Additional Phase Noise Research Articles

Control of stochastic and inverse stochastic resonances in a liquid-crystal electroconvection system using amplitude and phase noises

Stochastic and inverse stochastic resonances are counterintuitive phenomena, where noise plays a pivotal role in the dynamics of various biological and engineering systems. Even though these resonances have been identified in various systems, a transition between them has never been observed before. The present study demonstrates the presence of both resonances in a liquid crystal electroconvection system using combined amplitude and phase noises, which correspond to colored noises with appropriate cutoff frequencies (i.e., finite correlation times). We established the emergence of both resonances and their transition through systematic control of the electroconvection threshold voltage using these two noise sources. Our numerical simulations were experimentally confirmed and revealed how the output performance of the system could be controlled by combining the intensity and cutoff frequency of the two noises. Furthermore, we suggested the crucial contribution of a usually overlooked additional phase noise to the advancements in various noise-related fields.

Reconfigurable Low Phase Noise RF Carrier Generation up to W-Band in Silicon Photonics Technology

Reconfigurable radiofrequency (RF) signal generation in the 30–300 GHz range is attractive for many applications. W-band (75–110 GHz) is currently targeted by both wireless and satellite communications and similar frequency ranges are employed for on-board automotive radar systems. Distribution of high-precision and high-frequency synchronization signals in modern centralized radio access networks might be addressed by radio-over-fiber solutions, but the stringent phase noise (PN) requirements in case of broadband signals with high subcarriers density are not easily attainable through conventional electric-domain solutions. This article reports on the performance of a monolithically integrated silicon photonics (SiP) circuit employed for RF carrier synthesis. Up to sixfold frequency multiplication of an 18.5 GHz reference clock is demonstrated with low additional phase noise. The circuit includes a high-speed electro-optic phase modulator employed for optical frequency comb (OFC) generation and a tunable distributed feedback resonator (DFBR) filter for selecting the desired OFC harmonic. The beating of the OFC tone with the input laser mode in an off-chip photodiode generates the target RF carrier wave. By tuning the reference clock and the DFBR filter, reconfigurable frequency generation up to W-band and beyond is achieved. PN and time jitter (TJ) of the generated RF carriers are experimentally measured, demonstrating a similar performance as of an ideal frequency multiplier. The effect of the noise of DC sources employed for filter tuning is assessed and a counteracting solution is implemented. TJ robustness versus laser drifting is analyzed and the potential for up to elevenfold frequency multiplication (203.5 GHz) is shown.

A 12-GHz Reconfigurable Multicore CMOS DCO, With a Time-Variant Analysis of the Impact of Reconfiguration Switches on Phase Noise

This article introduces a 28-nm CMOS digitally controlled oscillator (DCO) based on eight oscillator cores, where the number of active cores can be reconfigured to be either 2, 4, 6, or 8, trading power consumption for phase noise without incurring an additional phase noise penalty. The impact of the reconfiguration pMOS switches on the phase noise performance is determined through a simple yet rigorous time-variant circuit analysis. The octa-core DCO covers a 27% frequency tuning range between 10.7 and 14.1 GHz with an average resolution of 6 MHz. A very low phase noise level of −126 dBc/Hz is measured at 1-MHz offset from 10.7 GHz with a power consumption of 173 mW, corresponding to a phase-noise figure-of-merit of −184 dBc/Hz that remains almost constant across the tuning range.

Coherent Optical Frequency Transfer via a 490 km Noisy Fiber Link

We demonstrate the coherent transfer of an ultrastable optical frequency reference over a 490 km noisy field fiber link. The fiber-induced phase noise power spectrum density per-unit-length at 1 Hz offset frequency can reach up to 510 rad2⋅Hz−1⋅km−1, which is much higher than the fiber noise observed in previous reports. This extreme level of phase noise is mainly due to the fiber link laying underground along the highway. Appropriate phase-locked loop parameters are chosen to complete the active compensation of fiber noise by measuring the intensity fluctuation of additional phase noise and designing a homemade digital frequency division phase discriminator with a large phase detection range of 212 π rad. Finally, a noise suppression intensity of approximately 40 dB at 1 Hz is obtained, with fractional frequency instability of 1.1 × 10−14 at 1 s averaging time, and 3.7 × 10−19 at 10000 s. The transfer system will be used for remote atomic clock comparisons and optical frequency distribution over a long-distance communication network established in China.

