Non-Gaussian statistics of an optical soliton in the presence of amplified spontaneous emission

A study was performed on non-Gaussian statistics of an optical soliton in the presence of amplified spontaneous emission. An approach based on the Fokker-Planck equation was applied to study the optical soliton parameters in the presence of additive noise. The rigorous method not only allowed to reproduce and justify the classical Gordon-Haus formula but also led to new exact results.

Gamma-shaped long-cavity normal-dispersion mode-locked Er-fiber laser for sub-nanosecond high-energy pulsed generation

We propose the design of a novel ?-shaped fiber laser resonator and apply it to build a long-cavity normaldispersion mode-locked Er-fiber laser which features enhanced functionalities for management and optimization of pulsed lasing regimes. We report the generation of sub-nanosecond pulses with the energy of ~0.5 µJ at a kilohertz-scale repetition rate in an all-fiber system based on the new laser design. A combination of special design solutions in the laser, such as polarization instability compensation in the ultra-long arm of the resonator, intra-cavity spectral selection of radiation with a broadband fiber Bragg grating, and polarization selection by means of a tilted refractive index grating, ensures low amplified spontaneous emission (ASE) noise and high stability of the laser system output parameters.

Impact of longitudinal power budget in coherent transmission systems employing digital back-propagation

We report the impact of longitudinal signal power profile on the transmission performance of coherently-detected 112 Gb/s m-ary polarization multiplexed quadrature amplitude modulation system after compensation of deterministic nonlinear fibre impairments. Performance improvements up to 0.6 dB (Q(eff)) are reported for a non-uniform transmission link power profile. Further investigation reveals that the evolution of the transmission performance with power profile management is fully consistent with the parametric amplification of the amplified spontaneous emission by the signal through four-wave mixing. In particular, for a non-dispersion managed system, a single-step increment of 4 dB in the amplifier gain, with respect to a uniform gain profile, at similar to 2/3(rd) of the total reach considerably improves the transmission performance for all the formats studied. In contrary a negative-step profile, emulating a failure (gain decrease or loss increase), significantly degrades the bit-error rate.

Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems

Limitations in the performance of coherent transmission systems employing digital back-propagation due to four-wave mixing impairments are reported for the first time. A significant performance constraint is identified, originating from four-wave mixing between signals and amplified spontaneous emission noise which induces a linear increase in the standard deviation of the received field with signal power, and linear dependence on transmission distance.

Gamma-shaped long-cavity normal-dispersion mode-locked Er-fiber laser for sub-nanosecond high-energy pulsed generation

We propose the design of a novel ?-shaped fiber laser resonator and apply it to build a long-cavity normaldispersion mode-locked Er-fiber laser which features enhanced functionalities for management and optimization of pulsed lasing regimes. We report the generation of sub-nanosecond pulses with the energy of ~0.5 µJ at a kilohertz-scale repetition rate in an all-fiber system based on the new laser design. A combination of special design solutions in the laser, such as polarization instability compensation in the ultra-long arm of the resonator, intra-cavity spectral selection of radiation with a broadband fiber Bragg grating, and polarization selection by means of a tilted refractive index grating, ensures low amplified spontaneous emission (ASE) noise and high stability of the laser system output parameters.

Population lensing vs thermal lensing in Yb:YAG rods and disks

The induced lenses in the Yb:YAG rods and disks end-pumped by a Gaussian beam were analyzed both analytically and numerically. The thermally assisted mechanisms of the lens formation were considered to include: the conventional volume thermal index changes ("dn/dT"), the bulging of end faces, the photoelastic effect, and the bending (for a disk). The heat conduction equations (with an axial heat flux for a disk and a radial heat flux for a rod), and quasi-static thermoelastic equations (in the plane-stress approximation with free boundary conditions) were solved to find the thermal lens power. The population rate equation with saturation (by amplified spontaneous emission or an external wave) was examined to find the electronic lens power in the active elements.

