Point-to-point stabilized optical frequency transfer with active optics

10 W super-wideband ultra-low-intensity-noise single-frequency fiber laser at 1 µm

A 10 W super-wideband ultra-low-intensity-noise single-frequency fiber laser (SFFL) at 1 µm is experimentally demonstrated, based on dual gain saturation effects from semiconductors and optical fibers, together with an analog-digital hybrid optoelectronic feedback loop. Three intensity-noise-inhibited units synergistically work, which actualizes a connection of effective bandwidth and enhancement of noise-suppressing amplitude. With the cascade action of the semiconductor optical amplifier and optical fiber amplifier, the laser power is remarkably boosted. Eventually, an SFFL with an output power of 10.8 W and a relative intensity noise (RIN) below -150 dB/Hz at the frequency range over 1 Hz is realized. More meaningfully, within the total frequency range of 10 Hz to 10 GHz exceeding 29 octaves, the RIN is controlled to below -160 dB/Hz, approaching the shot-noise limit (SNL) level. To the best of our knowledge, this is the lowest RIN result of SFFL within such an extensive frequency range, and this is the highest output power of the near-SNL super-wideband SFFL. Furthermore, a linewidth of less than 0.8 kHz, a long-term stable polarization extinction ratio of 20 dB, and an optical signal-to-noise ratio of over 60 dB are obtained simultaneously. This start-of-the-art SFFL has provided a systematic solution for high-power and low-noise light sources, which is competitive for sophisticated applications, such as free-space laser communication, space-based gravitational wave detection, and super-long-distance space coherent velocity measurement and ranging.

Free space optical link to a tethered balloon for frequency transfer and chronometric geodesy

We present the results of an optical link to a corner cube on board a tethered balloon at 300 m altitude including a Tip/Tilt compensation for the balloon tracking. Our experiment measures the carrier phase of a 1542 nm laser, which is the useful signal for frequency comparison of distant clocks. An active phase noise compensation of the carrier is implemented, demonstrating a fractional frequency stability of 8 × 10-19 after 16 s averaging, which slightly (factor ∼ 3) improves on best previous links via an airborne platform. This state-of-the-art result is obtained with a transportable set-up that enables a fast field deployment.

Atmospheric turbulence characterization with simultaneous measurement of phase, angle of arrival, and intensity in a retroreflected optical link

Free-space optical transmission through the Earth's atmosphere is applicable to high-speed data transmission and optical clock comparisons, among other uses. Fluctuations in the refractive index of the atmosphere limit the performance of atmospheric optical transmission by inducing phase noise, angle-of-arrival variation, and scintillation. The statistics of these deleterious effects are predicted by models for the spatial spectrum of the atmospheric refractive index structure. We present measurements of phase fluctuations, angle-of-arrival variations, and scintillation, taken concurrently and compared with models for the atmospheric refractive index structure. The measurements are also cross-compared by deriving independent estimates of the turbulence structure constant $C_n^2$. We find agreement within an order of magnitude for derived $C_n^2$ values for all three metrics.

Stabilized free space optical frequency transfer using digitally enhanced heterodyne interferometry

Free-space continuous-wave laser interferometry using folded links has applications in precision measurement for velocimetry, vibrometry, optical communications, and verification of frequency transfer for metrology. However, prompt reflections from the transceiver optics degrade the performance of these systems, especially when the power of the returning signal is equal to or less than the power of the prompt reflections. We demonstrate phase stabilized free-space continuous-wave optical frequency transfer that exploits the auto-correlation properties of pseudo-random binary sequences to filter out prompt reflections. We show that this system significantly improves the stability and robustness of optical frequency transfer over a 750 m turbulent free-space channel, achieving a best fractional frequency stability of 8 × 10^-20 at an integration time of τ = 512 s, and cycle-slip-free periods up to 162 min.

Wideband ultra-low intensity noise reduction via joint action of gain saturation and out-of-phase polarization mixing effect from a semiconductor optical amplifier

In this article, the vector dynamics of semiconductor optical amplifiers (SOAs) are systematically analyzed and developed to explore its mechanism of intensity noise suppression. First, theoretical investigation on the gain saturation effect and carrier dynamics is performed via a vectorial model, and the calculated result unravels desynchronized intensity fluctuations of two orthogonal polarization states. Particularly, it predicts an out-of-phase case, which allows the cancellation of the fluctuations via adding up the orthogonally-polarized components, then establishes a synthetic optical field with stable amplitude and dynamic polarization, and thereby enables a remarkable relative intensity noise (RIN) reduction. Here, we term this approach of RIN suppression as out-of-phase polarization mixing (OPM). To validate the OPM mechanism, we conduct an SOA-mediated noise-suppression experiment based on a reliable single-frequency fiber laser (SFFL) with the presence of relaxation oscillation peak, and subsequently carry out a polarization resolvable measurement. By this means, out-of-phase intensity oscillations with respect to the orthogonal polarization states are clearly demonstrated, and consequently enable a maximum suppression amplitude of >75 dB. Notably, the RIN of 1550-nm SFFL, suppressed by joint action of OPM and gain saturation effect, is dramatically reduced to -160 dB/Hz in a wideband of 0.5 MHz∼10 GHz, and the performance of which is excellent by comparing with the corresponding shot noise limit of -161.9 dB/Hz. The proposal of OPM here not only facilitates us to dissect the vector dynamics of SOA but also offers a promising solution to realize wideband near-shot-noise-limited SFFL.