Effects of the Space Plasma Density Oscillation on the Interspacecraft Laser Ranging for TianQin Gravitational Wave Observatory

AbstractThe TianQin space gravitational waves (GW) observatory will contain three geocentric and circularly orbiting spacecraft with an orbital radius of 105 km, to detect the GW in the milli‐hertz frequency band. Each spacecraft pair will establish a 1.7 × 105 km‐long laser interferometer immersed in the solar wind and the magnetospheric plasmas to measure the phase deviations induced by the GW. GW detection requires a high‐precision measurement of the laser phase. The cumulative effects of the long distance and the periodic oscillations of the plasma density may induce an additional phase noise. This study aims to model the plasma induced phase deviation of the interspacecraft laser signals, using a realistic orbit simulator and the Space Weather Modeling Framework model. Preliminary results show that the plasma density oscillation can induce the phase deviations close to 2 × 10−6 rad/Hz1/2 or 0.3 pm/Hz1/2 in the milli‐hertz frequency band and it is within the error budget assigned to the displacement noise of the interferometry. The amplitude spectrum density of phases along three arms become more separated when the orbital plane is parallel to the Sun‐Earth line or during a magnetic storm. Finally, the dependence of the phase deviations on the orbital radius is examined.

InAs/GaAs quantum dot single-section mode-locked lasers on Si (001) with optical self-injection feedback.

Silicon based InAs quantum dot mode locked lasers (QD-MLLs) are promising to be integrated with silicon photonic integrated circuits (PICs) for optical time division multiplexing (OTDM), wavelength division multiplexing (WDM) and optical clocks. Single section QD-MLL can provide high-frequency optical pulses with low power consumption and low-cost production possibilities. However, the linewidths of the QD-MLLs are larger than quantum well lasers, which generally introduce additional phase noise during optical transmission. Here, we demonstrated a single section MLL monolithically grown on Si (001) substrate with a repetition rate of 23.5 GHz. The 3-dB Radio Frequency (RF) linewidth of the QD-MLL was stabilized at optimized injection current under free running mode. By introducing self-injection feedback locking at a feedback strength of -24dB, the RF linewidth of MLL was significantly narrowed by two orders of magnitude from 900kHz to 8kHz.

4 × 32-Gbps Block-Wise QPSK 1200-km SSMF Direct Detection Transmission Based on Delta-Sigma Virtual Carrier Generation

Direct detection (DD) is one of the most attractive solutions for short and medium reach optical fiber transmission in comprehensive consideration of digital signal processing (DSP), power consumption, and cost. Various single side band (SSB) DD techniques have been widely investigated to detect and process the complex signal. In this paper, we propose a novel approach which uses only high-speed digital input/outputs (IO) to generate both quadrature phase shift keying (QPSK) signal and virtual carrier signal. A transmission of 4 × 32 Gb/s QPSK signal over 1200-km standard single mode fiber (SSMF) in block-wise manner has been successfully demonstrated. Only a single polarization in-phase-and-quadrature (IQ) modulator and one single photodiode (PD) are used for each channel. Compared with conventional DSP of coherent detection, the DSP in the proposed scheme is also simplified that only fixed frequency compensation is required without additional phase noise elimination. The overall system complexity has been greatly reduced.

Residual phase noise suppression for Pound-Drever-Hall cavity stabilization with an electro-optic modulator

We propose a simple method to suppress residual frequency/phase noise in Pound-Drever-Hall (PDH) cavity stabilization setups. This method makes use of the electro-optic modulator that is commonly used in PDH setups, and hence, only requires the addition of a simple electronic feedback circuit. Here, we apply this method to stabilize a commercially available continuous wave (cw) laser to a high-finesse cavity, and we demonstrate additional phase noise suppression of ~30 dB and more from DC to 100 kHz, compared to the use of a fast-piezo actuator alone. This method can be applied to almost all PDH systems to achieve feedback bandwidths in the multi-MHz range. Furthermore, this method does not require additional actuators, such as acousto-optic modulators, and it does not introduce parasitic amplitude modulation to the first order. The limitations and drawbacks of this approach are also discussed.

