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Integrated photonics has profoundly affected a wide range of technologies underpinning modern society1–4. The ability to fabricate a complete optical system on a chip offers unrivalled scalability, weight, cost and power efficiency5,6. Over the last decade, the progression from pure III–V materials platforms to silicon photonics has significantly broadened the scope of integrated photonics, by combining integrated lasers with the high-volume, advanced fabrication capabilities of the commercial electronics industry7,8. Yet, despite remarkable manufacturing advantages, reliance on silicon-based waveguides currently limits the spectral window available to photonic integrated circuits (PICs). Here, we present a new generation of integrated photonics by directly uniting III–V materials with silicon nitride waveguides on Si wafers. Using this technology, we present a fully integrated PIC at photon energies greater than the bandgap of silicon, demonstrating essential photonic building blocks, including lasers, amplifiers, photodetectors, modulators and passives, all operating at submicrometre wavelengths. Using this platform, we achieve unprecedented coherence and tunability in an integrated laser at short wavelength. Furthermore, by making use of this higher photon energy, we demonstrate superb high-temperature performance and kHz-level fundamental linewidths at elevated temperatures. Given the many potential applications at short wavelengths, the success of this integration strategy unlocks a broad range of new integrated photonics applications.

High-coherence visible and near-visible laser sources are centrally important to the operation of advanced position/navigation/timing systems as well as classical/quantum sensing systems. However, the complexity and size of these bench-top lasers are an impediment to their transition beyond the laboratory. Here, a system-on-chip that emits high-coherence near-visible lightwaves is demonstrated. The devices rely upon a new approach wherein wavelength conversion and coherence increase by self-injection locking are combined within a single nonlinear resonator. This simplified approach is demonstrated in a hybridly-integrated device and provides a short-term linewidth of around 4.7 kHz (10 kHz before filtering). On-chip converted optical power over 2 mW is also obtained. Moreover, measurements show that heterogeneous integration can result in a conversion efficiency higher than 25% with an output power over 11 mW. Because the approach uses mature III–V pump lasers in combination with thin-film lithium niobate, it can be scaled for low-cost manufacturing of high-coherence visible emitters. Also, the coherence generation process can be transferred to other frequency conversion processes, including optical parametric oscillation, sum/difference frequency generation, and third-harmonic generation.

Silicon nitride (SiN) waveguides with ultra-low optical loss enable integrated photonic applications including low noise, narrow linewidth lasers, chip-scale nonlinear photonics, and microwave photonics. Lasers are key components to SiN photonic integrated circuits (PICs), but are difficult to fully integrate with low-index SiN waveguides due to their large mismatch with the high-index III-V gain materials. The recent demonstration of multilayer heterogeneous integration provides a practical solution and enabled the first-generation of lasers fully integrated with SiN waveguides. However, a laser with high device yield and high output power at telecommunication wavelengths, where photonics applications are clustered, is still missing, hindered by large mode transition loss, non-optimized cavity design, and a complicated fabrication process. Here, we report high-performance lasers on SiN with tens of milliwatts output power through the SiN waveguide and sub-kHz fundamental linewidth, addressing all the aforementioned issues. We also show Hertz-level fundamental linewidth lasers are achievable with the developed integration techniques. These lasers, together with high-Q SiN resonators, mark a milestone towards a fully integrated low-noise silicon nitride photonics platform. This laser should find potential applications in LIDAR, microwave photonics and coherent optical communications., Achieving high output power and low noise integrated lasers is a major challenge. Here the authors experimentally demonstrate integrated lasers from a Si/SiN heterogeneous platform that shows Hertz-level linewidth, paving the way toward fully integrating low-noise silicon nitride photonics in volume using real devices for lasing.

Lasers with hertz linewidths at time scales of seconds are critical for metrology, timekeeping, and manipulation of quantum systems. Such frequency stability relies on bulk-optic lasers and reference cavities, where increased size is leveraged to reduce noise but with the trade-off of cost, hand assembly, and limited applications. Alternatively, planar waveguide–based lasers enjoy complementary metal-oxide semiconductor scalability yet are fundamentally limited from achieving hertz linewidths by stochastic noise and thermal sensitivity. In this work, we demonstrate a laser system with a 1-s linewidth of 1.1 Hz and fractional frequency instability below 10 −14 to 1 s. This low-noise performance leverages integrated lasers together with an 8-ml vacuum-gap cavity using microfabricated mirrors. All critical components are lithographically defined on planar substrates, holding potential for high-volume manufacturing. Consequently, this work provides an important advance toward compact lasers with hertz linewidths for portable optical clocks, radio frequency photonic oscillators, and related communication and navigation systems.

