Relative Phase Noise Research Articles

Parallel fiber amplifiers with carrier–envelope drift control for coherent combination of optical frequency combs

We demonstrated an active feed-forward method for compensating the relative phase drifts of fiber optical amplifiers. The frequency drifts of relative phase noise were well controlled in a variation range from ± 15 Hz of free-running, to approximately ± 1.5 Hz between the amplifier input and output. Coherent combination of two femtosecond fiber chirped-pulse amplifiers seeded by a Ti:S comb oscillator was achieved, which would benefit frequency comb combination to achieve high accuracy and high power.

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 induced impairment in CO-OFDM optical communication system with distributed fiber Raman amplifier.

In this Letter, we demonstrate that the interplay between Raman pump relative intensity noise and cross-phase modulation leads to a relative phase noise (RPN) that brings non-negligible performance degradation to coherent optical orthogonal frequency-division multiplexing (CO-OFDM) transmission systems with co-pumped Raman amplification. By theoretical analysis and numerical simulation, we proved that RPN brings more system impairment in terms of Q-factor penalty than the single carrier system, and relatively larger walk-off between pump and signal helps to suppress the RPN induced impairment. A higher-order modulated signal is less tolerant to RPN than a lower-order signal. With the same spectral efficiency, the quadrature-amplitude modulation format shows better tolerance to RPN than phase-shift keying. The reported findings will be useful for the design and optimization of Raman amplified CO-OFDM multi-carrier transmission systems.

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.

Transmission-link-induced intensity and phase noise in a 400-km interrogated fiber-optics hydrophone system using a phase-generated carrier scheme

Transmission-link induced-intensity noise, as well as the con- version of intensity fluctuation to demodulated phase noise in a 400-km interrogated hydrophone array with a phase-generated carrier (PGC) scheme are investigated. Theoretical and experimental results all show that a PGC scheme can increase the erbium-doped fiber amplifiers- induced phase noise level by ∼3.7 dB in intensity to phase noise conver- sion. However, it can significantly reduce the coherent double Rayleigh scattering (DRS)-induced phase noise by ∼11.7 dB when compared with the unmodulated DRS intensity noise. Considering the effects of these two kinds of noises, a PGC scheme still has significant advantages for noise suppression in the remote system, and the total phase noise of the 400-km hydrophone system is shown to be only 11 to 14 μrad∕ sqrt ðHzÞ. Moreover, it is demonstrated that the spectra of DRS-induced relative intensity noise and phase noise all have Lorentzian line shapes and the full widths at half maximum are twice the width of the laser source. This result is helpful for us to choose a suitable laser source in long- distance hydrophone systems. © 2013 Society of Photo-Optical Instrumentation

Relative phase noise induced impairment in M-ary phase-shift-keying coherent optical communication system using distributed fiber Raman amplifier

We show for the first time, to the best of our knowledge, that, in a coherent communication system that employs a phase-shift-keying signal and Raman amplification, besides the pump relative intensity noise (RIN) transfer to the amplitude, the signal's phase will also be affected by pump RIN through the pump-signal cross-phase modulation. Although the average pump power induced linear phase change can be compensated for by the phase-correction algorithm, a relative phase noise (RPN) parameter has been found to characterize pump RIN induced stochastic phase noise. This extra phase noise brings non-negligible system impairments in terms of the Q-factor penalty. The calculation shows that copumping leads to much more stringent requirements to pump RIN, and relatively larger fiber dispersion helps to suppress the RPN induced impairment. A higher-order phase-shift keying (PSK) signal is less tolerant to noise than a lower-order PSK.

Single-longitudinal-mode fiber ring laser employing a polarization-maintaining fiber Bragg grating made by the pre-stress method for wavelength match

Interferometric sensors based on fiber Bragg gratings (FBGs) with a time-division multiplexing (TDM) configuration are attractive for many applications. The laser source with the same output wavelength as the FBGs is an important component in the system. In this paper, a single-longitudinal-mode (SLM) fiber ring laser that incorporates a polarization-maintaining fiber Bragg grating (PM-FBG) acting as a wavelength selector in the laser cavity is introduced and the lasing occurs at the Bragg wavelength of the PM-FBG. A pre-stress method used to match the wavelength of the high-reflectivity PM-FBG and the low-reflectivity single-mode FBGs in the system is theoretically analyzed and experimentally demonstrated. SLM operation of the fiber ring laser is demonstrated and then the noise characteristics of the fiber ring laser are tested. The relative intensity noise (RIN) and phase noise are −120dB/Hz and −115dB/Hz at 1kHz respectively.

