Laser Phase Noise Research Articles

Geometrically Shaped Odd-Bit QAM Constellations Suitable for Principal Component-Based Phase Estimation

For high-speed optical communication systems, laser phase noise (LPN) stands as a pivotal factor influencing the quality of the received signal. Therefore, the employment of a highly accurate carrier phase recovery (CPR) algorithm at the receiving end is indispensable to ensure the reliability of transmission. While a CPR algorithm called principal component-based phase estimation (PCPE) has been proven to be capable of achieving low-complexity and high-performance phase recovery for even-bit quadrature amplitude modulation (QAM) (i.e., square QAM) signals, it is not compatible with traditional cross-shaped odd-bit QAM signals. To circumvent this problem, a signal constellation design scheme based on geometric shaping (GS) is proposed. The pair-wise optimization (PO) algorithm is used to optimize the constellation structure of 32QAM and 128QAM signals in order to obtain results that are compatible with the PCPE algorithm. Monte Carlo simulation results reveal that for odd-bit QAM signals utilizing PCPE for phase recovery, the proposed GS constellations enhance the mutual information (MI) performance across the entire measured signal-to-noise (SNR) range. Moreover, compared with regular 32QAM and 128QAM constellations using the well-known blind phase search (BPS) algorithm, the proposed GS and PCPE scheme can achieve SNR gains of 1.10 dB and 2.59 dB, respectively, when considering the 20% soft-decision forward error correction (SD-FEC) overhead. Verification through commercial simulation software corroborates these findings, demonstrating that the proposed GS constellations are particularly suitable for the PCPE algorithm, especially under conditions of high optical signal-to-noise ratio (OSNR). To the best of our knowledge, this is the first time that the incompatibility between the PCPE algorithm and odd-bit QAM signals has been investigated, and the proposed GS scheme has broadened the application scope of the low-complexity CPR algorithm.

Laser phase noise suppression method for a CO-OFDM-OQAM communication system with real-imaginary-alternate pilots

Laser phase noise suppression method for a CO-OFDM-OQAM communication system with real-imaginary-alternate pilots

Laser Frequency Modulation and PM-to-AM Noise Conversion in Atomic Clocks.

Laser wavelength stability is a necessity in present-day chip-scale atomic clocks (CSACs), in next-generation atomic clocks planned for Global Navigation Satellite Systems (GNSSs), and in many other atomic devices that generate their signals with lasers. Routinely, this is accomplished by modulating the laser's frequency about an atomic or molecular resonance, which in turn induces modulated laser-light absorption. The modulated absorption then generates a correction signal that stabilizes the laser wavelength. However, in addition to creating absorption modulation for laser wavelength stabilization, the modulated laser frequency can produce a time-dependent variance in transmitted laser intensity noise because of laser phase-noise (PM) to transmitted laser intensity-noise (AM) conversion. Here, we show that the time-varying PM-to-AM conversion can have a significant influence on the short-term frequency stability of vapor-cell atomic clocks. If diode-laser enabled vapor-cell atomic clocks are to break into the [Formula: see text] frequency-stability range, the amplitude of laser frequency modulation for wavelength stabilization will need to be chosen judiciously.

Integrated photonic molecule Brillouin laser with a high-power sub-100-mHz fundamental linewidth.

