Laser Phase Noise Research Articles

Spectral filtering of dual lasers with a high-finesse length-tunable cavity for rubidium atom Rydberg excitation* *Project supported by National Key Research and Development Program of China (Grant No. 2016YFA0302800), the National Natural Science Foundation of China (Grant Nos. U20A2074 and 12074391), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB 21010100), the Youth Innovation Promotion Association

We propose and demonstrate an alternative method for spectral filtering and frequency stabilization of both 780-nm and 960-nm lasers using a high-finesse length-tunable cavity (HFLTC). Firstly, the length of HFLTC is stabilized to a commercial frequency reference. Then, the two lasers are locked to this HFLTC using the Pound–Drever–Hall (PDH) method which can narrow the linewidths and stabilize the frequencies of both lasers simultaneously. Finally, the transmitted lasers of HFLTC with each power up to about 100 μW, which act as seed lasers, are amplified using the injection locking method for single-atom Rydberg excitation. The linewidths of obtained lasers are narrowed to be less than 1 kHz, meanwhile the obtained lasers’ phase noise around 750 kHz are suppressed about 30 dB. With the spectrally filtered lasers, we demonstrate a Rabi oscillation between the ground state and Rydberg state of single-atoms in an optical trap tweezer with a decay time of (67 ± 37) μs, which is almost not affected by laser phase noise. We found that the maximum short-term laser frequency fluctuation of a single excitation lasers is at ∼3.3 kHz and the maximum long-term laser frequency drift of a single laser is ∼46 kHz during one month. Our work develops a stable and repeatable method to provide multiple laser sources of ultra-low phase noise, narrow linewidth, and excellent frequency stability, which is essential for high precision atomic experiments, such as neutral atom quantum computing, quantum simulation, quantum metrology, and so on.

Ultraprecision quantum sensing and measurement based on nonlinear hybrid optomechanical systems containing ultracold atoms or atomic Bose–Einstein condensate

In this review, the authors study how a hybrid optomechanical system (OMS), in which a quantum micro- or nano-mechanical oscillator is coupled to the electromagnetic radiation pressure, consisting of an ensemble of ultracold atoms or an atomic Bose–Einstein condensate, can be used as an ultraprecision quantum sensor for measuring very weak signals. As is well-known in any precise quantum measurement, the competition between the shot noise and the backaction noise of measurement executes a limitation on the measurement precision which is the so-called standard quantum limit (SQL). In the case where the intensity of the signal is even lower than the SQL, one needs to perform an ultraprecision quantum sensing to beat the SQL. For this purpose, the authors review three important methods for surpassing the SQL in a hybrid OMS: (i) the backaction evading measurement of a quantum nondemolition variable of the system, (ii) the coherent quantum backaction noise cancelation, and (iii) the so-called parametric sensing, the simultaneous signal amplification, and added noise suppression below the SQL. Furthermore, the authors have shown in this article for the first time how the classical fluctuation of the driving laser phase, the so-called laser phase noise, affects the power spectrum of the output optical field in a standard OMS and induces an additional impression noise which makes the total system noise increase above the SQL. Also, for the first time in this review it has been shown that in the standard OMSs, it is impossible to amplify the signal while suppressing the noise below the SQL simultaneously.

Low-Overhead Low-Complexity Carrier Phase Recovery Technique for Coherent Multi-Band OFDM-Based Superchannel Systems Enabled by Optical Frequency Combs

Abstract In this paper, we have designed a low-overhead low-complexity carrier phase tracking scheme for OFDM-based superchannel transmission system enabled by optical frequency combs. In this scheme, taking advantage of the broadband phase coherence provided by optical frequency combs among the OFDM-bands, the carrier phase retrieved from pilot-subcarriers of the OFDM-band on the central wavelength channel is reused for the OFDM-bands on the other wavelength channels. In this case, the overall pilot-subcarrier overhead and DSP complexity is significantly reduced since the pilot-subcarriers occupy a small fraction of the overall OFDM bandwidth. The feasibility of this joint-carrier phase tracking scheme has been verified successfully via comprehensive simulation, where results show that the BER threshold for soft-decision FEC could be achieved for 50GHz-spaced 5-band 4-QAM, 8-QAM, 16-QAM and 32-QAM OFDM-based superchannel signals with zero guard-band and both laser and nonlinear phase noise effects after 7000km, 4000km, 3000km and 2000km SSMF transmission respectively. The simulation results show that there exist chromatic dispersion-induced differential phase offset among the OFDM-bands whose impact on joint-carrier phase tracking depends on the modulation format, channel count and fiber length. Finally, we demonstrate experimentally the feasibility performance of the designed master-slave carrier phase tracking technique for comb-based OFDM-based superchannels.

