Source Phase Noise Research Articles

Subspace tracking for phase noise source separation in frequency combs.

It is widely acknowledged that the phase noise of an optical frequency comb primarily stems from the common mode (carrier-envelope) and the repetition rate phase noise. However, owing to technical noise sources or other intricate intra-cavity factors, residual phase noise components, distinct from the common mode and the repetition rate phase noise, may also exist. We introduce a measurement technique that combines subspace tracking and multi-heterodyne coherent detection for the separation of different phase noise sources. This method allows us to break down the overall phase noise sources associated with a specific comb-line into distinct phase noise components associated with the common mode, the repetition rate and the residual phase noise terms. The measurement method allow us, for the first time, to identify and measure residual phase noise sources of a frequency modulated mode-locked laser.

Review of interferometric synthetic aperture sonar interferometric phase filtering methods

Interferometric synthetic aperture sonar (InSAS) is a novel three dimensional underwater mapping system, which is widely used in various fields. Interferometric phase filtering is a crucial process in InSAS signal processing. The study of interferogram filtering method has great significance to improve the signal-to-noise ratio (SNR) of interferogram, reduce the difficulty of phase unwrapping, and improve the accuracy of digital elevation maps. Firstly, this article introduces the sources of interferometric phase noise. Secondly, it illustrates the difference between real domain filter and complex domain filter by simulation experiment. Thirdly, the various methods of InSAS interferogram filtering are systematically studied, which can be classified into spatial domain filtering and transform domain filtering. The transform domain filtering can be further divided into frequency domain and wavelet transform filtering. Moreover, the advantages and disadvantages of various methods are analyzed theoretically. Finally, numerical simulation and real-data processing experiments are performed, and the advantages and shortcomings of several methods are compared using residue numbers, root mean square error (RMSE), and CPU time as evaluation criteria.

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.

Research on In-phase Signal Combining Method for Improving Phase Noise

In high-precision system design, the realization of target precision is often limited by the design of the frequency source. In the design and testing of frequency sources, phase noise is often listed as an assessment item that can characterize the performance of frequency sources. Due to the current design and manufacturing level of devices and circuits, it is difficult for conventional methods to get a significant improvement in the phase noise index. This paper explains the concept, source and characteristics of phase noise. According to the different combining characteristics of the main signal and the phase noise, an in-phase signal combining method is proposed to improve the phase noise index. Multiple S-band frequency sources were used to build the verification platform. This platform is used to verify the improvement of the in-phase signal combining method in phase noise index. Finally, this paper presents the difficulties and methods of in-phase signal combining in practical design and applications.

Analytic estimation of jitter and eye diagram based on transmission line time domain response considering skin effect and stochastic crosstalk

In this article, an analytic approach is proposed for estimation of oscillating signal jitter and eye diagram on a transmission line (TL). Basically, the jitter is a result of oscillator phase noise. There are two types of internal and external sources of phase noise which both are considered in the proposed stochastic estimation. Crosstalk between adjacent TLs is the main source of external phase noise on an oscillating signal of a system layout. This phenomenon on the victim TL is studied with stochastic input signal driving for the aggressor TL. For mathematical derivation, the skin effect of the TL is considered for better accuracy. The skin effect of the TL is considerable in high frequency like bit rate one. In addition, a magnetic near-field probe and test procedure are designed and proposed for the measurement of the TL operating stochastic signal without loading effect. A test board is designed and fabricated for verification of the proposed approach. The analytic derivations have good accuracy in estimation of bit rate of the TL less than 4% for the fabricated test board. For this test board, the crosstalk effect on the TL closes the eye diagram height by 30% in 20 GHz.