Photonic integrated lasers with an ultra-low fundamental linewidth and a high output power are important for precision atomic and quantum applications, high-capacity communications, and fiber sensing, yet wafer-scale solutions have remained elusive. Here we report an integrated stimulated Brillouin laser (SBL), based on a photonic molecule coupled resonator design, that achieves a sub-100-mHz fundamental linewidth with greater than 10-mW output power in the C band, fabricated on a 200-mm silicon nitride (Si3N4) CMOS-foundry compatible wafer-scale platform. The photonic molecule design is used to suppress the second-order Stokes (S2) emission, allowing the primary lasing mode to increase with the pump power without phase noise feedback from higher Stokes orders. The nested waveguide resonators have a 184 million intrinsic and 92 million loaded Q, over an order of magnitude improvement over prior photonic molecules, enabling precision resonance splitting of 198 MHz at the S2 frequency. We demonstrate S2-suppressed single-mode SBL with a minimum fundamental linewidth of 71±18 mHz, corresponding to a 23±6-mHz2/Hz white-frequency-noise floor, over an order of magnitude lower than prior integrated SBLs, with an ∼11-mW output power and 2.3-mW threshold power. The frequency noise reaches the resonator-intrinsic thermo-refractive noise from 2-kHz to 1-MHz offset. The laser phase noise reaches -155 dBc/Hz at 10-MHz offset. The performance of this chip-scale SBL shows promise not only to improve the reliability and reduce size and cost but also to enable new precision experiments that require the high-speed manipulation, control, and interrogation of atoms and qubits. Realization in the silicon nitride ultra-low loss platform is adaptable to a wide range of wavelengths from the visible to infrared and enables integration with other components for systems-on-chip solutions for a wide range of precision scientific and engineering applications including quantum sensing, gravitometers, atom interferometers, precision metrology, optical atomic clocks, and ultra-low noise microwave generation.

Impact of laser phase noise on the ranging accuracy of a cooperative MIMO FMCW photonic radar system

In this paper, a FMCW-based cooperative 2×2 MIMO photonic radar system using heterodyne detection is presented. The proposed system consists of two separate sensor nodes that use a linear frequency modulated continuous wave signal, which allows simultaneous monostatic and bistatic radar measurement, where the target range and angle of arrival information are extracted. The additional bistatic information enhances the target detection and estimation capabilities with improved accuracy. This accuracy in practicality is affected by the laser phase noise, which degrades the overall system performance. Here, the analytical laser phase noise model for the MIMO system is derived and implemented to analyze its impact on the ranging accuracy of the proposed system. Under the impact of standard white Gaussian laser phase noise assumption, the monostatic and bistatic response of the detected signal is measured and compared using statistics of measurement error. Further, the signal-to-noise ratio and SSB laser phase noise of the monostatic and bistatic response are measured and compared at different target ranges. At last, the phase-noise-limited ranging accuracy of the system is evaluated and analyzed. The concept shown in this work paves the way for advanced photonic radar system applications such as modern radar systems, electronic warfare systems, metrology, and automotive vehicle radar with multiperspective coherent detection.

Characterization of Laser Frequency Stability by Using Phase-Sensitive Optical Time-Domain Reflectometry

A new method to measure laser phase noise and frequency stability based on the phase-sensitive optical time-domain reflectometry is proposed. In this method, the laser under test is utilized in a phase-sensitive optical time-domain reflectometer, which employs phase-modulated dual pulses and acts as an optical frequency discriminator: laser frequency fluctuations are deduced from the analysis of the reflectometer data corresponded to phase fluctuations along the vibration-damped and thermally insulated fiber spool. The measurement results were validated by comparison with direct optical heterodyning of the tested and more coherent reference lasers. The use of dual pulses generated by an acousto-optic modulator makes it easy to adjust the time delay during measurements, which distinguishes favorably the proposed method from standard optical frequency discriminators. The method is suitable for testing highly coherent lasers and qualifying their parameters such as linear drift rate, random frequency walk rate, white frequency noise (which is directly related to laser instantaneous linewidth), and flicker noise level.

Compensating Chromatic Dispersion and Phase Noise using Parallel AFB-MBPS For FBMC-OQAM Optical Communication System

