Optical Phase Noise Research Articles

Optical Frequency Transfer on the Order of 10−19 Fractional Frequency Instability over a 64 m Free-Space Link

High-precision time–frequency is widely used in time measurement, satellite navigation, scientific research, and other fields. With the rapid development of optical clock technology, the fractional frequency instability and uncertainty of optical clock have reached 10−18 orders of magnitude, which is expected to contribute to generating the International Atomic Time and may even be used to redefine the “second” in the future. Therefore, the long-distance transfer of time–frequency signals between optical atomic clocks is of great significance. Free-space optical frequency transfer technology is one of the important technologies for solving the space-based optical clock comparison because of its high transfer precision and easy networking characteristics. In order to solve the long-distance space-based optical clock comparison, this paper investigates a free-space active phase noise compensation method using an Acousto-Optic Modulator (AOM), based on the traditional optical fiber phase noise compensation scheme. This new method is more flexible and scalable than the optical fiber time–frequency transfer technology. The optical frequency transfer over a 64 m free-space link is demonstrated. The fractional frequency transfer instability during free running is 9.50 × 10−16 at 1 s, and 4.44 × 10−16 at 2000 s, and the fractional frequency instability after compensation is 7.10 × 10−17 at 1 s, 3.07 × 10−19 at 2000 s, which is about 1–3 orders of magnitude better than that in free running, and provides a feasible scheme for space-based optical clock comparison.

A self-referenced optical phase noise analyzer for quantum technologies.

Second generation quantum technologies aim to outperform classical alternatives by utilizing engineered quantum systems. Maintaining the coherence required to enable any quantum advantage requires detailed knowledge and control over the noise that the hosting system is subjected to. Characterizing noise processes via their power spectral density is routinely done throughout science and technology and can be a demanding task. Determining the phase noise power spectrum in leading quantum technology platforms, for example, can be either outside the reach of many phase noise analyzers or prohibitively expensive. In this work, we present and characterize a low-complexity, low-cost optical phase noise analyzer based on the short-delay optical self-heterodyne measurements for quantum technology applications. Using this setup, we compare two ≈1Hz linewidth ultra-stable oscillators near 729nm. Their measurements are used as a baseline to determine and discuss the noise floor achieved in this measurement apparatus with a focus on limitations and their tradeoffs. The achieved noise floor in this all-stock-component implementation of an optical phase noise analyzer compares favorably with commercial offerings. This setup can be used particularly without a more stable reference or operational quantum system as a sensor as would be the case for many component manufacturers.

Coherent stepped-frequency waveform generation based on recirculating microwave photonic frequency conversion.

We propose a novel method for generating coherent and wideband stepped-frequency waveforms using recirculating microwave photonic frequency conversion (MWP-FC). By injecting a narrowband signal into an MWP-FC loop utilizing a dual-parallel Mach-Zehnder modulator (DPMZM), the signal frequency is continuously converted to produce a stepped-frequency waveform with a wide bandwidth. Within the MWP-FC loop, photo-electric conversion is achieved based on self-mixing detection, where the optical phase noise can be suppressed, guaranteeing stability and coherence of the generated signal. In a proof-of-concept experiment, a stepped-frequency signal with a frequency interval of 2 GHz and a bandwidth of about 16 GHz and a stepped-frequency chirp signal with a frequency interval of 3 GHz and a bandwidth of about 15 GHz are generated. In addition, coherence of the generated signals is verified by coherent integration and de-chirping.

Multiple-Branch Optical Frequency Transfer Without the Frequency Allocation Constraints

We report on the realization of a multiple-branch optical frequency transfer method, which can be adopted to deliver an optical reference to multiple independent remote sites. In comparison with the previous techniques, the proposed technique mitigates the frequency allocation constraints of the driving frequencies for the acousto-optic modulators (AOMs) at the remote sites by adding a short loop fiber link at the local site. The end-to-end optical path phase noise detection and compensation for each remote site is simultaneously performed at the remote site, which significantly simplifies the configuration at the local site, and can improve the signal-to-noise ratio (SNR) and reduce the cycle slip rate. We also conduct theoretical analysis for the effect of frequency aliasing from the perspective of different refractive index in triple-pass optical frequency transfer, analyze the effect of the SNR and cycle slips on the fractional frequency instability, and present a comprehensive equation for calculating noise contributions from end-to-end optical frequency transfer over the multiple-branch fiber network, demonstrating that the implementation of the fiber noise cancellation (FNC) for the each branch consisting of two fiber topologies with the single FNC setup is practical. This technique paves the way to integrate the optical frequency networks into the existing fiber communication networks with the higher compatibility and reliability.