Phase noise compensation experiment with frequency modulated continuous wave laser in atmospheric propagation

Experimental research is performed on a phase noise compensation (PNC) method to improve the signal-to-noise ratio of a frequency modulated continuous wave (FMCW) ladar under long-distance-detection and atmospheric propagation conditions. In the PNC method, a local self-coherent reference is generated where phase noise of the laser source is recorded. Then the phase noise of long-distance-target echo can be compensated by mean of the recorded source phase noise. The laser source of the ladar is chirped modulated from 1550-nm seed laser, whose bandwidth is 10 GHz. In the experiments, the target for test is an optical corner cube retro-reflector that placed over 10 km away from the ladar. The local self-coherent reference, also refer as auxiliary reference, is the heterodyne signal between the chirped laser source and the delay of itself. The delay path is a 5-km soundproofed fiber optic ring. A 2D data processing technique is proposed for ranging with the concatenately generated phase method applied to implement PNC. To verify the proposed technique under long-distance atmospheric propagation conditions, experiments are performed with the distances of the target as 12 and 19.5 km respectively, and the spectral linewidth of the seed laser as 100 Hz and 3 kHz respectively. By comparing the experimental results, the proposed technique is effective in compensating FMCW laser phase noise, even when the target is further and the phase noise of seed laser is worse.

Ultra-Low Phase Noise Measurement of Microwave Sources Using Carrier Suppression Enabled by a Photonic Delay Line

We propose and demonstrate a photonic delay line based carrier suppression interferometer system for measuring the phase noise of microwave sources. We show both theoretically and experimentally for the first time that carrier suppression is capable of suppressing the effects of the residual phase noise of the microwave amplifiers and the relative intensity noise of light in the system by up to 70 dB, and therefore effectively eliminates the contributions of these noise sources to the noise floor of the phase noise measurement system. Using a 2-km photonic delay line, we achieved phase noise measurement floors of −126 dBc/Hz at 1 kHz and −152 dBc/Hz at 10 kHz around a 10 GHz carrier, respectively, which are 15 and 20 dB lower than those of a frequency discriminator based phase noise measurement system using the same length of fiber delay and the same optical and microwave components. The noise floor of −152 dBc/Hz at 10 kHz is also 8 dB and 17 dB lower than those of a Keysight E5052B phase noise measurement system with 100-times cross-correlation and without cross-correlation, respectively. Even lower phase noise floors are expected for such a carrier suppression system if microwave phase shifters with lower residual phase noise or a longer photonics delay line are used.

Tunable Dual-Wavelength Bismuth Fiber Laser With 37.8-GHz Frequency Spacing

A tunable dual-wavelength Brillouin-bismuth fiber laser with a triple-Brillouin frequency spacing of ∼37.8 GHz was demonstrated by employing modular structures. The modular designs can be divided into two main cavities, whereby cavity 1 consisted of a 2-km single-mode fiber (SMF) and a loop mirror that was able to generate a single-spaced Brillouin shift, while cavity 2 comprised of 10-km dispersion compensating fiber (DCF) that was able to produce a double-spaced Brillouin shift. Based on this design, a stable dual-wavelength lasing was established with a low peak power fluctuation of 0.13 dB and 0.6 dB for the Brillouin pump (BP) and third Brillouin Stokes line (BS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ), respectively. By varying the center wavelength of the Brillouin pump, the dual-wavelength laser can be tuned across a 40 nm span, ranging from 1300 nm to 1340 nm. The frequency spacing of the Brillouin-bismuth fiber laser can also be easily switched between ∼12.6 GHz, ∼25.2 GHz, and ∼37.8 GHz by utilizing these modular structures. The proposed dual-wavelength laser has a promising potential for application as a low phase noise source for microwave generation.

Determining the source of phase noise: Response of a driven Duffing oscillator to low-frequency damping and resonance frequency fluctuations

We present an analytical calculation of the response of a driven Duffing oscillator to low-frequency fluctuations in the resonance frequency and damping. We find that fluctuations in these parameters manifest themselves distinctively, allowing them to be distinguished. In the strongly nonlinear regime, amplitude and phase noise due to resonance frequency fluctuations and amplitude noise due to damping fluctuations are strongly attenuated, while the transduction of damping fluctuations into phase noise remains of order 1. We show that this can be seen by comparing the relative strengths of the amplitude fluctuations to the fluctuations in the quadrature components, and suggest that this provides a means to determine the source of low-frequency noise in a driven Duffing oscillator.

