Primary Comb Research Articles

Dissipative Kerr soliton generation at 2μm in a silicon nitride microresonator

Chip-scale optical frequency combs enable the generation of highly-coherent pulsed light at gigahertz-level repetition rates, with potential technological impact ranging from telecommunications to sensing and spectroscopy. In combination with techniques such as dual-comb spectroscopy, their utilization would be particularly beneficial for sensing of molecular species in the mid-infrared spectrum, in an integrated fashion. However, few demonstrations of direct microcomb generation within this spectral region have been showcased so far. In this work, we report the generation of Kerr soliton microcombs in silicon nitride integrated photonics. Leveraging a high-Q silicon nitride microresonator, our device achieves soliton generation under milliwatt-level pumping at 1.97 µm, with a generated spectrum encompassing a 422 nm bandwidth and extending up to 2.25 µm. The use of a dual pumping scheme allows reliable access to several comb states, including primary combs, modulation instability combs, as well as multi- and single-soliton states, the latter exhibiting high stability and low phase noise. Our work extends the domain of silicon nitride based Kerr microcombs towards the mid-infrared using accessible factory-grade technology and lays the foundations for the realization of fully integrated mid-infrared comb sources.

High-speed data transmission over a microresonator frequency comb with dispersion compensation for augmented data rates and reach

Abstract Microresonator frequency comb-based high-speed data transmission provides a pathway towards augmented data capacity without increasing the number of laser sources. Their use with intensity-modulated direct detection modulation (IMDD) formats is especially pertinent in data center communications where minimizing cost, latency and complexity is paramount. This however implies that the same extent of digital signal processing techniques commonly used in coherent detection for the management of fiber impairments including chromatic dispersion are not available. With the proliferation of silicon photonics technologies in data center transceivers integrated dispersion compensation which can overcome fiber impairments would be of great merit. We demonstrate low power generation of the primary comb state in a silicon nitride microresonator and transmission of 25 Gb/s NRZ and 50 Gb/s PAM4 data over 20 km of single mode fiber. This represents the longest fiber reach demonstrated to date for the transmission of IMDD data using an integrated, microresonator frequency comb. An integrated, tunable grating device for dispersion compensation that reduces dispersion impairments after several fiber lengths generates significant improvements in the eye diagram, six orders of magnitude improvement in the bit-error rate and 14 dB improvement in the transmitter and dispersion eye closure quaternary values. Concurrently, doubling data transmission is demonstrated via polarization multiplexing a comb line and successful dispersion compensation of up to 20 km.

Turn-key Kerr soliton generation and tunable microwave synthesizer in dual-mode Si3N4 microresonators.

This study investigates the thermal compensation mechanism in dual-mode Si3N4 microresonators that demonstrates the ease of generation of single-solitons with nearly octave-wide spectral bandwidth. The deterministic creation of soliton frequency combs is achieved by merely switching the wavelength of a tunable laser or a semiconductor diode laser in a single step. The pump frequency detuning range that can sustain the soliton state is 30 gigahertz (GHz), which is approximately 100 times the resonance linewidth. Interestingly, these dual-mode resonators also support the coexistence of primary combs and solitons, enabling their utilization as functional microwave synthesizers. Furthermore, these resonators readily facilitate the generation of diverse multi-solitons and soliton crystals. This work presents a simplified system to access high-performance and versatile Kerr solitons, with wide-ranging applications in optical metrology, microwave photonics, and LiDAR.

Subharmonic instabilities in Kerr microcombs.

We report experimental observation of subharmonic mode excitation in primary Kerr optical frequency combs generated using crystalline whispering-gallery mode resonators. We show that the subcombs can be controlled and span a single or multiple free spectral ranges around the primary comb modes. In the spatial domain, the resulting multiscale combs correspond to an amplitude modulation of intracavity roll patterns. We perform a theoretical analysis based on eigenvalue decomposition that evidences the mechanism leading to the excitation of these combs.

Photo-induced cascaded harmonic and comb generation in silicon nitride microresonators.

