Laser Phase Noise Research Articles

Phase Noise Effects on Phase-Modulated Coherent Optical OFDM

One of the primary drawbacks of orthogonal frequency-division multiplexing (OFDM) is the large peak-to-average ratio (PAPR). It continues to contribute nonlinear degradations after it was introduced into optical fiber transmissions. However, phase-modulated OFDM can reduce the PAPR to the minimum, since its amplitude can be constant. In this paper, we conduct the theoretical and experimental study on the laser phase noise effect in phase-modulated coherent optical OFDM systems. Due to the laser phase noise, the phase transformation at the receiver is prone to errors due to phase wrapping. Consequently, we propose a mean-phase-compensation (MPC) method, which compensate for the mean phase offset for each OFDM symbol that has a Gaussian-distributed histogram. This method can avoid the problematic unwrapping function in phase transformation. We derive the closed-form expressions for the phase noise spreading and the corresponding signal-to-noise ratios (SNRs) based on the Wiener phase noise model. Unlike conventional coherent optical OFDM, the phase noise spreading to each OFDM subcarrier is decided by the reciprocal of the square of the subcarrier frequency, and the SNR can be improved by using a stronger PM modulation. We also discuss the SNR improvement by discarding a few affected subcarriers closing to dc. In a simulation, we demonstrate that our closed-form expressions are accurate. Finally, we experimentally verify our MPC method and our analysis.

A broadband passive cavity for analyzing and filtering the noise of a femtosecond laser

In this paper, the noise filtering effect on a femtosecond laser source via a broadband passive cavity is analyzed in detail. The results show that a passive optical cavity not only can be used as a low-pass noise filter, but also can inter-convert the phase and amplitude fluctuations of a light beam after transmission or reflection. Therefore, by measuring the intensity noise of the light field under test after transmission and reflection from a passive cavity, its phase noise properties can be explored. Based on this theoretical model, an eight-mirror ring passive cavity with a finesse of 1500 and a free spectral range of 75 MHz is designed and built. With a commercial Ti:sapphire femtosecond laser as a source, its intensity noises after transmission and reflection from the above cavity are measured with home-made self-homodyne detection setup. Furthermore, with the help of the noise conversion model of the passive cavity, the phase noise of the femtosecond laser as well as its evolution through the cavity transmission and reflection is indirectly derived. The result shows that after transmission through the passive cavity, both the amplitude and phase noise of the femtosecond laser source are evidently suppressed and reach the shot noise limit at the analyzing frequency of 2 MHz.

激光强度起伏及相位噪声对光学双频探测的影响

激光强度起伏及相位噪声对光学双频探测的影响

基于3×3 耦合器的窄线宽单频激光器噪声测量技术

A new delayed self-heterodyne technique using an unbalanced Michelson interferometer (MI) composed of a 3*3 optical fiber coupler is proposed. The principle of the technique to measure the laser phase and frequency noise are analyzed theoretically. The experimental setup is introduced. Also, the technique is used to characterize the phase noise power spectral density (PSD), frequency noise PSD and linewidth of two typical kinds of lasers, distributed feedback (DFB) semiconductor laser (Emcore) and super-narrow linewidth DFB fiber laser (NKT). The results show that the technique can measure the noise characters of different kinds of lasers and it confirms the correction and robustness of the proposed technique.

High order modulation format identification based on compressed sensing in optical fiber communication system

We propose a method of modulation format identification based on compressed sensing using a high-order cyclic cumulant combined with a binary tree classifier. Through computing the fourth-order cyclic cumulant of the pretreated band signal, which is obtained by compressed sensing with the sampling rate much less than the Nyquist sampling value, the feature vector for classification is extracted. Simulations are carried out in the optical coherent fiber communication system with different modulation formats of multiple phase-shift keying and multiple quadrature amplitude modulation. The results indicate that this method can identify these modulation formats correctly and efficiently. Meanwhile, the proposed method is insensitive to laser phase noise and signal noise.