All-optical repetition rate stabilization methods for ultrafast Yb-based SESAM mode-locked fiber oscillator

We demonstrate optical to radio frequency (RF) locking technique using all-fiber phase shifter. Phase shift at 1030 nm was achieved by pumping Er-doped fiber incorporated in the resonator. Pump induced refractive index change was fast enough to stabilize optical pulse repetition rate of ultrafast Yb-doped fiber oscillator and achieve sub-200 fs timing jitter. We also investigate the source of phase noise in soliton fiber oscillators and provide guidelines how to further reduce timing jitter.

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.

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.

Mitigation of phase noise and Doppler-induced frequency offsets in coherent random amplitude modulated continuous-wave LiDAR

We present a detailed analysis of techniques to mitigate the effects of phase noise and Doppler-induced frequency offsets in coherent random amplitude modulated continuous-wave (RAMCW) LiDAR. The analysis focuses specifically on a technique which uses coherent dual-quadrature detection to enable a sum of squares calculation to remove the input signal's dependence on carrier phase and frequency. This increases the correlation bandwidth of the matched-template filter to the bandwidth of the acquisition system, whilst also supporting the simultaneous measurement of relative radial velocity with unambiguous direction-of-travel. A combination of simulations and experiments demonstrate the sum of squares technique's ability to measure distance with consistently high SNR, more than 15 dB better than alternative techniques whilst operating in the presence of otherwise catastrophic phase noise and large frequency offsets. In principle, the technique is able to mitigate any sources of phase noise and frequency offsets common to the two orthogonal outputs of a coherent dual-quadrature receiver including laser frequency noise, speckle-induced phase noise, and Doppler frequency shifts due to accelerations.

Automated wide-ranged finely tunable microwave cavity for narrowband phase noise filtering.

Narrowband microwave filters have wide ranging applications, including the reduction in phase noise of microwave sources within a given frequency band. The prospect of developing an automated filter that tunes itself to an arbitrary desired frequency at maximum extinction promises many experimental advantages such as an enhanced efficiency in performing fine frequency detuning scans and saving time and effort as compared to manual tuning. We design, construct, and program such an automated system and present its hardware and software for reproducibility. It consists of a cylindrical cavity filter and two motors, which change the cavity length and the coupling strength of the microwave field into the cavity, respectively. By measuring the cavity response, an algorithm implemented in Python optimizes these two parameters to achieve the tuning of the filter cavity to the desired frequency with a precision of around 20 kHz, which is significantly better than the cavity linewidth (∼1 MHz). We also demonstrate the suppression of phase noise at the desired frequency by more than 10 dB.

Impact of VCO and PLL Phase Noise on Distributed Beamforming Arrays With Periodic Synchronization

Distributed beamforming between separate wireless nodes in a distributed antenna array requires significant coordination of the relative electrical states of the systems to achieve and maintain a phase-coherent state. A principal factor impacting distributed phase coherence is the relative stability of the local oscillators on each node. Ensuring a coherent state requires the distribution of a reference frequency such that all nodes are operating on the same basis frequency. To support distributed beamforming, the reference frequency must furthermore be distributed wirelessly, typically using a phase-locked loop (PLL) on the secondary nodes. In large arrays, the wireless link used for frequency distribution will have limited capacity, necessitating intermittent updates during which the oscillators are locked, and between which their frequencies will drift. The stability of the oscillator therefore plays an important role in the overall performance relative to the update time. In this paper, we discuss the sources of phase noise generated by the reference oscillator and the PLL, and analyze the impacts of phase noise and update interval on distributed beamforming performance. We provide a framework for analyzing distributed beamforming performance from oscillator and PLL parameters in general, and we analyze beamforming performance for two specific cases using nominal high-stability and low-stability voltage-controlled oscillators, with a parametric comparison between their impact on beamforming performance.

