Observation of correlation between route to formation, coherence, noise, and communication performance of Kerr combs

An Introduction to Nonlinear Integrated Photonics: Structures and Devices

The combination of integrated optics technologies with nonlinear photonics, which has led to growth of nonlinear integrated photonics, has also opened the way to groundbreaking new devices and applications. In a companion paper also submitted for publication in this journal, we introduce the main physical processes involved in nonlinear photonics applications and discuss the fundaments of this research area. The applications, on the other hand, have been made possible by availability of suitable materials with high nonlinear coefficients and/or by design of guided-wave structures that can enhance a material's nonlinear properties. A summary of the traditional and innovative nonlinear materials is presented there. Here, we discuss the fabrication processes and integration platforms, referring to semiconductors, glasses, lithium niobate, and two-dimensional materials. Various waveguide structures are presented. In addition, we report several examples of nonlinear photonic integrated devices to be employed in optical communications, all-optical signal processing and computing, or in quantum optics. We aimed at offering a broad overview, even if, certainly, not exhaustive. However, we hope that the overall work will provide guidance for newcomers to this field and some hints to interested researchers for more detailed investigation of the present and future development of this hot and rapidly growing field.

Stability analysis of mode-coupling-assisted microcombs in normal dispersion

We theoretically study the stability of mode-coupling-assisted frequency comb generation in normal-dispersion microresonators. With the aid of mode coupling, quantitative analysis of the modulational instability is explored in the parameter space of pump power and detuning. By exploring the coupled mode number, dispersion, and coupling strength in the normalized Lugiato-Lefever model, the modulational stability gain exists and yields extended spatial structures within the regime of eigenvalue bifurcations. Moreover, the dynamics and efficiency of microcombs are discussed, providing the accessibility of high-efficient, stable, and controllable combs. This work offers universal guidelines for operating mode-coupling-assisted combs in a normal-dispersion system.

Dissipative Kerr soliton microcombs for FEC-free optical communications over 100 channels

The demand for high-speed and highly efficient optical communication techniques has been rapidly growing due to the ever-increasing volume of data traffic. As well as the digital coherent communication used for core and metro networks, intensity modulation and direct detection (IM-DD) are still promising schemes in intra/inter data centers thanks to their low latency, high reliability, and good cost performance. In this work, we study a microresonator-based frequency comb as a potential light source for future IM-DD optical systems where applications may include replacing individual stabilized lasers with a continuous laser driven microresonator. Regarding comb line powers and spectral intervals, we compare a modulation instability comb and a soliton microcomb and provide a quantitative analysis with regard to telecom applications. Our experimental demonstration achieved a forward error correction (FEC) free operation of bit-error rate (BER) <10^-9 with a 1.45 Tbps capacity using a total of 145 lines over the entire C-band and revealed the possibility of soliton microcomb-based ultra-dense wavelength division multiplexing (WDM) with a simple, cost-effective IM-DD scheme, with a view to future practical use in data centers.

Effects of erbium-doped fiber amplifier induced pump noise on soliton Kerr frequency combs for 64-quadrature amplitude modulation transmission

We experimentally investigate the effects of erbium-doped fiber amplifier induced pump noise on soliton Kerr frequency combs for 64-quadrature amplitude modulation (QAM) transmission. We find that the optical carrier-to-noise ratios (OCNRs) of the comb lines across the C-band almost linearly depend on the pump OCNR and are similar for a constant input pump power and noise. For a specific three-soliton state, despite higher comb line power, there is no noticeable OCNR improvement compared to the single-soliton comb. When the ASE noise on the pump is varied by 10 dB in the stable single-soliton state, the comb linewidths remain relatively unchanged and similar to the pump linewidth. Furthermore, four lines of the single-soliton Kerr comb produced by a pump light at an OCNR larger than 52 dB are used as coherent light sources to transmit 20-Gbaud 64-QAM signals over a 25-km fiber with bit error rate below the forward-error correction threshold.

High-order coherent communications using mode-locked dark-pulse Kerr combs from microresonators

Microresonator frequency combs harness the nonlinear Kerr effect in an integrated optical cavity to generate a multitude of phase-locked frequency lines. The line spacing can reach values in the order of 100 GHz, making it an attractive multi-wavelength light source for applications in fiber-optic communications. Depending on the dispersion of the microresonator, different physical dynamics have been observed. A recently discovered comb state corresponds to the formation of mode-locked dark pulses in a normal-dispersion microcavity. Such dark-pulse combs are particularly compelling for advanced coherent communications since they display unusually high power-conversion efficiency. Here, we report the first coherent-transmission experiments using 64-quadrature amplitude modulation encoded onto the frequency lines of a dark-pulse comb. The high conversion efficiency of the comb enables transmitted optical signal-to-noise ratios above 33 dB, while maintaining a laser pump power level compatible with state-of-the-art hybrid silicon lasers.