A local oscillator for WCDMA band VII based on frequency multiplication

This work explores the generation of a local oscillator for WCDMA band VII based on frequency multiplication of a GSM reference. The frequency multiplier is based on a PLL, which includes a compact VCO based on a ring oscillator. A proper PLL design allows to sufficiently reject the relative high VCO phase noise, complying with the WCDMA requirements. The effectiveness of the proposed approach is proved with the design of the whole multiplier in a 90 nm CMOS technology. The generated oscillation ranges from 3 to 6 GHz, while the simulated phase noise is ?120 and ?144 dBc/Hz at a frequency offset of 0.6 and 20 MHz, respectively, dissipating 6.3 mW.

Characterization of the Excess Noise Conversion From Optical Relative Intensity Noise in the Photodetection of Mode-Locked Lasers for Microwave Signal Synthesis

Excess noise converted from the optical relative intensity noise (RIN) has limited the noise performance in the microwave signal synthesis application for mode-locked lasers. In this paper, a method for detailed characterization of the excess noise conversion from the optical RIN to the electrical pulse width jitter (PWJ), electrical relative amplitude noise (RAN) and electrical phase noise in the photodetection of mode-locked lasers is proposed. With the measured noise conversion ratios, one can predict the electrical RAN and phase noise power spectral densities under different input optical powers. The effect of the pulse width and peak power of the incident optical pulses and the effect of the saturation power of the photodetectors are also investigated. The results are used to suggest guidelines for achieving low-noise photodetection for microwave signal synthesis application.

Ultra-low-noise microwave extraction from fiber-based optical frequency comb

In this Letter we report on an all-optical-fiber approach to the generation of ultra-low-noise microwave signals. We make use of two erbium fiber mode-locked lasers phase locked to a common ultrastable laser source to generate an 11.55 GHz signal with an unprecedented relative phase noise of -111 dBc/Hz at 1 Hz from the carrier. The residual frequency instability of the microwave signals derived from the two optical frequency combs is below 2.3x10(-16) at 1 s and about 4x10(-19) at 6.5x10(4) s (in 5 Hz bandwidth, three days of continuous operation).

Simultaneous measurement of the phase noise on all optical modes of a mode-locked laser

We propose and experimentally demonstrate a method to simultaneously measure the relative phase noise of all modes of two mode-locked lasers. The method is based on the numerical analysis of a beat note of two lasers with slightly different pulse repetition rates. We carefully analyze and experimentally demonstrate the potential of this method. Compared to other methods, it has the unique advantage that it provides access to correlations of the phases of different modes.

64-Mb/s data transmission beyond the relaxation oscillation frequency using monolithically integrated two laterally coupled diode lasers

In this letter, we demonstrate the possibility of using two monolithically integrated laterally coupled diode lasers for data transmission beyond the intrinsic relaxation oscillation frequency of semiconductor lasers. The resonance of the lateral modes of such structure provides a peak in the small signal modulation response of the device above the relaxation oscillation frequency of the intrinsic emitters that is studied in terms of relative intensity noise and phase noise to characterize this new, simple, and compact device. Optical transmission of a 64-Mb/s pseudorandom bit sequence signal using a microwave carrier over this resonance peak of the lateral modes above the relaxation oscillation is demonstrated for the first time to our knowledge.

The effects of filtering RF source phase noise by a low noise, high quality factor actively modelocked laser on the laser’s absolute and relative phase noise

The phase noise of two low noise, high quality factor actively modelocked lasers is investigated. It is found that increasing the quality factor of a laser can increase the phase noise relative to the RF source used to modelock the laser, even though the absolute noise of the laser is decreased. The filtering of phase noise from the modelocking source that causes both the increase in relative noise and the decrease in absolute noise is exploited to reveal phase noise information otherwise obscured in a high quality factor laser.

Weak-light phase locking for LISA

The long armlengths of the LISA interferometer, and the finite aperture of the telescope, lead to an optical power attenuation of ∼10−10 of the transmitted to received light. Simple reflection at the end of the arm is therefore not an optimum interferometric design. Instead, a local laser is offset phase locked to the weak incoming beam, transferring the phase information of the incoming to the outgoing light. This paper reports on an experiment to characterize a weak-light phase-locking scheme suitable for LISA in which a diode-pumped, Nd:YAG, non-planar ring oscillator (NPRO) is offset phase locked to a low-power (13 pW) frequency stabilized master NPRO. Preliminary results of the relative phase noise of the slave laser shows shot noise limited performance above 0.4 Hz. Excess noise is observed at lower frequencies, most probably due to thermal effects in the optical arrangement and phase-sensing electronics.