Distributed optical fiber sensing system based on semiconductor lasers with mutual unbalanced double optical injection

A distributed optical fiber sensing system based on semiconductor lasers with mutual unbalanced double optical injection is proposed. Unequal lengths of the two injection paths enhance the nonlinear effect of the laser. The optical phase modulation caused by an external vibration acting on the sensing fiber is converted into the intensity modulation by the unbalanced double optical injection effect of the laser. Based on the synchronization effect of the mutually injected lasers, two waveform changes corresponding to the same external vibration emerge in the output signal of the system. The vibration position can be determined by the time difference between the two waveform changes. The period-one state of the system is employed to reduce the influence of optical phase noise and improve the sensing performance. The sensing system is modeled based on the rate equations of the mutually injected semiconductor lasers, and the working principle of the system is validated by numerical simulation. The location performance of the system is investigated experimentally. The average location error is less than 11 m on the 3.7 km-long sensing fiber. The experimental results show that the proposed system can work stably with a simple and accurate location method and does not require high coherence of the light source.

Quantum noise spectroscopy as an incoherent imaging problem

I point out the mathematical correspondence between an incoherent imaging model proposed by my group in the study of quantum-inspired superresolution [Tsang, Nair, and Lu, Physical Review X 6, 031033 (2016)] and a noise spectroscopy model also proposed by us [Tsang and Nair, Physical Review A 86, 042115 (2012); Ng et al., Physical Review A 93, 042121 (2016)]. Both can be regarded as random displacement models, where the probability measure for the random displacement depends on unknown parameters. The spatial-mode demultiplexing (SPADE) method proposed for imaging is analogous to the spectral photon counting method proposed in Ng et al. (2016) for optical phase noise spectroscopy -- Both methods are discrete-variable measurements that are superior to direct displacement measurements (direct imaging or homodyne detection) and can achieve the respective quantum limits. Inspired by SPADE, I propose a modification of spectral photon counting when the input field is squeezed -- simply unsqueeze the output field before spectral photon counting. I show that this method is quantum-optimal and far superior to homodyne detection for both parameter estimation and detection, thus solving the open problems in Tsang and Nair (2012) and Ng et al. (2016).

Phase Noise Analysis of Resonator-Enhanced Electro-Optic Comb-Based Analog Coherent Receivers

We present an architecture for wavelength-division-multiplexed coherent data center links employing resonator-enhanced electro-optic frequency comb generators as both transmitter and local oscillator (LO) sources. We show that in each frequency comb, the phase noise in all comb lines is determined completely by the optical phase noise of the seed laser and the phase noise of the microwave oscillator. We propose an analog coherent receiver that performs carrier recovery on all wavelength channels using only two phase-locked loops. We use an independent cascade of phase shifters driven by marker tone detection in each channel for polarization recovery and compensation of a static optical phase shift. We study design examples for quadrature phase-shift keying and 16-ary quadrature amplitude modulation (16-QAM), determining requirements on the transmitter and LO seed laser linewidths and the LO frequency modulation (FM) response. We find that for a dual-polarization (DP) 16-QAM link with 17 wavelength channels, each operating at 56 GBaud, if the combined linewidth of the transmitter and LO seed lasers is 100 kHz, the LO seed laser requires an FM response that is flat from d.c. to several hundred MHz to maintain a phase-error penalty below 1 dB.

Optical phase-locked loop phase noise in 5G mm-wave OFDM ARoF systems

The use of millimeter-wave (mm-wave) frequencies is required in order to support the increasing number of connected devices expected from the fifth generation (5G) of mobile communications. Subsequently, the generation of radio-frequency (RF) carriers ranging from 10GHz to 300GHz and their transport through optical distribution network (ODN) is a key element of the future 5G fronthaul. Optically assisted RF carrier generation is one of the most promising solutions to tackle this issue, allowing a wide use of analog radio-over-fiber (ARoF) architectures. However the main limitation of these optical methods is related to the finite coherence of lasers sources, which can dramatically degrade data transmission in analog formats. To mitigate its impact, the use of orthogonal frequency-division multiplexing (OFDM) as the 5G standard allows employing efficient phase noise compensation algorithms. Therefore, in this study, we present an experimental demonstration of a mm-wave generation technique based on an optical phase-locked loop (OPLL) that fulfills the frequency specifications for 5G. Then, an algorithm is introduced that improves data recovery at reception and reduces the impact of a possible high phase noise carrier. Finally, a back-to-back data transmission experiment is performed, demonstrating the efficiency of the algorithm to reach the 5G requirements. These results emphasize the use of OPLLs as a viable solution to generate mm-wave carriers for 5G and beyond.