Compact, low-noise microwave sources are required throughout a wide range of application areas including frequency metrology, wireless-communications and airborne radar systems. And the photonic generation of microwaves using soliton microcombs offers a path towards integrated, low noise microwave signal sources. In these devices, a so called quiet-point of operation has been shown to reduce microwave frequency noise. Such operation decouples pump frequency noise from the soliton’s motion by balancing the Raman self-frequency shift with dispersive-wave recoil. Here, we explore the limit of this noise suppression approach and reveal a fundamental noise mechanism associated with fluctuations of the dispersive wave frequency. At the same time, pump noise reduction by as much as 36 dB is demonstrated. This fundamental noise mechanism is expected to impact microwave noise (and pulse timing jitter) whenever solitons radiate into dispersive waves belonging to different spatial mode families., Here the authors explore the noise spectrum of soliton microcomb when the pump is decoupled from the solitons motion by balancing the Raman shift with the emitted dispersive wave. Based on the analysis of the phase noise and the soliton repetition rate, they identify the uncorrelated thermal fluctuations as underlying mechanism.

Driven by narrow-linewidth bench-top lasers, coherent optical systems spanning optical communications, metrology and sensing provide unrivalled performance. To transfer these capabilities from the laboratory to the real world, a key missing ingredient is a mass-produced integrated laser with superior coherence. Here, we bridge conventional semiconductor lasers and coherent optical systems using CMOS-foundry-fabricated microresonators with record high $Q$ factor over 260 million and finesse over 42,000. Five orders-of-magnitude noise reduction in the pump laser is demonstrated, and for the first time, fundamental noise below 1 Hz$^2$ Hz$^{-1}$ is achieved in an electrically-pumped integrated laser. Moreover, the same configuration is shown to relieve dispersion requirements for microcomb generation that have handicapped certain nonlinear platforms. The simultaneous realization of record-high $Q$ factor, highly coherent lasers and frequency combs using foundry-based technologies paves the way for volume manufacturing of a wide range of coherent optical systems., Comment: 19 pages, 11 figures

A semiconductor laser is self-injection-locked to a spiral, ultra-high-Q silicon-nitride resonator. The laser attains record-low frequency noise noise floor (0.006 Hz2/Hz or 40 mHz white-noise-linewidth) with stability at low-offset frequencies comparable to high-performance fiber lasers.

Pulsed pumping of a silica microcavity is used to generate single-soliton microcombs with conversion efficiency of 54%. Analytical expressions are developed by the Lagrangian approach and applied to model the results.

By integrating two periodic poling structures into a single high-Q lithium niobate microresonator, cascaded SHG and SFG achieved third-harmonic generation on-chip at a wavelength of 520 nm with an efficiency of 0.6%.

We demonstrate narrow linewidth, second-harmonic generation using a semi-conductor DFB laser self-injection locked with a high-Q lithium niobate microresonator. A second-harmonic linewidth of 31kHz is achieved from 36dB pump frequency noise suppression.

Dual-comb spectroscopy (DCS) offers high sensitivity and wide spectral coverage without the need for bulky spectrometers or mechanical moving parts. And DCS in the mid-infrared (mid-IR) is of keen interest because of inherently strong molecular spectroscopic signatures in these bands. We report GHz-resolution mid-IR DCS of methane and ethane that is derived from counter-propagating (CP) soliton microcombs in combination with interleaved difference frequency generation. Because all four combs required to generate the two mid-IR combs rely upon stability derived from a single high-Q microcavity, the system architecture is both simplified and does not require external frequency locking. Methane and ethane spectra are measured over intervals as short as 0.5 ms, a time scale that can be further reduced using a different CP soliton arrangement. Also, tuning of spectral resolution on demand is demonstrated. Although at an early phase of development, the results are a step towards mid-IR gas sensors with chip-based architectures for chemical threat detection, breath analysis, combustion studies, and outdoor observation of trace gases., Chip-based architectures for mid-infrared gas sensing could enable many applications. In this direction, the authors demonstrate a microcomb-based dual-comb spectroscopy sensor with GHz resolution in the mid-IR band, with stability completely determined by a single high-Q microresonator.

Optical microresonators with high quality ($Q$) factors are essential to a wide range of integrated photonic devices. Steady efforts have been directed towards increasing microresonator $Q$ factors across a variety of platforms. With success in reducing microfabrication process-related optical loss as a limitation of $Q$, the ultimate attainable $Q$, as determined solely by the constituent microresonator material absorption, has come into focus. Here, we report measurements of the material-limited $Q$ factors in several photonic material platforms. High-$Q$ microresonators are fabricated from thin films of SiO$_2$, Si$_3$N$_4$, Al$_{0.2}$Ga$_{0.8}$As and Ta$_2$O$_5$. By using cavity-enhanced photothermal spectroscopy, the material-limited $Q$ is determined. The method simultaneously measures the Kerr nonlinearity in each material and reveals how material nonlinearity and ultimate $Q$ vary in a complementary fashion across photonic materials. Besides guiding microresonator design and material development in four material platforms, the results help establish performance limits in future photonic integrated systems., Maodong Gao, Qi-Fan Yang and Qing-Xin Ji contributed equally to this work. 9 pages, 4 figures, 1 table

A conventional semiconductor DFB laser is self-injection-locked to a CMOS-foundry- fabricated ultra-high Q silicon nitride microresonator, suppressing high-offset frequency noise to 0.2 Hz2 Hz-1 and yielding instantaneous linewidth of 1.2 Hz.

A fundamental frequency noise of 9 mHz·Hz/Hz is demonstrated in an on-chip Brillouin laser. The noise measurement uses the frequency discrimination method enhanced by cross-correlator. The results set new performance targets for chip-based laser platforms.

Coherently pumped (Kerr) solitons in an ideal optical microcavity are expected to undergo random quantum motion that determines fundamental performance limits in applications of the soliton microcombs1. Here this random walk and its impact on Kerr soliton timing jitter are studied experimentally. The quantum limit is discerned by measuring the relative position of counter-propagating solitons2. Their relative motion features weak interactions and also presents common-mode suppression of technical noise, which typically hides the quantum fluctuations. This is in contrast to co-propagating solitons, which are found to have relative timing jitter well below the quantum limit of a single soliton on account of strong correlation of their mutual motion. Good agreement is found between theory and experiment. The results establish the fundamental limits to timing jitter in soliton microcombs and provide new insights on multisoliton physics. Quantum jitter fundamentally limits the performance of microresonator frequency combs. The timing jitter of the solitons that generate the comb spectra is analysed, reaching the quantum limit and establishing fundamental limits for soliton microcombs.

Microcomb based dual-comb spectroscopy of methane in the mid-infrared is demonstrated with GHz resolution. This fine resolution is enabled by generating spectrally densified mid-infrared combs via interleaved difference-frequency-generation.

The linewidth of regenerative oscillators is enhanced by amplitude–phase coupling of the oscillator field [Phys. Rev. 160, 290 (1967)]. In laser oscillators, this effect is well known for its impact on semiconductor laser performance. Here, this coupling is studied in Brillouin lasers. Because their gain is parametric, the coupling and linewidth enhancement are shown to originate from phase mismatch. The theory is confirmed by measurement of linewidth in a microcavity Brillouin laser, and enhancements as large as 50 × are measured. The results show that pump wavelength and device temperature should be carefully selected and controlled to minimize linewidth. More generally, this work provides a new perspective on the linewidth enhancement effect.

Optical frequency combs have a wide range of applications in science and technology(1). An important development for miniature and integrated comb systems is the formation of dissipative Kerr solitons in coherently pumped high-quality-factor optical microresonators(2-9). Such soliton microcombs(10) have been applied to spectroscopy(11-13), the search for exoplanets(14,15), optical frequency synthesis(16), time keeping(17) and other areas(10). In addition, the recent integration of microresonators with lasers has revealed the viability of fully chip-based soliton microcombs(18,19). However, the operation of microcombs requires complex startup and feedback protocols that necessitate difficult-to-integrate optical and electrical components, and microcombs operating at rates that are compatible with electronic circuits-as is required in nearly all comb systems-have not yet been integrated with pump lasers because of their high power requirements. Here we experimentally demonstrate and theoretically describe a turnkey operation regime for soliton microcombs co-integrated with a pump laser. We show the appearance of an operating point at which solitons are immediately generated by turning the pump laser on, thereby eliminating the need for photonic and electronic control circuitry. These features are combined with high-quality-factor Si3N4 resonators to provide microcombs with repetition frequencies as low as 15 gigahertz that are fully integrated into an industry standard (butterfly) package, thereby offering compelling advantages for high-volume production.

A record Q-factor of 1.1 billion is demonstrated in on-chip silica whispering-gallery resonators. Using the devices, sub-milliwatt parametric oscillation threshold is measured in 9 GHz free-spectral-range devices.

Generation of mid-infrared combs (3.3 micron band) with GigaHertz line spacing is demonstrated by interleaved difference-frequency-generation. The method, applied to a 22 GHz repetition-rate microcomb, is useful for spectral densification of sparse microcomb spectra.

The phase noise of the soliton repetition rate is experimentally characterized in silica microresonators. In conjunction with dispersive wave quieting of pump technical noise, spatio-temporal fluctuations of distinct transverse modes set a limit to performance.

theoretical calculation and supplement experiment data

We self-injection-lock a diode laser to a 1.41 m long, ultra-high Q integrated resonator. The hybrid integrated laser reaches a frequency noise floor of 0.006 H z 2 / H z at 4 MHz offset, corresponding to a Lorentzian linewidth below 40 mHz—a record among semiconductor lasers. It also exhibits exceptional stability at low-offset frequencies, with frequency noise of 200 H z 2 / H z at 100 Hz offset. Such performance, realized in a system comprised entirely of integrated photonic chips, marks a milestone in the development of integrated photonics; and, for the first time, to the best of our knowledge, exceeds the frequency noise performance of commercially available, high-performance fiber lasers.

A spectrometer is demonstrated using self-locked counter-propagating soliton frequency combs in a high-Q silica microresonator. Fast tuning laser waveforms and molecular absorption features are measured with kiloHertz to MegaHertz resolution.

Phonons at gigahertz frequencies interact with electrons, photons, and atomic systems in solids, and therefore have extensive applications in signal processing, sensing, and quantum technologies. Surface acoustic wave (SAW) resonators that confine surface phonons can play a crucial role in such integrated phononic systems due to small mode size, low dissipation, and efficient electrical transduction. To date, it has been challenging to achieve high quality (Q) factor and small phonon mode size for SAW resonators at gigahertz frequencies. Here, we present a methodology to design compact high-Q SAW resonators on lithium niobate operating at gigahertz frequencies. We experimentally verify out designs and demonstrate Q factors in excess of $2\times10^4$ at room temperature ($6\times10^4$ at 4 Kelvin) and mode area as low as $1.87 \lambda^2$. This is achieved by phononic band structure engineering, which provides high confinement with low mechanical loss. The frequency-Q products (fQ) of our SAW resonators are greater than $10^{13}$. These high-fQ and small mode size SAW resonators could enable applications in quantum phononics and integrated hybrid systems with phonons, photons, and solid-state qubits.

While soliton microcombs offer the potential for integration of powerful frequency metrology and precision spectroscopy systems, their operation requires complex startup and feedback protocols that necessitate difficult-to-integrate optical and electrical components. Moreover, CMOS-rate microcombs, required in nearly all comb systems, have resisted integration because of their power requirements. Here, a regime for turnkey operation of soliton microcombs co-integrated with a pump laser is demonstrated and theoretically explained. Significantly, a new operating point is shown to appear from which solitons are generated through binary turn-on and turn-off of the pump laser, thereby eliminating all photonic/electronic control circuitry. These features are combined with high-Q $Si_3N_4$ resonators to fully integrate into a butterfly package microcombs with CMOS frequencies as low as 15 GHz, offering compelling advantages for high-volume production., Comment: Boqiang Shen, Lin Chang, Junqiu Liu, Heming Wang and Qi-Fan Yang contributed equally to this work

High optical quality (Q) factors are critically important in optical microcavities, where performance in applications spanning nonlinear optics to cavity quantum electrodynamics is determined. Here, a record Q factor of over 1.1 billion is demonstrated for on-chip optical resonators. Using silica whispering-gallery resonators on silicon, Q-factor data is measured over wavelengths spanning the C/L bands (100 nm) and for a range of resonator sizes and mode families. A record low sub-milliwatt parametric oscillation threshold is also measured in 9 GHz free-spectral-range devices. The results show the potential for thermal silica on silicon as a resonator material.

With their compact size and semiconductor-chip-based operation, frequency microcombs can be an invaluable light source for gas spectrcoscopy. However, the generation of mid-infrared (mid-IR) frequency combs with gigahertz line spacing as required to resolve many gas spectra represents a significant challenge for these devices. Here, a technique referred to as interleaved difference-frequency generation (iDFG) is introduced that densifies the spectral line spacing upon conversion of near-IR comb light into the mid-IR light. A soliton microcomb is used as both a comb light source and microwave oscillator in a demonstration, and the spectrum of methane is measured to illustrate how the resulting mid-IR comb avoids spectral undersampling. Beyond demonstration of the iDFG technique, this work represents an important feasibility step towards more compact and potentially chip-based mid-IR gas spectroscopy modules.

We control the electronic structure of the silicon-vacancy (SiV) color-center in diamond by changing its static strain environment with a nano-electro-mechanical system. This allows deterministic and local tuning of SiV optical and spin transition frequencies over a wide range, an essential step towards multi-qubit networks. In the process, we infer the strain Hamiltonian of the SiV revealing large strain susceptibilities of order 1 PHz/strain for the electronic orbital states. We identify regimes where the spin-orbit interaction results in a large strain suseptibility of order 100 THz/strain for spin transitions, and propose an experiment where the SiV spin is strongly coupled to a nanomechanical resonator., Comment: 14 pages, 10 figures

In this paper, we provide a realistic framework that investors can use to optimize hedge fund portfolio strategy allocations. Our approach includes important aspects that investors need to address in the real world, such as how limited resources can restrict the ability to conduct multiple due diligences. Additionally, our approach is not based on a utility function, but on an easily quantifiable preference parameter, lambda. We need to account for higher moments of the return distribution within our optimization and approximate a best-fit distribution. Thus we replace the empirical return distributions, which are often skewed or exhibit excess kurtosis, with two normal distributions. We then use the estimated return distributions in the strategy optimization. Our dataset comes from the Lipper TASS Hedge Fund Database and covers the June 1996-December 2008 time period. Our results show in- and out-of-sample that our framework yields superior results to the Markowitz framework. It is also better able to manage regime switches, which tend to occur frequently during crises. Lastly, to test our results for stability, we use robustness tests, which allow for the time-varying correlation structures of the strategies.

We consider a Lucas-type exchange economy with two heterogeneous stocks (trees) and a representative investor with constant relative risk aversion. The dividend process for one stock follows a geometric Brownian motion with constant and known parameters. The expected dividend growth rate for the other tree is stochastic and in general unobservable, although there may be a signal from which the investor can learn about its current value. We find that the equilibrium quantities in our model significantly depend on the information structure and on the level of risk aversion. While an observable stochastic drift mainly makes the economy more risky, a latent expected growth rate process with learning significantly changes the equilibrium price-dividend ratios, price reactions to dividend and drift innovations, expected returns, volatilities, correlations, and differences between the stocks. These effects are the more pronounced the more risk averse the representative investor.

In this paper we analyze an economy with two heterogeneous investors who both exhibit misspecified filtering models for the unobservable expected growth rate of the aggregated dividend. A key result of our analysis with respect to long-run investor survival is that there are degrees of model misspecification on the part of one investor for which there is no compensation by the other investor's deficiency. The main finding with respect to the asset pricing properties of our model is that the two dimensions of asset pricing and survival are basically independent. In scenarios when the investors are more similar with respect to their expected consumption shares, return volatilities can nevertheless be higher than in cases when they are very different.

In this paper we analyze an economy with two heterogeneous investors who both exhibit misspecified filtering models for the unobservable expected growth rate of the aggregated dividend. A key result of our analysis with respect to long-run investor survival is that there are degrees of model misspecification on the part of one investor for which there is no compensation by the other investor's deficiency. The main finding with respect to the asset pricing properties of our model is that the two dimensions of asset pricing and survival are basically independent. In scenarios when the investors are more similar with respect to their expected consumption shares, return volatilities can nevertheless be higher than in cases when they are very different.

We consider an exchange economy with two groups of investors with identical CRRA utility function but heterogeneous beliefs. The stochastic central tendency of the dividend drift is not observable. Rational investors learn about it from the dividend drift and a signal, while irrational investors base their inference only on the dividend drift observations. The model shows that heterogeneous beliefs increase the bond yields and have strong impact on yield volatilities and correlations. The effect of the level of difference in beliefs is stronger for short term yields, while the effect of consumption share fluctuations between investor groups is stronger for medium and long term yields.