Bit-error probability for direct detection of optical RZ signal degraded by ASE noise and timing jitter

We analyze theoretically the interplay between optical return-to-zero signal degradation due to timing jitter and additive amplified-spontaneous-emission noise. The impact of these two factors on the performance of a square-law direct detection receiver is also investigated. We derive an analytical expression for the bit-error probability and quantitatively determine the conditions when the contributions of the effects of timing jitter and additive noise to the bit error rate can be treated separately. The analysis of patterning effects is also presented. © 2007 IEEE.

Performance enhancement of asymmetric filtered 40 Gb/s carrier suppressed return to zero-differential phase shift keying receiver in a 50 GHz grid

The authors present the impact of asymmetric filtering of strong (e.g. 35 GHz) optical filters on the performance of 42.7 Gb/s 67% (carrier suppressed return to zero)-differential phase shift keying systems. The performance is examined (in an amplified spontaneous emission (ASE) noise-limited regime and in the presence of chromatic dispersion) when offsetting the filter at the receiver by substantial amounts via balanced, constructive and destructive single-ended detections. It is found that with a slight offset (vestigial side band) or an offset of almost half of the modulation frequency (single-side band), there is a significant improvement in the calculated 'Q'. © The Institution of Engineering and Technology 2013.

Impact of longitudinal power budget in coherent transmission systems employing digital back-propagation

We report the impact of longitudinal signal power profile on the transmission performance of coherently-detected 112 Gb/s m-ary polarization multiplexed quadrature amplitude modulation system after compensation of deterministic nonlinear fibre impairments. Performance improvements up to 0.6 dB (Q(eff)) are reported for a non-uniform transmission link power profile. Further investigation reveals that the evolution of the transmission performance with power profile management is fully consistent with the parametric amplification of the amplified spontaneous emission by the signal through four-wave mixing. In particular, for a non-dispersion managed system, a single-step increment of 4 dB in the amplifier gain, with respect to a uniform gain profile, at similar to 2/3(rd) of the total reach considerably improves the transmission performance for all the formats studied. In contrary a negative-step profile, emulating a failure (gain decrease or loss increase), significantly degrades the bit-error rate.

Ultra-long range distributed fibre sensing using virtually transparent propagation

Distributed fibre sensors provide unique capabilities for monitoring large infrastructures with high resolution. Practically, all these sensors are based on some kind of backscattering interaction. A pulsed activating signal is launched on one side of the sensing fibre and the backscattered signal is read as a function of the time of flight of the pulse along the fibre. A key limitation in the measurement range of all these sensors is introduced by fibre attenuation. As the pulse travels along the fibre, the losses in the fibre cause a drop of signal contrast and consequently a growth in the measurement uncertainty. In typical single-mode fibres, attenuation imposes a range limit of less than 30km, for resolutions in the order of 1-2 meters. An interesting improvement in this performance can be considered by using distributed amplification along the fibre [1]. Distributed amplification allows having a more homogeneous signal power along the sensing fibre, which also enables reducing the signal power at the input and therefore avoiding nonlinearities. However, in long structures (≥ 50 km), plain distributed amplification does not perfectly compensate the losses and significant power variations along the fibre are to be expected, leading to inevitable limitations in the measurements. From this perspective, it is simple to understand intuitively that the best possible solution for distributed sensors would be offered by a virtually transparent fibre, i.e. a fibre exhibiting effectively zero attenuation in the spectral region of the pulse. In addition, it can be shown that lossless transmission is the working point that allows the minimization of the amplified spontaneous emission (ASE) noise build-up. © 2011 IEEE.

