Determining the Transverse Mode that Produces Frequency Combs in Microresonators

Globally, the long-haul transmission of ultra-high bandwidth data is enabled through coherent communications. Driven by the rapid pace of growth in interconnectivity over the last decade, long-haul data transmission has reached capacities on the order of tens to hundreds of terabits per second, over fiber reaches which may span thousands of kilometers. Data center communications operate in regimes featuring shorter reaches and higher cost sensitivity. While integrated microresonator frequency combs are poised to revolutionize light sources used for high-speed data transmission over fiber, recent progress has focused largely on coherent detection schemes. Furthermore, though state-of-the-art intensity modulators are advancing in speed, it has not been demonstrated in the literature if microresonator-based comb lines can accommodate higher intensity modulated direction data (IMDD) line rates in tandem with these advancements. In this manuscript, we demonstrate the use of microresonator frequency combs pumped with a single laser for the transmission of high-speed IMDD data. We demonstrate error-free transmission of 30 Gbs-1 per comb non-return-to-zero data over fiber lengths of 6 km, as well as bit error rates under the forward error correction limit for propagation through 20 km of optical fiber. 60 Gbs-1 and 42 Gbs-1 pulse modulation amplitude 4 (PAM4) data modulated on each frequency comb line is further quantified to have a bit error rate under the forward error correction limit for fiber reaches of up to 6 km and 20 km respectively. The results showcase CMOS-compatible microresonator frequency comb modulated using IMDD formats as a promising technology for high-speed transmission in the data center transceiver industry.

Multi-color solitons that are parametrically created in dual-pumped microresonators generate interleaved frequency combs that can be used to obtain combs at new frequencies and, when synchronized, can be used for low-noise microwave generation and potentially as an element in a chip-scale clockwork. Here, we first derive three-wave equations that describe multi-color solitons that appear in microresonators with a nearly quartic dispersion profile. These solitons are characterized by a single angular group velocity and different angular phase velocities. We then use these equations to explain the interleaved frequency combs that are observed at the output of the microresonator. Finally, we used these equations to describe the experimentally-observed soliton-OPO effect. In this effect, the pump frequency color interacts nonlinearly with a signal frequency color to create an idler frequency color in a new frequency range, somewhat analogous to an optical parametric oscillation (OPO) process, but in which the Kerr nonlinearity plays a role in matching the angular group velocity, analogous to soliton formation. These three colors then create an interleaved frequency comb in the output waveguide. We determine the conditions under which we expect this effect to occur. We anticipate that the three-wave equations and their extensions will be of use in designing new frequency comb systems and determining their stability and noise performance.

Microcombs are optical frequency combs in microresonators [1], [2]. Laser cavity-soliton (LCS) states can be achieved in a system comprising a nonlinear Kerr microresonator nested in a fibre laser [3], resulting in a self-emergent, robust [4], and efficient [5] microcomb. Generally, the platform generally produces a broader variety of states depending on the specific parameter settings of the system. The two critical experimental parameters that need to be adjusted to achieve solitary oscillation via self-emergence [4] are the gain, which controls the state energy, and the length of the main cavity, which governs the group velocity mismatch between the two cavities. When searching for solitary oscillations, these parameters must be spanned over large ranges. While detailed information can be obtained through accurate but time-consuming methods like laser scanning spectroscopy and interferometry, real-time approaches are preferable when handling large datasets. In this work, we introduce a rapid method to distinguish typical lasing states, including soliton states, based on simple experimental properties. Specifically, our approach utilises radiofrequency (RF) data and spectral analysis to map states within nonlinear optical systems in real time, with minimal computational effort when handling large datasets.

The aim of this work is to theoretically investigate the possibility of Kerr frequency combs in mechanical systems. In particular, whether microelectromechanical devices (MEMS) can be used to generate frequency combs in a manner that is analogous to the optical frequency combs generated in optical microresonators with Kerr-type nonlinearity. The analysis assumes a beam-like micromechanical structure, and starting from the Euler-Bernoulli beam equation derives the necessary conditions in parameter space for the comb generation. The chapter equally presents potential means for the physical implementation of mechanical Kerr combs.

We determine the regions in the parameter space of microresonators where cnoidal waves (Turing rolls) are stable. Solitons are included as a special limit. We identify conditions to efficiently obtain broadband frequency combs.

Optical frequency combs function as extremely broad bandwidth photonic synthesizers, capable of generating ultra-low noise signals from radio frequency to optical domains. We present synthesis results with both mode-locked laser and microresonator frequency combs.

