of soliton micro-comb technology.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Intermode Breather Solitons in Optical Microresonators

The observation of temporal dissipative Kerr solitons in optical microresonators provides, on the applied side, compact sources of coherent optical frequency combs that have already been applied in coherent communications, dual comb spectroscopy and metrology. On a fundamental level, it enables the study of soliton physics in driven nonlinear cavities. Microresonators are commonly multimode and, as a result, inter-mode interactions inherently occur among mode families - a condition referred to as "avoided mode crossings". Avoided mode crossings can cause soliton decay, but can also modify the soliton spectrum, leading to e.g. the formation of dispersive wave and inducing a spectral recoil. Yet, to date, the entailing temporal soliton dynamics from inter-mode interactions has rarely been studied, but is critical to understand regimes of soliton-stability. Here we report the discovery of an inter-mode breather soliton. Such breathing dynamics occurs within a laser detuning range where conventionally stationary dissipative solitons are expected. We demonstrate experimentally the phenomenon in two microresonator platforms (crystalline magnesium fluoride and photonic chip-based silicon nitride microresonators), and theoretically describe the dynamics based on a pair of coupled Lugiato-Lefever equations. We demonstrate experimentally that the breathing is associated with a periodic energy exchange between the soliton and another optical mode family. We further show that inter-mode interactions can be modeled by a response function acting on dissipative solitons. The observation of breathing dynamics in the conventionally stable soliton regime is critical to applications, ranging from low-noise microwave generation, frequency synthesis to spectroscopy. On a fundamental level, our results provide new understandings of the rich dissipative soliton dynamics in multimode nonlinear cavities.

Detuning-dependent properties and dispersion-induced instabilities of temporal dissipative Kerr solitons in optical microresonators

Temporal-dissipative Kerr solitons are self-localized light pulses sustained in driven nonlinear optical resonators. Their realization in microresonators has enabled compact sources of coherent optical frequency combs as well as the study of dissipative solitons. A key parameter of their dynamics is the effective-detuning of the pump laser to the thermally- and Kerr-shifted cavity resonance. Together with the free spectral range and dispersion, it governs the soliton-pulse duration, as predicted by an approximate analytical solution of the Lugiato-Lefever equation. Yet, a precise experimental verification of this relation was lacking so far. Here, by measuring and controlling the effective-detuning, we establish a new way of stabilizing solitons in microresonators and demonstrate that the measured relation linking soliton width and detuning deviates by less than 1 % from the approximate expression, validating its excellent predictive power. Furthermore, a detuning-dependent enhancement of specific comb lines is revealed, due to linear couplings between mode-families. They cause deviations from the predicted comb power evolution, and induce a detuning-dependent soliton recoil that modifies the pulse repetition-rate, explaining its unexpected dependence on laser-detuning. Finally, we observe that detuning-dependent mode-crossings can destabilize the soliton, leading to an unpredicted soliton breathing regime (oscillations of the pulse) that occurs in a normally-stable regime. Our results test the approximate analytical solutions with an unprecedented degree of accuracy and provide new insights into dissipative-soliton dynamics.

Self-referenced photonic chip soliton Kerr frequency comb

Self-referencing turns pulsed laser systems into self-referenced frequency combs. Such frequency combs allow counting of optical frequencies and have a wide range of applications. The required optical bandwidth to implement self-referencing is typically obtained via nonlinear broadening in optical fibers. Recent advances in the field of Kerr frequency combs have provided a path toward the development of compact frequency comb sources that provide broadband frequency combs, exhibit microwave repetition rates and are compatible with on-chip photonic integration. These devices have the potential to significantly expand the use of frequency combs. Yet to date, self-referencing of such Kerr frequency combs has only been attained by applying conventional, fiber-based broadening techniques. Here we demonstrate external broadening-free self-referencing of a Kerr frequency comb. An optical spectrum spanning two-thirds of an octave is directly synthesized from a continuous wave laser-driven silicon nitride microresonator using temporal dissipative Kerr soliton formation and soliton Cherenkov radiation. Using this coherent bandwidth and two continuous wave transfer lasers in a 2f–3f self-referencing scheme, we are able to detect the offset frequency of the soliton Kerr frequency comb. By stabilizing the repetition rate to a radio frequency reference, the self-referenced frequency comb is used to count and track the continuous wave pump laser’s frequency. This work demonstrates the principal ability of soliton Kerr frequency combs to provide microwave-to-optical clockworks on a chip.

Raman Self-Frequency Shift of Dissipative Kerr Solitons in an Optical Microresonator.

The formation of temporal dissipative Kerr solitons in microresonators driven by a continuous-wave laser enables the generation of coherent, broadband, and spectrally smooth optical frequency combs as well as femtosecond pulse sources with compact form factors. Here we report the observation of a Raman-induced soliton self-frequency shift for a microresonator dissipative Kerr soliton also referred to as the frequency-locked Raman soliton. In amorphous silicon nitride microresonator-based single soliton states the Raman effect manifests itself by a spectrum that is sech^{2} in shape and whose center is spectrally redshifted from the continuous wave pump laser. The shift is theoretically described by the first-order shock term of the material's Raman response, and we infer a Raman shock time of ∼20 fs for amorphous silicon nitride. Moreover, we observe that the Raman-induced frequency shift can lead to a cancellation or overcompensation of the soliton recoil caused by the formation of a coherent dispersive wave. The observations are in agreement with numerical simulations based on the Lugiato-Lefever equation with a Raman shock term. Our results contribute to the understanding of Kerr frequency combs in the soliton regime, enable one to substantially improve the accuracy of modeling, and are relevant to the understanding of the fundamental timing jitter of microresonator solitons.

Higher order mode suppression in high-Q anomalous dispersion SiN microresonators for temporal dissipative Kerr soliton formation.

High-Q silicon nitride (SiN) microresonators enable optical Kerr frequency comb generation on a photonic chip and have recently been shown to support fully coherent combs based on temporal dissipative Kerr soliton formation. For bright soliton formation, it is necessary to operate SiN waveguides in the multimode regime in order to produce waveguide induced anomalous group velocity dispersion. However, this regime can lead to local disturbances of the dispersion due to avoided crossings caused by coupling between different mode families and, therefore, prevent the soliton formation. Here, we demonstrate that a single-mode "filtering" section inside high-Q resonators enables efficiently suppression of avoided crossings, while preserving high quality factors (Q∼10(6)). We verify the approach by demonstrating single soliton formation in SiN resonators with a filtering section.

Photonic Damascene process for integrated high-Q microresonator based nonlinear photonics

High confinement, integrated silicon nitride (SiN) waveguides have recently emerged as attractive platform for on-chip nonlinear optical devices. The fabrication of high-Q SiN microresonators with anomalous group velocity dispersion (GVD) has enabled broadband nonlinear optical frequency comb generation. Such frequency combs have been successfully applied in coherent communication and ultrashort pulse generation. However, the reliable fabrication of high confinement waveguides from stoichiometric, high stress SiN remains challenging. Here we present a novel photonic Damascene fabrication process enabling the use of substrate topography for stress control and thin film crack prevention. With close to unity sample yield we fabricate microresonators with $1.35\,\mu\mathrm{m}$ thick waveguides and optical Q factors of $3.7\times10^{6}$ and demonstrate single temporal dissipative Kerr soliton (DKS) based coherent optical frequency comb generation. Our newly developed process is interesting also for other material platforms, photonic integration and mid infrared Kerr comb generation.