Optical fibre limits:an approach using ASE channel estimation

In this talk we investigate the usage of spectrally shaped amplified spontaneous emission (ASE) in order to emulate highly dispersed wavelength division multiplexed (WDM) signals in an optical transmission system. Such a technique offers various simplifications to large scale WDM experiments. Not only does it offer a reduction in transmitter complexity, removing the need for multiple source lasers, it potentially reduces the test and measurement complexity by requiring only the centre channel of a WDM system to be measured in order to estimate WDM worst case performance. The use of ASE as a test and measurement tool is well established in optical communication systems and several measurement techniques will be discussed [1, 2]. One of the most prevalent uses of ASE is in the measurement of receiver sensitivity where ASE is introduced in order to degrade the optical signal to noise ratio (OSNR) and measure the resulting bit error rate (BER) at the receiver. From an analytical point of view noise has been used to emulate system performance, the Gaussian Noise model is used as an estimate of highly dispersed signals and has had consider- able interest [3]. The work to be presented here extends the use of ASE by using it as a metric to emulate highly dispersed WDM signals and in the process reduce WDM transmitter complexity and receiver measurement time in a lab environment. Results thus far have indicated [2] that such a transmitter configuration is consistent with an AWGN model for transmission, with modulation format complexity and nonlinearities playing a key role in estimating the performance of systems utilising the ASE channel emulation technique. We conclude this work by investigating techniques capable of characterising the nonlinear and damage limits of optical fibres and the resultant information capacity limits. REFERENCES McCarthy, M. E., N. Mac Suibhne, S. T. Le, P. Harper, and A. D. Ellis, “High spectral efficiency transmission emulation for non-linear transmission performance estimation for high order modulation formats," 2014 European Conference on IEEE Optical Communication (ECOC), 2014. 2. Ellis, A., N. Mac Suibhne, F. Gunning, and S. Sygletos, “Expressions for the nonlinear trans- mission performance of multi-mode optical fiber," Opt. Express, Vol. 21, 22834{22846, 2013. Vacondio, F., O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems," Opt. Express, Vol. 20, 1022-1032, 2012.

Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems

In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dBSNR/dBPower suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error.

Picosecond soliton transmission using concatenated nonlinear optical loop-mirror intensity filters

The issues involved in employing nonlinear optical loop mirrors (NOLMs) as intensity filters in picosecond soliton transmission were examined in detail. It was shown that inserting NOLMs into a periodically amplified transmission line allowed picosecond solitons to be transmitted under conditions considered infeasible until now. The loop mirrors gave dual function, removing low-power background dispersive waves through saturable absorption and applying a negative feedback mechanism to control the amplitude of the solitons. The stochastic characteristics of the pulses that were due to amplifier spontaneous-emission noise were investigated, and a number of new properties were determined. In addition, the mutual interaction between pulses was also significantly different from that observed for longer-duration solitons. The impact of Raman scattering in the computations was included and it was shown that soliton self-frequency shifts may be eliminated by appropriate bandwidth restrictions.

Nonlinear spectral management:linearization of the lossless fiber channel

Using the integrable nonlinear Schrodinger equation (NLSE) as a channel model, we describe the application of nonlinear spectral management for effective mitigation of all nonlinear distortions induced by the fiber Kerr effect. Our approach is a modification and substantial development of the so-called eigenvalue communication idea first presented in A. Hasegawa, T. Nyu, J. Lightwave Technol. 11, 395 (1993). The key feature of the nonlinear Fourier transform (inverse scattering transform) method is that for the NLSE, any input signal can be decomposed into the so-called scattering data (nonlinear spectrum), which evolve in a trivial manner, similar to the evolution of Fourier components in linear equations. We consider here a practically important weakly nonlinear transmission regime and propose a general method of the effective encoding/modulation of the nonlinear spectrum: The machinery of our approach is based on the recursive Fourier-type integration of the input profile and, thus, can be considered for electronic or all-optical implementations. We also present a novel concept of nonlinear spectral pre-compensation, or in other terms, an effective nonlinear spectral pre-equalization. The proposed general technique is then illustrated through particular analytical results available for the transmission of a segment of the orthogonal frequency division multiplexing (OFDM) formatted pattern, and through WDM input based on Gaussian pulses. Finally, the robustness of the method against the amplifier spontaneous emission is demonstrated, and the general numerical complexity of the nonlinear spectrum usage is discussed. © 2013 Optical Society of America.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.