Filter Bank Multi-Carrier Offset-QAM (FBMC-OQAM) is one of the hottest topics in research for 5G multi-carrier methods because of its high efficiency in the spectrum, minimal leakage in the side lobes, zero cyclic prefix (CP), and multiphase filter design. Large-scale subcarrier configurations in optical fiber networks need the use of FBMC-OQAM. Chromatic dispersion is critical in optical fiber transmission because it causes different spectral waves (color beams) to travel at different rates. Laser phase noise, which arises when the phase of the laser output drifts with time, is a major barrier that lowers throughput in fiber-optic communication systems. This deterioration may be closely related among channels that share lasers in multichannel fiber-optic systems using methods like wavelength-division multiplexing with frequency combs or space-division multiplexing. In this research, we use parallel Analysis Filter Bank (AFB) equalizers in the receiver part of the FBMC OQAM Optical Communication system to compensate for chromatic dispersion (CD) and phase noise (PN). Following the equalization of CD compensation, the phase of the carriers in the received signal is tracked and compensated using Modified Blind Phase Search (MBPS). The CD and PN compensation techniques are simulated and analyzed numerically and graphically to determine their efficacy. To evaluate the FBMC's efficiency across various equalizers, 16-OQAM is taken into account. Bit Error Rate (BER), Optical Signal-to-Noise Ratio (OSNR), Q-Factor, and Mean Square Error (MSE) were the primary metrics we utilized to evaluate performance. Single-tap equalizer, multi-tap equalizer (N=3), ISDF equalizer with suggested Parallel Analysis Filter Banks (AFBs) (K=3), and MBPS were all set aside for comparison. When compared to other forms of Nonlinear compensation (NLC), the CD and PN tolerance attained by Parallel AFB equalization with MBPS is the greatest.

Weighted Decision Enabled Phase Retrieval Receiver With Adaptive Intensity Transformation

Phase-retrieval (PR) receivers can reconstruct complex-valued signals from two de-correlated intensity measurements by the use of iterative PR algorithm, without the assistance of any optical carriers. However, both the computational complexity with hundreds of iterations and the limited PR accuracy prevent it from being applied to high-speed photonic interconnections. In current submission, we propose a weighted decision enhanced PR receiver with adaptive intensity transformation (WD_AIT_PR). The weighted decision based on a compressed sigmoid nonlinear function is helpful to avoid the hard-decision (HD) errors, leading to the performance enhancement of the PR receiver, in terms of both convergence speed and PR accuracy. When the 56 GBaud 16QAM signal after transmission over 80 km standard single mode fiber (SSMF) is reconstructed, the WD_AIT_PR receiver is numerically verified to possess the faster convergency speed with only 70 iterations and the best steady BER performance by reducing the required optical signal-to-noise ratio (OSNR) by 0.8 dB, 1.8 dB and 1.8 dB in order to reach 7% HD forward error correction (HD-FEC), in comparison with the HD_AIT_PR receiver by replacing WD with HD, the PR receiver with the phase reset (PR_PR) and the PR receiver with adaptive intensity transformation (AIT_PR), respectively. Meanwhile, the WD_AIT_PR receiver is robust to transmission impairments, including transmitter-side I/Q imbalance, receiver-side skew, the noise imbalance between two intensity measurements, laser phase noise, and laser wavelength drift. Finally, the enhanced performance of the WD_AIT_PR receiver is experimentally verified through recovering 25 GBaud 16QAM signals under the condition of 40 km SSMF transmission.

Clock noise reduction in geometric time delay interferometry combinations

Time-delay interferometry (TDI) is a critical data post-processing technique in space-borne laser interferometer gravitational wave detection, which is developed to suppress the overwhelming laser phase noise below the instrumental noise floor by time-shifting and synthesizing the interferometric data streams. There are virous kinds of TDI combinations, and geometric TDI, as a special means to search TDI combination, has been widely used because of its clear physical significance, i.e. constructing virtual equal-arm interferometer to realize an excellent differential performance of the laser phase noise. To achieve the desired noise level, it is necessary to further suppress the phase fluctuations of the onboard ultra-stable oscillators (USO) used as reference clocks. In this paper, we analyze the characteristics of geometric TDI clock noise residual, and formulate it into a general expression. We find the intrinsic equal-arm length constraint of geometric TDI is a sufficient condition for clock noise reduction, which makes the clock noise terms only appear in differential form. Based on this, we propose a clock noise reduction scheme. Compared with the existing algorithms, our method benefits from the sufficient condition to avoid the problem that the clock noise terms without any time-shift operators cannot be properly handled.

