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Four-wave mixing has extensively been investigated for various applications such as communications, spectroscopy, metrology, quantum computing and bio-imaging. However, there is a clear desire to implement these functionalities in a small footprint nonlinear platform, being capable of efficient operation across a large optical bandwidth. Many such integrated platforms have been explored, but suffer from intrinsic significant performance degradation, because conventional approaches of nonlinear photonic waveguide geometry construction for dispersion engineering focus on waveguide cross section and result in always being multimode as a byproduct. Here we propose and demonstrate a methodology that utilizes not only the impact of the waveguide cross section on the modal and dispersion behavior of the waveguide but also includes the impact of the waveguide bend for cutting off high-order modes. This approach results in simultaneous single-mode operation and dispersion engineering for very broadband operation of four-wave mixing. While we implemented this in silicon nitride waveguides, which has emerged as a promising platform capable of continuous-wave optical parametric amplification, the design approach can be universally used with other platforms as well. By also considering both second- and fourth-order dispersion we achieve unprecedented amplification bandwidths of approximately 300 nm in super-low-loss silicon nitride nonlinear waveguides. In addition, penalty-free all-optical wavelength conversion of 100 Gbit/s data in a single optical carrier over 200 nm is realized, for the first time, without optical amplification of signal or idler waves. These single-mode hyper-dispersion-engineered nonlinear integrated waveguides can become practical building blocks in versatile nonlinear photonic devices and optical networks.

Narrow-linewidth yet tunable laser oscillators are one of the most important tools for precision metrology, optical atomic clocks, sensing and quantum computing. Commonly used tunable coherent oscillators are based on stimulated emission or stimulated Brillouin scattering; as a result, the operating wavelength band is limited by the gain media. Based on nonlinear optical gain, optical parametric oscillators (OPOs) enable coherent signal generation within the whole transparency window of the medium used. However, the demonstration of OPO-based Hertz-level linewidth and tunable oscillators has remained elusive. Here, we present a tunable coherent oscillator based on a multimode coherent OPO in a high-Q microresonator, i.e., a microcomb. Single-mode coherent oscillation is realized through self-injection locking (SIL) of one selected comb line. We achieve coarse tuning up to 20 nm, and an intrinsic linewidth down to sub-Hertz level, which is three orders of magnitude lower than the pump. Furthermore, we demonstrate that this scheme results into repetition rate stabilization of the microcomb. These results open exciting possibilities for generating tunable coherent radiation where stimulated emission materials are difficult to obtain, and the stabilization of microcomb sources beyond the limits imposed by the thermorefractive noise in the cavity.

Multiple applications of relevance in photonics, such as spectrally efficient coherent communications, microwave synthesis or the calibration of astronomical spectrographs, would benefit from soliton microcombs operating at repetition rates <50GHz. However, attaining soliton microcombs with low repetition rates using photonic integration technologies represents a formidable challenge. Expanding the cavity volume results in a drop of intracavity intensity that can only be offset by an encompassing rise in quality factor. In addition, reducing the footprint of the microresonator on a planar integrated circuit requires race-track designs that typically result into extra modal coupling losses and disruptions into the dispersion, preventing the generation of the dissipative single soliton state. Here, we report the generation of sub-50GHz soliton microcombs in dispersion-engineered silicon nitride microresonators. In contrast to other approaches, our devices feature an optimized racetrack design that minimizes the coupling to higher-order modes and reduces the footprint size by an order of magnitude to ~1mm2. The statistical intrinsic Q reaches 19 million, and soliton microcombs at 20.5GHz and 14.0GHz repetition rates are successfully generated. Importantly, the fabrication process is entirely subtractive, meaning that the devices can be directly patterned on the Si3N4 film. This standard approach facilitates integration with further components and devices.

