Photonic chip-based low-noise microwave oscillator.

Numerous modern technologies are reliant on the low-phase noise and exquisite timing stability of microwave signals. Substantial progress has been made in the field of microwave photonics, whereby low-noise microwave signals are generated by the down-conversion of ultrastable optical references using a frequency comb1-3. Such systems, however, are constructed with bulk or fibre optics and are difficult to further reduce in size and power consumption. In this work we address this challenge by leveraging advances in integrated photonics to demonstrate low-noise microwave generation via two-point optical frequency division4,5. Narrow-linewidth self-injection-locked integrated lasers6,7 are stabilized to a miniature Fabry-Pérot cavity8, and the frequency gap between the lasers is divided with an efficient dark soliton frequency comb9. The stabilized output of the microcomb is photodetected to produce a microwave signal at 20 GHz with phase noise of -96 dBc Hz-1 at 100 Hz offset frequency that decreases to -135 dBc Hz-1 at 10 kHz offset-values that are unprecedented for an integrated photonic system. All photonic components can be heterogeneously integrated on a single chip, providing a significant advance for the application of photonics to high-precision navigation, communication and timing systems.

Multi-harmonic near-infrared-ultraviolet dual-comb spectrometer.

Dual-comb spectroscopy in the ultraviolet (UV) and visible would enable broad bandwidth electronic spectroscopy with unprecedented frequency resolution. However, there are significant challenges in generation, detection, and processing of dual-comb data that have restricted its progress in this spectral region. In this work, we leverage robust 1550 nm few-cycle pulses to generate frequency combs in the UV-visible. We combine these combs with a wavelength multiplexed dual-comb spectrometer and simultaneously retrieve 100 MHz comb-mode-resolved spectra over three distinct harmonics at 386, 500, and 760 nm. The experiments highlight the path to continuous dual-comb coverage spanning 200-750 nm, offering extensive access to electronic transitions in atoms, molecules, and solids.

An optical-frequency synthesizer using integrated photonics.

Optical-frequency synthesizers, which generate frequency-stable light from a single microwave-frequency reference, are revolutionizing ultrafast science and metrology, but their size, power requirement and cost need to be reduced if they are to be more widely used. Integrated-photonics microchips can be used in high-coherence applications, such as data transmission 1 , highly optimized physical sensors 2 and harnessing quantum states 3 , to lower cost and increase efficiency and portability. Here we describe a method for synthesizing the absolute frequency of a lightwave signal, using integrated photonics to create a phase-coherent microwave-to-optical link. We use a heterogeneously integrated III-V/silicon tunable laser, which is guided by nonlinear frequency combs fabricated on separate silicon chips and pumped by off-chip lasers. The laser frequency output of our optical-frequency synthesizer can be programmed by a microwave clock across 4 terahertz near 1,550 nanometres (the telecommunications C-band) with 1 hertz resolution. Our measurements verify that the output of the synthesizer is exceptionally stable across this region (synthesis error of 7.7 × 10-15 or below). Any application of an optical-frequency source could benefit from the high-precision optical synthesis presented here. Leveraging high-volume semiconductor processing built around advanced materials could allow such low-cost, low-power and compact integrated-photonics devices to be widely used.

Compact, portable, thermal-noise-limited optical cavity with low acceleration sensitivity.

We develop and demonstrate a compact (less than 6 mL) portable Fabry-Pérot optical reference cavity. A laser locked to the cavity is thermal noise limited at 2 × 10-14 fractional frequency stability. Broadband feedback control with an electro-optic modulator enables near thermal-noise-limited phase noise performance from 1 Hz to 10 kHz offset frequencies. The additional low vibration, temperature, and holding force sensitivity of our design makes it well suited for out-of-the-lab applications such as optically derived low noise microwave generation, compact and mobile optical atomic clocks, and environmental sensing through deployed fiber networks.

Precision Doppler shift measurements with a frequency comb calibrated laser heterodyne radiometer.

We report precision atmospheric spectroscopy of CO2 using a laser heterodyne radiometer (LHR) calibrated with an optical frequency comb. Using the comb calibrated LHR, we record spectra of atmospheric CO2 near 1572.33 nm with a spectral resolution of 200 MHz, using sunlight as a light source. The measured CO2 spectra exhibit frequency shifts by approximately 11 MHz over the course of the 5-h measurement, and we show that these shifts are caused by Doppler effects due to wind along the spectrometer line of sight. The measured frequency shifts are in excellent agreement with an atmospheric model, and we show that our measurements track the wind-induced Doppler shifts with a relative frequency precision of 2 MHz (3 m·s-1) for a single 10 s measurement, improving to 100 kHz (15 cm·s-1) after averaging (equivalent to a fractional precision of a few parts in 1010). These results demonstrate that frequency comb calibrated LHR enables precision velocimetry that can be of use in applications ranging from climate science to astronomy.

