Laser Phase Noise Research Articles

Minimizing Measurement Error of Phase Noise of a Narrow-Band Laser Using a Fiber-Based Mach–Zehnder Interferometer with Polarization Maintenance

A device for measurements of phase noise with the use of the Mach–Zehnder interferometer is proposed, in which all fi ber components are made based on fiber with polarization state maintenance. This permits not using a basic radiation source in the device, and thereby reducing significantly the installation cost. Two interference signals from orthogonally polarized waves are formed in the device and are then divided by a polarizing demultiplexor that eliminates the effect of external noise on the measurement result. An algorithm for calculating phase noise is described and an estimate of the effect of temperature instability is presented. A comparison of the characteristics of phase noise between calculated and specified in modeling was performed in order to assess the operational capability of the installation and algorithm for signal processing.

Phase-noise model for actively linearized frequency-modulated continuous-wave ladar.

Understanding the effects of laser phase noise on frequency-modulated continuous-wave distance measurements is important in evaluating ranging accuracy. The standard white-frequency-noise assumption is commonly used to predict the ranging performance. However, other noise sources are typically present that can further degrade the heterodyne beat signal and make this assumption invalid. In addition, many ranging systems employ active sweep linearization techniques that can impact the phase noise. Here, we present a phase-noise model for assessing the accuracy of a phase-locked swept laser source.

Pseudo-Pilot Coding Based Phase Noise Estimation for Coherent Optical FBMC-OQAM Transmissions

We propose a cost-efficient scheme called pseudo-pilot coding based phase noise estimation (PC-PNE) to compensate laser phase noises for filter-bank multicarrier (FBMC) transmission systems. The performance of the proposed PC-PNE with rectangular quadratic-amplitude modulation (QAM) is evaluated and compared with the state-of-the-art modified blind phase search (M-BPS) approach via extensive Monte Carlo simulations. Under 200 kHz combined laser linewidth, 32 Gbaud 256-subcarriers FBMC optical transmission equipped with PC-PNE provides a comparable performance with the complicated M-BPS method for QPSK, 16QAM and 64QAM. Moreover, a significant reduction in computational complexity (up to 50 times) is obtained with PC-PNE in comparison with M-BPS method at the cost of 3.1% spectral efficiency loss.

Non-orthogonal basis expansion based laser phase noise suppression in CO-OFDM systems

A laser phase noise suppression approach, based on non-orthogonal basis expansion (NOBE), is proposed for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. In the NOBE approach, the time-varying laser phase noise is (sub-) optimally reconstructed using a bank of non-orthogonal expansion bases. Theoretical derivation of the non-orthogonal basis expansion matrices using the minimum mean-square error (MMSE) criteria is presented analytically. Compared with the conventional inverse discrete Fourier transform (IDFT)-based orthogonal basis expansion (OBE) method, the proposed NOBE approach, with the same expansion order L, offers higher accuracy in carrier phase estimation. Numerical analysis shows that the system’s tolerance to laser phase noise is significantly enhanced by the new method thanks to the lower modeling error. For example, the laser linewidth-symbol period product in an ∼ 100-Gbps 16QAM CO-OFDM system at an optical signal-to-noise-ratio (OSNR) of 22 dB achieves 3.87×10−2 with the NOBE (L=3), which is approximately twice that with the OBE. The impact of residual carrier frequency offset (CFO) on the NOBE is also semi-analytically investigated, which shows that the NOBE has robust performance for the residual CFO up to 2 MHz under a subcarrier spacing of 31.25 MHz. By taking advantage of the elaborately-designed comb-type pilot subcarriers pattern, the computational complexity of NOBE is also lower than that of the OBE. Since the NOBE with a sub-optimal basis expansion matrix does not require a priori knowledge of the product of laser linewidth and symbol period, it is well-suited for practical implementations.