Optical amplifiers are essential in numerous photonic applications. Parametric amplifiers, relying on a nonlinear material to create amplification, are uniquely promising as they can amplify without generating excess noise. Here, we demonstrate amplification based on the 3rd order nonlinearity in a single chip, while in addition reporting a noise figure significantly below the conventional quantum limit when operated in phase-sensitive mode. Our results show the potential of nanophotonics for realizing continuous-wave parametric amplification that can enable applications in optical communications, signal processing and quantum optics across a wide range of frequencies., Comment: Parts of this works were presented at CLEO-PDP and OFC-PDP

Receiver sensitivity is a particularly important metric in optical communication links operating at low signal-to-noise ratios (SNRs), for example in deep-space communication, since it directly limits the maximum achievable reach and data rate. Pulse position modulation (PPM) with direct detection photon-counting detectors are the most power-efficient solution known, however, the sensitivity gain comes at the expense of reduced spectral efficiency. We show that quadrature phase-shift keying (QPSK) modulation with a phase-sensitive ultralow noise pre-amplified coherent receiver outperforms other well-known power-efficient multi-dimensional coherent modulation formats, while simultaneously having higher spectral efficiency. It also results in better sensitivity than PPM for orders up to 64 with ideal direct detection using photon-counting receivers. This is because of the bit error rate characteristics favoring the QPSK format when forward error correction with a large overhead is considered.

We propose a simple approach to implement a tunable, high power and narrow linewidth laser source based on a series of highly coherent tones from an electro-optic frequency comb and a set of 3 DFB slave lasers. We experimentally demonstrate approximately 1.25 THz (10 nm) of tuning within the C-Band centered at 192.9 THz (1555 nm). The output power is approximately 100 mW (20 dBm), with a side band suppression ratio greater than 55 dB, and a linewidth below 400 Hz across the full range of tunability. This approach is scalable and may be extended to cover a significantly broader optical spectral range.

Many physical systems display quantized energy states. In optics, interacting resonant cavities show a transmission spectrum with split eigenfrequencies, similar to the split energy levels that result from interacting states in bonded multi-atomic, i.e. molecular, systems. Here, we study the nonlinear dynamics of photonic diatomic molecules in linearly coupled microresonators and demonstrate that the system supports the formation of self-enforcing solitary waves when a laser is tuned across a split energy level. The output corresponds to a frequency comb (microcomb) whose characteristics in terms of power spectral distribution are unattainable in single-mode (atomic) systems. Photonic molecule microcombs are coherent, reproducible, and reach high conversion efficiency and spectral flatness whilst operated with a laser power of a few milliwatts. These properties can favor the heterogeneous integration of microcombs with semiconductor laser technology and facilitate applications in optical communications, spectroscopy and astronomy.

Noise fundamentally limits the capacity and reach in all communication links. In optical space communications, noise primarily originates from the detection process and limits the signal fidelity. . Therefore, the receiver sensitivity plays a key role, dictating the minimum power needed to recover the information transmitted. The widely explored approach of using the pulse-position modulation format trades-off sensitivity against receiver bandwidth and thus data-rate. Here we report on a novel, spectrally efficient, approach based on a coherent receiver with a near-noiseless phase-sensitive pre-amplifier operating at room temperature and demonstrate a sensitivity of one photon-per-bit of incident power at a data rate of 10 Gb/s. The results provide a path to future high-capacity inter-satellite and deep space, and other free-space communication links, Comment: 12 pages, 3 figures