High-frequency broadband laser phase noise cancellation using a delay line.

Laser phase noise remains a limiting factor in many experimental settings, including metrology, time-keeping, as well as quantum optics. Hitherto this issue was addressed at low frequencies ranging from well below 1 Hz to maximally 100 kHz. However, a wide range of experiments, such as, e.g., those involving nanomechanical membrane resonators, are highly sensitive to noise at higher frequencies in the range of 100 kHz to 10 MHz, such as nanomechanical membrane resonators. Here we employ a fiber-loop delay line interferometer optimized to cancel laser phase noise at frequencies around 1.5 MHz. We achieve noise reduction in 300 kHz-wide bands with a peak reduction of more than 10 dB at desired frequencies, reaching phase noise of less than -160 dB(rad2/Hz) with a Ti:Al2O3 laser. These results provide a convenient noise reduction technique to achieve deep ground-state cooling of mechanical motion.

Frequency drift mitigation of Φ-OTDR using difference-fitting method.

A difference-fitting method is proposed to mitigate the low frequency drift of a phase-sensitive optical time domain reflectometry (Φ-OTDR) system caused by laser phase noise. The effective difference region for phase demodulation is theoretically analyzed and experimentally verified, which should be greater than the convolution of the spatial resolution and the length of disturbed optical fiber. Then, a median-fitting algorithm is used to obtain the phase noise of the differential region. The vibration signal of 0.2 Hz is first demodulated with the SNR of 41.79 dB on the optical fiber of 11 km. The low-frequency vibration signals of 0.05 Hz and 0.02 Hz are then successfully restored by using the difference-fitting method, which can effectively eliminate the influence of low frequency drift.

DISPERSION COMPENSATION USING ELECTRONIC METHODS BROADCASTING SYSTEM

System distortions due to chromatic dispersion (CD), polarization mode dispersion (PMD), laser phase noise and fiber nonlinearities have a significant impact on the performance of high-speed fiber optic networks. In connection with the need to improve the quality of information transmission in high-speed fiber-optic communication systems, coherent detection with a digital signal processing unit is of particular interest. The main goal of the DSP block is to reduce the impact of linear and nonlinear effects that degrade the quality of information transfer. In this direction, the use of adaptive filters with adaptation algorithms for filter coefficients plays an important role. The Constant Modulus Algorithm (CMA) and the Least Mean Square (LMS) method used to compensate for dispersion distortions are presented. The load on transport networks based on fiber-optic transmission systems is increasing at an accelerating rate. This paper discusses the possibility and limitations of increasing the throughput of fiber-optic transmission systems by reducing the distance between carriers. A comparison is made between fixed and flexible grids in terms of the spectral bandwidth efficiency. It is concluded that the use of flexible mesh technology is promising when switching to channel speeds above 100 Gbit/s.

Metrology of Optical Communication Systems Using Error Vector Magnitude

Error vector magnitude (EVM) as a performance metric for M-ary quadrature amplitude modulation (QAM) formats in optical coherent systems is presented. It is shown that the calibrated BER, which would otherwise be under-estimated without the correction factor, can reliably monitor the performance of optical coherent systems near the target BER of 10?3 for quadrature phase shift keying (QPSK), 16-QAM, and 64-QAM employing carrier phase recovery with differential decoding to compensate for laser phase noise. The impact on the number of symbols used to estimate the BER from EVM analysis is also presented and compared to the BER obtained by error counting.

Reduction of Phase-Modulation to Intensity-Modulation Conversion Noise Effect Using Delayed Self-Homodyne Optical Orthogonal Frequency Division Multiplexing System

Self-homodyne optical orthogonal frequency division multiplexing (OFDM) transmission system is a variant of self-coherent systems with a relaxed laser linewidth requirement as opposed to a full coherent system. The system is designed by transmitting a carrier together with the subcarriers, ensuring a strong phase-correlation between them at a receiver compared to the coherent system where only the subcarriers are transmitted. Despite the strong phase-correlation, the laser phase noise (PN) can still degrade the self-homodyne system performance due to the interaction of the PN with a chromatic dispersion (CD) induces a phase-modulation to intensity-modulation (PM-to-IM) conversion noise which cannot be canceled using a balanced-receiver. This imposes a high noise pedestal underneath each subcarrier, with the highest pedestal's peak imposed beneath the subcarriers that are farthest away from the carrier. This in turn produces a phase-decorrelation between the carrier and subcarriers which degrades the Q-factor between the lowest and highest subcarrier frequencies. In this work, the effect of the PM-to-IM conversion noise is reduced for the transmission of up to 174 Gb/s using a simple delay-line assigned to realign the phase-decorrelation of the subcarriers. With this technique, the subcarriers Q-degradation can be improved and the total transmission length can be tripled with Q-improvements of 5.4, 5.3, and 5-dB for 16-quadrature amplitude modulation (QAM) over 1360 km, 32- QAM over 800 km, and 64-QAM over 480 km, respectively, using 10-MHz LW with a 15-GHz total signal bandwidth. For 29 GHz signal bandwidth, the phase-walk-off of the high frequency subcarrier becomes more severe where the introduced delay can increase the transmission length by 2.5 times than without the delay, which increased the signal tolerance to the conversion noise.

Laser Phase Noise in Ring Resonator Assisted Direct Detection Data Transmission

We introduce an analytical model describing the statistical and spectral properties of laser phase noise induced intensity noise in ring-resonator-based modulation. The model is validated with single sideband orthogonal frequency division multiplexing (SSB-OFDM) implemented with a silicon photonics resonantly-assisted Mach-Zehnder modulator (RA-MZM). Excellent agreement of experimental data with full link simulations, in which phase noise conversion is treated with the analytical model, confirms its validity. Moreover, we demonstrate 30 Gb/s raw data rate transmission with SSB-OFDM over 20 km of single-mode fiber with a bit error ratio below the 20% forward error correction (FEC) limit for three independently run channels of the RA-MZM, each supplied with off-the-shelf 1 MHz linewidth distributed feedback lasers.

(Invited) Temperature Stable III-V/Si/Si3N4 Heterogeneous Integrated Laser

Silicon nitride (Si3N4) is a widely used complementary metal–oxide–semiconductor (CMOS) compatible material in modern IC industry and recent years have witnessed tremendous development of Si3N4 in photonics. The benefits of Si3N4 in photonics include low loss, low thermo optic coefficient and negligible nonlinear absorption at telecom wavelengths. Devices based on Si3N4 waveguides innovates in the field of nonlinear photonics, sensing, microwave photonics and so on. However, they are all dependent on the excellent passive properties of Si3N4. There are no successful demonstrations of fully integrated laser with Si3N4 yet.For an external cavity laser design, it is beneficial to have a low loss waveguide. A low loss waveguide platform can enable a long optical cavity which can greatly reduce the laser phase noise. Butt-coupled hybrid integrated lasers are extensively studied using Si3N4 cavity, but they are based on separate chips and are not scalable for large volume integration.Heterogeneous integration of III-V material and Si has achieved great success in the past years, offering the silicon photonics industry with low-cost, high-performance silicon photonic integrated circuits fully integrated with lasers. For the heterogeneous integration of III-V material with Si3N4, the biggest challenge is the large index mismatch. Typical III-V epi used for heterogeneous lasers is about 2 μm thick and extreme tapering cannot facilitate a high coupling efficiency between the III-V layer and Si3N4 layer.In this work, we used an intermediate Si layer to bridge the index mismatch between the III-V and Si3N4 layer. By using multilayer heterogeneous integration shown in Fig.1 (a), we enable a III-V/Si/Si3N4 structure to efficiently couple the mode between III-V/Si and Si/Si3N4. Based on this structure, we designed the III-V/Si/Si3N4 laser using an external Si3N4 spiral grating as the feedback cavity. This spiral grating provides the narrow-band optical feedback and determines the laser wavelength. The laser configuration is shown in Fig. 1(b).The laser performance is summarized in Fig. 1 (c)-(e). The lasing wavelength is at 1546 nm and the laser has over 58 dB side mode suppression ratio (SMSR). This shows the excellent mode selectivity from the 20 mm long Si3N4 spiral grating. We measured the frequency noise of the laser. With optimized loop mirror reflectivity, the laser fundamental linewidth is about 4 KHz. This linewidth can be further improved by lowering the Si3N4 waveguide loss. We anticipate the laser fundamental linewidth can be reduced to below 100 Hz using this design.Another advantage of integrating Si3N4 into the laser cavity is to have much higher temperature stability. By comparison, III-V/Si/Si3N4 laser wavelength shifts by only 0.47 nm for 45 oC change, while for a III-V/Si DBR laser this wavelength shift is 3.3 nm. This is over 7x difference and is a result of the low thermo-optic coefficient of Si3N4. When combined with Si3N4 based arrayed waveguide gratings, our laser can be potentially used in dense wavelength-division-multiplexing (DWDM) systems.The successful demonstration of this multilayer heterogeneous integration will enable a whole new class of devices that require low loss waveguides and are presently not integrated. This is a key step in fully exploiting the capabilities of wafer-bonding technologies. We anticipate this platform can take narrow-linewidth semiconductor laser performance to a new level. Figure 1

Amplitude randomness of spontaneous emission influence on the coherence properties of a laser.

Based on the randomness of spontaneous emission, the statistical characteristics of phase noise are discussed. A theoretical analysis model, focusing on the amplitude randomness of spontaneous emission, is established to calculate laser phase noise. Then, the coherence of a laser before and after phase-locked control is calculated when an ideal laser and nonideal laser are used as a reference light in an optical phase-locked loop (OPLL). The effects of the amplitude randomness of spontaneous emission on phase-locked laser coherence are analyzed in detail. The results show that phase noise randomness increases with the increase of the expectation or variance of spontaneous emission amplitude, which represents amplitude randomness. When an ideal light is used as reference light, if the expectation and the variance of spontaneous emission amplitude are about 10 and 100, respectively, the time constant of an OPLL should be set as 1 ns, while a favorable noise suppression result can be achieved. However, to achieve a favorable noise suppression result, the time constant of an OPLL should be set as 0.1 ns when a nonideal laser is used as reference light.

Optical Heterodyne Analog Radio-Over-Fiber Link for Millimeter-Wave Wireless Systems

Optical heterodyne analog radio-over-fiber (A-RoF) links provide an efficient solution for future millimeter wave (mm-wave) wireless systems. The phase noise of the photo-generated mm-wave carrier limits the performance of such links, especially, for the transmission of low subcarrier baud rate multi-carrier signals. In this work, we present three different techniques for the compensation of the laser frequency offset (FO) and phase noise (PN) in an optical heterodyne A-RoF system. The first approach advocates the use of an analog mm-wave receiver; the second approach uses standard digital signal processing (DSP) algorithms, while in the third approach, the use of a photonic integrated mode locked laser (MLL) with reduced DSP is advocated. The compensation of the FO and PN with these three approaches is demonstrated by successfully transmitting a 1.95 MHz subcarrier spaced orthogonal frequency division multiplexing (OFDM) signal over a 25 km 61 GHz mm-wave optical heterodyne A-RoF link. The advantages and limitations of these approaches are discussed in detail and with regard to recent 5G recommendations, highlighting their potential for deployment in next generation wireless systems.

Dynamical decoupling of laser phase noise in compound atomic clocks

The frequency stability of many optical atomic clocks is limited by the coherence of their local oscillator. Here, we present a measurement protocol that overcomes the laser coherence limit. It relies on engineered dynamical decoupling of laser phase noise and near-synchronous interrogation of two clocks. One clock coarsely tracks the laser phase using dynamical decoupling; the other refines this estimate using a high-resolution phase measurement. While the former needs to have a high signal-to-noise ratio, the latter clock may operate with any number of particles. The protocol effectively enables minute-long Ramsey interrogation for coherence times of few seconds as provided by the current best ultrastable laser systems. We demonstrate implementation of the protocol in a realistic proof-of-principle experiment, where we interrogate for 0.5 s at a laser coherence time of 77 ms. Here, a single lattice clock is used to emulate synchronous interrogation of two separate clocks in the presence of artificial laser frequency noise. We discuss the frequency instability of a single-ion clock that would result from using the protocol for stabilisation, under these conditions and for minute-long interrogation, and find expected instabilities of σy(τ) = 8 × 10−16(τ/s)−1/2 and σy(τ) = 5 × 10−17(τ/s)−1/2, respectively.

Geometric Shaping of 2-D Constellations in the Presence of Laser Phase Noise

In this article, we propose a geometric shaping (GS) strategy to design 8, 16, 32, and 64-ary modulation formats for the optical fibre channel impaired by both additive white Gaussian (AWGN) and phase noise. The constellations were optimised to maximise generalised mutual information (GMI) using a mismatched channel model. The presented formats demonstrate an enhanced signal-to-noise ratio (SNR) tolerance in high phase noise regimes when compared with their quadrature amplitude modulation (QAM) or AWGN-optimised counterparts. By putting the optimisation results in the context of the 400ZR implementation agreement, we show that GS alone can either relax the laser linewidth (LW) or carrier phase estimation (CPE) requirements of 400 Gbit/s transmission links and beyond. Following the GMI validation, the performance of the presented formats was examined in terms of post forward error correction (FEC) bit-error-rate (BER) for a soft decision (SD) extended Hamming code (128, 120), implemented as per the 400ZR implementation agreement. We demonstrate gains of up to 1.2 dB when compared to the 64-ary AWGN shaped formats.

Noise-suppressing and lock-free optical interferometer for cold atom experiments.

A novel noise-suppressing and lock-free interferometer is proposed and experimentally demonstrated in the study of the quantum non-destructive (QND) interaction of cold atoms. A QND measurement based on far-off resonant dispersive probing is usually carried out by a Mach-Zehnder type interferometer. It is an experimental challenge in its own right to reduce the classical noise, such as acoustic noise, phase noise and amplitude noise of lasers, and to lock the interferometer at the white-light position that corresponds to a nearly zero path-length difference. Here, we report an interferometer with an inserted acousto-optic modulator (AOM). It is noise immune and lock-free in principle. The experiments show that the new interferometer is able to measure cold atoms for more than 30 minutes and reduce the phase noise by about 30 dB.

Reanalyzing Atomic Beam Interferometric Gyroscopes: Dependence of Sensitivity on Experimental Parameters

As an important technique for developing high-precision gyroscopes, atom interferometry with continuous atomic beams has exhibited advantages of high short-term sensitivity and dynamic response relative to that with periodically launched atom clouds. This article reanalyzes the characteristics of an atomic beam interferometric gyroscope from perspectives including the continuous operation mode and the modified sensitivity dependence on laser and atomic sources. Specific requirements on certain experimental parameters are explored including the Raman beam diameter, detection beam diameter, atomic flux, laser power, laser phase noise, atomic longitudinal and transverse velocity distributions. The parameter determining strategy is discussed to achieve target sensitivity with controlled conditions such as system volume and operating bandwidth. The results would provide strong support on analytical method and data reference for further improvement of atomic beam interferometric gyroscopes.

Flexible Coherent Communication System With Adaptable SNR and Laser Phase Noise Tolerance for Probabilistically Shaped QAM

Probabilistic-shaped quadrature amplitude modulation (PS-QAM) based on Maxwell-Boltzmann (MB) distribution has been extensively studied in recent years in the SNR limited coherent communication system to approach the Shannon capacity. However, MB distribution is not the optimal distribution when the transmission system suffers from serious laser phase noise. To improve the laser phase noise tolerance of MB distribution, a novel Maxwell-Boltzmann/Angular-distance-directed (MB/ADD) distribution is proposed in this article. The benefits of PS-QAM exist in the case of limited SNR, as well as large laser phase noise. The proposed distribution is verified through simulations and experiments. In our simulation analysis, the ADD part enables the reduction of SNR penalty when laser phase noise increases. The results are validated by experimental data, in which both digitally generated and distributed-feed-back (DFB) laser generated phase noise are employed to evaluate laser phase noise tolerance. In the scenario of large phase noise, MB/ADD shaping can achieve lower pre-FEC BER and higher GMI compared with MB shaping, without inserting pilot symbols. Moreover, the improvement of applying MB/ADD distribution can be obtained no matter whether BPS or V&V based algorithm is adopted for carrier phase estimation (CPE). Different shaping parameters are also tested, where the capability to agilely adapt to various channel conditions of the MB/ADD distribution is shown. And the proposed MB/ADD shaping can be applied with similar complexity with MB shaping, if the Kullback–Leibler (KL) divergence between the generated and the expected 2-D QAM distribution is required to be lower than 10−3.

Stable complex conjugate artifact removal in OCT using circularly polarized light as reference

In Fourier domain optical coherence tomography (FDOCT), the depth profile is mirrored about the zero delay between the sample and reference optical paths, limiting the imaging depth to half of the entire ranging space and undermining the optimal sensitivity window. We present a new method, to the best of our knowledge, to remove the complex conjugate artifact by using circularly polarized light as reference. Quadrature detection of the complex fringe is achieved by utilizing the intrinsic λ/4 delay between two polarization channels. We use passive broadband polarization optics to control the polarization state of the light in the reference and sample arms and a balanced polarization diversity detection unit to simultaneously detect phase-shifted fringes. We demonstrate a 40 dB artifact suppression ratio with a swept-source optical coherence tomography system. Our proposed method is immune to sample motion and laser phase noise, and imposes no restrictions to the source bandwidth, imaging speed, or computational power. In vivo images of the human finger, as well as the cornea and retina of a non-human primate, were demonstrated.

Investigation of the phase noise of a microresonator soliton comb.

Optical frequency combs generated from microresonators (especially microresonator soliton combs) have been attracting significant attentions because of the potential to be fully chip-scale. Among various promising applications of soliton combs, coherent optical communications and mm/THz wireless communications require low phase noise of the comb modes and low relative phase noise between the comb modes, respectively. Here, we measure the phase noise of a soliton comb, investigating how the thermorefractive noise of a microresonator influences on the phase noise. We observe the quadratic increase of the phase noise of the comb modes, as the comb mode number, counted from the wavelength of a pump cw laser, increases. In addition, we measure the relative phase noise between the comb modes, showing less influence of the phase noise of pump cw lasers by comparing soliton combs generated from pump cw lasers with low and large phase noise.

Mode Locked Laser Phase Noise Reduction Under Optical Feedback for Coherent DWDM Communication

Single section quantum dash (QDash) mode locked lasers (MLL) can provide a flat and broadband optical frequency comb with low energy consumption, operational simplicity and large-scale low-cost production possibilities. MLL longitudinal modes can be employed as single carriers with a regular spectral spacing in a dense wavelength division multiplexing (DWDM) link, making them promising components for next generation DWDM transceivers. However, individual modes of a MLL suffer from relatively high phase noise while high capacity coherent transmission requires carriers with low phase noise. Optical feedback, which is a well-known method to reduce the linewidth of a single mode laser, can be used to stabilize comb lasers. This article reports on the investigation of phase noise properties of comb lines delivered from a single section QDash MLL under optical feedback and shows that each MLL longitudinal mode optical linewidth can be drastically narrowed. It enables coherent transmission with extended link budget over 50 km at Tbit/s line rates.