Silicon nitride (Si3N4) is an ever-maturing integrated platform for nonlinear optics but mostly considered for third-order [χ(3)] nonlinear interactions. Recently, second-order [χ(2)] nonlinearity was introduced into Si3N4 via the photogalvanic effect, resulting in the inscription of quasi-phase-matched χ(2) gratings. However, the full potential of the photogalvanic effect in microresonators remains largely unexplored for cascaded effects. Here, we report combined χ(2) and χ(3) nonlinear effects in a normal dispersion Si3N4 microresonator. We demonstrate that the photo-induced χ(2) grating also provides phase-matching for the sum-frequency generation process, enabling the initiation and successive switching of primary combs. In addition, the doubly resonant pump and second-harmonic fields allow for effective third-harmonic generation, where a secondary optically written χ(2) grating is identified. Last, we reach a broadband microcomb state evolved from the sum-frequency-coupled primary comb. These results expand the scope of cascaded effects in microresonators.

Repetition-rate multiplicable soliton microcomb generation and stabilization via phase-modulated pumping scheme

We numerically demonstrate repetition rate multiplicable soliton microcomb generation using the phase-modulation pump scheme (PMS). Dissipative Kerr solitons are directly obtained avoiding the primary comb and chaotic modulation-instability stage and the repetition rate can be multiplied by changing the modulation frequency with fixed intensity. The PMS can not only help to stabilize emitted solitons with inhibited temporal drift against the Raman self-frequency shift effect, but also achieve soliton spacing equalization recovered from certain position fluctuations. Such approach can enable delicate manipulation on soliton behaviors, and provide a feasible route to soliton microcombs with even higher repetition rates and improved stabilities.

A mechanically tuned Kerr comb in a dispersion-engineered silica microbubble resonator

This paper discusses the developement and investigation of a silica microbubble resonator (MBR) that is optimized to cancel mode dispersion with material dispersion, at a wavelength of approximately $1550\mathrm{\,nm}$and maintain a quality factor of an optical mode as large as $5.4\times10^{7}$.Benefitting from the near-zero dispersion and high quality factor,a primary optical comb is generated in the MBR using cascaded four-wavemixing processes, which span over $300\,\mathrm{nm}$ with severaltens of teeth. Furthermore, the frequency comb could be graduallytuned by mechanically stretching the MBR. This tunable Kerr comb has multiple potential applications in precision measurements and sensing applications, suchas molecular spectroscopy and ranging.

Gate-tunable frequency combs in graphene-nitride microresonators.

Optical frequency combs, which emit pulses of light at discrete, equally spaced frequencies, are cornerstones of modern-day frequency metrology, precision spectroscopy, astronomical observations, ultrafast optics and quantum information1-7. Chip-scale frequency combs, based on the Kerr and Raman nonlinearities in monolithic microresonators with ultrahigh quality factors8-10, have recently led to progress in optical clockwork and observations of temporal cavity solitons11-14. But the chromatic dispersion within a laser cavity, which determines the comb formation15,16, is usually difficult to tune with an electric field, whether in microcavities or fibre cavities. Suchelectrically dynamic control couldbridge optical frequency combs and optoelectronics, enabling diverse comb outputs in one resonator with fast and convenient tunability. Arising from its exceptional Fermi-Dirac tunability and ultrafast carrier mobility17-19, graphene has a complex optical dispersion determined by its optical conductivity, which can be tuned through a gate voltage20,21. This has brought about optoelectronic advances such as modulators22,23, photodetectors 24 and controllable plasmonics25,26. Here we demonstrate the gated intracavity tunability of graphene-based optical frequency combs, by coupling the gate-tunable optical conductivity to a silicon nitride photonic microresonator, thus modulating its second- and higher-order chromaticdispersions by altering the Fermi level. Preserving cavity quality factors up to 106 in the graphene-based comb, we implement a dual-layer ion-gel-gated transistor to tune the Fermi level of graphene across the range 0.45-0.65 electronvolts, under single-volt-level control. We use this to produce charge-tunable primary comb lines from 2.3 terahertz to 7.2 terahertz, coherent Kerr frequency combs, controllable Cherenkov radiation and controllable soliton states, all in a single microcavity. We further demonstrate voltage-tunable transitions from periodic soliton crystals to crystals with defects, mapped by our ultrafast second-harmonic optical autocorrelation. This heterogeneous graphene microcavity, which combines single-atomic-layer nanoscience and ultrafast optoelectronics, will help to improve our understanding of dynamical frequency combs and ultrafast optics.

Type-II micro-comb generation in a filter-driven four wave mixing laser [Invited

We experimentally demonstrate the generation of highly coherent Type-II micro-combs based on a microresonator nested in a fiber cavity loop, known as the filter-driven four wave mixing (FD-FWM) laser scheme. In this system, the frequency spacing of the comb can be adjusted to integer multiples of the free-spectral range (FSR) of the nested micro-resonator by properly tuning the fiber cavity length. Sub-comb lines with single FSR spacing around the primary comb lines can be generated. Such a spectral emission is known as a “Type-II comb.” Our system achieves a fully coherent output. This behavior is verified by numerical simulations. This study represents an important step forward in controlling and manipulating the dynamics of an FD-FWM laser.

Optimization of primary Kerr optical frequency combs for tunable microwave generation.

We analyze the condition under which Kerr combs generate the highest microwave output power after photodetection. These optimal comb states correspond to configurations in which the sidemode-to-pump ratio is the highest possible. For the case of primary combs, we show how the interplay between the power and frequency of the pump laser critically influences this ratio, which has a direct influence on the phase noise performance of the generated microwaves. We also experimentally demonstrate primary combs with a sidemode-to-pump ratio as high as -2 dB, thereby leading to efficient energy conversion from the lightwave to the microwave frequency range.

Numerical simulation and temporal characterization of dual-pumped microring-resonator-based optical frequency combs

Dual-pumped microring-resonator-based optical frequency combs (OFCs) and their temporal characteristics are numerically investigated and experimentally explored. The calculation results obtained by solving the driven and damped nonlinear Schrodinger equation indicate that an ultralow coupled pump power is required to excite the primary comb modes through a non-degenerate four-wave-mixing (FWM) process and, when the pump power is boosted, both the comb mode intensities and spectral bandwidths increase. At low pump powers, the field intensity profile exhibits a cosine variation manner with frequency equal to the separation of the two pumps, while a roll Turing pattern is formed resulting from the increased comb mode intensities and spectral bandwidths at high pump powers. Meanwhile, we found that the power difference between the two pump fields can be transferred to the newly generated comb modes, which are located on both sides of the pump modes, through a cascaded FWM process. Experimentally, the dual-pumped OFCs were realized by coupling two self-oscillating pump fields into a microring resonator. The numerically calculated comb spectrum is verified by generating an OFC with 2.0 THz mode spacing over 160 nm bandwidth. In addition, the formation of a roll Turing pattern at high pump powers is inferred from the measured autocorrelation trace of a 10 free spectral range (FSR) OFC. The experimental observations accord well with the numerical predictions. Due to their large and tunable mode spacing, robustness, and flexibility, the proposed dual-pumped OFCs could find potential applications in a wide range of fields, including arbitrary optical waveform generation, high-capacity optical communications, and signal-processing systems.

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.

Dual-pump generation of high-coherence primary Kerr combs with multiple sub-lines.

We experimentally generate high-coherence primary Kerr combs with multiple sub-lines by using dual pumps and demonstrate the application of a primary comb state in multichannel communications. We find that more than 10 primary comb lines can be generated within the spectrum of modulation instability gain in our microring resonator. The generation is also verified by numerical simulations and the measured linewidth confirms the high coherence of the generated primary comb lines. We also demonstrate the high-coherence characteristics in a coherent communication experiment, in which each comb line is encoded with 20 Gbaud quadrature phase-shift-keyed signals.

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.