Modern optical communication systems transmit multiple frequency channels, each operating very close to its theoretical limit. The total bandwidth can reach 10THz limited by the optical amplifiers. Maximizing spectral efficiency, the throughput per bandwidth is thus crucial. Replacing independent lasers with an optical frequency comb can enable very dense packing by overcoming relative drifts. However, to date, interference from non-ideal spectral shaping prevents exploiting the full potential of frequency combs. Here, we demonstrate comb-enabled multi-channel digital signal processing, which overcomes these limitations. Each channel is detected using an independent coherent receiver and processed at two samples-per-symbol. By accounting for the unique comb stability and exploiting aliasing in the design of the dynamic equalizer, we show that the optimal spectral shape changes, resulting in a higher signal to noise ratio that pushes the optimal symbol rate towards and even \emph{above} the channel spacing, resulting in the first example of frequency-domain super-Nyquist transmission with multi-channel detection for optical systems. The scheme is verified both in back-to-back configuration and in single span transmission of a 21 channel superchannel originating from a 25GHz-spaced frequency comb. By jointly processing 3 wavelength channels at a time, we achieve spectral efficiency beyond what is possible with independent channels. At the same time, one significantly relaxes the hardware requirements on digital-to-analog resolution and bandwidth, and well as filter tap numbers. Our results show that comb-enabled multi-channel processing can overcome the limitations of classical dense wavelength division multiplexing systems by enabling tighter spacing to reach the ultimate spectral efficiency in optical communications., Comment: 9 pages, 8 figures

Microresonator frequency combs (microcombs) are enabling new applications in frequency synthesis and metrology from high-speed laser ranging to coherent optical communications. One critical parameter that dictates the performance of the microcomb is the optical quality factor (Q) of the microresonator. Microresonators fabricated in planar structures such as silicon nitride (Si3N4) allow for dispersion engineering and the possibility to monolithically integrate the microcomb with other photonic devices. However, the relatively large refractive index contrast and the tight optical confinement required for dispersion engineering make it challenging to attain Si3N4 microresonators with Qs > 10 000 000 using standard subtractive processing methods. In this work, we achieve ultra-smooth Si3N4 microresonators featuring mean intrinsic Qs around 11 million. The cross-section geometry can be precisely engineered in the telecommunications band to achieve either normal or anomalous dispersion, and we demonstrate the generation of mode-locked dark-pulse Kerr combs as well as soliton microcombs. Such high-Qs allow us to generate soliton microcombs with photodetectable repetition rates, demonstrated here for the first time in Si3N4 microresonators fabricated using a subtractive processing method. These results enhance the possibilities for co-integration of microcombs with high-performance photonic devices, such as narrow-linewidth external-cavity diode lasers, ultra-narrow filters and demultiplexers., Comment: 9pages, 4 figures

Fiber-optical networks are a crucial telecommunication infrastructure in society. Wavelength division multiplexing allows for transmitting parallel data streams over the fiber bandwidth, and coherent detection enables the use of sophisticated modulation formats and electronic compensation of signal impairments. In the future, optical frequency combs may replace multiple lasers used for the different wavelength channels. We demonstrate two novel signal processing schemes that take advantage of the broadband phase coherence of optical frequency combs. This approach allows for a more efficient estimation and compensation of optical phase noise in coherent communication systems, which can significantly simplify the signal processing or increase the transmission performance. With further advances in space division multiplexing and chip-scale frequency comb sources, these findings pave the way for compact energy-efficient optical transceivers., Comment: 17 pages, 9 figures

Optical communication systems have come through five orders of magnitude improvement in data rate over the last three decades. The increased demand in data traffic and the limited optoelectronic component bandwidths have led to state-of-the-art systems employing hundreds of separate lasers in each transmitter. Given the limited optical amplifier bandwidths, focus is now shifting to maximize the spectral efficiency, SE. However, the frequency jitter from neighbouring lasers results in uncertainties of the exact channel wavelength, requiring large guardbands to avoid catastrophic channel overlap. Optical frequency combs with optimal line spacings (typically around 10-50 GHz) can overcome these limitations and maximize the SE. Recent developments in microresonator-based soliton frequency combs (hereafter microcombs) promise a compact, power efficient multi-wavelength and phase-locked light source for optical communications. Here we demonstrate a microcomb-based communication link achieving state-of-the-art spectral efficiency that has previously only been possible with bulk-optics systems. Compared to previous microcomb works in optical communications, our microcomb features a narrow line spacing of 22.1 GHz. In addition, it provides a four order-of-magnitude more stable line spacing compared to free-running lasers. The optical signal-to-noise ratio (OSNR) is sufficient for information encoding using state-of-the-art high-order modulation formats. This enables us to demonstrate transmission of a 12 Tb/s superchannel over distances ranging from a single 82 km span with an SE exceeding 10 bits/s/Hz, to 2000 km with an SE higher than 6 bits/s/Hz. These results demonstrate that microcombs can attain the SE that will spearhead future optical networks.