Quantum Dash Passively Mode-Locked Lasers for Coherent Wavelength Conversion System

We demonstrate an all-optical wavelength conversion system based on four-wave mixing in semiconductor optical amplifiers for quadrature phase shift keying (QPSK) and 16-quadrature amplitude modulation (16-QAM) signals using tunable dual-correlated pumps provided by the combination of a quantum dash passively mode-locked laser (QD-PMLL) and a programmable tunable optical filter. We investigate the effects of additional phase noise transfer to the wavelength converted idler due to non-ideal correlation between the comb lines of the QD-PMLL. Our studies of the wavelength conversion of QPSK and 16-QAM signals at 12.5 Gbaud using the proposed scheme find that the bit error rate performance was below the 7% forward error correction (FEC) limit over a range of pump spacing exceeding 300 GHz for QPSK signals, and conversion of 16-QAM signals was limited by the wavelength conversion scheme though was nonetheless below the 20% FEC limit.

Lock threshold deterioration induced by antenna vibration and signal coupling effects in hypersonic vehicle carrier tracking system of Ka band

The envelope of a hypersonic vehicle is affected by severe fluctuating pressure, which causes the airborne antenna to vibrate slightly. This vibration mixes with the transmitted signals and thus introduces additional multiplicative phase noise. Antenna vibration and signal coupling effects as well as their influence on the lock threshold of the hypersonic vehicle carrier tracking system of the Ka band are investigated in this study. A vibration model is initially established to obtain phase noise in consideration of the inherent relationship between vibration displacement and electromagnetic wavelength. An analytical model of the Phase-Locked Loop (PLL), which is widely used in carrier tracking systems, is established. The coupling effects on carrier tracking performance are investigated and quantitatively analyzed by imposing the multiplicative phase noise on the PLL model. Simulation results show that the phase noise presents a Gaussian distribution and is similar to vibration displacement variation. A large standard deviation in vibration displacement exerts a significant effect on the lock threshold. A critical standard deviation is observed in the PLL of Binary Phase Shift Keying (BPSK) and Quadrature Phase Shift Keying (QPSK) signals. The effect on QPSK signals is more severe than that on BPSK signals. The maximum tolerable standard deviations normalized by the wavelength of the carrier are 0.04 and 0.02 for BPSK and QPSK signals, respectively. With these critical standard deviations, lock thresholds are increased from −12 and −4 dB to 3 and −2 dB, respectively.

Upper limit to the transverse to longitudinal motion coupling of a waveguide mirror

Waveguide mirrors (WGMs) possess nano-structured surfaces which can potentially provide a significant reduction in thermal noise over conventional dielectric mirrors. To avoid introducing additional phase noise from the motion of the mirror transverse to the reflected light, however, they must possess a mechanism to suppress the phase effects associated with the incident light translating across the nano-structured surface. It has been shown that with carefully chosen parameters this additional phase noise can be suppressed. We present an experimental measurement of the coupling of transverse to longitudinal displacements in such a WGM designed for 1064 nm light. We place an upper limit on the level of measured transverse to longitudinal coupling of one part in seventeen thousand with 95% confidence, representing a significant improvement over a previously measured grating mirror.