Optical linewidth of soliton microcombs

Soliton microcombs provide a versatile platform for realizing fundamental studies and technological applications. To be utilized as frequency rulers for precision metrology, soliton microcombs must display broadband phase coherence, a parameter characterized by the optical phase or frequency noise of the comb lines and their corresponding optical linewidths. Here, we analyse the optical phase-noise dynamics in soliton microcombs generated in silicon nitride high-Q microresonators and show that, because of the Raman self-frequency shift or dispersive-wave recoil, the Lorentzian linewidth of some of the comb lines can, surprisingly, be narrower than that of the pump laser. This work elucidates information about the physical limits in phase coherence of soliton microcombs and illustrates a new strategy for the generation of spectrally coherent light on chip.

Near ultraviolet photonic integrated lasers based on silicon nitride

Low phase noise lasers based on the combination of III–V semiconductors and silicon photonics are well established in the near-infrared spectral regime. Recent advances in the development of low-loss silicon nitride-based photonic integrated resonators have allowed them to outperform bulk external diode and fiber lasers in both phase noise and frequency agility in the 1550 nm-telecommunication window. Here, we demonstrate for the first time a hybrid integrated laser composed of a gallium nitride-based laser diode and a silicon nitride photonic chip-based microresonator operating at record low wavelengths as low as 410 nm in the near-ultraviolet wavelength region suitable for addressing atomic transitions of atoms and ions used in atomic clocks, quantum computing, or for underwater LiDAR. By self-injection locking of the Fabry–Pérot diode laser to a high-Q (0.4 × 106) photonic integrated microresonator, we reduce the optical phase noise at 461 nm by a factor greater than 100×, limited by the device quality factor and back-reflection.

Digital Doppler-Cancellation Servo for Ultrastable Optical Frequency Dissemination Over Fiber.

Progress made in optical references, including ultrastable Fabry-Perot cavities, optical frequency combs, and optical atomic clocks, has driven the need for ultrastable optical fiber networks. Telecom-wavelength ultrapure optical signal transport has been demonstrated on distances ranging from the laboratory scale to the continental scale. In this article, we present a Doppler-cancellation setup based on a digital phase-locked loop (PLL) for ultrastable optical signal dissemination over fiber. The optical phase stabilization setup is based on a usual heterodyne Michelson-interferometer setup, while the software-defined radio (SDR) implementation of the PLL is based on a compact commercial board embedding a field-programmable gate array and analog-to-digital and digital-to-analog converters. Using three different configurations, including an undersampling method, we demonstrate a 20-m-long fiber link with residual fractional frequency instability as low as 10-18 at 1000 s and optical phase noise of -70 dBc/Hz at 1 Hz with a telecom frequency carrier.

Thermal noise reduction in soliton microcombs via laser self-cooling.

Thermal noise usually dominates the low-frequency region of the optical phase noise of soliton microcombs, which leads to decoherence that limits many aspects of applications. In this work, we demonstrate a simple and reliable way to mitigate this noise by laser cooling with a pump laser. The key is rendering the pump laser to simultaneously excite two neighboring cavity modes from different families that are respectively red and blue detuned, one for soliton generation and the other for laser cooling.

Analysis of squeezed light source in band of alkali atom transitions based on cascaded optical parametric amplifiers

The squeezed light field in the band of alkali metal atomic transitions is an important quantum resource in the field of quantum information and precision measurement. The wavelengths of atomic transition lines (760–860 nm) are relatively short. Limited by the gray-tracking effect of nonlinear crystals, the squeezing degree of the squeezed light in this band generated by the optical parametric amplifiers is low. Now, the squeezing is about 3–5 dB. Considering the problems in the experimental generation of the squeezed light at the wavelengths of atomic transitions, the variation law of quantum noise of the light field output from the single optical parametric amplifier with its physical parameters is studied theoretically, and the optimal physical parameters are obtained. To further improve the squeezing in the band of alkali metal atomic transitions, the cascaded optical parametric amplifiers are considered. Based on the basic theory of the optical parametric amplifiers, the theoretical model of the cascaded optical parametric amplifiers is constructed, in which the optical loss and phase noise of the cascaded optical loops are considered. Based on this, the quantum noise characteristics of the light field output from the cascaded system versus the optical loss and phase noise are analyzed at the frequencies of 2 MHz and 100 kHz, respectively. It is found that for the squeezing at 2 MHz, cascading 2 to 3 optical parametric amplifiers can significantly improve the squeezing under the premise of the low optical path loss and phase noise; for the squeezing in the low-frequency band, the enhancement of the squeezing for the cascaded system is quite weak. Under the current experimental parameters, the squeezing at 2 MHz of the squeezed light on rubidium resonance can be improved from –5 dB to –7 dB by cascading another DOPA. For the squeezing at low frequency band, the cascaded system proves to be useless, and the efforts should be made to reduce the technique noise in the low frequency band. Furthermore, the quantum limit and spectral characteristics of the squeezed light field output from the cascaded system are further explored. This study can provide reference and guidance for the improvement in the squeezing degree of the band of atomic transitions.