Pull-in analysis of dither optical phase-lock loop

The pull-in behavior of dither optical phase-lock loop (OPLL) is analyzed, neglecting the shot noise and phase noise of the loop. Expressions are derived analytically for computing the pull-in voltage, pull-in limit and acquisition time for a second-order type-II dither OPLL that employs an active low pass loop filter. The influence of dither signal on the acquisition of the dither OPLL is studied in detail. It is found that dither signal allows pull-in from much larger frequency offset, decreases the acquisition time of the loop and also improves the acquisition characteristics of the OPLL in terms of the pull-in voltage. This paper also analyzes the effect of loop-delay on the pull-in behavior of the dither OPLL. The performance of the dither OPLL regarding the phase-error variance and noise bandwidth is investigated considering laser phase noise, photo-detector shot noise and dither noise. Analytical results are supported by simulations.

Influence on the Lifetime of 87Rb Bose–Einstein Condensation for Far-Detuning Single-Frequency Lasers with Different Phase Noises**Supported by the National Key Research and Development Program of China under Grant Nos 2016YFA0301600 and 2016YFA0301602, the National Natural Science Foundation of China under Grant Nos 11234008, 11474188 and 11704234, and the Fund for Shanxi ‘1331 Project’ Key Subjects Construction.

We study the influence of the phase noises of far detuning single frequency lasers on the lifetime of Bose–Einstein condensation (BEC) of 87Rb in an optical dipole trap. As a comparison, we shine a continuous-wave single-frequency Ti:sapphire laser, an external-cavity diode laser and a phase-locked diode laser on BEC. We measure the heating and lifetime of BEC in two different hyperfine states: and . Due to the narrow linewidth and small phase noise, the continuous-wave single-frequency Ti:sapphire laser has less influence on the lifetime of 87Rb BEC than the external-cavity diode laser. To reduce the phase noise of the external-cavity diode laser, we use an optical phase-locked loop for the external-cavity diode laser to be locked on a Ti:sapphire laser. The lifetime of BEC is increased when applying the phase-locked diode laser in contrast with the external-cavity diode laser.

Influence of Time Delay on Pull-in Behaviour of Dither Optical Phase-Lock Loop

ABSTRACTThis paper analyses the impact of loop propagation delay on the pull-in behaviour of dither optical phase-lock loop (OPLL), neglecting the shot noise and phase noise of the loop. Analytical expressions of pull-in voltage, pull-in range, and acquisition time are presented in terms of all the parameters affecting the loop acquisition. Also, the influence of dither signal on the pull-in performance of dither OPLL is studied in the presence of loop propagation delay. It is found that the time delay associated with the filtering process within the loop gives rise to degradation in acquisition capability. In addition, dither signal allows pull-in from much larger frequency offset, decreases the acquisition time of the loop, and improves the acquisition characteristics of dither OPLL in terms of the pull-in voltage in the presence of loop delay. The tracking performance of dither OPLL regarding phase-error variance is investigated considering laser phase noise, photo-detector shot noise, and loop propagation delay. Simulation results are given in support of the analytical results.

Terabit Faster-Than-Nyquist PDM 16-QAM WDM Transmission With a Net Spectral Efficiency of 7.96 b/s/Hz

In this paper, we experimentally demonstrate a 1.28 Tb/s faster-than-Nyquist (FTN) wavelength division multiplexing (WDM) system with polarization division multiplexed (PDM) 16-ary quadrature amplitude modulation (16-QAM) signal and coherent detection. Note that intersymbol interference (ISI) and intercarrier interference (ICI) are two major problems in FTN-WDM systems. In our experiment, we use a digital brick-wall filter at the transmitter to reduce the signal bandwidth and fit the FTN-WDM channel spacing. In doing so, the ICI can be mostly suppressed when aggregating the WDM channels. The aggressive filtering induced ISI is compensated based on duobinary signal processing at the receiver. Through numerical simulation, we evaluate the robustness of the receiver-side duobinary signal processing against bandwidth truncation ratio of the digital brick-wall filter, the ICI from neighboring channels, and laser phase noise. The FTN WDM transmission is based on five-channel 32 Gbaud PDM 16-QAM signal with 29 GHz channel spacing. The gross data capacity is 1.28 Tb/s (5 × 256 Gb/s). After 80 km standard single-mode fiber transmission, the bit-error rates of the five WDM channels are all below than 7% hard-decision forward error correction threshold of 4.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . The net bit rate is 1.15 Tb/s and the net optical spectral efficiency achieves a record of 7.96 b/s/Hz for PDM 16-QAM format. To our best knowledge, our work is the first report of Terabit FTN-WDM system with high-order modulation of PDM 16-QAM signal.

