Self-phase Modulation Compensation Research Articles

Enabling Technologies for Fiber Nonlinearity Mitigation in High Capacity Transmission Systems

Fiber nonlinearity has become a major limiting transmission impairment factor. In this paper, we discuss various nonlinearity mitigation techniques in electrical and optical domains. In electrical domain, multiple reduced complexity digital back-propagation algorithms were developed, including perturbation back-propagation. One drawback is that they can compensate for intra-channel self-phase modulation (SPM) effects only. The inter-channel fiber nonlinearity mitigation can be done in optical domain. For example, digital subcarrier multiplexing (SCM) can effectively mitigate both SPM and cross-phase modulation (XPM) effects. It can become even more beneficial for higher symbol rate systems (e.g., 64 Gbaud and 128 Gbaud) and has a capability to deliver longer reach than single carrier 32 Gbaud DP-16QAM signals and only slightly shorter reach (by up to 7%) compared to 32 Gbaud SCM systems. Another technique, the total intensity directed phase modulation, can provide per-span SPM and XPM compensation. However, this technique is limited to compensation of a few channels only. On the other hand, the proposed enhanced pre-dispersed spectral inversion can effectively compensate for SPM/XPM effects of multiple channels and become more practical by removing limitation to link symmetry even in nonuniform transmission links. Finally, subcarrier power pre-emphasis in optical superchannels can equalize performance of all subcarriers by mitigating intersubcarrier XPM and extend transmission reach by 20%.

Self-phase modulation pre-compensation of narrowlinewidth pulsed fiber lasers

High peak power, single frequency nanosecond fiber lasers have aroused the intense interest in their applications such as nonlinear frequency generation, LIDAR, and remote sensing. However, self-phase modulation (SPM) will induce a temporally dependent phase shift φNL (L, t)=|Ap (0, t)|2γLeff, where Ap is the amplitude of pump wave, γ is the nonlinear parameter, and Leff is the effective fiber length. The nonlinear phase shift will broaden the spectral linewidth of pulsed laser, which degrades the coherence of the laser and influences the performance of the laser. In order to obtain laser pulses with narrower linewidth, we can phase-modulate the pulsed laser with a value of-φNL(L,t). Thus, the SPM induced the nonlinear phase shift can be eliminated, and the spectra of pulsed laser can remain during the amplification and transmission in the fiber. Stimulated Brillouin scattering (SBS) has very low threshold and should be taken into consideration in narrow linewidth fiber lasers. The SBS threshold, which is dependent on the linewidth of laser, will be changed at the same time when the SPM is pre-compensated for. Because the SPM pre-compensation will change the linewidth of the pulsed laser. According to three coupled amplitude equations, we numerically analyze the influence of SPM pre-compensation on SBS threshold and spectral characteristics. The stimulation results show that in a master oscillator power amplifier structured fiber laser system, when SPM is completely compensated for (φM(t)=φNL(L,t)), the spectrum of the output pulsed laser can be maintained as that of the laser seed, but the SBS threshold usually decreases. When the SPM is compensated for incompletely (φM(t) φNL(L,t)), the spectral linewidth of the output laser cannot be compressed to that of the laser seed, and the SBS threshold in this situation is lower than the SBS threshold obtained when φM(t)=φNL(L,t). When the SPM is overcompensated for (φM(t) > φNL(L, t)), the spectral linewidth of the output laser cannot be compressed to that of the laser seed either, but the the SBS threshold in this situation is higher than the SBS threshold when φM(t)=φNL(L,t). We also build an experimental setup to verify the feasibility of SPM compensation. In our experiment, the linewidth of the pulsed laser is reduced from 1.4 GHz to 120 MHz when SPM is compensated for by phase modulation. The SBS threshold of the system are measured before and after SPM pre-compensation, and correctness of theoretical simulation is experimentally verified. This analysis method can provide the design guidelines for narrow-linewidth pulsed fiber laser systems.

Contrast enhancement in an optical time-domain reflectometer via self-phase modulation compensation by chirped probe pulses

In the present paper we propose a novel method for optical time-domain reflectometer (OTDR)–reflectogram contrast enhancement via compensation of nonlinear distortions of propagating probe pulse, which arise due to the self-phase modulation (SPM) effect in optical fiber. The compensation is performed via preliminary frequency modulation (chirp) of the initial probe pulse according to the specific law. As a result the OTDR contrast at some distant predefined fiber point is fully restored to the value of non-distorted probe pulse at the beginning of the fiber line. As a result, the performance of the phase OTDR increases. The point of full SPM compensation could be shifted to any other point of the fiber line via preliminary frequency modulation index change. The feasibility of the proposed method is theoretically proved and experimentally demonstrated.