Characterization and Optimization of Coherent MZI-Based Nanophotonic Neural Networks Under Fabrication Non-Uniformity

Silicon-photonic neural networks (SPNNs) and artificial intelligence (AI) accelerators have emerged as promising successors to electronic accelerators by offering orders of magnitude lower latency and higher energy efficiency. Nevertheless, the underlying silicon photonic devices in SPNNs are sensitive to inevitable fabrication-process variations (FPVs) stemming from optical lithography imperfections. Consequently, the inferencing accuracy in an SPNN can be highly impacted by FPVs—e.g., can drop to below 10%—the impact of which is yet to be fully studied. In this paper, we, for the first time, model and explore the impact of optical phase noise due to FPVs in the waveguide width, silicon-on-insulator (SOI) thickness, and etch depth in coherent SPNNs that use Mach–Zehnder interferometers (MZIs). Leveraging such models, we propose a novel variation-aware, design-time optimization solution to improve MZI tolerance to different FPVs in SPNNs. Simulation results for two example SPNNs of different scales under realistic and correlated FPVs indicate that using the optimized MZIs can lead to significant improvements in the network inferencing accuracy. The proposed one-time optimization imposes low area overhead and hence is applicable even to resource-constrained designs.

Artificial Intelligence Techniques Evaluation for Modulation Format Identification in Optical Networks

In an elastic network paradigm, where the transceiver is able to control several characteristics of the transmitted signal according to the optical link quality and capacity demand, receivers able to automatically detect the modulation format are fundamental to recover the transmitted signal without the necessity of headers that reduce system capacity. This work presents a simulated performance comparison of six methods for blind identification of modulation format in high-capacity optical systems: k-nearest neighbors (KNN), k-means, fuzzy c-means, deep neural networks, support-vector machine (SVM) and peak-to-average power ratio (PAPR). The transmitted channels were 64-GBd modulated with the following modulation formats available at the transceiver: QPSK, 16QAM, 64QAM, and 256QAM. The optical link was emulated considering several impairments, as amplified spontaneous emission from optical amplifiers, frequency and phase noise from lasers, and polarization rotation and differential group delay from the propagation. The support-vector machine algorithm presented the most robust results.

Orthogonalizing the control of frequency combs for optical clockworks.

Frequency combs play a crucial supporting role for optical clocks by allowing coherent frequency division of their output signals into the electronic domain. This task requires stabilization of the comb's offset frequency and of an optical comb mode to the clock laser. However, the two actuators used to control these quantities often influence both degrees of freedom simultaneously. This non-orthogonality leads to artificial limits to the control bandwidth and unwanted noise in the comb. Here, we orthogonalize the two feedback loops with a linear combination of the measured signals in a field-programmable gate array. We demonstrate this idea using a fiber frequency comb stabilized to a clock laser at 259 THz, half the frequency of the 1S0→3P0 Yb transition. The decrease in coupling between the loops reduces the comb's optical phase noise by 20 dB. This approach could improve the performance of any comb stabilized to any optical frequency standard.

SI-traceable frequency dissemination at 1572.06 nm in a stabilized fiber network with ring topology.

Frequency dissemination in phase-stabilized optical fiber networks for metrological frequency comparisons and precision measurements are promising candidates to overcome the limitations imposed by satellite techniques. However, in an architecture shared with telecommunication data traffic, network constraints restrict the availability of dedicated channels in the commonly-used C-band. Here, we demonstrate the dissemination of an SI-traceable ultrastable optical frequency in the L-band over a 456 km fiber network with ring topology, in which data traffic occupies the full C-band. We characterize the optical phase noise and evaluate a link instability of 4.7 × 10-16 at 1 s and 3.8 × 10-19 at 2000 s integration time, and a link accuracy of 2 × 10-18. We demonstrate the application of the disseminated frequency by establishing the SI-traceability of a laser in a remote laboratory. Finally, we show that our metrological frequency does not interfere with data traffic in the telecommunication channels. Our approach combines an unconventional spectral choice in the telecommunication L-band with established frequency-stabilization techniques, providing a novel, cost-effective solution for ultrastable frequency-comparison and dissemination, and may contribute to a foundation of a world-wide metrological network.