Carrier Frequency Offset Estimation for CO-OFDM: The Matched-Filter Approach

This paper proposes a novel carrier frequency offset (CFO) estimator for the coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems using the matched-filter (MF) concept. We consider an OFDM symbol with $N$ subcarriers so that the receiver takes $N$ time samples of the received noisy CO-OFDM signal. Our idea is to first append these $N$ received samples with $(L-1)N$ zeros at the end to get a sequence of $LN$ time samples. By taking the discrete Fourier transform of these $LN$ samples, we compute the spectrum of the CO-OFDM symbol at $LN$ discrete frequency points. We think of this spectrum as being made up of $L$ sets of $N$ points each, each set consisting of the frequency points $\lbrace \frac{2\pi }{LN}l, \frac{2\pi }{LN}l+\frac{2\pi }{N}, \ldots, \frac{2\pi }{LN}l+\frac{2\pi (N-1)}{N}\rbrace$ , for each value of $l$ , where $l=0,1,\ldots,L-1$ . Each set of $N$ points for one value of $l$ can be considered as the spectrum of the CO-OFDM symbol corresponding to one hypothesized value $\frac{2\pi }{LN}l$ of the CFO. The receiver can now obtain the maximum likelihood (ML) CFO estimate by determining the hypothesized value that best matches the spectrum of the CO-OFDM symbol received from the channel. In the case of data-aided (DA) ML estimation, we treat the OFDM symbol as a pilot symbol in which we know the data in all the subcarriers, and this pilot symbol is used as the reference signal for the MF. In the case of blind (BL) ML estimation, the data in all the subcarriers are unknown, and the receiver uses an OFDM symbol with no data modulation in all the subcarriers as the reference signal. After making the ML decision of the hypothesized value of the CFO, a fine search will be carried out to determine the actual value more accurately. It turns out only one step is necessary to locate the actual value of the CFO. The DA MF ML algorithm can achieve full-range (integral and fractional part) CFO estimation with high accuracy, while the BL MF ML algorithm has low computational complexity but focuses on the fractional CFO estimation only. We discuss the complexity and performance of this MF ML algorithm, and present simulation results to demonstrate the estimation error variance for 16-PSK/QAM modulations. The simulation results show that the estimation error variance of the DA MF ML algorithm can achieve the Cramer–Rao lower bound in the absence of the laser phase noise.

High-Power, Ultra-Low Noise Hybrid Lasers for Microwave Photonics and Optical Sensing

This paper describes the design, fabrication, and excellent performance achieved with prototype hybrid lasers incorporating a high performance gain chip coupled into a fiber external cavity including a novel fiber Bragg grating (FBG) reflector. Packaged ultra-low noise (ULN) hybrid lasers operating at 1550 nm and at 1319 nm with high output power, >100 mW, and extremely low relative intensity noise (RIN) are described. Devices provide extremely stable singlemode output with high side-mode suppression ratio (SMSR), typically above 70 dB, with worst case measured RIN at microwave frequencies (1–20 GHz) being below –165 dBc/Hz. Operation of these high power, low RIN devices within an analog optical link demonstrates a Spurious Free Dynamic Range as high as 114.6 dB.Hz 2/3. In addition to high power and very low RIN, the ULN hybrid lasers provide extremely small low frequency phase noise, with Lorentzian linewidths down to 15 Hz, enabling key Microwave Photonics and Optical Sensing applications. A comparison of the phase noise and Lorentzian linewidth of ULN lasers with different FBG designs / external cavity lengths is described, demonstrating the novel hybrid approach for achieving extremely low phase noise lasers.