Dark-pulse combs may be useful for coherent communications since they display high power conversion efficiency. Here, the authors report the first demonstration of coherent wavelength division multiplexing using dark pulse microresonator combs high signal-to-noise while maintaining a low on-chip pump power.

On-chip dual-comb source for spectroscopy

Dual-comb spectroscopy is a powerful technique for real-time, broadband optical sampling of molecular spectra, which requires no moving components. Recent developments with microresonator-based platforms have enabled frequency combs at the chip scale. However, the need to precisely match the resonance wavelengths of distinct high quality-factor microcavities has hindered the development of on-chip dual combs. We report the simultaneous generation of two microresonator combs on the same chip from a single laser, drastically reducing experimental complexity. We demonstrate broadband optical spectra spanning 51 THz and low-noise operation of both combs by deterministically tuning into soliton mode-locked states using integrated microheaters, resulting in narrow (<10 kHz) microwave beat notes. We further use one comb as a reference to probe the formation dynamics of the other comb, thus introducing a technique to investigate comb evolution without auxiliary lasers or microwave oscillators. We demonstrate high signal-to-noise ratio absorption spectroscopy spanning 170 nm using the dual-comb source over a 20-μs acquisition time. Our device paves the way for compact and robust spectrometers at nanosecond time scales enabled by large beat-note spacings (>1 GHz).

Long-haul coherent communications using microresonator-based frequency combs

Microresonator-based frequency combs are strong contenders as light sources for wavelength-division multiplexing (WDM). Recent experiments have shown the potential of microresonator combs for replacing a multitude of WDM lasers with a single laser-pumped device. Previous demonstrations have however focused on short-distance few-span links reaching an impressive throughput at the expense of transmission distance. Here we report the first long-haul coherent communication demonstration using a microresonator-based comb source. We modulated polarization multiplexed (PM) quadrature phase-shift keying-data onto the comb lines allowing transmission over more than 6300 km in a single-mode fiber. In a second experiment, we reached beyond 700 km with the PM 16 quadrature amplitude modulation format. To the best of our knowledge, these results represent the longest fiber transmission ever achieved using an integrated comb source.

Pump-linewidth-tolerant wavelength multicasting using soliton Kerr frequency combs

We experimentally demonstrate pump-linewidth-tolerant wavelength multicasting using microresonator-based soliton Kerr frequency combs. When Kerr comb lines serve as coherent pumps in a periodically poled lithium niobate waveguide, the linewidth of the multicast signal almost remains that of the original signal at different linewidths of Kerr combs, ranging from 100 kHz to 1 MHz. However, in conventional multicasting where free-running (FR) pumps are used, the linewidth of the converted signal significantly increases. Furthermore, the error vector magnitude (EVM) performance demonstrates eight-fold error-free multicasting of 10 Gbaud 16-quadrature amplitude modulation signals, even when the linewidths of the Kerr combs are as broad as 1 MHz (no Kalman filtering algorithm in the receiver). In contrast, the EVM performance of the signal copy is degraded with an FR laser as a dummy pump.

Investigation of the local dispersion change in anomalous dispersion microcavity and quantitative analysis of the phase-matching in Kerr comb generation

We numerically simulate Kerr comb generation in an anomalous dispersion microcavity by modal expansion method and demonstrate that the initiation of comb generation is affected by the change of local dispersion possibly caused by avoided mode crossings. We also quantitatively analyze the instantaneous phase matching of different modes and reveal the characteristics of energy distribution in different modes in the dynamics of comb generation. We demonstrate that the local dispersion change can control the Kerr comb to transform between Type I and Type II combs. We also find that local dispersion is closely related to the stability of the power of Kerr comb lines, something that can change the dynamical state of the system near the Hamiltonian-Hopf bifurcation under an anomalous dispersion regime from a quasi-periodic oscillation state to a periodic state (Turing patterns).

Dependence of a microresonator Kerr frequency comb on the pump linewidth

We experimentally investigate the dependence of Kerr comb generation, comb linewidth, and coherent system performance on the pump linewidth in a microresonator. We find that the generation of the primary comb can have a larger tolerance to the pump linewidth compared with that of the low-phase-noise comb. In addition, the linewidths of the generated combs are almost linearly dependent on the pump linewidth in the primary and low-phase-noise states. Furthermore, the optical signal-to-noise ratio penalty between the pump and generated Kerr combs in a coherent communication system is less than 0.2 dB in both the primary and low-phase-noise states, showing that Kerr frequency combs in these two states can have similar coherent system performance to the pump.