Towards optical frequency geopotential difference measurements via a flying drone

Geopotential and orthometric height differences between distant points can be measured via timescale comparisons between atomic clocks. Modern optical atomic clocks achieve statistical uncertainties on the order of 10^-18, allowing height differences of around 1 cm to be measured. Frequency transfer via free-space optical links will be needed for measurements where linking the clocks via optical fiber is not possible, but requires line of sight between the clock locations, which is not always practical due to local terrain or over long distances. We present an active optical terminal, phase stabilization system, and phase compensation processing method robust enough to enable optical frequency transfer via a flying drone, greatly increasing the flexibility of free-space optical clock comparisons. We demonstrate a statistical uncertainty of 2.5×10^-18 after 3 s of integration, corresponding to a height difference of 2.3 cm, suitable for applications in geodesy, geology, and fundamental physics experiments.

Adaptive optics LEO uplink pre-compensation with finite spatial modes

Adaptive optics pre-compensation of free-space optical communications uplink from ground to space is complicated by the "point ahead angle" due to spacecraft velocity and the finite speed of light, as well as anisoplanatism of the uplink beam and the wavefront beacon. This Letter explores how pre-compensation varies with the number of spatial modes applied and how it varies with a beacon at the point-ahead angle versus a downlink beacon. Using a w₀ = 16 cm Gaussian beam propagating through a modified Hufnagel-Valley model as an example, we find pre-compensation performance plateaus beyond ∼100 applied modes regardless of integrated turbulence strength, and that a point ahead beacon provides a 1-4 dB gain in median received power and an order-of-magnitude reduction in scintillation over a downlink beacon at wavelengths typical of optical communications. Modeling tailored to specific scenarios should be conducted to determine whether implementing a resource-intensive point ahead beacon is the optimum path to meeting link requirements.

Demonstration of 100 Gbps coherent free-space optical communications at LEO tracking rates

Free-space optical communications are poised to alleviate the data-flow bottleneck experienced by spacecraft as traditional radio frequencies reach their practical limit. While enabling orders-of-magnitude gains in data rates, optical signals impose much stricter pointing requirements and are strongly affected by atmospheric turbulence. Coherent detection methods, which capitalize fully on the available degrees of freedom to maximize data capacity, have the added complication of needing to couple the received signal into single-mode fiber. In this paper we present results from a coherent 1550 nm link across turbulent atmosphere between a deployable optical terminal and a drone-mounted retroreflector. Through 10 Hz machine vision optical tracking with nested 200 Hz tip/tilt adaptive optics stabilisation, we corrected for pointing errors and atmospheric turbulence to maintain robust single mode fiber coupling, resulting in an uninterrupted 100 Gbps optical data link while tracking at angular rates of up to 1.5 deg/s, equivalent to that of spacecraft in low earth orbit. With the greater data capacity of coherent communications and compatibility with extant fiber-based technologies being demonstrated across static links, ground-to-low earth orbit links of Terabits per second can ultimately be achieved with capable ground stations.

The time-programmable frequency comb and its use in quantum-limited ranging

Two decades after its invention, the classic self-referenced frequency comb laser is an unrivalled ruler for frequency, time and distance metrology owing to the rigid spacing of its optical output^1,2. As a consequence, it is now used in numerous sensing applications that require a combination of high bandwidth and high precision^3-5. Many of these applications, however, are limited by the trade-offs inherent in the rigidity of the comb output and operate far from quantum-limited sensitivity. Here we demonstrate an agile programmable frequency comb where the pulse time and phase are digitally controlled with ±2-attosecond accuracy. This agility enables quantum-limited sensitivity in sensing applications as the programmable comb can be configured to coherently track weak returning pulse trains at the shot-noise limit. To highlight its capabilities, we use this programmable comb in a ranging system, reducing the required power to reach a given precision by about 5,000-fold compared with a conventional dual-comb system. This enables ranging at a mean photon per pulse number of 1/77 while retaining the full accuracy and precision of a rigid frequency comb. Beyond ranging and imaging^6-12, applications in time and frequency metrology^1,2,5,13-23, comb-based spectroscopy^24-32, pump-probe experiments³³ and compressive sensing^34,35 should benefit from coherent control of the comb-pulse time and phase.