Microwave generation with photonic frequency octupling using a DPMZM in a Sagnac loop

A photonic microwave signal generation scheme with frequency octupling is proposed and experimentally demonstrated. The scheme is based on bi-directional use of a dual-parallel Mach–Zehnder modulator (DPMZM) in a Sagnac loop. The two sub-modulators in the DPMZM are driven by two low-frequency signals with a π/2 phase difference, and the dc biases of the modulator are all set at the maximum transmission points. Due to the velocity mismatch of the modulator, only the light wave along the clockwise direction is effectively modulated by the drive signals to generate an optical signal with a carrier and ±4th order sidebands, while the modulation of the light wave along the counterclockwise direction is far less effective and can be ignored. By properly adjusting the polarization of the light wave output from the Sagnac loop, the optical carrier can be significantly suppressed at a polarizer, and then an optical signal with only ±4th order sidebands is generated. In the experiment, a pure 24-GHz microwave signal without additional phase noise from the optical system is generated using a 3-GHz local oscillator signal. As no electrical or optical filter is used, the photonic frequency octupler is of good frequency tunability.

Relative Phase Noise-Induced Phase Error and System Impairment in Pump Depletion/Nondepletion Regime

Although the pump relative intensity noise transfer phenomenon in traditional Raman amplified amplitude-shift keying fiber communication systems has been investigated intensively, the stochastic intensity fluctuation of Raman pump laser will interplay with fiber nonlinearity and leads to additional phase noise of signal in the multilevel modulated coherent optical communication system. Such phase noise is defined as relative phase noise (RPN). In this paper, we present comprehensive analysis regarding the characteristics and impairments of RPN through both theoretical derivation and Monte Carlo simulation. We derive the analytical expressions of phase error variance for M-ary PSK and 16QAM modulation formats in consideration of RPN using decision-aided maximum-likelihood phase estimation algorithm. The analysis can be used to predict RPN induced impairment theoretically. Bit error rate (BER) performance is evaluated and compared for QPSK, 8PSK, 16PSK, and 16QAM modulation formats, and the result shows that in the context of RPN 16QAM signal outperforms 16PSK which has the same spectral efficiency. Finally, we extend the analytical result obtained in pump nondepletion regime to depletion regime via numerical analysis. It is observed by comparison that Q-factor penalty will increase in depletion regime.

Relative phase noise estimation and mitigation in Raman amplified coherent optical communication system

The interplay between the stochastic intensity fluctuation of Raman pump laser and cross-phase modulation (XPM) effect in transmission optical fiber leads to additional phase noise, namely, relative phase noise (RPN) of signal in multi-level modulated coherent optical communication system. Both theoretical analysis and quantitative simulation have been performed to investigate the characteristics and impact of RPN. Being low-pass in nature, RPN is different from XPM induced phase noise in PSK/OOK hybrid system, and has not been considered yet. The noise power of RPN can accumulate incoherently along transmission links. With a proper signal model, we study the impact of RPN to the coherent optical communication system through Monte Carlo simulation. RPN will cause more cycle slips in Viterbi-and-Viterbi (V-V) phase estimation (PE), and the quantitative analysis of cycle slip probability is carried out. When using sliding window V-V without any optimization, the Q factor penalty of RPN on DQPSK signal can be as large as around 5 dB in strong RPN condition. However, it can be reduced by over 3 dB when using an optimal block size or optimal averaging weights.

Interferometer phase noise due to beam misalignment on diffraction gratings

All-reflective interferometer configurations have been proposed for the next generation of gravitational wave detectors, with diffractive elements replacing transmissive optics. However, an additional phase noise creates more stringent conditions for alignment stability. A framework for alignment stability with the use of diffractive elements was required using a Gaussian model. We successfully create such a framework involving modal decomposition to replicate small displacements of the beam (or grating) and show that the modal model does not contain the phase changes seen in an otherwise geometric planewave approach. The modal decomposition description is justified by verifying experimentally that the phase of a diffracted Gaussian beam is independent of the beam shape, achieved by comparing the phase change between a zero-order and first-order mode beam. To interpret our findings we employ a rigorous time-domain simulation to demonstrate that the phase changes resulting from a modal decomposition are correct, provided that the coordinate system which measures the phase is moved simultaneously with the effective beam displacement. This indeed corresponds to the phase change observed in the geometric planewave model. The change in the coordinate system does not instinctively occur within the analytical framework, and therefore requires either a manual change in the coordinate system or an addition of the geometric planewave phase factor.