Analysis of SNR penalty in Brillouin optical time-domain analysis sensors induced by laser source phase noise

In this paper, we analyze numerically the effect of phase noise from the laser in Brillouin optical time-domain analysis (BOTDA) sensors. Due to laser phase noise, the phase shift between pump and probe beams is a stochastic variable with zero mean and variance changing with the position along the fiber. The numerical results, carried out for various fiber lengths and pump pulse durations, show that laser phase noise induces a reduction of the average Brillouin gain, as well as an increase of the overall system noise. Preliminary experimental results, carried out by use of a conventional BOTDA system and two DFB diode lasers having different linewidth (63 and 900 kHz), support the numerical analysis.

Laser phase noise compensation in long-range OFDR by using an optical fiber delay loop

We propose and experimentally demonstrate a novel technique to compensate the laser phase noise in long-range OFDR by using an optical fiber delay loop, which mainly consists of a delay fiber and a frequency shifter. The delay fiber is used to shorten the optical path difference between two arms of the interferometer, and the frequency shifter works as a counter for taking the number of lightwave circulated in the loop. The preliminary experiment shows a successful compensation effect, and a 10cm spatial resolution over 30km measurement range is realized by using this method.

Machine Learning Techniques in Optical Communication

Machine learning techniques relevant for nonlinearity mitigation, carrier recovery, and nanoscale device characterization are reviewed and employed. Markov Chain Monte Carlo in combination with Bayesian filtering is employed within the nonlinear state-space framework and demonstrated for parameter estimation. It is shown that the time-varying effects of cross-phase modulation (XPM) induced polarization scattering and phase noise can be formulated within the nonlinear state-space model (SSM). This allows for tracking and compensation of the XPM induced impairments by employing approximate stochastic filtering methods such as extended Kalman or particle filtering. The achievable gains are dependent on the autocorrelation (AC) function properties of the impairments under consideration which is strongly dependent on the transmissions scenario. The gain of the compensation method are therefore investigated by varying the parameters of the AC function describing XPM-induced polarization scattering and phase noise. It is shown that an increase in the nonlinear tolerance of more than 2 dB is achievable for 32 Gbaud QPSK and 16-quadratic-amplitude modulation (QAM). It is also reviewed how laser rate equations can be formulated within the nonlinear state-space framework which allows for tracking of nonLorentzian laser phase noise lineshapes. It is experimentally demonstrated for 28 Gbaud 16-QAM signals that if the laser phase noise shape strongly deviates from the Lorentzian, phase noise tracking algorithms employing rate equation-based SSM result in a significant performance improvement ( $>$ 8 dB) compared to traditional approaches using digital phase-locked loop. Finally, Gaussian mixture model is reviewed and employed for nonlinear phase noise compensation and characterization of nanoscale devices structure variations.

Novel MDM-PON scheme utilizing self-homodyne detection for high-speed/capacity access networks.

In this paper, we propose a cost-effective, energy-saving mode-division-multiplexing passive optical network (MDM-PON) scheme utilizing self-homodyne detection for high-speed/capacity access network based on low modal-crosstalk few-mode fiber (FMF) and all-fiber mode multiplexer/demultiplexer (MUX/DEMUX). In the proposed scheme, one of the spatial modes is used to transmit a portion of signal carrier (namely pilot-tone) as the local oscillator (LO), while the others are used for signal-bearing channels. At the receiver, the pilot-tone and the signal can be separated without strong crosstalk and sent to the receiver for coherent detection. The spectral efficiency (SE) is significantly enhanced when multiple spatial channels are used. Meanwhile, the self-homodyne detection scheme can effectively suppress laser phase noise, which relaxes the requirement for the lasers line-width at the optical line terminal or optical network units (OLT/ONUs). The digital signal processing (DSP) at the receiver is also simplified since it removes the need for frequency offset compensation and complex phase correction, which reduces the computational complexity and energy consumption. Polarization division multiplexing (PDM) that offers doubled SE is also supported by the scheme. The proposed scheme is scalable to multi-wavelength application when wavelength MUX/DEMUX is utilized. Utilizing the proposed scheme, we demonstrate a proof of concept 4 × 40-Gb/s orthogonal frequency division multiplexing (OFDM) transmission over 55-km FMF using low modal-crosstalk two-mode FMF and MUX/DEMUX with error free operation. Compared with back to back case, less than 1-dB Q-factor penalty is observed after 55-km FMF of the four channels. Signal power and pilot-tone power are also optimized to achieve the optimal transmission performance.