Analog transmission of time-frequency signal in atmospheric turbulence environment

The high-precision time-frequency transfer of the optical atomic clock signals over ground-to-satellite and terrestrial free-space laser paths is of great significance in the fields of fundamental and applied sciences. However, the phase noises caused by atmospheric turbulence severely degrade the measurement precision. In this paper, a new method to simulate the transmission of time-frequency signal propagating through atmospheric turbulence is investigated. An analog transmission system comparable to the practical out-field link has been demonstrated, which can provide a deep insight into the phase distortion of time-frequency signal of free-space optical communication links.

Frequency comb-to-comb stabilization over a 1.3-km free-space atmospheric optical link

Stabilizing a frequency comb to an ultra-stable optical frequency reference requires a multitude of optoelectronic peripherals that have to operate under strict ambient control. Meanwhile, the frequency comb-to-comb stabilization aims to synchronize a slave comb to a well-established master comb with a substantial saving in required equipment and efforts. Here, we report an utmost case of frequency comb-to-comb stabilization made through a 1.3 km free-space optical (FSO) link by coherent transfer of two separate comb lines along with a feedback suppression control of atmospheric phase noise. The FSO link offers a transfer stability of 1.7 × 10^-15 at 0.1 s averaging, while transporting the master comb's stability of 1.2 × 10^-15 at 1.0 s over the entire spectrum of the slave comb. Our remote comb-to-comb stabilization is intended to expedite diverse long-distance ground-to-ground or ground-to-satellite applications; as demonstrated here for broadband molecular spectroscopy over a 6 THz bandwidth as well as ultra-stable microwaves generation with phase noise of -80 dBc Hz^-1 at 1 Hz.

Generation of a coherent distributed RF array with a strong positive correlation

In this work, we present a coherent distributed radio frequency (RF) array, discover and quantitatively describe the strong positive correlation between reconstructed signals for the first time. Eight replicable parallel receivers are connected to the phase-locked common trunk link via eight optical couplers spaced 1 km apart. The forward and backward signals at each receiver, extracted from two ports of optical couplers, are recovered to RF signals separately and then mixed to achieve upward frequency conversion. The link delay jitter is counteracted by wavelength-tuning of the optical carrier. With the long-term stability of point-to-multipoint fiber-optic RF dissemination effectively improved, the coherent distributed array is generated, and further the relative frequency stability between signals at different receivers is studied. The proposed correlation coefficient at 10³ s is ∼0.8 and shows a slight downward trend with the increase of averaging time based on our experimental results.

High-gain narrowband radio frequency signal amplifier based on a dual-loop optoelectronic oscillator

A novel photonic-assisted method for radio frequency (RF) signal amplification with high-gain and narrowband based on a dual-loop optoelectronic oscillator (OEO) is proposed and experimentally demonstrated. In the proposed system, the low-power RF signal is injected into a dual-loop OEO which is below the threshold oscillation state. And the maximum gain is obtained when the frequency of the RF signal matches with the potential oscillation mode of the dual-loop OEO. The approach provides an average gain greater than 22 dB for the RF signal which matches with oscillation mode. After amplification, the signal-to-noise ratio (SNR) turns out to be 40 dB. Furthermore, the 3 dB bandwidth of the suggested system can be narrower than 1.2 kHz which can effectively remove the out-of-band noise and spurious effects. Meanwhile, the performance of sensitivity and phase noise are also investigated.

Angle-of-arrival variability of retroreflected lasers despite atmospheric reciprocity

Corner cube retroreflectors are commonly used as cooperative targets in free-space laser applications. The previous literature suggests that due to path reciprocity, a retroreflected beam is self-corrected across a turbulent atmosphere and should show no angle-of-arrival variability in the near field. This is at odds with recent experiments that rely on angle-of-arrival measurements in retroreflected beams for effective tip/tilt correction. In this Letter we investigate the mechanism behind observed angle-of-arrival variability using numerical field propagation to model various transceiver and retroreflector geometries. We determine that asymmetric truncation of a curved wavefront at the retroreflector, transceiver, or both, results in a difference in tip/tilt between the transmitted and reflected wavefronts. This difference propagates as angle-of-arrival variation at the transceiver despite reciprocity, providing the error signal necessary for adaptive optics tip/tilt correction without a remote beacon.

Ultrastable Free-Space Laser Links for a Global Network of Optical Atomic Clocks

A global network of optical atomic clocks will enable unprecedented measurement precision in fields including tests of fundamental physics, dark matter searches, geodesy, and navigation. Free-space laser links through the turbulent atmosphere are needed to fully exploit this global network, by enabling comparisons to airborne and spaceborne clocks. We demonstrate frequency transfer over a 2.4 km atmospheric link with turbulence comparable to that of a ground-to-space link, achieving a fractional frequency stability of 6.1×10^{-21} in 300 s of integration time. We also show that clock comparison between ground and low Earth orbit will be limited by the stability of the clocks themselves after only a few seconds of integration. This significantly advances the technologies needed to realize a global timescale network of optical atomic clocks.