Transverse mode interaction via stimulated Raman scattering comb in a silica microcavity

Comb generation in different mode families via a stimulated Raman scattering (SRS) process is studied using a silica toroid microcavity. The broad gain bandwidth of SRS in silica allows us to excite longitudinal modes at long wavelengths belonging to mode families that are either the same as or different from the pump mode. We found through experiment and numerical analysis, that an SRS comb in a different mode family with a high quality factor (Q) is excited when we pump in a low-Q mode. No transverse mode interaction occurs when we excite in a high-Q mode resulting the generation of a single comb family. We studied the condition of the transverse mode interaction while varying the mode overlap and Q of the Raman mode. Our experimental results are in good agreement with the analysis and this enables us to control the generation of one- and two-mode combs.

On the phase noise performance of microwave and millimeter-wave signals generated with versatile Kerr optical frequency combs

We investigate the phase noise performance of micro- and millimeter-wave signals generated using a ultra-high Q whispering gallery mode disk-resonator with Kerr nonlinearity. Our study focuses on the stability of the optical spectra and on the performances of the corresponding microwave and millimeter-wave beat notes in terms of power and phase noise. The blue slope of an optical mode of the resonator, allowing for the generation of optical frequency combs, is accurately explored in order to identify various comb patterns. Each of these patterns is characterized in the optical and radio-frequency domains. Phase noise levels below -100 dBc/Hz at 10 kHz offset have been achieved for beat notes in the radio-frequency spectrum at 12 GHz, 18 GHz, 24 GHz, 30 GHz, and 36 GHz with the same resonator.

Design of a polymer-filled silicon nitride strip/slot asymmetric hybrid waveguide for realizing both flat dispersion and athermal operation

An asymmetric strip/slot hybrid silicon nitride waveguide is designed to simultaneously realize athermal operation and flat dispersion. The slot filling and upper cladding materials are negative thermal-optical coefficient (TOC), low refractive index polyurethane acrylate, while the left and right cladding layers are positive TOC, high refractive index silicon nitride. With suitable waveguide parameter selection, an optimum strip/slot hybrid silicon nitride waveguide exhibits an effective TOC of 1.263×10^-7/K at 1550 nm, flattened dispersion in the wavelength range from 1200 to 1800 nm with the maximum dispersion of 30.51 ps/(nm·km), and a minimum of 10.89 ps/(nm·km). The proposed hybrid waveguide has great potential in building up broadband athermal microresonator optical frequency combs.

Coherent mid-infrared frequency combs in silicon-microresonators in the presence of Raman effects

We demonstrate the first low-noise mid-IR frequency comb source using a silicon microresonator. Our observation of strong Raman scattering lines in the generated comb suggests that interplay between Raman and four-wave mixing plays a role in the generated low-noise state. In addition, we characterize, the intracavity comb generation dynamics using an integrated PIN diode, which takes advantage of the inherent three-photon absorption process in silicon.

Effect of a breather soliton in Kerr frequency combs on optical communication systems

In this study, we numerically investigate the effect of Kerr-comb-generated breather soliton pulses on optical communication systems. The breather soliton pulse amplitude and spectrum envelope oscillate periodically in time. Simulations show that the spectrum of each comb line in the breather soliton state has multiple sub-teeth due to the periodic oscillation of the comb spectrum. In the simulation, the comb output is modulated with different formats. We find that the sub-teeth distort quadrature phase-shift-keyed signals but have less of an effect on on-off-keyed signals.

Tunable frequency combs based on dual microring resonators

In order to achieve efficient parametric frequency comb generation in microresonators, external control of coupling between the cavity and the bus waveguide is necessary. However, for passive monolithically integrated structures, the coupling gap is fixed and cannot be externally controlled, making tuning the coupling inherently challenging. We design a dual-cavity coupled microresonator structure in which tuning one ring resonance frequency induces a change in the overall cavity coupling condition. We demonstrate wide extinction tunability with high efficiency by engineering the ring coupling conditions. Additionally, we note a distinct dispersion tunability resulting from coupling two cavities of slightly different path lengths, and present a new method of modal dispersion engineering. Our fabricated devices consist of two coupled high quality factor silicon nitride microresonators, where the extinction ratio of the resonances can be controlled using integrated microheaters. Using this extinction tunability, we optimize comb generation efficiency as well as provide tunability for avoiding higher-order mode-crossings, known for degrading comb generation. The device is able to provide a 110-fold improvement in the comb generation efficiency. Finally, we demonstrate open eye diagrams using low-noise phase-locked comb lines as a wavelength-division multiplexing channel.