Adaptive Phase Noise Cancellation Technique for Fiber-Optic Interferometric Sensors

The optical source phase noise is one of the main factors influencing the noise performance of fiber-optic interferometric measurement systems. The phase noise is directly proportional to the optical path length difference of the interferometer and wavelength instability of the optical source. Conventional phase noise suppression techniques involve the use of highly stable optical sources and reduction of path length differences of sensing interferometers. However, such methods are not always appropriate for all interferometric configurations. Alternative phase noise suppression techniques suggest the use of an auxiliary reference interferometer for independent measurements of the phase noise. In this case, the phase noise signal can be directly subtracted from the sensor signal. But equal path length differences are required for all interferometers in the measurement system. In this paper, an adaptive phase noise cancellation technique for fiber-optic interferometric sensors is presented. The proposed technique is based on the real-time evaluation of optical path length differences for all interferometers in the measurement system. This approach doesn't require identical path length differences and takes into account their variations caused by environmental conditions. Thus, the optical source phase noise can be independently measured by the reference interferometer and subtracted from the sensor signal with the required attenuation. The results of experimental investigations of the proposed technique for two types of interferometric schemes are presented. It is shown that the proposed technique demonstrates the phase noise reduction up to 30 dB in the frequency range up to 500 Hz.

Quantum dash multi-wavelength lasers for Tbit/s coherent communications and 5G wireless networks

We report on the design, growth, fabrication, and performance of InAs/InP quantum dash (QD) multi-wavelength lasers (MWLs) developed by the National Research Council (NRC) Canada. The key technical specifications investigated include optical and RF beating spectra, relative intensity noise (RIN), and optical phase noise of each individual wavelength channel. Data bandwidth transmission capacity of 5.376 Tbit/s and 10.8 Tbit/s respectively in the PAM-4 and 16-QAM modulation formats are demonstrated using only a single C-band QD 34.2-GHz MWL chip. We have also developed a monolithic InAs/InP QD dual-wavelength (DW) DFB laser as a compact optical beat source to generate millimeter-wave (MMW) signals. Due to the common cavity, highly coherent and correlated optical modes with optical linewidth as low as 15.83 kHz, spectrally pure MMW signals around 46.8 GHz with a linewidth down to 26.1 kHz were experimentally demonstrated. By using this QD DW-DFB laser, a one GBaud (2 Gbps) MMW over-fiber transmission link is demonstrated with PAM-4 signals. The results show that the demonstrated device is suitable for high speed high capacity MMW fiber-wireless integrated fronthaul of 5G networks.

InAs/InP quantum dash buried heterostructure mode-locked laser for high capacity fiber-wireless integrated 5G new radio fronthaul systems.

We have developed and experimentally demonstrated a highly coherent and low noise InP-based InAs quantum dash (QDash) buried heterostructure (BH) C-band passively mode-locked laser (MLL) with a pulse repetition rate of 25 GHz for fiber-wireless integrated fronthaul 5G new radio (NR) systems. The device features a broadband spectrum providing over 46 equally spaced highly coherent and low noise optical channels with an optical phase noise and integrated relative intensity noise (RIN) over a frequency range of 10 MHz to 20 GHz for each individual channel typically less than 466.5 kHz and -130 dB/Hz, respectively, and an average total output power of ∼50 mW per facet. Moreover, the device exhibits low RF phase noise with measured RF beat-note linewidth down to 3 kHz and estimated timing jitter between any two adjacent channels of 5.5 fs. By using this QDash BH MLL device, we have successfully demonstrated broadband optical heterodyne based radio-over-fiber (RoF) fronthaul wireless links at 5G NR in the underutilized spectrum of around 25 GHz with a total bit rate of 16-Gb/s. The device performance is experimentally evaluated in an end-to-end fiber-wireless system in real-time in terms of error vector magnitude (EVM) and bit error rate (BER) by generating, transmitting and detecting 4-Gbaud 16-QAM RF signals over 0.5-m to 2-m free-space indoor wireless channel through a total length of 25.22 km standard single mode fiber (SSMF) with EVM and BER under 8.4% and 2.9 × 10-5, respectively. The intrinsic characteristics of the device in conjunction with its system transmission performance indicate that QDash BH MLLs can be readily used in fiber-wireless integrated systems of 5G and beyond wireless communication networks.