Presence Of Laser Phase Noise Research Articles

Effect of laser phase noise on the steady-state field-mirror entanglement and ground-state cooling in a Laguerre-Gaussian optorotational system

Cavity optomechanical systems are considered as one of the best platforms for studying macroscopic quantum phenomena. In this paper, we studied the effect of laser phase noise on the steady-state entanglement between a cavity mode and a rotating mirror in a Laguerre-Gaussian (L-G) optorotational system. We found that the effect of laser phase noise was non-negligible on the field-mirror entanglement especially at a larger input power and a larger angular momentum. We also investigated the influence of laser phase noise on the ground-state cooling of the rotating mirror. In the presence of laser phase noise, the ground-state cooling of the rotating mirror can still be realized within a range of input powers.

Optimum Constellation Size for Probabilistically Shaped Signals in the Presence of Laser Phase Noise

Higher cardinality modulation formats are generally adopted for probabilistically shaped (PS) signals to achieve the same entropy as uniformly shaped (US) signals. As a result, despite the shaping gain, PS signals are more sensitive to the laser phase noise since the phase margin is smaller than that of US signals. In this work, we investigate the optimum constellation size for PS signals by considering the effects from both shaping gain and laser phase noise. The constellation size we consider is not restricted to values given by 2^k, where k is an integer. Here, we compare the performances of US-64 QAM, PS-100 QAM, PS-144 QAM, PS-196 QAM and PS-256 QAM with the same information rate under the circumstance of different laser linewidths. The carrier phase recovery (CPR) is conducted by applying a modified two-stage pilot-symbols-aided carrier phase estimator. Consequently, we also study the CPR performance of the five modulation formats with different combinations of the block size in the first stage and the window size in the second stage. In our experimental demonstration, a coherent detection based optical back-to-back system is built with 100-kHz linewidth transmitter laser and local oscillator. For homodyne detection, PS-256 QAM performs best owing to the largest shaping gain. However, PS-144 QAM becomes the optimal choice for 200-kHz sum linewidth heterodyne detection benefiting from both the shaping gain and relatively large phase margin.

Geometric Shaping of 2-D Constellations in the Presence of Laser Phase Noise

In this article, we propose a geometric shaping (GS) strategy to design 8, 16, 32, and 64-ary modulation formats for the optical fibre channel impaired by both additive white Gaussian (AWGN) and phase noise. The constellations were optimised to maximise generalised mutual information (GMI) using a mismatched channel model. The presented formats demonstrate an enhanced signal-to-noise ratio (SNR) tolerance in high phase noise regimes when compared with their quadrature amplitude modulation (QAM) or AWGN-optimised counterparts. By putting the optimisation results in the context of the 400ZR implementation agreement, we show that GS alone can either relax the laser linewidth (LW) or carrier phase estimation (CPE) requirements of 400 Gbit/s transmission links and beyond. Following the GMI validation, the performance of the presented formats was examined in terms of post forward error correction (FEC) bit-error-rate (BER) for a soft decision (SD) extended Hamming code (128, 120), implemented as per the 400ZR implementation agreement. We demonstrate gains of up to 1.2 dB when compared to the 64-ary AWGN shaped formats.

Force measurement in squeezed dissipative optomechanics in the presence of laser phase noise.

We investigate the force measurement sensitivity in a squeezed dissipative optomechanics within the free-mass regime under the influence of shot noise (SN) from the photon number fluctuations, laser phase noise from the pump laser, thermal noise from the environment, and optical losses from outcoupling and detection inefficiencies. Generally, squeezed light could generate a reduced SN on the squeezed quadrature and an enlarged quantum backaction noise (QBA) due to the antisqueezed conjugate quadrature. With an appropriate choice of phase angle in homodyne detection, QBA is cancellable, leading to an exponentially improved measurement sensitivity for the SN-dominated regime. By now, the effects of laser phase noise that is proportional to laser power emerge. The balance between squeezed SN and phase noise can lead to an sub-SQL sensitivity at an exponentially lower input power. However, the improvement by squeezing is limited by optical losses because high sensitivity is delicate and easily destroyed by optical losses.