SOLITONS: NOVEL APPROACH FOR DISPERSION MANAGEMENT

Soliton is a special kind of wave packet that travels distortion less over long distances. It is a pulse able to maintain its shape and width due to compensation of Self Phase Modulation (SPM) process which is a non-linear effect based on refractive index variation and Group Velocity Dispersion (GVD) process which is a linear effect. For long range communication, soliton pulses are very suitable as the pulse width remain constant over the entire transmission distance. It eliminates the need to cope with any type of dispersion. The transmission of light in optical fiber given by Nonlinear Schrodinger equation has been discussed in the paper. The performance of fiber with soliton parameters is compared to that with fiber without soliton parameters using OptiSystem Software.

Self-phase modulation compensation in a regenerative amplifier using cascaded second-order nonlinearities

Self-phase modulation limits the amplification of short optical pulses because of spatial self-focusing and spectral broadening. Cascaded nonlinearities are theoretically and experimentally investigated for intracavity nonlinearity compensation in a neodymium-doped yttrium-lithium-fluoride (Nd:YLF) regenerative amplifier. Experimental results are in good agreement with simulations. Spectral broadening is significantly reduced, allowing for efficient amplification in a Nd:YLF power amplifier.

High-peak-power, single-frequency, single-mode, linearly polarized, nanosecond all-fiber laser based on self-phase modulation compensation

We demonstrated a high-peak-power, single-frequency, single-mode, linearly polarized, nanosecond all-fiber laser in master oscillator power amplifier configuration. The pulsed seed was generated by modulating a single-frequency continuous wave laser at 1064 nm. The short pulse width (∼3.2 ns) of the pulsed seed prevented the onset of stimulated Brillouin scattering in the 10 μm-core single-transverse-mode polarization-maintaining ytterbium-doped fiber of the main amplifier. In order to compensate self-phase modulation-induced spectral broadening, a phase modulator was employed to control the phase of the pulsed seed, and the linewidth of the output pulses were reduced from ∼1.22 GHz to ∼185 MHz at the peak power of 1.47 kW.

Polarization multiplexed 16QAM transmission employing modified digital back-propagation

We experimentally demonstrate performance enhancements enabled by weighted digital back propagation method for 28 Gbaud PM-16QAM transmission systems, over a 250 km ultra-large area fibre, using only one back-propagation step for the entire link, enabling up to 3 dB improvement in power tolerance with respect to linear compensation only. We observe that this is roughly the same improvement that can be obtained with the conventional, computationally heavy, non-weighted digital back propagation compensation with one step per span. As a further benchmark, we analyze performance improvement as a function of number of steps, and show that the performance improvement saturates at approximately 20 steps per span, at which a 5 dB improvement in power tolerance is obtained with respect to linear compensation only. Furthermore, we show that coarse-step self-phase modulation compensation is inefficient in wavelength division multiplexed transmission.

Pilot-based cross-phase modulation compensation for coherent optical orthogonal frequency division multiplexing long-haul optical communications systems

A pilot-based nonlinearity compensator (PB-NLC) is shown in this Letter to be an effective method for compensating cross-phase modulation (XPM) in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. An unmodulated pilot tone is transmitted at the center of each OFDM channel to detect phase errors caused by the Kerr effect, which converts intensity fluctuations from all channels to phase errors. The pilots are then used to cancel the XPM phase errors for each OFDM channel at the receiver after each channel's self-phase modulation (SPM) has been compensated, using its intensity waveform to determine its SPM. Numerical simulations of a 58 Gb/s single polarization 2375 km system with inline dispersion compensation show that the signal quality, Q, at the optimal launch power is increased by 2.4 dB if SPM compensation is used before the PB-NLC. This contrasts with only a 0.9 dB improvement if the PB-NLC is used without an SPM compensator for the same link. This shows the PB-NLC can effectively mitigate XPM but not SPM.

Mitigation of fiber nonlinear impairments in polarization division multiplexed OFDM transmission

Fiber nonlinear effects are found to cause severe signal degradation in long-haul coherent optical OFDM (CO-OFDM) transmission, particularly in dispersion-managed transmission. We present promising techniques to mitigate the fiber nonlinear impairments in both single-channel and wavelength division multiplexed (WDM) transmission. For single-channel transmission, we discuss a joint self-phase modulation (SPM) compensation scheme that is applicable to polarization division multiplexed (PDM) CO-OFDM signals. Experimental demonstration of this joint SPM compensation scheme is also presented. For WDM transmission, we describe an OFDM frame design and a dispersion management scheme that reduce the cross-phase-modulation (XPM) penalty among the WDM channels. The impact of XPM from WDM channels with different signal formats and data rates is briefly discussed. é 2010 Alcatel-Lucent.

