Compensating for dispersion and the nonlinear Kerr effect without phase conjugation

Spectrally efficient pilot tone-based compensation of inter-channel cross-phase modulation noise in a WDM coherent transmission using injection locking

We propose the precise and wideband compensation of the nonlinear phase noise caused by cross-phase modulation (XPM) among WDM channels using a pilot tone (PT) and injection locking for short-reach, higher-order QAM transmission. A high spectral efficiency is maintained by sharing a single PT among multiple channels. We describe a 60 ch, 3 Gbaud PDM-256 QAM transmission over 160 km, where the bit error rate was improved from 6 × 10^-3 to 2 × 10^-3 by employing the proposed XPM compensation technique, with a spectral efficiency of 10.3 bit/s/Hz. We also analyze the influence of the group delay caused by fiber chromatic dispersion that determines the compensation range achievable with a single PT. We obtained good agreement with the experimental results.

Injection-locked 256 QAM WDM coherent transmissions in the C- and L-bands

We demonstrate WDM 256 QAM coherent transmissions with injection locking in the C- and L-bands and compare the transmission performance in the two bands. Although four-wave mixing (FWM) is more significant in an L-band EDFA than in a C-band EDFA, the FWM did not accumulate through the transmission and the FWM components were hidden by the ASE noise level. Since the FWM was weakened by the decorrelation of the WDM signals during the transmission, the transmission performance in the L-band was the same as that in the C-band. The injection locking circuit enabled precise carrier-phase synchronization between a data signal and a local oscillator regardless of the transmission band. By using this circuit, we successfully transmitted 58.2 and 57.6 Tbit/s 256 QAM WDM signals over 160 km with a spectral efficiency of 12 bit/s/Hz in the C- and L-bands, respectively.

Suppression of large error floor in 1024 QAM digital coherent transmission by compensating for GAWBS phase noise

There is a large error floor in an ultra multi-level digital coherent transmission signal of 1024 QAM or higher, and we have yet to determine its origin. In this paper, we show that this large error floor results from guided acoustic-wave Brillouin scattering (GAWBS) phase noise. We prove experimentally that such an error floor can be greatly reduced by compensating for the GAWBS noise with a phase modulation technique. We show that the BER of a 1024 QAM signal was reduced from 8.7 × 10^-4 to 2.7 × 10^-4 after a 160 km transmission with GAWBS noise compensation. Furthermore, we successfully extend the transmission distance from 160 to 240 km with a 7% overhead forward error correction.

Single-channel 200 Gbit/s, 10 Gsymbol/s-1024 QAM injection-locked coherent transmission over 160 km with a pilot-assisted adaptive equalizer

We demonstrate a 10 Gsymbol/s, 1024 quadrature amplitude modulation (QAM) 160 km coherent transmission with an injection locking technique. Our newly developed, pilot-assisted adaptive equalizer has greatly improved the precision of waveform distortion compensation, and this has enabled us to increase the symbol rate to 10 Gsymbol/s in a 1024 QAM transmission. Thus, we could realize a 200 Gbit/s, 1024 QAM transmission over 160 km with a potential spectral efficiency of 12.6 bit/s/Hz.

42.3 Tbit/s, 18 Gbaud 64 QAM WDM coherent transmission over 160 km in the C-band using an injection-locked homodyne receiver with a spectral efficiency of 9 bit/s/Hz

We demonstrate a 235-channel wavelength division multiplexing (WDM), polarization-multiplexed (pol-mux) 18-Gbaud 64 QAM coherent transmission of 160 km over the full C-band. By applying an injection-locked homodyne detection circuit to WDM coherent transmission, we have achieved low noise optical carrier-phase locking between transmitted data and a local oscillator over the full C-band range. As a result, a potential capacity of 42.3 Tbit/s data with a spectral efficiency of 9 bit/s/Hz was transmitted.

320 Gbit/s, 20 Gsymbol/s 256 QAM coherent transmission over 160 km by using injection-locked local oscillator

We demonstrate 20 Gsymbol/s, 256 QAM polarization multiplexed (pol-mux) 320 Gbit/s coherent transmission. By employing an LD-based injection locking circuit, we achieved low noise optical carrier-phase locking between the LO and the data signal. Furthermore, frequency domain equalization and digital back-propagation enabled us to realize precise compensation for transmitted waveform distortions. As a result, a 320 Gbit/s data was successfully transmitted over 160 km with a potential spectral efficiency of 10.9 bit/s/Hz. This is the highest symbol rate yet achieved in a pol-mux 256 QAM coherent transmission. In addition, we also describe a pol-mux 256 QAM transmission at a symbol rate of 10 Gsymbol/s.