Lifetime-Limited Interrogation of Two Independent ^{27}Al^{+} Clocks Using Correlation Spectroscopy.

Laser decoherence limits the stability of optical clocks by broadening the observable resonance linewidths and adding noise during the dead time between clock probes. Correlation spectroscopy avoids these limitations by measuring correlated atomic transitions between two ensembles, which provides a frequency difference measurement independent of laser noise. Here, we apply this technique to perform stability measurements between two independent clocks based on the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+}. By stabilizing the dominant sources of differential phase noise between the two clocks, we observe coherence between them during synchronous Ramsey interrogations as long as 8s at a frequency of 1.12×10^{15} Hz. The observed contrast in the correlation spectroscopy signal is consistent with the 20.6s ^{3}P_{0} state lifetime and represents a measurement instability of (1.8±0.5)×10^{-16}/sqrt[τ/s] for averaging periods longer than the probe duration when dead time is negligible.

Coherent beam combining of multipass thin-disk lasers with active phase control

Coherent beam combining and the development of thin-disk lasers have provided the ability to increase the output power of solid-state laser systems. Here, coherent beam combining by active phase control of one multipass thin-disk laser amplifier and one similar multipass setup is demonstrated with powers below 100 mW. Piston phase disturbances are measured via optical heterodyne detection and compensated for by piezo mirrors. For one double pass over the disk, a root mean square phase error of λ/69 was achieved. Mechanical vibrations &lt; 5 kHz inside the multipass setup caused by the water cooling of the disk are the main source of phase noise. Thermal effects by the pumping diodes with 1 kW of optical power are negligible.

W-Band Optoelectronic Oscillator

We demonstrate the first W-band optoelectronic oscillator (OEO), that oscillates at 94.5 GHz with a measured single side band (SSB) phase noise of -101 dBc/Hz at an offset frequency of 10 kHz from the carrier. Side mode suppression of more than 65 dB has been achieved by using injection locking. This OEO has potential application as a signal source in emerging W-band applications (e.g. fiber-wireless links) and opens a path to low phase noise sources beyond 100 GHz.

Picometer scale vibrometry in the human middle ear using a surgical microscope based optical coherence tomography and vibrometry system.

We have developed a highly phase stable optical coherence tomography and vibrometry system that attaches directly to the accessory area of a surgical microscope common to both the otology clinic and operating room. Careful attention to minimizing sources of phase noise has enabled a system capable of measuring vibrations of the middle ear with a sensitivity of < 5 pm in an awake human patient. The system is shown to be capable of collecting a wide range of information on the morphology and function of the ear in live subjects, including frequency tuning curves below the hearing threshold, maps of tympanic membrane vibrational modes and thickness, and measures of distortion products due to the nonlinearities in the cochlear amplifier.

Phase Noise in FMCW Radar Systems

Phase noise is one of the fundamental performance parameters in modern radar, communication, spectroscopic, and metrological systems. In this paper, a phase noise theory has been developed for FMCW radar systems. A new design equation has been derived to specify the maximum bound on the allowable source phase noise level in radar systems. The nonlinear phase noise decorrelation function due to coherent mixing has been analyzed for propagation delays less than the coherence time of the reference oscillator, and the spectral broadening of target responses has been discussed for delay times greater than the coherence time. The effects of the subsystems in the transceiver chain are presented and a new model of phase noise in ADCs is discussed. Phase noise modeling techniques are presented, followed by a comparison of a PLL frequency synthesizer with a low-noise frequency synthesizer to demonstrate the reduction of phase noise sidebands for improved detection and tracking performance. Practical measurements from two millimeter wave FMCW radar systems utilizing the two frequency synthesizers have been presented to validate the developed theory.