Deterministic single soliton generation and compression in microring resonators avoiding the chaotic region

A path within the parameter space of detuning and pump power is demonstrated in order to obtain a single cavity soliton (CS) with certainty in SiN microring resonators in the anomalous dispersion regime. Once the single CS state is reached, it is possible to continue a path to compress it, broadening the corresponding single free spectral range (FSR) Kerr frequency comb. The first step to achieve this goal is to identify the stable regions in the parameter space via numerical simulations of the Lugiato-Lefever equation (LLE). Later, using this identification, we define a path from the stable modulation instability (SMI) region to the stable cavity solitons (SCS) region avoiding the chaotic and unstable regions.

Spectro-temporal dynamics of Kerr combs with parametric seeding

We report a joint theoretical and experimental investigation of the parametric seeding of a primary Kerr optical frequency comb. Electro-optic modulation sidebands matching multiple free-spectral ranges of an ultrahigh-Q millimeter-size magnesium fluoride disk resonator are used as seed signals. These seed signals interact through four-wave mixing with the spectral components of a stable primary comb and give rise to complex spectro-temporal patterns. We show that the new frequency combs feature multiscale frequency spacing, with major frequency gaps in the order of a few hundred gigahertz, and minor frequency spacing in the order of a few tens of gigahertz. The experimental results are in agreement with numerical simulations using the Lugiato-Lefever equation. We expect such versatile and coherent optical frequency combs to have potential applications in optical communications systems where frequency management assigns predefined spectral windows at the emitter stage.

Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications

Optical Kerr frequency combs are known to be effective coherent multiwavelength sources for ultrahigh capacity fiber communications. These combs are the frequency-domain counterparts of a wide variety of spatiotemporal dissipative structures, such as cavity solitons, chaos, or Turing patterns (rolls). In this Letter, we demonstrate that Turing patterns, which correspond to the so-called primary combs in the spectral domain, are optimally coherent in the sense that for the same pump power they provide the most robust carriers for coherent data transmission in fiber communications using advanced modulation formats. Our model is based on a stochastic Lugiato-Lefever equation which accounts for laser pump frequency jitter and amplified spontaneous emission noise induced by the erbium-doped fiber amplifier. Using crystalline whispering-gallery-mode resonators with quality factor Q∼10^{9} for the comb generation, we show that when the noise is accounted for, the coherence of a primary comb is significantly higher than the coherence of their solitonic or chaotic counterparts for the same pump power. In order to confirm this theoretical finding, we perform an optical fiber transmission experiment using advanced modulation formats, and we show that the coherence of the primary comb is high enough to enable data transmission of up to 144  Gbit/s per comb line, the highest value achieved with a Kerr comb so far. This performance evidences that compact crystalline photonic systems have the potential to play a key role in a new generation of coherent fiber communication networks, alongside fully integrated systems.

Classical-to-quantum transition with broadband four-wave mixing

A key question of quantum optics is how nonclassical biphoton correlations at low power evolve into classical coherence at high power. Direct observation of the crossover from quantum to classical behavior is desirable, but difficult due to the lack of adequate experimental techniques that cover the ultrawide dynamic range in photon flux from the single photon regime to the classical level. We investigate biphoton correlations within the spectrum of light generated by broadband four-wave mixing over a large dynamic range of ∼80  dB in photon flux across the classical-to-quantum transition using a two-photon interference effect that distinguishes between classical and quantum behavior. We explore the quantum-classical nature of the light by observing the interference contrast dependence on internal loss and demonstrate quantum collapse and revival of the interference when the four-wave mixing gain in the fiber becomes imaginary.

Phase steps and resonator detuning measurements in microresonator frequency combs

Experiments and theoretical modelling yielded significant progress toward understanding of Kerr-effect induced optical frequency comb generation in microresonators. However, the simultaneous Kerr-mediated interaction of hundreds or thousands of optical comb frequencies with the same number of resonator modes leads to complicated nonlinear dynamics that are far from fully understood. An important prerequisite for modelling the comb formation process is the knowledge of phase and amplitude of the comb modes as well as the detuning from their respective microresonator modes. Here, we present comprehensive measurements that fully characterize optical microcomb states. We introduce a way of measuring resonator dispersion and detuning of comb modes in a hot resonator while generating an optical frequency comb. The presented phase measurements show unpredicted comb states with discrete π and π/2 steps in the comb phases that are not observed in conventional optical frequency combs.