Performance analysis of a deterministic channel estimator for block transmission systems with null guard intervals

A deterministic algorithm was proposed for channel identification in block communication systems. The method assumed that the channel has a finite impulse response (FIR) and that null guard intervals of length greater than the channel order are inserted between successive blocks to prevent interblock interference and allow block synchronization. In the absence of noise, the algorithm provides error-free channel estimates, using a finite number of received data, without requiring training sequences and without imposing a restriction neither on the channel, except for finite order and time invariance, nor on the symbol constellation. Using small perturbation analysis, we derive approximate expressions of the estimated channel covariance matrix, which are used to quantify the resilience of the estimation algorithm to additive noise and channel fluctuations. Specifically, we consider channel fluctuations induced by transmitter/receiver relative motion, asynchronism, and oscillators' phase noise. We also compare the channel estimation accuracy with the Cramer-Rao bound (CRB) and prove that our estimation method is statistically efficient at practical SNR values for any data block length. Finally, we validate our theoretical analysis with simulations and compare our transmission scheme with an alternative system using training sequences for channel estimation.

Optical Fiber Communication Systems

The Communications Toolbox: Introduction. Probability and Random Variables. Some Important Probability Distributions. Signals and Systems. Random Processes. Spectral Analysis. Narrowband Signals and Systems. Elements of Detection Theory. From Light to Signals. Basic Optical Fiber Communications Components: Introduction. The Refractive Index and the Laws of Reflection and Refraction. Total Internal Refraction. Step Index Fibers and Slab Waveguides. Maxwell's Equations in the Slab Waveguide. Even Propagation Modes. Odd Propagation Modes. Number of Modes and Single-Mode Fibers. Phase Velocity. Group Velocity. Attenuation and Dispersion. Dispersion-Shifted and Dispersion-Flattened Fibers. Polarization-Maintaining and Single-Polarization Fibers. The P-N Junction. Single Heterostructure. Double Heterostructure. LED Physical Structure. The LED Rate Equation. LED Output Spectrum. LED Modulation Response. The Fabry-Perot Resonator. Semiconductor Laser Physical Structure. Laser Output Spectrum--Spectral Width and Linewidth. Bragg Reflections. Distributed Feedback (DFB) and Distributed Bragg Reflection (DBR) Lasers. Rate Equations. The Steady-State Solution to the Rate Equations. Laser Modulation--Step Response. Laser Modulation--Sinusoidal Frequency Response. Relative Intensity Noise (RIN), Phase and Frequency Noise, Chirp. Laser Package. The PIN Photodiode. The Avalanche Photodiode, ADP. Basic Binary Optical Communication System: Introduction. System Description. Performance Evaluation. Coherent Systems: Motivations and Basics. Fundamental Receiver Sensitivity--Homodyne Systems. Heterodyne Systems--Synchronous Detection. Heterodyne Systems--Asynchronous Detection. Heterodyne Systems--Weakly Synchronous Detection. Summary and Comparison of Fundamental Sensitivities. Optical Hybrids. Phase Noise and Linewidth. Synchronous Systems. Asynchronous Systems. Weakly Synchronous Systems. How to Deal with Phase Noise--Summary. Polarization Fluctuations. Appendix A--Statistics of Phase Noise to Amplitude Conversion. Appendix B--Evaluation of Averages by Quadrature Rules. Optical Amplifiers: Introduction. Semiconductor Amplifiers. Erbium-Doped Fiber Amplifier. Comparison of Major SOA and EDFA Characteristics. Other Fiber Amplifiers. Soliton Systems: Intuitive Explanation of Solitons. Advantages of Solitons for Long Distance Transmission. Derivation of Solitons. Amplitude, Duration, Energy, and Power. Higher-Order Solitons. Qualitative Physical Explanation of Solitons. Estimation of Peak Pulse Power Required for Solitons. Fiber Loss and its Compensation. Lumped Amplifiers in Soliton Systems. Polarization Dispersion. Amplified Spontaneous Emission Noise in Soliton Systems. Error Rates in Soliton Systems. Soliton Experiments. Using Recirculating Loops. Wavelength Division Multiplexing with Solitons. Bidirectional Soliton Systems. Sources of Soliton Pulses. Beyond the Gordon-Haus Limit. Multichannel Systems: Introduction. Time-Division Multiplexing (TDM). Wavelength-Division Multiplexing. Subcarrier Multiplexing. Code-Division Multiplexing. Space-Division Multiplexing. Network Issues.