Wide-range tunability, thermal locking, and mode-crossing effects in Kerr optical frequency combs

We theoretically and experimentally investigate some effects related to the Kerr optical frequency comb generation, using a millimeter-size magnesium fluoride ultrahigh quality disk resonator. We show that the Kerr comb tunability can be extremely wide in the Turing pattern (or primary comb) regime, with an intermodal frequency that can be tuned from 4 to 229 multiple free spectral ranges (corresponding to a frequency spacing ranging from 24 GHz to 1.35 THz). We also discuss the role played by thermal locking while pumping the res- onator, as well as the effect of modal crossing when broadband combs are generated. © 2014 Society of Photo-Optical

Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes

We propose a detailed stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering-gallery-mode resonators when they are pumped in either the anomalous- or normal-dispersion regime. We analyze the spatial bifurcation structure of the stationary states depending on two parameters that are experimentally tunable; namely, the pump power and the cavity detuning. Our study demonstrates that, in both the anomalous- and normal-dispersion cases, nontrivial equilibria play an important role in this bifurcation map because their associated eigenvalues undergo critical bifurcations that are actually foreshadowing the existence of localized and extended spatial dissipative structures. The corresponding bifurcation maps are evidence of a considerable richness from a dynamical standpoint. The case of anomalous dispersion is indeed the most interesting from the theoretical point of view because of the considerable variety of dynamical behavior that can be observed. For this case we study the emergence of super- and subcritical Turing patterns (or primary combs) in the system via modulational instability. We determine the areas where bright isolated cavity solitons emerge, and we show that soliton molecules can emerge as well. Very complex temporal patterns can actually be observed in the system, where solitons (or soliton complexes) coexist with or without mutual interactions. Our investigations also unveil the mechanism leading to the phenomenon of breathing solitons. Two routes to chaos in the system are identified; namely, a route via the destabilization of a primary comb, and another via the destabilization of solitons. For the case of normal dispersion, we unveil the mechanism leading to the emergence of weakly stable Turing patterns. We demonstrate that this weak stability is justified by the distribution of stable and unstable fixed points in the parameter space (flat states). We show that dark cavity solitons can emerge in the system, and also show how these solitons can coexist in the resonator as long as they do not interact with each other. We find evidence of breather solitons in this normal dispersion regime as well. The Kerr frequency combs corresponding to all these spatial dissipative structures are analyzed in detail, along with their stability properties. A discussion is led about the possibility to gain unifying comprehension of the observed spectra from the dynamical complexity of the system.

Cell lineage and differentiation on the male foreleg of Drosophila melanogaster

Cell lineage was studied in the epidermis of the basitarsus of the foreleg of male Drosophila melanogaster. This was accomplished by “marking” single cells, and their descendants, with genotypes different from the rest of the tissues. The mosaic basitarsi thus produced had areas with yellow chaetae on a background of black chaetae. On the basis of cell lineage data, the male basitarsus can be divided in two main parts. Region A occupies most of the segment including the primary sex comb and the central bristle. It does not include the area of the longitudinal rows 1, 2, and 3 and that of the secondary sex comb which shows a close developmental relation to rows 1 and 2. These areas constitute region B. Within region A cell lineage data yield a subdivision into A-1 which includes longitudinal row 1′, the transverse rows, longitudinal rows 7 and 6 and 5.5, the primary sex comb and the central bristle; and A-2 the remaining area which includes longitudinal rows 4 and 5. In region A-1 the following developmental relations were found. (a) The descendants of a yellow cell tend to form longitudinal strips of tissue both along the longitudinal rows and in the area of the transverse rows. (b) The proximal teeth of the sex comb and the central bristle are closely related to the posterior part of the transverse rows. (c) The middle teeth are closely related to the middle and the anterior parts of the transverse rows and to row 7. (d) The bractless bristles 5.5 are closely related to the distal teeth within the middle part of the sex comb. (e) The distal teeth of the sex comb are closely related to longitudinal row 6, and less closely, to row 7. The data suggest that the prospective area of the primary sex comb initially occupies the same distal part of the basitarsus as the most distal transverse rows of the female basitarsus. They suggest further that in the male the tissue of this area shifts anteriorly, whereby it changes its direction by approximately 90 degrees. This not only is deduced from the results of the cell lineage studies, but explains the position of the bracts at the base of the sex comb teeth and the direction assumed by the teeth, both of which deviate by about 90 degrees from that of the other chaetae of the segment. The above results on pure male basitarsi were confirmed by cell lineage studies of gynandric basitarsi. Systematic deviations from the norm in the location and direction of the male sex comb teeth and of female chaetae at the distal part of the segment are the result of the differential morphogenesis of the male and female tissues in this area.