Single-channel 40 Gbit/s digital coherent QAM quantum noise stream cipher transmission over 480 km

We demonstrate the first 40 Gbit/s single-channel polarization-multiplexed, 5 Gsymbol/s, 16 QAM quantum noise stream cipher (QNSC) transmission over 480 km by incorporating ASE quantum noise from EDFAs as well as the quantum shot noise of the coherent state with multiple photons for the random masking of data. By using a multi-bit encoded scheme and digital coherent transmission techniques, secure optical communication with a record data capacity and transmission distance has been successfully realized. In this system, the signal level received by Eve is hidden by both the amplitude and the phase noise. The highest number of masked signals, 7.5 x 10(4), was achieved by using a QAM scheme with FEC, which makes it possible to reduce the output power from the transmitter while maintaining an error free condition for Bob. We have newly measured the noise distribution around I and Q encrypted data and shown experimentally with a data size of as large as 2(25) that the noise has a Gaussian distribution with no correlations. This distribution is suitable for the random masking of data.

448 Gbit/s, 32 Gbaud 128 QAM coherent transmission over 150 km with a potential spectral efficiency of 10.7 bit/s/Hz

We realized a single-carrier, polarization-multiplexed 32 Gbaud 128 QAM coherent transmission. Digital frequency-domain equalization enabled us to achieve waveform distortion compensation of a wideband data signal with high frequency resolution. Thus, we successfully increased the QAM multiplicity to 128 at 32 Gbaud, and transmitted 448 Gbit/s data over 150 km with a potential spectral efficiency of 10.7 bit/s/Hz. This is the highest multiplicity and spectral efficiency yet achieved in a coherent QAM transmission at a baud rate of as high as 32 Gbaud.

PROUD-based method for simple real-time in-line characterization of propagation-induced distortions in NRZ data signals

A simple, in-line method for real-time full characterization (amplitude and phase) of propagation distortions arising because of group velocity dispersion and self-phase modulation on 10-20 Gbps transmitted NRZ optical signals is reported. It is based on phase reconstruction using optical ultrafast differentiation (PROUD), a linear and self-referenced technique. The flexibility of the technique is demonstrated by characterizing different data stream scenarios. Experimental results were modeled using conventional propagation equations, showing good agreement with the measured data. It is envisaged that the proposed method could be used in combination with DSP techniques for the estimation and compensation of propagation distortions in fiber links, not only in conventional IM/DD systems, but also in coherent systems with advanced modulation formats.

2048 QAM (66 Gbit/s) single-carrier coherent optical transmission over 150 km with a potential SE of 15.3 bit/s/Hz

We describe a 2048 QAM single-carrier coherent optical transmission over 150 km in detail. The OSNR at the transmitter was increased by 5 dB and the phase noise at the receiver was reduced from 0.35 to 0.17 degrees compared with a previous 1024 QAM transmission. Furthermore, we employed an A/D converter with a higher ENOB (7 bit) to guarantee the SNR of the digital QAM data, and introduced a polarization-demultiplexing algorithm to fast track the polarization state transition. As a result, a 66 Gbit/s polarization-multiplexed 2048 QAM signal was successfully transmitted within an optical bandwidth of 3.6 GHz including a pilot tone, and a potential SE of 15.3 bit/s/Hz under a 20% FEC overhead was achieved.

400 Gbit/s 256 QAM-OFDM transmission over 720 km with a 14 bit/s/Hz spectral efficiency by using high-resolution FDE

We demonstrate 400 Gbit/s frequency-division-multiplexed and polarization-division-multiplexed 256 QAM-OFDM transmission over 720 km with a spectral efficiency of 14 bit/s/Hz by using high-resolution frequency domain equalization (FDE) and digital back-propagation (DBP) methods. A detailed analytical evaluation of the 256 QAM-OFDM transmission is also provided, which clarifies the influence of quantization error in the digital coherent receiver on the waveform distortion compensation with DBP.

Marked performance improvement of 256 QAM transmission using a digital back-propagation method

We demonstrate substantial performance improvements in 256 QAM transmission in terms of both data rate and distance that we realized by using a digital back-propagation (DBP) method. 160 Gbit/s-160 km and 64 Gbit/s-560 km transmissions were successfully achieved with a polarization-multiplexed 256 QAM signal, in which the symbol rate and transmission distance were greatly increased by compensating for the interplay between dispersion and nonlinearity, which is responsible for the transmission impairment especially for a higher symbol rate and longer distance.