High-performance, compact optical standard.

We describe a high-performance, compact optical frequency standard based on a microfabricated Rb vapor cell and a low-noise, external cavity diode laser operating on the Rb two-photon transition at 778 nm. The optical standard achieves an instability of 1.8×10-13τ-1/2 for times less than 100 s and a flicker noise floor of 1×10-14 out to 6000 s. At long integration times, the instability is limited by variations in optical probe power and the ac Stark shift. The retrace was measured to 5.7×10-13 after 30 h of dormancy. Such a simple, yet high-performance optical standard could be suitable as an accurate realization of the meter or, if coupled with an optical frequency comb, as a compact atomic clock comparable to a hydrogen maser.

All-fiber frequency comb at 2 µm providing 1.4-cycle pulses.

We report an all-fiber approach to generating sub-2-cycle pulses at 2 µm and a corresponding octave-spanning optical frequency comb. Our configuration leverages mature erbium:fiber laser technology at 1.5 µm to provide a seed pulse for a thulium-doped fiber amplifier that outputs 330 mW average power at a 100 MHz repetition rate. Following amplification, nonlinear self-compression in fiber decreases the pulse duration to 9.5 fs, or 1.4 optical cycles. The spectrum of the ultrashort pulse spans from 1 to beyond 2.4 µm and enables direct measurement of the carrier-envelope offset frequency. Our approach employs only commercially available fiber components, resulting in a design that is easy to reproduce in the larger community. As such, this system should be useful as a robust frequency comb source in the near-infrared or as a pump source to generate mid-infrared frequency combs.

Mid-infrared frequency comb with 6.7 W average power based on difference frequency generation.

We report on the development of a high-power mid-infrared frequency comb with 100 MHz repetition rate and 100 fs pulse duration. Difference frequency generation is realized between two branches derived from an Er:fiber comb, amplified separately in Yb:fiber and Er:fiber amplifiers. Average powers of 6.7 W and 14.9 W are generated in the 2.9 µm idler and 1.6 µm signal, respectively. With high average power, excellent beam quality, and passive carrier-envelope phase stabilization, this light source is a promising platform for generating broadband frequency combs in the far infrared, visible, and deep ultraviolet.

Mid-infrared frequency combs at 10 GHz.

We demonstrate mid-infrared (MIR) frequency combs at 10 GHz repetition rate via intra-pulse difference-frequency generation (DFG) in quasi-phase-matched nonlinear media. Few-cycle pump pulses (≲15fs, 100 pJ) from a near-infrared electro-optic frequency comb are provided via nonlinear soliton-like compression in photonic-chip silicon-nitride waveguides. Subsequent intra-pulse DFG in periodically poled lithium niobate waveguides yields MIR frequency combs in the 3.1-4.8 µm region, while orientation-patterned gallium phosphide provides coverage across 7-11 µm. Cascaded second-order nonlinearities simultaneously provide access to the carrier-envelope-offset frequency of the pump source via in-line f-2f nonlinear interferometry. The high-repetition rate MIR frequency combs introduced here can be used for condensed phase spectroscopy and applications such as laser heterodyne radiometry.

Mid-Infrared Frequency Comb Generation and Spectroscopy with Few-Cycle Pulses and χ

The mid-infrared atmospheric window of 3-5.5 µm holds valuable information regarding molecular composition and function for fundamental and applied spectroscopy. Using a robust, mode-locked fiber-laser source of <11 fs pulses in the near infrared, we explore quadratic (χ^{(2)}) nonlinear optical processes leading to frequency comb generation across this entire mid-infrared atmospheric window. With experiments and modeling, we demonstrate intrapulse difference frequency generation that yields few-cycle mid-infrared pulses in a single pass through periodically poled lithium niobate. Harmonic and cascaded χ^{(2)} nonlinearities further provide direct access to the carrier-envelope offset frequency of the near infrared driving pulse train. The high frequency stability of the mid-infrared frequency comb is exploited for spectroscopy of acetone and carbonyl sulfide with simultaneous bandwidths exceeding 11 THz and with spectral resolution as high as 0.003 cm^{-1}. The combination of low noise and broad spectral coverage enables detection of trace gases with concentrations in the part-per-billion range.