Performance improvement of RoF transmission link by using 120° hybrid coupler in OSSB generation

This paper presents an analysis, simulation and comparison of the performance of Optical single sideband radio over fiber system based on a dual drive Mach Zehender modulator using 90° and 120° hybrid coupler including the effects of phase noise from RF signal oscillator and laser source, fiber dispersion. Signal to noise ratio (SNR) is significantly influenced by phase noise from RF signal oscillator. On comparison with conventional 90° hybrid coupler system, the performance of the considered system improves by 0.78 dB in terms of SNR, when RF and laser phase noises are increased.

Numerical Analysis of Phase Noise Characteristics of SGDBR Lasers

Detailed analyses of the phase noise characteristics of tunable sampled grating distributed Bragg reflector (SGDBR) lasers are presented in this paper. Based on the transmission line laser model, we derive the Langevin rate equations for the photon number and the electric-field phase in the cavity of SGDBR lasers. This model includes the spontaneous emission white noise in active section and the carrier shot noise in passive tuning sections, both of which contribute to the enhancement of the laser phase noise. Based on this model, the frequency modulation (FM) noise spectrum is calculated from the instantaneous laser phase fluctuation. The white noise linewidth and carrier shot noise linewidth are then calculated according to the FM noise spectrum. The linewidth tuning curves as a function of the currents in passive sections are simulated and the laser linewidth is strongly dependent on the tuning currents. Lower white noise linewidth is obtained when the longitudinal mode is located on the longer wavelength side of the total reflection-peak wavelength of the front and back gratings. However, the carrier shot noise linewidth increases with the increase of the injected current within each longitudinal mode. Finally, the impact of structural parameters on the linewidth is discussed.

Low-Complexity Tracking of Laser and Nonlinear Phase Noise in WDM Optical Fiber Systems

In this paper, the wavelength division multiplexed (WDM) fiber optic channel is considered. It is shown that for ideal distributed Raman amplification (IDRA), the Wiener process model is suitable for the non-linear phase noise due to cross phase modulation from neighboring channels. Based on this model, a phase noise tracking algorithm is presented. We approximate the distribution of the phase noise at each time instant by a mixture of Tikhonov distributions, and derive a closed form expression for the posterior probabilities of the input symbols. This reduces the complexity dramatically compared to previous trellis-based approaches, which require numerical integration. Further, the proposed method performs very well in low-to-moderate signal-to-noise ratio (SNR), where standard decision directed (DD) methods, especially for high-order modulation, fail. The proposed algorithm does not rely on averaging, and therefore does not experience high error floors at high SNR in severe phase noise scenarios. The laser linewidth (LLW) tolerance is thereby increased for the entire SNR region compared to previous DD methods. In IDRA WDM links, the algorithm is shown to effectively combat the combined effect of both laser phase noise and non-linear phase noise, which cannot be neglected in such scenarios. In a more practical lumped amplification scheme, we show near-optimal performance for 16 QAM, 64 QAM, and 256 QAM with LLW up to 100 kHz, and reasonable performance for LLW of 1 MHz for 16 QAM and 64 QAM, at the moderate received SNR region. The performance in these cases is close to the information rate achieved by the above mentioned trellis processing.