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.

Silicon nitride is awell-established material for photonic devices and integrated circuits. It displays a broad transparency window spanning from the visible to the mid-IR and waveguides can be manufactured with low losses. An absence of nonlinear multi-photon absorption in the erbium lightwave communications band has enabled various nonlinear optic applications in the past decade. Silicon nitride is a dielectric material whose optical and mechanical properties strongly depend on the deposition conditions. In particular, the optical bandgap can be modified with the gas flow ratio during low-pressure chemical vapor deposition (LPCVD). Here we show that this parameter can be controlled in a highly reproducible manner, providing an approach to synthesize the nonlinear Kerr coefficient of the material. This holistic empirical study provides relevant guidelines to optimize the properties of LPCVD silicon nitride waveguides for nonlinear optics applications that rely on the Kerr effect.

Microresonator-based frequency combs are strong contenders as light sources for wavelength-division multiplexing (WDM). Recent demonstrations have shown the potential of microresonator combs for replacing tens of WDM lasers with a single laser-pumped device. These experiments relied on microresonators displaying anomalous dispersion. Devices operating in the normal dispersion offer the prospect of attaining high power conversion efficiency - an aspect that will be crucial in the future for enabling energy-efficient coherent communications with higher order modulation formats or lighting several spatial channels in space-division multiplexing. Here we report the experimental demonstration of coherent communications using normal dispersion microresonator combs. With polarization multiplexed (PM) quadrature phase-shift keying, we transmitted data over more than 6300 km in single-mode fiber. In a second experiment, we reached beyond 700 km with PM 16 quadrature amplitude modulation format and an aggregate data rate above 900 Gbit/s assuming 6% error correction overhead. These results represent the longest fiber transmission ever achieved using an integrated comb source., Comment: 7 pages, 6 figures

Dual-comb interferometry is a measurement technique that uses two laser frequency combs to retrieve complex spectra in a line-by-line basis. This technique can be implemented with electro-optic frequency combs, offering intrinsic mutual coherence, high acquisition speed and flexible repetition-rate operation. A challenge with the operation of this kind of frequency comb in dual-comb interferometry is its limited optical bandwidth. Here, we use coherent spectral broadening and demonstrate electro-optic dual-comb interferometry over the entire telecommunications C band (200 lines covering ~ 40 nm, measured within 10 microseconds at 100 signal-to-noise ratio per spectral line). These results offer new prospects for electro-optic dual-comb interferometry as a suitable technology for high-speed broadband metrology, for example in optical coherence tomography or coherent Raman microscopy.

We experimentally investigate mutual information and generalized mutual information for coherent optical transmission systems. The impact of the assumed channel distribution on the achievable rate is investigated for distributions in up to four dimensions. Single channel and wavelength division multiplexing (WDM) transmission over transmission links with and without inline dispersion compensation are studied. We show that for conventional WDM systems without inline dispersion compensation, a circularly symmetric complex Gaussian distribution is a good approximation of the channel. For other channels, such as with inline dispersion compensation, this is no longer true and gains in the achievable information rate are obtained by considering more sophisticated four-dimensional (4D) distributions. We also show that for nonlinear channels, gains in the achievable information rate can also be achieved by estimating the mean values of the received constellation in four dimensions. The highest gain for such channels is seen for a 4D correlated Gaussian distribution.