Parallelized Kalman Filters for Mitigation of the Excess Phase Noise of Fast Tunable Lasers in Coherent Optical Communication Systems

Numerical and experimental investigations are carried out on the performance of parallelized Kalman filters applied for mitigation of the excess phase noise of fast tunable lasers. Based on the characterization of the phase noise of a sampled grating distributed Bragg reflector (SG-DBR) laser, the proposed carrier phase recovery (CPR) scheme using Kalman filters is introduced. By performing simulations of data transmission with various advanced modulation formats in the presence of the excess phase noise, the Kalman filter based CPR scheme shows its ability to overcome the excess phase noise and this method is suitable for parallel processing. Then the results are further demonstrated by 12.5 Gbaud QPSK and 16-QAM transmission experiments employing the SG-DBR laser. We find that the Kalman filters have better performance than the 2nd-order phase-locked loop in parallel systems due to a better phase noise tolerance. The bit error rate performance is also examined in the whole tuning range (∼30 nm) of the tunable laser, which further proves the feasibility of the proposed scheme.

Improving the phase response of an atom interferometer by means of temporal pulse shaping

We study theoretically and experimentally the influence of temporally shaping the light pulses in an atom interferometer, with a focus on the phase response of the interferometer. We show that smooth light pulse shapes allow rejecting high frequency phase fluctuations (above the Rabi frequency) and thus relax the requirements on the phase noise or frequency noise of the interrogation lasers driving the interferometer. The light pulse shape is also shown to modify the scale factor of the interferometer, which has to be taken into account in the evaluation of its accuracy budget. We discuss the trade-offs to operate when choosing a particular pulse shape, by taking into account phase noise rejection, velocity selectivity, and applicability to large momentum transfer atom interferometry.

Phase Noise Influence in a Dual-Frequency Laser Phase-Shift Range Finder

The influence of phase noise in a dual-frequency laser phase-shift range finder is theoretically and experimentally investigated. The proposed range finder is based on the use of a coherent dual-frequency laser and direct detection of the backscattered laser. The effects of laser phase noise and noise from an acousto-optic frequency shifter (AOFS) on the dual-frequency laser phase-shift range finder are analyzed. Expressions of the power spectral density and the phase noise of the dual-frequency laser beat note are deduced. In addition, we find that noise from the AOFS has a considerable impact on beat note noise conversion. The theoretical results can be used to estimate the influence of laser phase noise, noise induced by the AOFS and delay length in the dual-frequency laser range finder. An experiment involving the dual-frequency laser range finder is performed on outdoor targets at a distance of 200 m, and the phase jitter observed in the experiment is in good agreement with the model of beat note phase noise.

Modeling the adiabatic creation of ultracold polar 23Na40K molecules

In this work we model and realize stimulated Raman adiabatic passage (STIRAP) in the diatomic $\mathrm{^{23}Na^{40}K}$ molecule from weakly bound Feshbach molecules to the rovibronic ground state via the $\left|v_d=5,J=\Omega=1\right\rangle$ excited state in the $d^3\Pi$ electronic potential. We demonstrate how to set up a quantitative model for polar molecule production by taking into account the rich internal structure of the molecules and the coupling laser phase noise. We find excellent agreement between the model predictions and the experiment, demonstrating the applicability of the model in the search of an ideal STIRAP transfer path. In total we produce 5000 fermionic groundstate molecules. The typical phase-space density of the sample is 0.03 and induced dipole moments of up to 0.54 Debye could be observed.

Chromatic dispersion estimation based on heterodyne detection for coherent optical communication systems

We propose an accurate and nondata-aided chromatic dispersion (CD) estimation method involving the use of the cross-correlation function of two heterodyne detection signals for coherent optical communication systems. Simulations are implemented to verify the feasibility of the proposed method for 28-GBaud coherent systems with different modulation formats. The results show that the proposed method has high accuracy for measuring CD and has good robustness against laser phase noise, amplified spontaneous emission noise, and nonlinear impairments.

