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.

Fiber-coupled 2 mL vacuum-gap Fabry-Perot reference cavity for portable laser stabilization.

Vacuum-gap Fabry-Perot cavities are indispensable for the realization of frequency-stable lasers, with applications across a diverse range of scientific and industrial pursuits. However, making these cavity-based laser stabilization systems compact, portable, and rugged enough for use outside of controlled laboratory conditions has proven difficult. Here, we present a fiber-coupled 1396 nm laser stabilization system requiring no free-space optics or alignment, built for a portable strontium optical lattice clock. Based on a 2 mL vacuum-gap Fabry-Perot cavity, this system demonstrates thermal noise-limited performance and 1 × 10-14 fractional frequency instability. Fiber-integrated optical components have been instrumental in both advancing the field of optics and leveraging those advances across disciplines to facilitate other fields of study. This portable system represents a major step toward making the frequency stability of cavity-based systems broadly accessible.

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.

Calculation of the impulse response and phase noise of a high-current photodetector using the drift-diffusion equations.

We describe a procedure to calculate the impulse response and phase noise of high-current photodetectors using the drift-diffusion equations while avoiding computationally expensive Monte Carlo simulations. We apply this procedure to a modified uni-traveling-carrier (MUTC) photodetector. In our approach, we first use the full drift-diffusion equations to calculate the steady-state photodetector parameters. We then perturb the generation rate as a function of time to calculate the impulse response. We next calculate the fundamental shot noise limit and cut-off frequency of the device. We find the contributions of the electron, hole, and displacement currents. We calculate the phase noise of an MUTC photodetector. We find good agreement with experimental and Monte Carlo simulation results. We show that phase noise is minimized by having an impulse response with a tail that is as small as possible. Since, our approach is much faster computationally than Monte Carlo simulations, we are able to carry out a broad parameter study to optimize the device performance. We propose a new optimized structure with less phase noise and reduced nonlinearity.

Optical amplification and pulse interleaving for low-noise photonic microwave generation.

We investigate the impact of pulse interleaving and optical amplification on the spectral purity of microwave signals generated by photodetecting the pulsed output of an Er:fiber-based optical frequency comb. It is shown that the microwave phase noise floor can be extremely sensitive to delay length errors in the interleaver, and the contribution of the quantum noise from optical amplification to the phase noise can be reduced ∼10 dB for short pulse detection. We exploit optical amplification, in conjunction with high power handling modified unitraveling carrier photodetectors, to generate a phase noise floor on a 10 GHz carrier of -175 dBc/Hz, the lowest ever demonstrated in the photodetection of a mode-locked fiber laser. At all offset frequencies, the photodetected 10 GHz phase noise performance is comparable to or better than the lowest phase noise results yet demonstrated with stabilized Ti:sapphire frequency combs.

Broadband noise limit in the photodetection of ultralow jitter optical pulses.

Applications with optical atomic clocks and precision timing often require the transfer of optical frequency references to the electrical domain with extremely high fidelity. Here we examine the impact of photocarrier scattering and distributed absorption on the photocurrent noise of high-speed photodiodes when detecting ultralow jitter optical pulses. Despite its small contribution to the total photocurrent, this excess noise can determine the phase noise and timing jitter of microwave signals generated by detecting ultrashort optical pulses. A Monte Carlo simulation of the photodetection process is used to quantitatively estimate the excess noise. Simulated phase noise on the 10 GHz harmonic of a photodetected pulse train shows good agreement with previous experimental data, leading to the conclusion that the lowest phase noise photonically generated microwave signals are limited by photocarrier scattering well above the quantum limit of the optical pulse train.

Photonic microwave generation with high-power photodiodes.

We utilized and characterized high-power, high-linearity modified unitraveling carrier (MUTC) photodiodes for low-phase-noise photonic microwave generation based on optical frequency division (OFD). When illuminated with picosecond pulses from a repetition-rate-multiplied gigahertz Ti:sapphire modelocked laser, the photodiodes can achieve a 10 GHz signal power of +14 dBm. Using these diodes, we generated a 10 GHz microwave tone with less than 500 attoseconds absolute integrated timing jitter (1 Hz-10 MHz) and a phase noise floor of -177 dBc/Hz.We also characterized the electrical response, amplitude-to-phase conversion, saturation, and residual noise of the MUTC photodiodes.