Mode spectrum and temporal soliton formation in optical microresonators

The formation of temporal dissipative solitons in optical microresonators enables compact, high-repetition rate sources of ultrashort pulses as well as low noise, broadband optical frequency combs with smooth spectral envelopes. Here we study the influence of the microresonator mode spectrum on temporal soliton formation in a crystalline MgF2 microresonator. While an overall anomalous group velocity dispersion is required, it is found that higher order dispersion can be tolerated as long as it does not dominate the resonator's mode structure. Avoided mode crossings induced by linear mode coupling in the resonator mode spectrum are found to prevent soliton formation when affecting resonator modes close to the pump laser frequency. The experimental observations are in excellent agreement with numerical simulations based on the nonlinear coupled mode equations. The presented results provide for the first time design criteria for the generation of temporal solitons in optical microresonators.

Bandwidth shaping of microresonator-based frequency combs via dispersion engineering

We investigate experimentally and theoretically the role of group-velocity dispersion and higher-order dispersion on the bandwidth of microresonator-based parametric frequency combs. We show that the comb bandwidth and the power contained in the comb can be tailored for a particular application. Additionally, our results demonstrate that fourth-order dispersion plays a critical role in determining the spectral bandwidth for comb bandwidths on the order of an octave.

Coherent terabit communications with microresonator Kerr frequency combs

Optical frequency combs have the potential to revolutionize terabit communications¹. Generation of Kerr combs in nonlinear microresonators² represents a particularly promising option³ enabling line spacings of tens of GHz. However, such combs may exhibit strong phase noise^4-6, which has made high-speed data transmission impossible up to now. Here we demonstrate that systematic adjustment of pump conditions for low phase noise^4,7-9 enables coherent data transmission with advanced modulation formats that pose stringent requirements on the spectral purity of the comb. In a first experiment, we encode a data stream of 392 Gbit/s on a Kerr comb using quadrature phase shift keying (QPSK) and 16-state quadrature amplitude modulation (16QAM). A second experiment demonstrates feedback-stabilization of the comb and transmission of a 1.44 Tbit/s data stream over up to 300 km. The results show that Kerr combs meet the highly demanding requirements of coherent communications and thus offer an attractive solution towards chip-scale terabit/s transceivers.

Comparative analysis of spectral coherence in microresonator frequency combs

Microresonator combs exploit parametric oscillation and nonlinear mixing in an ultrahigh-Q cavity. This new comb generator offers unique potential for chip integration and access to high repetition rates. However, time-domain studies reveal an intricate spectral coherence behavior in this type of platform. In particular, coherent, partially coherent or incoherent combs have been observed using the same microresonator under different pumping conditions. In this work, we provide a numerical analysis of the coherence dynamics that supports the above experimental findings and verify particular design rules to achieve spectrally coherent microresonator combs. A particular emphasis is placed in understanding the differences between so-called Type I and Type II combs.

Self-injection locking and phase-locked states in microresonator-based optical frequency combs

Microresonator-based optical frequency combs have been a topic of extensive research during the last few years. Several theoretical models for the comb generation have been proposed; however, they do not comprehensively address experimental results that show a variety of independent comb generation mechanisms. Here, we present frequency-domain experiments that illuminate the transition of microcombs into phase-locked states, which show characteristics of injection locking between ensembles of comb modes. In addition, we demonstrate the existence of equidistant optical frequency combs that are phase stable but have nondeterministic phase relationships between individual comb modes.

On timing jitter of mode locked Kerr frequency combs

We study fundamental timing jitter in repetition rate of a mode locked Kerr frequency comb generated in an externally pumped nonlinear ring resonator. We show that the increase in the integrated power of the comb harmonics, and the corresponding decrease of the duration of the associated pulse, results in the increase of low frequency noise, and a decrease in high frequency noise.

Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip

We report a novel geometry for OPOs based on nonlinear microcavity resonators. This approach relies on a self-locked scheme that enables OPO emission without the need for thermal locking of the pump laser to the microcavity resonance. By exploiting a CMOS-compatible microring resonator, we achieve oscillation featured by a complete absence of "shutting down", i.e. the self-terminating behavior that is a very common and detrimental occurrence in externally pumped OPOs. Further, our scheme consistently produces very wide bandwidth (>300nm, limited by our experimental set-up) combs that oscillate at a spacing equal to the FSR of the micro cavity resonance.