An effective scheme of optical pilot aided carrier phase estimation for a time packing Nyquist optical communication system

An optical domain pilot aided carrier phase estimation (PA-CPE) scheme in a double-carrier time packing Nyquist system is proposed, in which the middle pilot can be used for carrier phase estimation in both side time packing signal channels. The proposed PA-CPE method can effectively overcome the scale of the inter-symbol interference (ISI) introduced by time packing, with the good characteristics of high phase noise tolerance and simple hardware complexity. The comprehensive mathematical descriptions of laser phase noise model and PA-CPE scheme are provided. The analyses show that the proposed PA-CPE can estimate the phase noise successfully despite ISI caused by time packing. In the double-carrier time packing Nyquist system mentioned above, using the proposed PA-CPE algorithm, the linewidth tolerance value of 6×10−5 can be reached with 1dB OSNR penalty at the bit error rate (BER) of 1×10−3 even though the compression factor α is as small as 0.625.

Subpicotesla Diamond Magnetometry

Diamond defect centers are promising solid state magnetometers. Single centers allow for high spatial resolution field imaging but are limited in their magnetic field sensitivity to around 10 nT/Hz^(1/2) at room-temperature. Using defect center ensembles sensitivity can be scaled as N^(1/2) when N is the number of defects. In the present work we use an ensemble of 1e11 defect centers for sensing. By carefully eliminating all noise sources like laser intensity fluctuations, microwave amplitude and phase noise we achieve a photon shot noise limited field sensitivity of 0.9 pT/Hz^(1/2) at room-temperature with an effective sensor volume of 8.5e-4 mm^3. The smallest field we measured with our device is 100 fT. While this denotes the best diamond magnetometer sensitivity so far, further improvements using decoupling sequences and material optimization could lead to fT/Hz^(1/2) sensitivity.

Virtual Carrier-Assisted Direct-Detection MB-OFDM Next-Generation Ultra-Dense Metro Networks Limited by Laser Phase Noise

The impact of the phase-to-intensity conversion of the laser phase noise due to the optical band selector (BS) used for band extraction on the performance of direct-detection (DD) optical multiband orthogonal frequency-division multiplexing (MB-OFDM) networks employing single-sideband (SSB) modulation is assessed. Compared to conventional double-sideband DD systems, in which the amplitude shape of the optical filter is quasi-symmetric relative to the centre of the signal spectrum, ultra-dense optical SSB-MB-OFDM networks employing virtual carrier-assisted DD are differently affected by the phase-to-intensity conversion. This is due to the detuned BS required by these networks, which modify the converted phase noise (CPN) features. A reduction of the power spectral density of the CPN achieving 30 dB can occur along the frequency range in which the BS bandwidth and detuning lead to a filtering attenuation that is similar in both sides of the virtual carrier. For single band, when the ratio between the BS detuning and bandwidth increases from 0% to 28%, an error vector magnitude improvement of 7 dB due to the CPN reduction is observed. The optical signal-to-noise ratio (OSNR) penalty due to the laser phase noise in 112-Gb/s SSB-MB-OFDM networks comprising 12 OFDM bands and employing an ultra-dense band spacing of 3.125 GHz is lower than 1 dB for external cavity lasers and is 1.6 dB for distributed feedback lasers. These OSNR penalties are obtained for an optimized ratio between the BS detuning and bandwidth of 14%.

Performance analysis of an OSSB RoF link using 90o & 120o Hybrid coupler

This paper presents an analysis, simulation and comparison of the performance of Optical single sideband (OSSB) radio over fiber (RoF) system based on a dual drive Mach Zehender modulator (DD-MZM) using 90o and 120o hybrid coupler including the effects of phase noise from RF signal oscillator and laser source, input RF signal power and fiber dispersion. Signal to Noise ratio (SNR) is significantly influenced by phase noise from RF signal oscillator and input RF signal power. On comparison with conventional 90o hybrid coupler system, the performance of the considered system improves by 5.64 and 0.67dB in terms of SNR, when RF and laser phase noises are increased.