Optimization of Transmitter-Side Signal Rotations in the Presence of Laser Phase Noise

The effects of transmitter-side multidimensional signal rotations on the performance of multichannel optical transmission are studied in the presence of laser phase noise. In particular, the laser phase noise is assumed to be uncorrelated between channels. To carry out this study, a simple multichannel laser-phase-noise model that has been experimentally validated for weakly-coupled multicore-fiber transmission is considered. As the considered rotation scheme is intended to work in conjunction with receiver-side carrier phase estimation (CPE), the model is modified to further assume that imperfect CPE has taken place, leaving residual phase noise in the processed signal. Based on this model, two receiver structures are derived and used to numerically optimize transmitter-side signal rotations through Monte Carlo simulations. For reasonable amounts of residual phase noise, rotations based on Hadamard matrices are found to be near-optimal for transmission of 4-D signals. Furthermore, Hadamard rotations can be performed for any dimension that is a power of two. By exploiting this property, an increase of up to 0.25 bit per complex symbol in an achievable information rate is observed for transmission of higher-order constellations.

Resolved-Sideband Cooling of a Levitated Nanoparticle in the Presence of Laser Phase Noise.

We investigate the influence of laser phase noise heating on resolved sideband cooling in the context of cooling the center-of-mass motion of a levitated nanoparticle in a high-finesse cavity. Although phase noise heating is not a fundamental physical constraint, the regime where it becomes the main limitation in Levitodynamics has so far been unexplored and hence embodies from this point forward the main obstacle in reaching the motional ground state of levitated mesoscopic objects with resolved sideband cooling. We reach minimal center-of-mass temperatures comparable to T_{min}=10 mK at a pressure of p=3×10^{-7} mbar, solely limited by phase noise. Finally we present possible strategies towards motional ground state cooling in the presence of phase noise.

Effects of laser phase fluctuation on force sensing for a free particle in a dissipative optomechanical system

In this paper, we study the effects of laser phase noise on the detection of a weak classical mechanical force on a free particle based upon dissipative optomechanical coupling. We show that for an optimum choice of various parameters, one can realize force sensing below the standard quantum limit even in the presence of laser phase noise. Moreover, we also investigate the effect of mechanical damping and thermal noise on force measurement in the presence of laser phase fluctuations. We show that force sensing strongly depends upon the phase fluctuations associated with the driving laser.

Dispersive interaction of a Bose-Einstein condensate with a movable mirror of an optomechanical cavity in the presence of laser phase noise

We theoretically investigate the dispersive interaction of a Bose-Einstein condensate (BEC) trapped inside an optomechanical cavity with a moving end mirror in the presence of the laser phase noise (LPN) as well as the atomic collisions. We assume that the effective frequency of the optical mode is much greater than those of the mechanical and the Bogoliubov modes of the movable mirror and the BEC . In the adiabatic approximation where the damping rate of the cavity is faster than those of the other modes, the system behaves as an effective two-mode model in which the atomic and mechanical modes are coupled to each other through the mediation of the optical field by an effective coupling parameter. We show that in the effective two-mode model, the LPN appears as a classical stochastic pump term which drives the amplitude quadratures of the mechanical and the Bogoliubov modes. It is also shown that a strong stationary mirror-atom entanglement can be established just in the dispersive and Doppler regimes where the two modes come into resonance with each other and the effect of the LPN gets very low.

Joint-Polarization Phase-Noise Estimation and Symbol Detection for Optical Coherent Receivers

The problem of optimal symbol detection in the presence of laser phase noise is studied, for uncoded polarization-multiplexed fiber-optic transmission. To this end, the maximum a posteriori (MAP) symbol detector is presented. Specifically, it is emphasized that obtaining phase-noise point estimates, and treating them as the true values of the phase noise, is in general suboptimal. Furthermore, a pilot-based algorithm that approximates the MAP symbol detector is developed, using approaches adopted from the wireless literature. The algorithm performs joint-polarization phase-noise estimation and symbol detection, for arbitrary modulation formats. Through Monte Carlo simulations, the algorithm is compared to existing solutions from the optical communications literature. It is demonstrated that joint-polarization processing can significantly improve upon the single-polarization case, with respect to linewidth tolerance. Finally, it is shown that with less than 3% pilot overhead the algorithm can be used with lasers having up to 6 times larger linewidths than the most well-performing blind algorithms can tolerate.

Novel Rx IQ mismatch compensation considering laser phase noise for CO-OFDM system

In this paper, a novel compensation scheme for receiver (Rx) in-phase/quadrature (IQ) mismatch is proposed in coherent optical orthogonal frequency division multiplexing (CO-OFDM) system in the presence of laser phase noise. In this scheme, laser phase noise and channel distortion were combined as a new channel transfer factor, the IQ mismatch factor and initial channel transfer factor can be estimated independently based on the relationship of IQ mismatch factors. And the channel transfer factor can be updated on a symbol-by-symbol basis which retrieves an estimation of the phase noise value by extracting and averaging the phase drift of all OFDM sub-channels. Numerical results indicate that when the phase and amplitude mismatch are 10° and 2dB respectively, a 1.6dB optical signal-to noise ratio is improved at laser linewidth of 60kHz. Furthermore, the complexity of the proposed method is analyzed in terms of the number of required complex multiplications per bit.