The photodetection of ultrashort optical pulse trains for low noise microwave signal generation.

Electrical signals derived from optical sources have achieved record-low levels of phase noise, and have demonstrated the highest frequency stability yet achieved in the microwave domain. Attaining such ultrastable phase and frequency performance requires high-fidelity optical-to-electrical conversion, typically performed via a high-speed photodiode. This paper reviews characteristics of the direct photodetection of optical pulses for the intent of generating high power, low phase noise microwave signals from optical sources. The two most popular types of photodiode detectors used for low noise microwave generation are discussed in terms of electrical pulse characteristics, achievable microwave power, and photodetector nonlinearities. Noise sources inherent to photodetection, such as shot noise, flicker noise, and photocarrier scattering are reviewed, and their impact on microwave phase fidelity is discussed. General guidelines for attaining the lowest noise possible from photodetection that balances power saturation, optical amplification, and amplitude-to-phase conversion, are also presented.

Demonstration of on-sky calibration of astronomical spectra using a 25 GHz near-IR laser frequency comb.

We describe and characterize a 25 GHz laser frequency comb based on a cavity-filtered erbium fiber mode-locked laser. The comb provides a uniform array of optical frequencies spanning 1450 nm to 1700 nm, and is stabilized by use of a global positioning system referenced atomic clock. This comb was deployed at the 9.2 m Hobby-Eberly telescope at the McDonald Observatory where it was used as a radial velocity calibration source for the fiber-fed Pathfinder near-infrared spectrograph. Stellar targets were observed in three echelle orders over four nights, and radial velocity precision of ∼10 m/s (∼6 MHz) was achieved from the comb-calibrated spectra.

Chip-based laser with 1-hertz integrated linewidth.

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.

Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider.

We present an optical frequency divider based on a 200 MHz repetition rate Er:fiber mode-locked laser that, when locked to a stable optical frequency reference, generates microwave signals with absolute phase noise that is equal to or better than cryogenic microwave oscillators. At 1 Hz offset from a 10 GHz carrier, the phase noise is below -100 dBc/Hz, limited by the optical reference. For offset frequencies >10 kHz, the phase noise is shot noise limited at -145 dBc/Hz. An analysis of the contribution of the residual noise from the Er:fiber optical frequency divider is also presented.

Low-noise, low repetition rate, semiconductor-based mode-locked laser source suitable for high bandwidth photonic analog-digital conversion.

A semiconductor-based mode-locked laser source with low repetition rate, ultralow amplitude, and phase noise is introduced. A harmonically mode-locked semiconductor-based ring laser is time demultiplexed at a frequency equal to the cavity fundamental frequency (80MHz), resulting in a low repetition rate pulse train having ultralow amplitude and phase noise, properties usually attributed to multigigahertz repetition rate lasers. The effect of time demultiplexing on the phase noise of harmonically mode-locked lasers is analyzed and experimentally verified.

Coherent optical clock down-conversion for microwave frequencies with 10-18 instability.

Optical atomic clocks are poised to redefine the Système International (SI) second, thanks to stability and accuracy more than 100 times better than the current microwave atomic clock standard. However, the best optical clocks have not seen their performance transferred to the electronic domain, where radar, navigation, communications, and fundamental research rely on less stable microwave sources. By comparing two independent optical-to-electronic signal generators, we demonstrate a 10-gigahertz microwave signal with phase that exactly tracks that of the optical clock phase from which it is derived, yielding an absolute fractional frequency instability of 1 × 10-18 in the electronic domain. Such faithful reproduction of the optical clock phase expands the opportunities for optical clocks both technologically and scientifically for time dissemination, navigation, and long-baseline interferometric imaging.

Ultrafast electro-optic light with subcycle control.

Light sources that are ultrafast and ultrastable enable applications like timing with subfemtosecond precision and control of quantum and classical systems. Mode-locked lasers have often given access to this regime, by using their high pulse energies. We demonstrate an adaptable method for ultrastable control of low-energy femtosecond pulses based on common electro-optic modulation of a continuous-wave laser light source. We show that we can obtain 100-picojoule pulse trains at rates up to 30 gigahertz and demonstrate sub-optical cycle timing precision and useful output spectra spanning the near infrared. Our source enters the few-cycle ultrafast regime without mode locking, and its high speed provides access to nonlinear measurements and rapid transients.