Narrow-Linewidth 852-nm DBR-LD with Self-Injection Lock Based on High-Finesse Optical Cavity Filtering

Narrow-linewidth lasers have a high spectral purity, long coherent length, and low phase noise, so they have important applications in atomic clocks, precision measurement, and quantum computing. We inject a transmitted laser from a narrow-linewidth (∼15 kHz) flat-concave Fabry–Perot (F-P) cavity made from ultra-low expansion (ULE) optical glass into an 852 nm distributed Bragg reflector-type laser diode (DBR-LD), of which the comprehensive linewidth is 1.67 MHz for the free running case. With an increase in the self-injection power, the laser linewidth gradually narrows, and the injection locking current range gradually increases. The narrowest linewidth measured by the delayed frequency-shifted self-heterodyne (DFSSH) method is about 365 Hz, which is about 1/4500 of the linewidth for the free running case. Moreover, to characterize the laser phase noise, we use a detuned F-P cavity to measure the conversion signal from the laser phase noise to the intensity noise for both the free running case and the self-injection lock case. The laser phase noise for the self-injection lock case is significantly suppressed in the analysis frequency range of 0.1–10 MHz compared to the free running case. In particular, the phase noise is suppressed by more than 30 dB at an analysis frequency of 100 kHz.

FPGA-driven random walk noise generation for tunable laser linewidth control

We propose a novel approach for real-time generation of random walk noise. Our approach aims to generate natural laser phase noise and construct a linewidth tunable laser. By utilizing field- programmable gate array circuits and digital-to-analog converters, we generate noise that is subsequently combined with low-frequency analog noise. This combined noise is then fed into a lithium niobate phase modulator to emulate phase fluctuations. Our method facilitates accurate control over the laser linewidth spectrum, closely approximating actual noise characteristics.

3D integration enables ultralow-noise isolator-free lasers in silicon photonics

Photonic integrated circuits are widely used in applications such as telecommunications and data-centre interconnects1–5. However, in optical systems such as microwave synthesizers6, optical gyroscopes7 and atomic clocks8, photonic integrated circuits are still considered inferior solutions despite their advantages in size, weight, power consumption and cost. Such high-precision and highly coherent applications favour ultralow-noise laser sources to be integrated with other photonic components in a compact and robustly aligned format—that is, on a single chip—for photonic integrated circuits to replace bulk optics and fibres. There are two major issues preventing the realization of such envisioned photonic integrated circuits: the high phase noise of semiconductor lasers and the difficulty of integrating optical isolators directly on-chip. Here we challenge this convention by leveraging three-dimensional integration that results in ultralow-noise lasers with isolator-free operation for silicon photonics. Through multiple monolithic and heterogeneous processing sequences, direct on-chip integration of III–V gain medium and ultralow-loss silicon nitride waveguides with optical loss around 0.5 decibels per metre are demonstrated. Consequently, the demonstrated photonic integrated circuit enters a regime that gives rise to ultralow-noise lasers and microwave synthesizers without the need for optical isolators, owing to the ultrahigh-quality-factor cavity. Such photonic integrated circuits also offer superior scalability for complex functionalities and volume production, as well as improved stability and reliability over time. The three-dimensional integration on ultralow-loss photonic integrated circuits thus marks a critical step towards complex systems and networks on silicon.

Intracavity filtering in SESAM mode-locked fiber lasers: soliton effects and noise performance.

We characterized and analyzed the effect of intracavity spectral filtering in the Er:fiber laser mode-locked with a semiconductor saturable absorber mirror (SESAM). We studied the dispersive properties of bandpass filters and their influence on the characteristics of generated soliton pulses. Our analysis showed that various sideband structures were induced by the filter dispersion profiles and shaped through the interaction of the soliton with the dispersive wave. In addition, intracavity filtering improved the intensity and phase noise of the laser significantly, and we showed optimal filtering conditions for both types of noise. By adding a 10 nm bandpass filter to the laser resonator, the intensity and phase noise were improved 2- and 2.6 times, respectively.