An efficient combining technique to analyze the performance of non-ideal ASK optical systems

In this paper, we propose a new method to detect binary optical homodyne and heterodyne amplitude shift keying (ASK) signals in the presence of laser phase noise and receiver shot noise. This method relies on an efficient least square (LS) algorithm to mitigate the negative effects of phase noise error. The error rate performance of non-ideal ASK systems is investigated under LS detection and the signal-to-noise ratio (SNR) gain penalty of heterodyne system over homodyne system is observed. For design purposes, we also provide tabulated results for the number of required photoelectrons to achieve a certain error rate level for the system under investigation. To show the effectiveness of the proposed LS combining technique we compare our results for non-ideal systems with some previous results in the literature. The numerical results obtained through this work show that LS technique has the ability to reduce the SNR gain penalty caused by the lasers phase error, and hence, can be used in any wire-line or wireless coherent systems that suffer from imperfect (non-ideal) phase recovery. • Propose a new method to detect optical signals in the presence of laser phase noise. • This technique has the ability to reduce the SNR gain penalty. • The new method is superior to the envelope detection method by at least 1 dB. • Glass pore contact angle varies with liquid surface tension and chemical structure. • The number of photoelectrons required in ideal systems to obtain a certain BER can be maintained.

Theoretical calculation on ICI reduction using digital coherent superposition of optical OFDM subcarrier pairs in the presence of laser phase noise.

Digital coherent superposition (DCS) of optical OFDM subcarrier pairs with Hermitian symmetry can reduce the inter-carrier-interference (ICI) noise resulted from phase noise. In this paper, we show two different implementations of DCS-OFDM that have the same performance in the presence of laser phase noise. We complete the theoretical calculation on ICI reduction by using the model of pure Wiener phase noise. By Taylor expansion of the ICI, we show that the ICI power is cancelled to the second order by DCS. The fourth order term is further derived out and only decided by the ratio of laser linewidth to OFDM subcarrier symbol rate, which can greatly simplify the system design. Finally, we verify our theoretical calculations in simulations and use the analytical results to predict the system performance. DCS-OFDM is expected to be beneficial to certain optical fiber transmissions.

Architecture of a Single-Chip 50 Gb/s DP-QPSK/BPSK Transceiver With Electronic Dispersion Compensation for Coherent Optical Channels

The architecture of a single-chip dual-polarization QPSK/BPSK 50 Gigabits per second (Gb/s) DSP-based transceiver for coherent optical communications is presented. The receiver compensates the chromatic dispersion (CD) of more than 3,500 km of standard single-mode fiber using a frequency-domain equalizer. A time-domain four-dimensional MIMO transversal equalizer compensates up to 200 ps of differential group delay (DGD) and 8000 ps <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of second-order polarization-mode dispersion (SOPMD). Other key DSP functions of the receiver include carrier and timing recovery, automatic gain control, channel diagnostics, etc. A novel low-latency parallel-processing carrier recovery implementation which is robust in the presence of laser phase noise and frequency jitter is proposed. The chip integrates the transmitter, receiver, framer and host interface functions and features a 4-channel 25 Gs/s 6-bit ADC with a figure of merit (FOM) of 0.4 pJ/conversion. Each ADC channel is based on an 8-way interleaved flash architecture. The DSP uses a 16-way parallel processing architecture. Extensive measurement results are presented which confirm the design targets. Measured optical signal-to-noise ratio (OSNR) penalty when compensating 200 ps DGD and 8000 ps <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is 0.1 dB, while OSNR penalty when compensating 55 ns/nm CD (corresponding to 3,500 km of standard single-mode fiber) is 0.5 dB.

Pilot-Aided Channel Equalization in RGI-PDM-CO-OFDM Systems

A pilot-aided channel equalizer (PACE) is proposed to mitigate the impairments caused by the polarization mode dispersion and laser phase noise simultaneously in reduced-guard-interval polarization-division-multiplexing coherent-optical orthogonal-frequency-division-multiplexing (RGI-PDM-CO-OFDM) transmission systems. Since PACE updates the channel state information symbol-by-symbol, it enables us to track the drifts in the optical channel. Adaptive PACE (APACE) and boosted PACE (BPACE) are then proposed to further improve the performance of PACE. Numerical simulations are carried out to compare the performance of APACE and BPACE with a conventional training symbols aided channel equalizer (TSACE) and adaptive decision-direct channel equalizer for a 108-Gb/s (56-GS/s) RGI-PDM-CO-OFDM system. It is revealed that both APACE and BPACE offer superior performances over the other two equalizers in the presence of laser phase noise, and they can tolerate lasers with a line width around <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\beta=2000~{\rm k}$</tex></formula> ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$2\pi\beta T_{s}=2.24\times 10$</tex></formula> when it is normalized to the symbol rate <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$1/T_{s}$</tex></formula> ). We also show that only small additional computation efforts are required for APACE and BPACE when compared with TSACE.