Dual-comb interferometry via repetition rate switching of a single frequency comb.

We experimentally demonstrate a versatile technique for performing dual-comb interferometry using a single frequency comb. By rapid switching of the repetition rate, the output pulse train can be delayed and heterodyned with itself to produce interferograms. The full speed and resolution of standard dual-comb interferometry is preserved while simultaneously offering a significant experimental simplification and cost savings. We show that this approach is particularly suited for absolute distance metrology due to an extension of the nonambiguity range as a result of the continuous repetition rate switching.

Tunable mid-infrared generation via wide-band four-wave mixing in silicon nitride waveguides.

We demonstrate wide-band frequency down-conversion to the mid-infrared (MIR) using four-wave mixing (FWM) of near-infrared (NIR) femtosecond-duration pulses from an Er:fiber laser, corresponding to 100 THz spectral translation. Photonic-chip-based silicon nitride waveguides provide the FWM medium. Engineered dispersion in the nanophotonic geometry and the wide transparency range of silicon nitride enable large-detuning FWM phase-matching and results in tunable MIR from 2.6 to 3.6 µm on a single chip with 100-pJ-scale pump-pulse energies. Additionally, we observe up to 25 dB broadband parametric gain for NIR pulses when the FWM process is operated in a frequency up-conversion configuration. Our results demonstrate how integrated photonic circuits pumped with fiber lasers could realize multiple nonlinear optical phenomena on the same chip and lead to engineered synthesis of broadband, tunable, and coherent light across the NIR and MIR wavelength bands.

Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis.

We report accurate phase stabilization of an interlocking pair of Kerr-microresonator frequency combs. The two combs, one based on silicon nitride and one on silica, feature nearly harmonic repetition frequencies and can be generated with one laser. The silicon-nitride comb supports an ultrafast-laser regime with three-optical-cycle, 1-picosecond-period soliton pulses and a total dispersive-wave-enhanced bandwidth of 170 THz, while providing a stable phase-link between optical and microwave frequencies. We demonstrate nanofabrication control of the silicon-nitride comb's carrier-envelope offset frequency and spectral profile. The phase-locked combs coherently reproduce their clock with a fractional precision of <6×10-13/τ, a behavior we verified through 2 h of measurement to reach <3×10-16. Our work establishes Kerr combs as a viable technology for applications like optical-atomic timekeeping and optical synchronization.

Mid-infrared frequency comb generation via cascaded quadratic nonlinearities in quasi-phase-matched waveguides.

We experimentally demonstrate a simple configuration for mid-infrared (MIR) frequency comb generation in quasi-phase-matched lithium niobate waveguides using the cascaded-χ(2) nonlinearity. With nanojoule-scale pulses from an Er:fiber laser, we observe octave-spanning supercontinuum in the near-infrared with dispersive wave generation in the 2.5-3 µm region and intrapulse difference frequency generation in the 4-5 µm region. By engineering the quasi-phase-matched grating profiles, tunable, narrowband MIR and broadband MIR spectra are both observed in this geometry. Finally, we perform numerical modeling using a nonlinear envelope equation, which shows good quantitative agreement with the experiment-and can be used to inform waveguide designs to tailor the MIR frequency combs. Our results identify a path to a simple single-branch approach to mid-infrared frequency comb generation in a compact platform using commercial Er:fiber technology.

Deuterated silicon nitride photonic devices for broadband optical frequency comb generation.

We report and characterize low-temperature, plasma-deposited deuterated silicon nitride films for nonlinear integrated photonics. With a peak processing temperature less than 300°C, it is back-end compatible with complementary metal-oxide semiconductor substrates. We achieve microresonators with a quality factor of up to 1.6×106 at 1552 nm and >1.2×106 throughout λ=1510-1600 nm, without annealing or stress management (film thickness of 920 nm). We then demonstrate the immediate utility of this platform in nonlinear photonics by generating a 1 THz free-spectral-range, 900 nm bandwidth modulation-instability microresonator Kerr comb and octave-spanning, supercontinuum-broadened spectra.

Quasi-Phase-Matched Supercontinuum Generation in Photonic Waveguides.

Supercontinuum generation (SCG) in integrated photonic waveguides is a versatile source of broadband light, and the generated spectrum is largely determined by the phase-matching conditions. Here we show that quasi-phase-matching via periodic modulations of the waveguide structure provides a useful mechanism to control the evolution of ultrafast pulses during supercontinuum generation. We experimentally demonstrate a quasi-phase-matched supercontinuum to the TE_{20} and TE_{00} waveguide modes, which enhances the intensity of the SCG in specific spectral regions by as much as 20 dB. We utilize higher-order quasi-phase-matching (up to the 16th order) to enhance the intensity in numerous locations across the spectrum. Quasi-phase-matching adds a unique dimension to the design space for SCG waveguides, allowing the spectrum to be engineered for specific applications.

Thermal and Nonlinear Dissipative-Soliton Dynamics in Kerr-Microresonator Frequency Combs.

We explore the dynamical response of dissipative Kerr solitons to changes in pump power and detuning and show how thermal and nonlinear processes couple these parameters to the frequency-comb degrees of freedom. Our experiments are enabled by a Pound-Drever-Hall (PDH) stabilization approach that provides on-demand, radio-frequency control of the frequency comb. PDH locking not only guides Kerr-soliton formation from a cold microresonator but opens a path to decouple the repetition and carrier-envelope-offset frequencies. In particular, we demonstrate phase stabilization of both Kerr-comb degrees of freedom to a fractional frequency precision below 10^{-16}, compatible with optical-time-keeping technology. Moreover, we investigate the fundamental role that residual laser-resonator detuning noise plays in the spectral purity of microwave generation with Kerr combs.

Frequency stability characterization of a broadband fiber Fabry-Pérot interferometer.

An optical etalon illuminated by a white light source provides a broadband comb-like spectrum that can be employed as a calibration source for astronomical spectrographs in radial velocity (RV) surveys for extrasolar planets. For this application the frequency stability of the etalon is critical, as its transmission spectrum is susceptible to frequency fluctuations due to changes in cavity temperature, optical power and input polarization. In this paper we present a laser frequency comb measurement technique to characterize the frequency stability of a custom-designed fiber Fabry-Pérot interferometer (FFP). Simultaneously probing the stability of two etalon resonance modes, we assess both the absolute stability of the etalon and the long-term stability of the cavity dispersion. We measure mode positions with MHz precision, which corresponds to splitting the FFP resonances by a part in 500 and to RV precision of ≈ 1 m s-1. We address limiting systematic effects, including the presence of parasitic etalons, that need to be overcome to push the metrology of this system to the equivalent RV precision of 10 cm s-1. Our results demonstrate a means to characterize environmentally-driven perturbations of etalon resonance modes across broad spectral bandwidths, as well as motivate the benefits and challenges of FFPs as spectrograph calibrators.

Self-referenced frequency combs using high-efficiency silicon-nitride waveguides.

We utilize silicon-nitride waveguides to self-reference a telecom-wavelength fiber frequency comb through supercontinuum generation, using 11.3 mW of optical power incident on the chip. This is approximately 10 times lower than conventional approaches using nonlinear fibers and is enabled by low-loss (<2 dB) input coupling and the high nonlinearity of silicon nitride, which can provide two octaves of spectral broadening with incident energies of only 110 pJ. Following supercontinuum generation, self-referencing is accomplished by mixing 780-nm dispersive-wave light with the frequency-doubled output of the fiber laser. In addition, at higher optical powers, we demonstrate f-to-3f self-referencing directly from the waveguide output by the interference of simultaneous supercontinuum and third harmonic generation, without the use of an external doubling crystal or interferometer. These hybrid comb systems combine the performance of fiber-laser frequency combs with the high nonlinearity and compactness of photonic waveguides, and should lead to low-cost, fully stabilized frequency combs for portable and space-borne applications.

Tunable resolution terahertz dual frequency comb spectrometer.

Terahertz dual frequency comb spectroscopy (THz-DFCS) yields high spectral resolution without compromising bandwidth. Nonetheless, the resolution of THz-DFCS is usually limited by the laser repetition rate, which is typically between 80 MHz and 1 GHz. In this paper, we demonstrate a new method to achieve sub-repetition rate resolution in THz-DFCS by adaptively modifying the effective laser repetition rate using integrated Mach-Zehnder electro-optic modulators (MZ-EOMs). Our results demonstrate that it is possible to improve the 100 MHz resolution of a terahertz frequency comb by at least 20x (down to 5 MHz) across the terahertz spectrum without compromising the average output power, and to a large extent, its bandwidth. Our approach can augment a wide range of existing THz-DFCS systems to provide a significant and easily adaptable resolution improvement.