RF injection locked 18 GHz regeneratively mode-locked semiconductor laser.

In this manuscript, a semiconductor based fiber ring cavity mode-locked laser regeneratively driven at 18 GHz is presented. The optical spectrum of the laser is centered at 1578 nm. The laser is RF injection locked via an external source at 18 GHz. The phase noise of the mode-locked laser is measured and the integrated timing jitter was found to be 10.8 fs (from 100 Hz to 20 MHz) and 13.3 fs (from 100 Hz to Nyquist frequency). The integrated amplitude fluctuation (from 100 Hz to 20 MHz) was less than 0.02%. The laser phase and amplitude noise responses to various injected RF power levels were also investigated. The injection RF power has significant effect on the phase noise and the best jitter value is around 40 dB lower than the cavity regenerated RF power.

Minimization of the measurement error of narrow-band laser phase noise us-ing pm-fiber based mach–zehnder interferometer

Minimization of the measurement error of narrow-band laser phase noise us-ing pm-fiber based mach–zehnder interferometer

Laser Phase Noise Tolerance in Direct Detection Optical OFDM Transmission Using Laser Linewidth Emulator

Laser phase noise tolerance in direct detection optical orthogonal frequency division multiplexing (OFDM) transmission system is experimentally demonstrated using laser linewidth emulator. With this linewidth emulator, the linewidth of the laser can be broadened independently without inducing other laser's noise characteristics such as relative intensity noise and chirping. The results show the effect of phase-to-intensity noise conversion due to the laser's phase noise and chromatic dispersion. This induces noise pedestals not only onto the optical carrier, but also to each of the subcarriers, and thus produces intersubcarriers interference. Measurements show 6 dB Q-degradation is suffered by the system when 10 MHz linewidth is used as compared to using narrowest emulator linewidth of 256 kHz. Transmission with the linewidth emulator set to 20 MHz is also shown where it can still be tolerated by 400 km of fiber at the Q of 9.606 dB with respect to $1.6\,\times \,10^{{\rm - 3}}$ bit error rate. Simulation of 16 quadratic-amplitude modulation (QAM) (∼128 Gb/s) and 4 QAM (∼100 Gb/s) using VPItransmissionMaker are also presented to demonstrate the effect of carrier's phase-to-intensity noise conversion when a high data rate and wide OFDM signal bandwidth are used with the linewidth emulator as the system's laser source. The results show that a phase rotation term is insignificant for lower M -size QAM with fiber length less than 500 km. This presents the high effectiveness and reliability of the laser linewidth emulator to discretely determine an independent phase noise tolerance from the other laser's noise characteristics in the optical OFDM transmission system.

Blind modulation format identification using nonlinear power transformation.

This paper proposes and experimentally demonstrates a blind modulation format identification (MFI) method delivering high accuracy (> 99%) even in a low OSNR regime (< 10 dB). By using nonlinear power transformation and peak detection, the proposed MFI can recognize whether the signal modulation format is BPSK, QPSK, 8-PSK or 16-QAM. Experimental results demonstrate that the proposed MFI can achieve a successful identification rate as high as 99% when the incoming signal OSNR is 7 dB. Key parameters, such as FFT length and laser phase noise tolerance of the proposed method, have been characterized.

Pilot-Based Phase Noise, IQ Mismatch, and Channel Distortion Estimation for PDM CO-OFDM System

In this letter, a pilot-based method is proposed to suppress three non-ideal factors, including channel distortion, transmitter in-phase and quadrature (IQ) mismatch, and laser phase noise for polarization division multiplexed coherent optical orthogonal frequency division multiplexing systems. Compared with the conventional phase noise and IQ mismatch estimation methods which only consider one of the two non-ideal factors, we deduce a novel mathematical model considering both and compensate them with special designed pilots: the channel distortion and IQ mismatch are compensate by the block-type pilot while the comb-type pilot is used to estimate phase noise. The simulation results proved that our method can not only better compensate the non-idealities factors, but also can provide high speed transmission with 120 Gb/s over 400-km transmission compared with the conventional methods.