Impact of the second order dispersion on compensation of SPM in an adaptive pulse pre-shaping quasi-CPA system

A model of quasi-CPA (chirped pulse amplification) system, in which the input is the transform-limited Gaussian pulses, is set up numerically to investigate the impact of the second order dispersion on the adaptive compensation of self-phase modulation (SPM) effect. The adaptive phase pre-shaping controlled by differential evolution algorithm is introduced to the input pulse before amplification and recompression. With maximizing the peak power of the output pulse, the simulation results show that the normal dispersion is really helpful to eliminate the side lobes of the output pulse and increase the pulse peak power.

Experimental demonstration of XPM compensation for WDM fibre transmission

Distributed compensation for cross-phase modulation (XPM) by solving the coupled nonlinear Schrodinger equations in digital backward propagation is demonstrated experimentally. The results show that XPM compensation provides significant improvement over self-phase modulation compensation.

107 Gb/s electronic predistortion transmitter using commercial FPGAs and D/A converters implementing real-time DSP for chromatic dispersion and SPM compensation

We present an experimental demonstration of simultaneous chromatic dispersion and self-phase modulation compensation at 10.7 Gb/s using real-time electronic digital signal processing. This was achieved using a pre-distorting transmitter based on commercially available field programmable gate arrays and 21.4 GS/s, 6-bit resolution digital-to-analog converters. The digital signal processing employed look-up tables stored in RAM. This resulted in the achievement of a BER of 10(-6) at an OSNR of 16 dB after transmission over a 450 km link of uncompensated standard single mode fiber with + 4 dBm launch power.

Scaling of femtosecond Yb-doped fiber amplifiers to tens of microjoule pulse energy via nonlinear chirped pulse amplification

We demonstrate that the compensation of self-phase modulation by third-order dispersion can be exploited in the design of fiber amplifiers with tens of microjoules pulse energy. At the highest energies, the amplified pulse accumulates nonlinear phase shift as large as 17 pi. Gain-narrowing occurs in the final amplifier stage, but shorter pulses are still generated with larger nonlinear phase shifts. A large-mode-area Yb-doped photonic crystal fiber amplifier generates diffraction-limited 30 microJ pulses, which are compressed to 240 fs duration. These are converted to the second harmonic with 48% conversion efficiency, as expected theoretically, which confirms the pulse quality.

Compensation of self-phase modulation in fiber-based chirped-pulse amplification systems

We demonstrate a simple, all-fiber technique for removing nonlinear phase due to self-phase modulation in fiber-based chirped-pulse amplification (CPA) systems. Using a LiNbO3 electro-optic phase modulator to emulate a negative nonlinear index of refraction, we are able to remove 1.0 pi rad of self-phase modulation acquired by pulses during amplification and eliminate nearly all pulse distortion. Our technique is high speed, removes nonlinear phase on a pulse-to-pulse basis, and can be readily integrated into existing CPA systems.

Femtosecond Transform-Limited Pulse Generation by Compensating for the Linear Chirp of SPM Spectra in Dispersion Shifted Fibers

A simple technique of pulse compression, based on the linear chirp compensation of self-phase modulation (SPM) spectra in dispersion shifted fibers, is demonstrated. The optimization procedure is carried out, for a short span of a single-mode fiber, using a parabolic law, which describes the behavior of the squared output pulse width versus the pump peak power in the case of Gaussian pulses. The experimental results give a minimum pulse duration of 233 fs, which is in good agreement with the model. Shorter and coherent pulses, down to 90 fs, have been obtained by inserting an interference filter at the optical output.

Compensation of self-phase modulation in chirped-pulse amplification laser systems

Small amounts of self-phase modulation can lead to significant pulse distortions in chirped-pulse amplifiers. However, we show the surprising result that the strong chirp of the pulse can be exploited to remove these distortions completely by linear pulse shaping before amplification.

Compensation of self-phase modulation in a QND measurement of photon number based on the optical Kerr effect

The authors study a quantum non-demolition (QND) set-up for the measurement of photon number, employing the optical Kerr effect. A method for the compensation of the negative effects of self-phase modulation is discussed. Losses are taken into account. It is seen that the performance of the device is limited in the first place by losses, rather than by self-phase modulation.

Complete compensation of self-phase modulation in cesium vapor at 1.06 μ

We have observed a complete cancellation of self-phase modulation in 1.06-μ pulses propagating through cesium vapor. The negative nonlinear refractive index responsible for this is measured as n2/N=−(2.5±0.5) ×10−30 esu, in good agreement with the theoretical value −2.62×10−30 esu.

Compensation of self-phase modulation by cesium vapor

Compensation of self-phase modulation by cesium vapor