Regenerative Wavelength Conversion of DPSK Signals Through FWM in an SOA

We experimentally investigate broadband regenerative capability of four-wave mixing (FWM) in a semiconductor optical amplifier (SOA) for nonreturn-to-zero differential phase-shift keying signals at 10 Gb/s. This scheme exploits the amplitude-limiting properties of the FWM process, when proper SOA gain saturation and α-factor depletion result in almost negligible additional phase noise for the converted signal after delay-interferometer demodulation. We report characterization in both the wavelength down- and up-conversion operations, demonstrating sound <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> -factor improvement (through a factor comprised between 1.4 and 2.4) over a conversion range of about 50 nm.

The Effect of Phase-Correlated Returns and Spatial Smoothing on the Accuracy of Radar Refractivity Retrievals

Abstract Radar refractivity retrievals have the potential to accurately capture near-surface humidity fields from the phase change of ground clutter returns. In practice, phase changes are very noisy and the required smoothing will diminish large radial phase change gradients, leading to severe underestimates of large refractivity changes (ΔN). To mitigate this, the mean refractivity change over the field (〈ΔN〉field) must be subtracted prior to smoothing. However, both observations and simulations indicate that highly correlated returns (e.g., when single targets straddle neighboring gates) result in underestimates of 〈ΔN〉field when pulse-pair processing is used. This may contribute to reported differences of up to 30 N units between surface observations and retrievals. This effect can be avoided if 〈ΔN〉field is estimated using a linear least squares fit to azimuthally averaged phase changes. Nevertheless, subsequent smoothing of the phase changes will still tend to diminish the all-important spatial perturbations in retrieved refractivity relative to 〈ΔN〉field; an iterative estimation approach may be required. The uncertainty in the target location within the range gate leads to additional phase noise proportional to ΔN, pulse length, and radar frequency. The use of short pulse lengths is recommended, not only to reduce this noise but to increase both the maximum detectable refractivity change and the number of suitable targets. Retrievals of refractivity fields must allow for large ΔN relative to an earlier reference field. This should be achievable for short pulses at S band, but phase noise due to target motion may prevent this at C band, while at X band even the retrieval of ΔN over shorter periods may at times be impossible.

Alleviation of additional phase noise in fiber optical parametric amplifier based signal regenerator

We theoretically and numerically explain the power saturation and the additional phase noise brought by the fiber optical parametric amplifier (FOPA). An equation to calculate an approximation to the saturated signal output power is presented. We also propose a scheme for alleviating the phase noise brought by the FOPA at the saturated state. In simulation, by controlling the decisive factor dispersion difference term Δk of the FOPA, amplitude-noise and additional phase noise reduction of quadrature phase shift keying (QPSK) based on the saturated FOPA is studied, which can provide promising performance to deal with PSK signals.

A new method to enhance frequency operation of CMOS ring oscillators

This article proposes a frequency-boosting method for CMOS ring oscillators. It consists of adding RC-based differentiators in delay cells to speed up their transient responses. Two novel delay cells for simple and differential versions are presented. On using MOS transistor components to implement the differentiators, the resulting increase of surface area is observed to be moderate, and this allows frequency tuning by voltage control, without inducing additional phase noise. The presented circuits are suitable for low-voltage operation. Simulation results on the proposed circuits have shown significant frequency enhancement with a competitive factor of merit.

Low-Power Divider Retiming in a 3–4 GHz Fractional-N PLL

The resynchronization of a frequency divider output is routinely used in the design of low-noise phase-locked loops (PLLs) in order to remove additional phase noise and avoid modulus-dependent nonlinearity. However, metastability issues cause PLLs to fail to lock or to degrade jitter at certain synthesized frequencies. This brief proposes a novel automatic retiming circuit, which mitigates metastability issues and avoids induced noise degradation, without adding a relevant increase in power consumption. A 3-4-GHz PLL implementing this technique has been fabricated in 65-nm CMOS technology. Measured root mean square jitter below 500 fsec over the whole tuning range and added current consumption of 51 μA from a voltage supply of 1.2 V prove the effectiveness of the proposed solution.