ИЗМЕРЕНИЕ ФАЗОВЫХ И АМПЛИТУДНЫХ ШУМОВ ПОЛУПРОВОДНИКОВЫХ ЛАЗЕРОВ. МЕТОДИКА ИЗМЕРЕНИЙ. КАЛИБРОВКА. РЕЗУЛЬТАТЫ

The application of the frequency detector method for measuring the phase noise spectrum of semiconductor lasers has been experimentally demonstrated. The frequency detector is based on an unbalanced Mach-Zehnder interferometer and a photodetector. Analytical relations are obtained that allow one to choose the parameters of the Mach-Zehnder interferometer and perform experimental calibration of the measuring system. A technique is proposed for measuring the spectral components of the phase noise of lasers in the presence of a slow drift of the delay in fiber-optic lines and the frequency of the laser under study. The results of measuring the phase noise of a low-noise DX-1 laser module and high-noise laser diodes LSDLD155 (DFB) and LSFLD155 (FP) are presented. A strong correlation between the amplitude and phase noise levels of these lasers is found. The decisive influence of the noise of LSDLD155 and LSFLD155 lasers on the level of phase noise of optoelectronic (OE) microwave generators built using them is shown. It has been suggested that the low-noise laser module DX-1, which has a phase noise level 20–60 dB lower (in different parts of the spectrum), is not decisive in the level of phase and amplitude noise of an optoelectronic microwave generator. The investigated OE generator was built during the research in this work. The generator has low phase noise: −120 dBc/Hz at a frequency detuning of 10 kHz. Oscillation frequency 6.8 GHz; fiber optic delay line length 200 m.

Noise Compensation Methods for Optical Fiber Frequency Sweeping Interferometry: A Review

Noise induced by the fluctuation of laser phase, frequency, intensity, etc., can deteriorate the point spread function (PSF) in distributed optical fiber sensing and testing systems, which is the core concern for measurement performance, such as measurement spatial resolution, length range, accuracy and dynamic range. In this paper, we review the development of noise compensation methods for improving the PSF in optical fiber frequency sweeping interferometry (OFFSI) systems and provide a reference to select appropriate compensation methods in different applications (e.g., fiber optics component characterization, optical fiber network diagnosis). A discussion of noise impacts on PSF is made, including laser source phase noise, laser source intensity noise and ambient noise. The most serious noise is the laser source phase noise involved in frequency tunable lasers, including deterministic frequency tuning nonlinearity and stochastic laser phase noise. Also, a comprehensive and detailed classification of the compensation strategies for different noise is provided according to the dominant noise in the laser source. Recent progress on each kind of compensation method is analyzed based on the principles, performance, advantages and limitations, and a comparison of compensation methods is presented. Finally, an overview of trends and future developments is given.

Suppression of laser phase noise by using updated common arm locking

The space-borne gravitational wave (GW) detectors, e.g., LISA, TianQin, TaiJi, are designed to measure the GW in the low-frequency regime (0.1 mHz to 1 Hz). The arm length mismatches in the flying constellation prevent exact laser phase noise cancellation. For a typical Michelson interferometric design such as LISA, the two arms will differ by a few percent and the uncanceled fluctuation from the ultra-stable laser is about 5 orders larger than the sensitivity goal in the science band (0.1 mHz to 1 Hz). In this work, we try to resolve this discrepancy in real time by using an arm locking technique. Unlike the analysis in previous literatures, we use the subtraction of one closed loop phase meter output from another one at the main spacecraft to cancel the laser phase noise further. We find that, with a careful design of the arm locking controller, the laser phase noise can be suppressed below the level of secondary noises in most parts of the science band. We point out that since the nulls always exist in the presence the GW transfer function of Michelson interferometer, there is no need to move the nulls to outside the science band by using a complicated arm locking sensor. Then, a study on the Doppler frequency pulling for the system has been carried out, and the result suggests that the pulling rate can meet the requirement. Finally, a good agreement between the time-series simulation in Simulink and theoretical result indicates the feasibility of this scheme. Therefore, the suppression of laser phase noise can possibly be realized in real time with prestabilization and updated common arm locking techniques. Our work can provide a back-up strategy for the implementation of arm locking in future space-borne GW detectors.