1024 QAM (60 Gbit/s) single-carrier coherent optical transmission over 150 km

We demonstrate a record QAM multiplicity of 1024 levels in a single-carrier coherent transmission. A frequency-domain equalization technique and a back-propagation method are adopted to compensate for distortions caused by hardware imperfections and fiber impairments, respectively. As a result, 60 Gbit/s polarization-multiplexed transmission over 150-km has been achieved at 3 Gsymbol/s within an optical bandwidth of only 4.05 GHz.

Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems

Backpropagation has been shown to be the most effective method for compensating intra-channel fiber nonlinearity in long-haul optical communications systems. However, effective compensation is computationally expensive, as it requires numerous steps and possibly increased sampling rates compared with the baud rate. This makes backpropagation difficult to implement in real-time. We propose: (i) low-pass filtering the compensation signal (the intensity waveform used to calculate the nonlinearity compensation) in each backpropagation step and (ii) optimizing the position of the nonlinear section in each step. With numerical simulations, we show that these modifications to backpropagation improve system performance, reducing the number of backpropagation steps and reducing the oversampling for a given system performance. Using our 'filtered backpropagation', with four backpropagation steps operating at the same sampling rate as that required for linear equalizers, the Q at the optimal launch power was improved by 2 dB and 1.6 dB for single wavelength CO-OFDM and CO-QPSK systems, respectively, in a 3200 km (40 x 80 km) single-mode fiber link, with no optical dispersion compensation. With previously proposed backpropagation methods, 40 steps were required to achieve an equivalent performance. A doubling in the sampling rate of the OFDM system was also required. We estimate this is a reduction in computational complexity by a factor of around ten.

Stabilization and destabilization of second-order solitons against perturbations in the nonlinear Schrödinger equation

We consider splitting and stabilization of second-order solitons (2-soliton breathers) in a model based on the nonlinear Schrodinger equation, which includes a small quintic term, and weak resonant nonlinearity management (NLM), i.e., time-periodic modulation of the cubic coefficient, at the frequency close to that of shape oscillations of the 2-soliton. The model applies to the light propagation in media with cubic-quintic optical nonlinearities and periodic alternation of linear loss and gain and to Bose-Einstein condensates, with the self-focusing quintic term accounting for the weak deviation of the dynamics from one dimensionality, while the NLM can be induced by means of the Feshbach resonance. We propose an explanation to the effect of the resonant splitting of the 2-soliton under the action of the NLM. Then, using systematic simulations and an analytical approach, we conclude that the weak quintic nonlinearity with the self-focusing sign stabilizes the 2-soliton, while the self-defocusing quintic nonlinearity accelerates its splitting. It is also shown that the quintic term with the self-defocusing/focusing sign makes the resonant response of the 2-soliton to the NLM essentially broader in terms of the frequency.

Efficient backward-propagation using wavelet-based filtering for fiber backward-propagation

With the goal of reducing the number of operations required for digital backward-propagation used for fiber impairment compensation, wavelet-based filtering is presented. The wavelet-based design relies on signal decomposition using time-limited basis functions and hence is more compatible with the dispersion operator, which is also time-limited. This is in comparison with inverse-Fourier filter design which by definition is not time-limited due to the use of harmonic basis functions for signal decomposition. Artificial, after-the-fact windowing may be employed in this case; however only a limited amount of saving in the number of operations can be achieved, compared to the wavelets-base filter design. Wavelet-based filter design procedure and numerical simulations which validate this approach are presented in this paper.

Phase fluctuations of linearly chirped solitons in a noisy optical fiber channel with varying dispersion, nonlinearity, and gain

The phase fluctuations of arbitrarily nonlinearity- and dispersion-managed solitons propagating in a noisy fiber channel are studied both analytically and numerically. We begin by discussing the stability problem of such linearly chirped solitons with a full linear stability analysis. It is shown that these sophisticated solitons possess an enhanced stability against perturbations and therefore hold promise for applications in optical telecommunications. We then make an approach to the phase statistics of these solitons, which stems from an inevitable random walk in phase evolutions due to amplified spontaneous emission noise. By using the variational approach together with impulse-response (Green) functions, an elegant closed-form expression for the phase variance is derived based on an unconstrained self-similar soliton ansatz in which the effect of chirp fluctuations has been critically taken into account as well as the dispersive and nonlinear effects. An inspection of the intriguing subtleties of the interplay among these effects reveals that the chirp fluctuations effect does play an important role in the control of nonlinear phase noise via fiber dispersion, independently of whether the input solitons are initially chirped or not. Our analytical result also offers many possibilities of optimally manipulating nonlinear phase noise with engineered fiber parameters that may lead to the steady pulse propagation, broadening, or compression under favorable parametric conditions. Last, we demonstrate our result by several convincible examples and show an excellent agreement between analytical predictions and numerical simulations.