Designing coherent optical wireless systems for high speed indoor telecom applications

This paper focuses on several design issues of coherent optical wireless systems as a means of providing high data rate optical links in indoor environments enabling the realization of ultra-broadband wireless local area networks. We show how the performance specifications can be translated into signal-to-noise ratio requirements inside the coverage area, taking into account the laser phase noise mitigation scheme. We then discuss the power budget details using Gaussian beam optics incorporating the transceiver positioning and the optical systems used at the transmitter and receiver side. We also treat the influence of ambient light noise. We show that coherent optical wireless systems are characterized by excellent signal-to-noise performance enabling networking at very high data rates. Our results indicate that 2Gb/s and 10Gb/s data rates can be easily sustained at 3m distances over a circular coverage area of 1m radius using Class-1 lasers for the transmitter and the local oscillator. We also discuss the power gain compared to intensity modulated/direct detection optical wireless and show that it can be as high as 20dB, especially near the edge of the coverage area.

Chromatic dispersion measurement with double sideband phase noise canceled OFDR

OTDR is the realistic method for measuring chromatic dispersion of already deployed fibers because it is one end measurement technique. Furthermore, it can measure chromatic dispersion of each fiber segment connected together in the fiber link. On the other hand, though OFDR has better spatial resolution and sensitivity than OTDR, its measurable distance is limited by laser phase noise. We have proposed Double Sideband Phase Noise Canceled OFDR (DB-PNC-OFDR), which enables the long distance measurement. In this paper, we have used our proposed DB-PNC-OFDR to measure chromatic dispersion in a 50km long fiber link made up of three fiber segments. Also chromatic dispersion of each fiber segment in the fiber link have been measured. Moreover, the chromatic dispersion of a standard single-mode fiber was measured. To confirm the accuracy of the proposed method, the measured chromatic dispersion was compared with a widely used phase shift method.

Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multi-channel digital back-propagation

Superchannel transmission spaced at the symbol rate, known as Nyquist spacing, has been demonstrated for effectively maximizing the optical communication channel capacity and spectral efficiency. However, the achievable capacity and reach of transmission systems using advanced modulation formats are affected by fibre nonlinearities and equalization enhanced phase noise (EEPN). Fibre nonlinearities can be effectively compensated using digital back-propagation (DBP). However EEPN which arises from the interaction between laser phase noise and dispersion cannot be efficiently mitigated, and can significantly degrade the performance of transmission systems. Here we report the first investigation of the origin and the impact of EEPN in Nyquist-spaced superchannel system, employing electronic dispersion compensation (EDC) and multi-channel DBP (MC-DBP). Analysis was carried out in a Nyquist-spaced 9-channel 32-Gbaud DP-64QAM transmission system. Results confirm that EEPN significantly degrades the performance of all sub-channels of the superchannel system and that the distortions are more severe for the outer sub-channels, both using EDC and MC-DBP. It is also found that the origin of EEPN depends on the relative position between the carrier phase recovery module and the EDC (or MC-DBP) module. Considering EEPN, diverse coding techniques and modulation formats have to be applied for optimizing different sub-channels in superchannel systems.

Impact of laser phase and amplitude noises on streak camera temporal resolution.

Streak cameras are now reaching sub-picosecond temporal resolution. In cumulative acquisition mode, this resolution does not entirely rely on the electronic or the vacuum tube performances but also on the light source characteristics. The light source, usually an actively mode-locked laser, is affected by phase and amplitude noises. In this paper, the theoretical effects of such noises on the synchronization of the streak system are studied in synchroscan and triggered modes. More precisely, the contribution of band-pass filters, delays, and time walk is ascertained. Methods to compute the resulting synchronization jitter are depicted. The results are verified by measurement with a streak camera combined with a Ti:Al2O3 solid state laser oscillator and also a fiber oscillator.