Initialized autoencoders to find constellations robust to residual laser phase noise

Autoencoder (AE) has been used to find quadrature amplitude modulation (QAM) constellations robust to optical impairments, such as residual laser phase noise or fiber nonlinearities. We examine AE for constellations for fiber links with residual phase noise following phase recovery. We study 1) improved constellations via AE neural network (NN) initialization, 2) bit-to-symbol mappings for AE constellations, and 3) performance enhancement from the AE decoder as a detection algorithm. We compare our performance to several other phase-noise-optimized constellations, using an identical phase recovery method for fair comparison. We confirm the improved performance of our constellations experimentally as well as via simulation. Our AE initialization technique (using previous constellations found experimentally, empirically, numerically, etc.) is shown to improve constellations for 16QAM and 64QAM. A bit-to-symbol mapping is essential to benefit fully from AE constellations, but is intractable to optimize. We use an ad hoc approach that derives mappings from our initialization constellations. Our AE initialization technique leads to performance improvements over the previous QAM constellations under all metrics: generalized mutual information (GMI), bit error rate (BER) and symbol error rate (SER). We examine the gap between BER and SER due to non-optimal bit-to-symbol mappings. The AE approach to constellation design has as a byproduct an optimized detector: the AE decoder. We quantify the improvement of this detector over the classic maximum likelihood detection that neglects phase noise.

Analysis of the encryption penalty in a QAM-based quantum noise stream cipher.

Quantum noise stream cipher based on quadrature-amplitude-modulation (QAM/QNSC) is a kind of physical layer encryption technology. However, the additional encryption penalty will significantly affect the practical deployment of QNSC, especially in the high capacity and long-haul transmission system. With our research, the encryption process of QAM/QNSC degrades the transmission performance of plaintext information. In this paper, we quantitatively analyze the encryption penalty of QAM/QNSC based on the proposed concept of effective minimum Euclidean distance. We calculate the theoretical signal-to-noise ratio sensitivity and encryption penalty of QAM/QNSC signals. A modified feedforward pilot-aided two-stage carrier phase recovery scheme is used to reduce the effect of laser phase noise and the encryption penalty. Experimental results achieve single-channel 205.9 Gbit/s 640km transmission with single carrier polarization-diversity-multiplexing 16-QAM/QNSC signal.

High accurate and modulation transparent frequency offset compensation scheme using data-aided feedback structure in coherent optical communication systems

The high-order modulation format has the advantages of high spectral efficiency and large system capacity. However, the traditional frequency offset estimation and compensation algorithms, such as fast Fourier transform-based frequency offset estimation (FFT-FOE) that relies on a large number of complex FFT operations and differential frequency offset estimation (Diff-FOE) that relies on finite phase difference between adjacent symbols, are difficult to meet the frequency offset estimation requirements for any high-order modulation format. In this work, a novel FOE scheme using QPSK training symbols aided feedback structure is proposed. The performance of the proposed FOE scheme is evaluated in a polarization multiplexing QPSK-aided 32/64-quadrature amplitude modulation (QAM) simulation platforms with a symbol rate of 28 GBaud. The results show that has the technical advantages of low complexity, suitable for arbitrarily high-order modulation, tolerance for laser phase noise and wide tracking frequency offset range.

On the Nonlinear Shaping Gain With Probabilistic Shaping and Carrier Phase Recovery

The performance of different probabilistic amplitude shaping (PAS)techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques—namely, sphere shaping, shell mapping with different number of shells, and constant composition DM—and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1\times 180$</tex-math></inline-formula> km, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$15\times 80$</tex-math></inline-formula> km, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$27\times 80$</tex-math></inline-formula> km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm.