Fault-tolerant four-dimensional constellation for coherent optical transmission systems.

We propose a 4-dimensional 2-ary amplitude ring-switched modulation format with 64 symbols, which is denoted as 4D-2A-RS64 encoded over two polarization tributaries to improve the transmission performance over long-haul optical fibers in the presence of the non-linear Kerr effect. At a spectral efficiency of 6 bits per 4D, simulation results show that this format outperforms the polarization division multiplexed (PDM) 8QAM-star modulation as well as the 4D-2A-8PSK over links without inline dispersion management. We evaluate the performance for a WDM transmission of 11 × 90~Gbaud channels over a multi-span SSMF link. For an achievable information rate of 4.8bit/s/Hz, the maximum transmission distance is improved by 10.6% (400 km) and 4% (160 km) compared to PDM-8QAM-star and 4D-2A-8PSK respectively. The achieved gains are composed of a linear part and a non-linear part, respectively from the improved Euclidean-distance distribution and the constant power property of the 4D modulation. The geometric shaping of the proposed scheme is easy to implement and is robust to Mach-Zehnder modulator (MZM) imbalances and quantization errors stemming from the finite digital-to-analog converter (DAC) resolution. This robustness is compared to the one of other geometric-shaped non-linearity tolerant 4D schemes such as the 4D-2A-8PSK and the 4D-64PRS that can be both outperformed by our scheme in severe conditions.

Experimental realization of Fermi-Pasta-Ulam-Tsingou recurrence in a long-haul optical fiber transmission system.

The integrable nonlinear Schrödinger equation (NLSE) is a fundamental model of nonlinear science which also has important consequences in engineering. The powerful framework of the periodic inverse scattering transform (IST) provides a description of the nonlinear phenomena modulational instability and Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in terms of exact solutions. It associates the complex nonlinear dynamics with invariant nonlinear spectral degrees of freedom that may be used to encode information. While optical fiber is an ideal testing ground of its predictions, maintaining integrability over sufficiently long distances to observe recurrence, as well as synthesizing and measuring the field in both amplitude and phase on the picosecond timescales of typical experiments is challenging. Here we report on the experimental realization of FPUT recurrence in terms of an exact space-time-periodic solution of the integrable NLSE in a testbed for optical communication experiments. The complex-valued initial condition is constructed by means of the finite-gap integration method, modulated onto the optical carrier driven by an arbitrary waveform generator and launched into a recirculating fiber loop with periodic amplification. The measurement with an intradyne coherent receiver after a predetermined number of revolutions provides a non-invasive full-field characterization of the space-time dynamics. The recurrent space-time evolution is in close agreement with theoretical predictions over a distance of 9000 km. Nonlinear spectral analysis reveals an invariant nonlinear spectrum. The space-time scale exceeds that of previous experiments on FPUT recurrence in fiber by three orders of magnitude.

Polarization-division multiplexing based on the nonlinear Fourier transform.

Polarization-division multiplexed (PDM) transmission based on the nonlinear Fourier transform (NFT) is proposed for optical fiber communication. The NFT algorithms are generalized from the scalar nonlinear Schrödinger equation for one polarization to the Manakov system for two polarizations. The transmission performance of the PDM nonlinear frequency-division multiplexing (NFDM) and PDM orthogonal frequency-division multiplexing (OFDM) are determined. It is shown that the transmission performance in terms of Q-factor is approximately the same in PDM-NFDM and single polarization NFDM at twice the data rate and that the polarization-mode dispersion does not seriously degrade system performance. Compared with PDM-OFDM, PDM-NFDM achieves a Q-factor gain of 6.4 dB. The theory can be generalized to multi-mode fibers in the strong coupling regime, paving the way for the application of the NFT to address the nonlinear effects in space-division multiplexing.

Arbitrary-shaped Brillouin microwave photonic filter by manipulating a directly modulated pump.

We present a cost-effective gigahertz-wide arbitrary-shaped microwave photonic filter based on stimulated Brillouin scattering in fiber using a directly modulated laser (DML). After analyzing the relationship between the spectral power density and the modulation current of the DML, we manage to precisely adjust the optical spectrum of the DML, thereby controlling the Brillouin filter response arbitrarily for the first time, to the best of our knowledge. The filter performance is evaluated by amplifying a 500 Mb/s non-return-to-zero on-off keying signal using a 1 GHz rectangular filter. The comparison between the proposed DML approach and the previous approach adopting a complex IQ modulator shows similar filter flexibility, shape fidelity, and noise performance, proving that the DML-based Brillouin filter technique is a cost-effective and valid solution for microwave photonic applications.

Software-defined microwave photonic filter with high reconfigurable resolution.

Microwave photonic filters (MPFs) are of great interest in radio frequency systems since they provide prominent flexibility on microwave signal processing. Although filter reconfigurability and tunability have been demonstrated repeatedly, it is still difficult to control the filter shape with very high precision. Thus the MPF application is basically limited to signal selection. Here we present a polarization-insensitive single-passband arbitrary-shaped MPF with ~GHz bandwidth based on stimulated Brillouin scattering (SBS) in optical fibre. For the first time the filter shape, bandwidth and central frequency can all be precisely defined by software with ~MHz resolution. The unprecedented multi-dimensional filter flexibility offers new possibilities to process microwave signals directly in optical domain with high precision thus enhancing the MPF functionality. Nanosecond pulse shaping by implementing precisely defined filters is demonstrated to prove the filter superiority and practicability.

Ultra-selective flexible add and drop multiplexer using rectangular optical filters based on stimulated Brillouin scattering.

We demonstrate an ultra-selective flexible reconfigurable add and drop multiplexer (ROADM) structure enablingseparation and aggregation operations for multi-band orthogonal frequency division multiplexing(MB-OFDM) signal with ~2-GHz spectral granularity and 300-MHz guard band. The ROADM employs rectangular optical filters based on stimulated Brillouin effect (SBS) in fiber, which have steepedges, ~1-dB passband ripple and tunable bandwidth from 100 MHz to 3 GHz realized by two different kinds of electrical feedback pump control approaches. The ROADM performance is measured with MB-OFDM signals inquadrature-phase-shift-keying (QPSK) and 16-quadrature-amplitude-modulation (16-QAM) formats. For QPSK format signal, the SBS-ROADM induced penalty is ~0.7 dB while the performance for 16-QAM format is also acceptable.

Bandwidth-tunable narrowband rectangular optical filter based on stimulated Brillouin scattering in optical fiber.

We propose a rectangular optical filter based on stimulated Brillouin scattering (SBS) in optical fiber with bandwidth tuning from 50 MHz to 4 GHz at less than 15-MHz resolution. The rectangular shape of the filter is precisely achieved utilizing digital feedback control of the comb-like pump spectral lines. The passband ripple is suppressed to ~1 dB by mitigating the nonlinearity influences of the comb-like pump lines generated in electrical and optical components and fibers. Moreover a fiber with a single Brillouin peak is employed to further reduce the in-band ripple and the out-of-band SBS gain at the same time. Finally, we analyze the noise performance of the filter at different bandwidth cases and demonstrate the system performance of the proposed filter with 2.1-GHz bandwidth and 19-dB gain by amplifying a 2-GHz orthogonal frequency-division-multiplexing (OFDM) signal with quadrature-phase-shift-keying (QPSK) and 16-quadrature-amplitude-modulation (16-QAM) on each subscriber.

1 kW peak power, 110 ns single-frequency thulium doped fiber amplifier at 2050 nm.

We report a high power, single frequency, linearly polarized master oscillator power amplifier emitting 110 ns, 1 kW peak power pulses at 2050 nm. A 20% slope efficiency and a beam quality of M2=1.21 are achieved with three-stage double-clad Tm(3+)-doped fiber architecture. Various pump schemes are compared leading to the conclusion that 793 nm pump wavelength is the most efficient for amplification at 2050 nm. Based on numerical simulations, the Brillouin gain coefficient around 2 µm in Tm(3+) highly doped silica fiber is estimated to 1.2×10(-11) m/W. Output peak power is limited by stimulated Brillouin scattering to 535 W without mitigation and to 1 kW with application of a strain distribution along the doped fiber.

Polarization-time coding for PDL mitigation in long-haul PolMux OFDM systems.

In this paper, we present a numerical, theoretical and experimental study on the mitigation of Polarization Dependent Loss (PDL) with Polarization-Time (PT) codes in long-haul coherent optical fiber transmissions using Orthogonal Frequency Division Multiplexing (OFDM). First, we review the scheme of a polarization-multiplexed (PolMux) optical transmission and the 2 × 2 MIMO model of the optical channel with PDL. Second, we introduce the Space-Time (ST) codes originally designed for wireless Rayleigh fading channels, and evaluate their performance, as PT codes, in mitigating PDL through numerical simulations. The obtained behaviors and coding gains are different from those observed on the wireless channel. In particular, the Silver code performs better than the Golden code and the coding gains offered by PT codes and forward-error-correction (FEC) codes aggregate. We investigate the numerical results through a theoretical analysis based on the computation of an upper bound of the error probability of the optical channel with PDL. The derived upper bound yields a design criterion for optimal PDL-mitigating codes. Furthermore, a transmission experiment of PDL-mitigation in a 1,000 km optical fiber link with inline PDL validates the numerical and theoretical findings. The results are shown in terms of Q-factor distributions. The mean Q-factor is improved with PT coding and the variance is also narrowed.

Nonsinusoidal phase modulations for high-power laser performance control: stimulated Brillouin scattering and FM-to-AM conversion.

High-power lasers, such as the Laser MegaJoule (LMJ), have to be phase modulated to avoid stimulated Brillouin scattering (SBS) that may strongly damage optics at the end of the laser chain. Current spectral broadening on LMJ is performed with a sinusoidal phase modulation. This pure sinusoidal phase modulation leads to inhomogeneous spectral power densities (SPD). Thus, for a same SBS power threshold, the sinusoidal phase-modulated spectrum has to be larger than the equivalent ideal SPD with isoenergetic peaks. We present in this paper a technique to generate energy-balanced Dirac peaks spectra thanks to nonsinusoidal phase modulations. Thus, we can build a narrower spectrum with a nonsinusoidal phase modulation that has the same SBS threshold as a sinusoidal phase modulation, and we show that FM-to-AM conversion can be strongly reduced, which is of great interest for LMJ laser performance, with reductions up to 40%.

Microbending behavior of large-effective-area Bragg fibers.

We use a phase-sensitive optical low-coherence interferometry technique and camera imaging to identify microbend-induced mode couplings in Bragg fibers. Results show the importance of the quality of fabrication of Bragg fibers on their modal content when they are subject to microbends. Design strategies to improve the microbending robustness are identified.

Self-referenced and single-ended method to measure Brillouin gain in monomode optical fibers.

We present a new self-referenced and single-ended method to measure the Brillouin-gain coefficient in monomode optical fibers accurately with high reliability. Our comparative measurements on several different fibers show that a fiber with a smaller optical effective mode area can nevertheless have a higher Brillouin threshold, thus confirming the significance of acousto-optic effective mode area.

FM-to-AM conversion in high-power lasers.

FM-to-AM conversion is an important issue that could prevent fusion ignition with high-power lasers, such as the Laser MegaJoule (LMJ). We first overview the whole problem of FM-to-AM conversion in high-power lasers and we explain why AM spectral content of FM-to-AM conversion is important, although this information was not used in previous studies. We then propose simple analytical models to simulate FM-to-AM conversion in the LMJ frequency conversion system. We succeed in isolating every cause of spectrum distortion and give, for each of them, FM-to-AM predictions that are in very good agreement with simulations of a complex propagation code. Finally, we show how the last grating filters most of the FM-to-AM conversion. We conclude that the FM-to-AM conversion distortion criterion will be, on LMJ, below 40% in the last optics and 10% on the target.

Simultaneous demodulation and slow light of differential phase-shift keying signals using stimulated-Brillouin-scattering-based optical filtering in fiber.

For the first time to our knowledge, we demonstrate simultaneous demodulation and slow-light delay of differential phase-shift keying (DPSK) signals at flexible bit rates using the stimulated-Brillouin-scattering-based optical filtering effect in optical fiber. Both 10 and 2.5 Gbit/s DPSK signals have been demodulated and delayed with excellent performances. In the case of the 10 Gbit/s DPSK signal, after demodulation the tunable delay range with error-free operation is about 50 ps, which we believe is the best result obtained for 10 Gbit/s slow-light demonstrations. For the 2.5 Gbit/s DPSK signal, the optimal sensitivity after demodulation is -36.5 dBm, which is comparable with the back-to-back sensitivity of a 2.5 Gbit/s nonreturn-to-zero signal.

Optical low-coherence reflectometry for complete chromatic dispersion characterization of few-mode fibers.

A phase-sensitive optical low-coherence reflectometry (OLCR) technique is demonstrated to simultaneously measure the absolute chromatic dispersion values of each guided LP mode of a few-mode fiber. We show that the OLCR technique requires only short samples of fiber (<1 m) and has no need for high-ratio mode converters to reach an accurate wavelength-dependent group delay evolution of every mode. As an example we present for the first time to our knowledge a direct and complete analysis of few-mode fibers with high, low, positive, and negative modal dispersion values, leading to chromatic dispersion parameters in good agreement with theoretical predictions.

Full characterization of modern transmission fibers for Raman amplified-based communication systems.

Telecommunication carriers have to estimate the Raman parameters of the fibers installed on their optical transport networks in order to facilitate the design of the next generation of high bit-rate Raman amplified-based transmission systems. This paper reports a very complete characterization of the most popular modern transmission fibers in terms of Raman efficiency, noise figure and double Rayleigh backscattering crosstalk. Our experiment is based on an averaged power analysis, applied to a counter-pumped long-haul distributed fiber Raman amplifier. We evaluate as well at 40 Gb/s for these different fiber types the double Rayleigh backscattering impact in terms of Q-factor penalty for various Raman gains and RZ modulation formats with different duty cycles.

Improved slow-light performance of 10 Gb/s NRZ, PSBT and DPSK signals in fiber broadband SBS.

We have demonstrated error-free operations of slow-light via stimulated Brillouin scattering (SBS) in optical fiber for 10-Gb/s signals with different modulation formats, including non-return-to-zero (NRZ), phase-shaped binary transmission (PSBT) and differential phase-shiftkeying (DPSK). The SBS gain bandwidth is broadened by using current noise modulation of the pump laser diode. The gain shape is simply controlled by the noise density function. Super-Gaussian noise modulation of the Brillouin pump allows a flat-top and sharp-edge SBS gain spectrum, which can reduce slow-light induced distortion in case of 10-Gb/s NRZ signal. The corresponding maximal delay-time with error-free operation is 35 ps. Then we propose the PSBT format to minimize distortions resulting from SBS filtering effect and dispersion accompanied with slow light because of its high spectral efficiency and strong dispersion tolerance. The sensitivity of the 10-Gb/s PSBT signal is 5.2 dB better than the NRZ case with a same 35-ps delay. The maximal delay of 51 ps with error-free operation has been achieved. Futhermore, the DPSK format is directly demodulated through a Gaussian-shaped SBS gain, which is achieved using Gaussian-noise modulation of the Brillouin pump. The maximal error-free time delay after demodulation of a 10-Gb/s DPSK signal is as high as 81.5 ps, which is the best demonstrated result for 10-Gb/s slow-light.

Evidence of thermal effects in a high-power Er3+-Yb3+ fiber laser.

We analyze the influence of heat generation caused by nonradiative transitions in a high-power 1.55 microm double-clad erbium-ytterbium fiber laser on the Stark level population. At strong pumping rates, 1 microm lasing can start as a result of parasitic reflections. We present a model that allows us to simulate the effect of self-generated heat on the Stark level population by using the MacCumber relation. Heat generation plays a significant role and improves the 1.5 microm laser's efficiency by increasing the 1 microm lasing threshold.

Phase-sensitive optical low-coherence reflectometry technique applied to the characterization of photonic crystal fiber properties.

Localized measurements of group-velocity dispersion and birefringence of photonic crystal fibers are achieved with a phase-sensitive optical low-coherence reflectometry technique. This technique is efficient for fiber samples no longer than 1 m. Theoretical simulations are in good agreement with experimental results. As a result, the stress-induced birefringence proves to be at most 1 order of magnitude below the geometrical-shape birefringence.

Double-clad 10-W Yb3+-doped fiber master oscillator power fiber amplifier for He3+ optical pumping.

We describe an all-fiber ytterbium-doped laser followed by a double-stage ytterbium-doped double-clad fiber amplifier of 10-W output power for helium pumping. Different cavity designs are investigated with the goal of achieving high-power multimode emission at 1083 nm, wavelength tunability over the helium absorption bands, and linewidth envelope control over the range 1-3 GHz. We point out the domains with unstable output power and discuss their origin.