Shaping lightwaves in time and frequency for optical fiber communication.

In optical communications, sphere shaping is used to limit the energy of lightwaves to within a certain value over a period. This minimizes the energy required to contain information, allowing the rate of information transmission to approach the theoretical limit if the transmission medium is linear. However, when shaped lightwaves are transmitted through optical fiber, Kerr nonlinearity manifests itself as nonlinear interference in a peculiar way, potentially lowering communications capacity. In this article, we show that the impact of sphere shaping on Kerr nonlinearity varies with chromatic dispersion, shaping block length and symbol rate, and that this impact can be predicted using a novel statistical measure of light energy. As a practical consequence, by optimally controlling the parameters of sphere-shaped lightwaves, it is experimentally demonstrated that the information rate can be increased by up to 25% in low-dispersion channels on a 2824 km dispersion-managed wavelength-division multiplexed optical fiber link.

Publisher Correction: Long-haul optical transmission link using low-noise phase-sensitive amplifiers.

The original version of this Article incorrectly listed an affiliation of Samuel L.I. Olsson as 'Thomas Johann Seebeck Department of Electronics, Tallinn University of Technology, Tallinn 19086, Estonia', instead of the correct 'Present address: Nokia Bell Labs, 791 Holmdel Road, Holmdel, NJ 07733, USA'. Similarly, Egon Astra had an incorrect affiliation of 'Present address: Nokia Bell Labs, 791 Holmdel Road, Holmdel, NJ 07733, USA', instead of the correct 'Thomas Johann Seebeck Department of Electronics, Tallinn University of Technology, Tallinn 19086, Estonia'. This has been corrected in both the PDF and HTML versions of the Article.

Phase-sensitive amplifier link with distributed Raman amplification.

We demonstrate long-haul transmission using a hybrid amplifier approach combining distributed Raman amplification and lumped phase-sensitive amplification. Aside from the well-known resulting SNR improvement, distributed Raman amplification is included in an effort to improve the nonlinearity mitigation capability of the phase-sensitive amplifiers. When changing from phase-insensitive operation to phase-sensitive operation in a link employing distributed Raman amplification, the transmission reach at BER = 10-3 is increased from 15 to 44 spans of length 81 km while simultaneously increasing the optimal launch power by 2 dB.

Long-haul optical transmission link using low-noise phase-sensitive amplifiers.

The capacity and reach of long-haul fiber optical communication systems is limited by in-line amplifier noise and fiber nonlinearities. Phase-sensitive amplifiers add 6 dB less noise than conventional phase-insensitive amplifiers, such as erbium-doped fiber amplifiers, and they can provide nonlinearity mitigation after each span. Realizing a long-haul transmission link with in-line phase-sensitive amplifiers providing simultaneous low-noise amplification and nonlinearity mitigation is challenging and to date no such transmission link has been demonstrated. Here, we demonstrate a multi-channel-compatible and modulation-format-independent long-haul transmission link with in-line phase-sensitive amplifiers. Compared to a link amplified by conventional erbium-doped fiber amplifiers, we demonstrate a reach improvement of 5.6 times at optimal launch powers with the phase-sensitively amplified link operating at a total accumulated nonlinear phase shift of 6.2 rad. The phase-sensitively amplified link transmits two data-carrying waves, thus occupying twice the bandwidth and propagating twice the total power compared to the phase-insensitively amplified link.

Probabilistically shaped PDM 4096-QAM transmission over up to 200 km of fiber using standard intradyne detection.

We demonstrate transmission of a probabilistically shaped polarization-division multiplexed 3-GBd 4096-QAM signal over up to 200 km of backward Raman amplified Corning® Vascade® EX2000 fiber. The 3-GBd signal with a root-raised-cosine roll-off of 0.01 has the potential to generate a spectral efficiency of 19.77 bit/s/Hz over 50 km of fiber.

Dispersion management for nonlinearity mitigation in two-span 28 GBaud QPSK phase-sensitive amplifier links.

We present an investigation of dispersion map optimization for two-span single-channel 28 GBaud QPSK transmission systems with phase-sensitive amplifiers (PSAs). In experiments, when the PSA link is operated in a highly nonlinear regime, a 1.4 dB error vector magnitude (EVM) improvement is achieved compared to a one-span optimized dispersion map link due to improved nonlinearity mitigation. The two-span optimized dispersion map of a PSA link differs from the optimized dispersion map of a dispersion managed phase-insensitive amplifier (PIA) link. Simulations show that the performance of the two-span dispersion map optimized PSA link does not improve by residual dispersion optimization. Further, by using the two-span optimized dispersion maps repeatedly in a long-haul PSA link instead of one-span optimized maps, the maximum transmission reach can be improved 1.5 times.

Mitigation of nonlinear distortion in hybrid Raman/phase-sensitive amplifier links.

Hybrid systems combining distributed Raman amplification and phase-sensitive amplifiers (PSAs) are investigated in numerical simulations. We focus on the mitigation of fiber nonlinearities and the impact of the span power map which is also important in systems employing optical phase conjugation or phase-conjugated twin waves. We simulate multi-span PSA links with and without distributed Raman amplification and show that by including distributed Raman amplification, the transmission distance increases more at optimum launch power than in the linear regime. For a 5-channel WDM QPSK PSA-amplified system, we observe a transmission reach increase by a factor of 8.1 by including ideal distributed Raman amplification.

Nonlinear phase noise mitigation in phase-sensitive amplified transmission systems.

We investigate the impact of in-line amplifier noise in transmission systems amplified by two-mode phase-sensitive amplifiers (PSAs) and present the first experimental demonstration of nonlinear phase noise (NLPN) mitigation in a modulation format independent PSA-amplified transmission system. The NLPN mitigation capability is attributed to the correlated noise on the signal and idler waves at the input of the transmission span. We study a single-span system with noise loading in the transmitter but the results are expected to be applicable also in multi-span systems. The experimental investigation is supported by numerical simulations showing excellent agreement with the experiments. In addition to demonstrating NLPN mitigation we also present a record high sensitivity receiver, enabled by low-noise PSA-amplification, requiring only 4.1 photons per bit to obtain a bit error ratio (BER) of 1 × 10(-3) with 10 GBd quadrature phase-shift keying (QPSK) data.

Quadrature demultiplexing using a degenerate vector parametric amplifier.

We report on quadrature demultiplexing of a quadrature phase-shift keying (QPSK) signal into two cross-polarized binary phase-shift keying (BPSK) signals with negligible penalty at bit-error rate (BER) equal to 10(-9). The all-optical quadrature demultiplexing is achieved using a degenerate vector parametric amplifier operating in phase-insensitive mode. We also propose and demonstrate the use of a novel and simple phase-locked loop (PLL) scheme based on detecting the envelope of one of the signals after demultiplexing in order to achieve stable quadrature decomposition.

Injection locking-based pump recovery for phase-sensitive amplified links.

An injection locking-based pump recovery system for phase-sensitive amplified links, capable of handling 40 dB effective span loss, is demonstrated. Measurements with 10 GBd DQPSK signals show penalty-free recovery of a pump wave, phase modulated with two sinusoidal RF-tones at 0.1 GHz and 0.3 GHz, with 64 dB amplification. The operating power limit for the pump recovery system is experimentally investigated and is governed by the noise transfer and phase modulation transfer characteristics of the injection-locked laser. The corresponding link penalties are explained and quantified. This system enables, for the first time, WDM compatible phase-sensitive amplified links over significant lengths.