A performance investigation of correlation-based and pilot-tone-assisted frequency offset compensation method for CO-OFDM

We carry out a comprehensive analysis to examine the performance of our recently proposed correlation-based and pilot-tone-assisted frequency offset compensation method in coherent optical OFDM system. The frequency offset is divided into two parts: fraction part and integer part relative to the channel spacing. Our frequency offset scheme includes the correlation-based Schmidl algorithm for fraction part estimation as well as pilot-tone-assisted method for integer part estimation. In this paper, we analytically derive the error variance of fraction part estimation methods in the presence of laser phase noise using different correlation-based algorithms: Schmidl, Cox and Cyclic Prefix based. This analytical expression is given for the first time in the literature. Furthermore, we give a full derivation for the pilot-tone-assisted integer part estimation method using the OFDM model.

Optomechanical entanglement in the presence of laser phase noise

We study the simplest optomechanical system in the presence of laser phase noise using the covariance matrix formalism. We show that the destructive effect of the phase noise is especially strong in the bistable regime. This explains why ground state cooling is still possible in the presence of phase noise, as it happens far away from the bistable regime. On the other hand, the optomechanical entanglement is strongly affected by phase noise.

Maximum likelihood sequence detection in laser phase noise-impaired coherent optical systems

A maximum likelihood sequence detection (MLSD) receiver is used to detect data sequences in single-carrier coherent optical systems in the presence of laser phase noise. It requires no explicit phase estimation and involves only linear operations. It consistently shows improvement in the OSNR penalty (e.g., 1.1 dB at BER = 10⁻⁴ with memory length L =3) and the laser linewidth tolerance (e.g., around 4 times that of DAML at 1dB OSNR penalty at BER = 10⁻⁴ with memory length L =3) over the well-known DAML and Mth power approaches in laser phase noise (LPN)-impaired coherent optical systems.

Compensation of Frequency Offset for Differentially Encoded 16- and 64-QAM in the Presence of Laser Phase Noise

The compensation of frequency offset for differentially encoded 16- and 64-ary quadrature amplitude modulation (QAM) in the presence of laser phase noise is investigated. Differential encoding is employed to solve the four-fold phase ambiguity problem in a nondata-aided transmission system with square QAM constellations. Simulation results show that frequency offset and phase noise can successfully be compensated using a second-order digital filter loop for the square QAM constellations.

Beyond 100 Gb∕s Optical Transmission Based on Polarization Multiplexed Coded-OFDM With Coherent Detection

We propose a coded-modulation scheme suitable for beyond 100 Gb∕s transmission and 100 Gb∕s Ethernet. It is based on polarization multiplexed coded-orthogonal frequency division multiplexing (OFDM). By using 32-QAM-based polarization multiplexed coded-OFDM, we are able to achieve the aggregate rate of 100 Gb∕s, while the OFDM signal bandwidth is only 10 GHz, resulting in a spectral efficiency of 10 bits∕s∕Hz. The spectral efficiency of the proposed scheme is twice higher than that of the polarization diversity OFDM scheme. We show that the proposed multicarrier scheme is insensitive to polarization mode dispersion (PMD), while the PMD represents a major source of performance degradation in single carrier systems, in addition to fiber nonlinearities. We also describe how to determine the symbols' log-likelihood ratios in the presence of laser phase noise.

Alamouti-type polarization-time coding in coded-modulation schemes with coherent detection

We present the Almouti-type polarization-time (PT) coding scheme suitable for use in multilevel (M>or=2) block-coded modulation schemes with coherent detection. The PT-decoder is found it to be similar to the Alamouti combiner. We also describe how to determine the symbols log-likelihood ratios in the presence of laser phase noise. We show that the proposed scheme is able to compensate even 800 ps of differential group delay, for the system operating at 10 Gb/s, with negligible penalty. The proposed scheme outperforms equal-gain combining polarization diversity OFDM scheme. However, the polarization diversity coded-OFDM and PT-coding based coded-OFDM schemes perform comparable. The proposed scheme has the potential of doubling the spectral efficiency compared to polarization diversity schemes.