Microresonator frequency combs can be an enabling technology for optical frequency synthesis and timekeeping in low size, weight, and power architectures. Such systems require comb operation in low-noise, phase-coherent states such as solitons, with broad spectral bandwidths (e.g., octave-spanning) for self-referencing to detect the carrier-envelope offset frequency. However, accessing such states is complicated by thermo-optic dispersion. For example, in the Si3N4 platform, precisely dispersion-engineered structures can support broadband operation, but microsecond thermal time constants often require fast pump power or frequency control to stabilize the solitons. In contrast, here we consider how broadband soliton states can be accessed with simple pump laser frequency tuning, at a rate much slower than the thermal dynamics. We demonstrate octave-spanning soliton frequency combs in Si3N4 microresonators, including the generation of a multi-soliton state with a pump power near 40 mW and a single-soliton state with a pump power near 120 mW. We also develop a simplified two-step analysis to explain how these states are accessed without fast control of the pump laser, and outline the required thermal properties for such operation. Our model agrees with experimental results as well as numerical simulations based on a Lugiato-Lefever equation that incorporates thermo-optic dispersion. Moreover, it also explains an experimental observation that a member of an adjacent mode family on the red-detuned side of the pump mode can mitigate the thermal requirements for accessing soliton states.

We describe our measurements on high-precision microresonators and microresonator-based optical frequency combs, including full stabilization of planar frequency microcombs, with an instrument-limited instability at 3.6-mHz-per-root-tau and tooth-to-tooth relative uncertainty to 50mHz. Noise in thermally-compensated ultrahigh-Q microresonators and lasers are demonstrated at the thermodynamical limits.

We perform optical frequency division of an ultra-stable laser by using a crystalline-based Kerr frequency comb as a transfer oscillator. We demonstrate absolute phase noise levels of −110 dBc/Hz at 200-Hz offset from a 14 GHz carrier. © 2019 The Author(s)

Sinc-shaped temporal pulse trains have a spectrally efficient, rectangular Nyquist spectrum. We demonstrate the simultaneous and reconfigurable optical generation of multiple Nyquist-shaped wavelength-division-multiplexed (WDM) channels having temporal sinc-shaped pulse trains as data carriers. The channels are generated through the insertion of coherent lines using cascaded continuous-wave amplitude modulation around the spectral lines of a microresonator-based Kerr optical frequency comb. For each of nine Kerr frequency comb lines, we insert sub-groups of uniform and coherent lines to generate nine WDM channels. The deviations from ideal Nyquist pulses for the nine channels at repetition rates of 6 and 2GHz are between 4.2%-6.1% and 2%-4.5%, respectively. Each WDM channel is modulated with on-off keying (OOK) at 6 Gbit/s. In addition, we show the reconfigurability of this method by varying the number of WDM channels, the generated sinc-shaped pulse train repetition rates, the duration, and the number of zero-crossings.

Since their discovery, microresonator frequency combs have made considerable progress [1]. Octave spanning combs [2, 3], data transmission applications [4] and mode-locking [5, 6] have been demonstrated. There have also been advances in understanding the properties and the generation process of the frequency combs inside the resonators [7].

We demonstrate a new type of Kerr frequency comb with expanded parametric range, where the momentum conservation is ensured by azimuthal modulation of the cavity dispersion. A coherent multispectral frequency comb covering telecommunication O, C, L, and 2 μm bands is observed and characterized.

We show that both the power and repetition rate of a frequency comb generated\nin a nonlinear ring resonator, pumped with continuous wave (cw) coherent light,\nare modulated. The modulation is brought about by the interaction of the cw\nbackground with optical pulses excited in the resonator, and occurs in\nresonators with nonzero high-order chromatic dispersion and\nwavelength-dependent quality factor. The modulation frequency corresponds to\nthe detuning of the pump frequency from the eigenfrequency of the pumped mode\nin the resonator.\n

We report the experimental observation of a modulation instability induced Kerr frequency comb in an all fiber Fabry-Pérot resonator. We fully characterized, in intensity and phase, the frequency comb using a commercial 10 MHz resolution heterodyne detection system to reveal more than 125 comb teeth within each of the modulation instability sidelobes. Moreover, we were able to reveal the fine temporal structure in phase and intensity of the output Turing patterns. The experimental results are generally in good agreement with numerical simulations.

On-chip Kerr frequency combs open up unprecedented opportunities for developing compact, low-cost, and high-density wavelength-division multiplexing (WDM) techniques for optical communications and optical interconnects. However, to achieve high-density WDM channels, a large-radius microring could be used to develop a Kerr frequency comb with a small free spectral range (FSR), inevitably increasing the comb's footprint and threshold. Herein, we theoretically study a dual-mode Kerr frequency comb based on a graphene-on-silicon (GOS) microring to overcome the limitation. Theoretical results show that a TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -mode comb with a 50-dB bandwidth of 200 nm and FSR of 170 GHz, and a TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -mode comb with a 50-dB bandwidth of 130 nm and FSR of 212.4 GHz could be generated in the single GOS microring. Moreover, the TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -mode and TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -mode combs could be selectively activated via modulating the Fermi level of the graphene nanoribbons integrated on the silicon microring. The study is expected to provide a useful technique for developing on-chip coherent light sources for high-speed optical communications.