Nonlinear wave mixing and susceptibility properties of negative refractive index materials

We present an analysis of second-order and third-order nonlinear susceptibilities and wave-mixing properties of negative refractive index materials. We show that the nonlinear susceptibilities for noncentrosymmetric and centrosymmetric media may be positive or negative and away from resonance depending on the frequency of interest relative to the resonant frequencies of the material. Manipulation of the signs of the nonlinear susceptibilities is important in the field of optics, particularly for solitons and compensation of nonlinear effects. We also show that three- and four-wave mixing can be naturally phase matched in the material.

Resonant nonlinearity management for nonlinear Schrödinger solitons

We consider effects of a periodic modulation of the nonlinearity coefficient on fundamental and higher-order solitons in the one-dimensional NLS equation, which is an issue of direct interest to Bose-Einstein condensates in the context of the Feshbach-resonance control, and fiber-optic telecommunications as concerns periodic compensation of the nonlinearity. We find from simulations, and explain by means of a straightforward analysis, that the response of a fundamental soliton to the weak perturbation is resonant, if the modulation frequency omega is close to the intrinsic frequency of the soliton. For higher-order n-solitons with n=2 and 3, the response to an extremely weak perturbation is also resonant, if omega is close to the corresponding intrinsic frequency. More importantly, a slightly stronger drive splits the 2- or 3-soliton, respectively, into a set of two or three moving fundamental solitons. The dependence of the threshold perturbation amplitude, necessary for the splitting, on omega has a resonant character too. Amplitudes and velocities of the emerging fundamental solitons are accurately predicted, using exact and approximate conservation laws of the perturbed NLS equation.

All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification

All-optical regeneration of differential phase-shift keying signals based on phase-sensitive amplification is described. Nearly ideal phase regeneration can be achieved in the undepleted-pump regime, and simultaneous amplitude and phase regeneration can be realized in the depleted-pump regime.

Effect of chromatic dispersion on nonlinear phase noise

We consider the combined effects of amplified spontaneous emission noise, optical Kerr nonlinearity, and chromatic dispersion on phase noise in an optical communication system. The effect of amplified spontaneous emission noise and Kerr nonlinearity were considered previously by Gordon and Mollenauer [Opt. Lett. 15, 1351 (1990)], and the effect of nonlinearity was found to be severe. We investigate the effect of chromatic dispersion on phase noise and show that it can either enhance or suppress the nonlinear noise amplification. For large absolute values of dispersion the nonlinear effect is suppressed, and the phase noise is reduced to its linear value. For a range of negative values of dispersion, however, nonlinear phase noise is enhanced and exhibits a maximum related to the modulation instability found in amplitude fluctuations. Nonlinear phase noise is quenched by these effects even in dispersion-compensated systems; the degree of suppression is sensitively dependent on the dispersion map. We demonstrate these results analytically with a simple linearized model.

Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation

We show that significant improvements in transmission performance can be achieved in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation (NPSC). A simple device that provides NPSC is described. In a 10-Gbit/s single-channel system based on dispersion-managed solitons, an improvement in performance (Q(2)) of almost 6dB is realized by NPSC after 6000km of transmission. In dense wavelength-division multiplexed systems, interchannel cross-phase modulation reduces the effectiveness of NPSC slightly.

Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission

A novel scheme for postnonlinearity compensation is proposed to reduce the phase jitter in phase-shift keying transmission. A phase modulator is used to modulate the phase of the data pulses in front of the receiver. The magnitude of the phase modulation is proportional to the detected pulse intensity, and the sign is opposite to that of the nonlinear phase shift caused by self-phase modulation. Thus, the nonlinear phase noise induced by amplitude fluctuation and self-phase modulation is partially compensated for. We show by numerical simulations that a differential phase-shift keying dispersion-managed soliton system at 10Gbits/s with such postnonlinearity compensation can provide greater than 3dB of improvement in ultralong-haul dense wavelength-division multiplexing transmissions.

Nonlinearity management in a dispersion-managed system

We propose using a nonlinear phase-shift interferometric converter (NPSIC), a new device, for lumped compensation for nonlinearity in optical fibers. The NPSIC is a nonlinear analog of the Mach-Zehnder interferometer and provides a way to control the sign of the nonlinear phase shift. We investigate a potential use of the NPSIC for compensation for nonlinearity to develop a dispersion-managed system that is closer to an ideal linear system. More importantly, the NPSIC can be used to essentially improve single-channel capacity in the nonlinear regime.