The effects of filtering RF source phase noise by a low noise, high quality factor actively modelocked laser on the laser's absolute and relative phase noise.

The phase noise of two low noise, high quality factor actively modelocked lasers is investigated. It is found that increasing the quality factor of a laser can increase the phase noise relative to the RF source used to modelock the laser, even though the absolute noise of the laser is decreased. The filtering of phase noise from the modelocking source that causes both the increase in relative noise and the decrease in absolute noise is exploited to reveal phase noise information otherwise obscured in a high quality factor laser.

Two-mode beat phase noise of actively modelocked lasers.

An analytic expression for the phase noise spectrum is estimated when two arbitrary longitudinal modes are selected for beating from the output of an actively mode-locked laser. A separate experiment confirmed the theory qualitatively. It was found that two-mode beating possesses more phase noise than the beating involving the entire mode spectrum, especially at low offset frequency, even though two mode beating noise is decoupled from the RF oscillator noise to the first order.

State-of-the-art RF signal generation from optical frequency division.

We present the design of a novel, ultralow-phase-noise frequency synthesizer implemented with extremely-low-noise regenerative frequency dividers. This synthesizer generates eight outputs, viz. 1.6 GHz, 320 MHz, 160 MHz, 80 MHz, 40 MHz, 20 MHz, 10 MHz and 5 MHz for an 8 GHz input frequency. The residual single-sideband (SSB) phase noises of the synthesizer at 5 and 10 MHz outputs at 1 Hz offset from the carrier are -150 and -145 dBc/Hz, respectively, which are unprecedented phase noise levels. We also report the lowest values of phase noise to date for 5 and 10 MHz RF signals achieved with our synthesizer by dividing an 8 GHz signal generated from an ultra-stable optical-comb-based frequency division. The absolute SSB phase noises achieved for 5 and 10 MHz signals at 1 Hz offset are -150 and -143 dBc/Hz, respectively; at 100 kHz offset, they are -177 and -174 dBc/Hz, respectively. The phase noise of the 5 MHz signal corresponds to a frequency stability of approximately 7.6 × 10(-15) at 1 s averaging time for a measurement bandwidth (BW) of 500 Hz, and the integrated timing jitter over 100 kHz BW is 20 fs.

Jitter reduction by intracavity active phase modulation in a mode-locked semiconductor laser.

We experimentally verify the theory of Haus et al. [IEEE J. Quantum Electron. 40, 41 (2004)] on the effects of timing jitter using intracavity phase modulation on the pulse train of a mode-locked laser. The theory is based on the solution of the Heisenberg-Langevin equation in the presence of dispersion and intracavity phase modulation. Using active intracavity phase modulation, we have reduced the timing jitter on a 10.24 GHz mode-locked diode laser by 50% from 304 to 150 fs integrated from 1 Hz to the Nyquist frequency of 5.12 GHz.

Measurement of the comb dynamics for feedback control of an etalon-based coupled optoelectronic oscillator.

The response of an optical frequency comb from an etalon-based coupled optoelectronic oscillator to changes in drive current, optoelectronic loop phase, modulator bias, and laser cavity length has been measured. It is found that controlling the phase of the optoelectronic loop is best suited for control of the pulse repetition rate, whereas controlling the laser cavity length is best for stabilization of the optical carrier frequency. Moreover, by measuring the instabilities of the carrier frequency at the fixed-point frequency of the optoelectronic phase, changes to the optoelectronic phase can be decoupled from changes to the laser cavity.

Ultralow-jitter and -amplitude-noise semiconductor-based actively mode-locked laser.

We report a semiconductor-based, low-noise, 10.24 GHz actively mode-locked laser with 4.65 fs of relative timing jitter and a 0.0365% amplitude fluctuation (1 Hz to 100 MHz) of the optical pulse train. The keys to obtaining this result were the laser's high optical power and the low phase noise of the rf source used to mode lock the laser. The low phase noise of the rf source not only improves the absolute and relative timing jitter of the laser, but also prevents coupling of the rf source phase noise to the pulse amplitude fluctuations by the mode-locked laser.