Fokker-Planck equation approach to the description of soliton statistics in optical fiber transmission systems

We derive rigorously the Fokker-Planck equation that governs the statistics of soliton parameters in optical transmission lines in the presence of additive amplifier spontaneous emission. We demonstrate that these statistics are generally non-Gaussian. We present exact marginal probability-density functions for soliton parameters for some cases. A WKB approach is applied to describe the tails of the probability-density functions. © 2005 Optical Society of America.

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.

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.

A lower bound on the per soliton capacity of the nonlinear optical fibre channel

A closed-form expression for a lower bound on the per soliton capacity of the nonlinear optical fibre channel in the presence of (optical) amplifier spontaneous emission (ASE) noise is derived. This bound is based on a non-Gaussian conditional probability density function for the soliton amplitude jitter induced by the ASE noise and is proven to grow logarithmically as the signal-to-noise ratio increases.

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.

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.

Optical and Spin Properties of Defect-Bound Excitons in Semiconductors

Thesis (Ph.D.)--University of Washington, 2016-08

Détection et caractérisation de nouveaux disques circumstellaires autour d’étoiles de faibles masses et naines brunes jeunes.

La présence de disques circumstellaires signale la formation actuelle ou passée de systèmes planétaires, pour lesquels les processus de formation sont encore mal compris. Ce mémoire porte sur la détection et la caractérisation de disques circumstellaires autour d’étoiles de faibles masses (types spectraux > K5) et de naines brunes qui sont candidates ou membres d’associations cinématiques jeunes. Nous présentons ici les résultats de cette recherche ainsi que son implication pour la compréhension des processus de formation et d’évolution des systèmes planétaires. De l’échantillon initial composé de ∼ 1600 objets provenant des relevés BANYAN de Malo et al. ainsi que Gagné et al., dont seulement 600 satisfont nos critères de qualité sur les données, quatre nouveaux candidats de disque ont été découverts en détectant leur excès d’émission infrarouge dans les données d’archive de la mission WISE. Les données du relevé 2MASS ainsi que les spectres synthétiques BT-Settl ont été conjointement utilisés pour modéliser l’émission des étoiles. Les nouveaux candidats, dont les types spectraux sont tardifs (M4.5 à L0) et les masses se situent entre ∼ 13 et 120 M_Jup, ont des températures de disque de ∼ 135–520 K et des luminosités fractionnaires de 0,021–0,15. Pour deux des cibles, nous avons obtenu des spectres dans les longueurs d’onde visibles et infrarouges proches. Ces nouveaux spectres montrent respectivement des signes d’émission en Hα et Paβ, indiquant la présence d’accrétion, et ainsi de gaz, et renforçant l’hypothèse que ces objets sont réellement jeunes. Ces deux objets, vraisemblablement âgés de 40 Ma, pourraient représenter la première détection et caractérisation de disques porteurs de gaz plus vieux que 20 Ma.

Détection et caractérisation de nouveaux disques circumstellaires autour d’étoiles de faibles masses et naines brunes jeunes

La présence de disques circumstellaires signale la formation actuelle ou passée de systèmes planétaires, pour lesquels les processus de formation sont encore mal compris. Ce mémoire porte sur la détection et la caractérisation de disques circumstellaires autour d’étoiles de faibles masses (types spectraux > K5) et de naines brunes qui sont candidates ou membres d’associations cinématiques jeunes. Nous présentons ici les résultats de cette recherche ainsi que son implication pour la compréhension des processus de formation et d’évolution des systèmes planétaires. De l’échantillon initial composé de ∼ 1600 objets provenant des relevés BANYAN de Malo et al. ainsi que Gagné et al., dont seulement 600 satisfont nos critères de qualité sur les données, quatre nouveaux candidats de disque ont été découverts en détectant leur excès d’émission infrarouge dans les données d’archive de la mission WISE. Les données du relevé 2MASS ainsi que les spectres synthétiques BT-Settl ont été conjointement utilisés pour modéliser l’émission des étoiles. Les nouveaux candidats, dont les types spectraux sont tardifs (M4.5 à L0) et les masses se situent entre ∼ 13 et 120 M_Jup, ont des températures de disque de ∼ 135–520 K et des luminosités fractionnaires de 0,021–0,15. Pour deux des cibles, nous avons obtenu des spectres dans les longueurs d’onde visibles et infrarouges proches. Ces nouveaux spectres montrent respectivement des signes d’émission en Hα et Paβ, indiquant la présence d’accrétion, et ainsi de gaz, et renforçant l’hypothèse que ces objets sont réellement jeunes. Ces deux objets, vraisemblablement âgés de 40 Ma, pourraient représenter la première détection et caractérisation de disques porteurs de gaz plus vieux que 20 Ma.

Study on the practical realization of a device able to generate an in-space 3D luminous image

Gli ologrammi sono parte integrante della cultura pop a partire dagli anni 50, tanto che ad oggi sentirne parlare non desta più scalpore. Dal lato pratico, invece, solo negli ultimi anni sono state fatte ricerche approfondite con lo scopo di realizzarli. Fra i dispositivi attualmente in commercio, in pochi sono degni di nota e presentano numerose limitazioni, questo perché è molto difficile riuscire a progettare un sistema che permetta di illuminare dei punti specifici in uno spazio tridimensionale per lunghi periodi. In questa tesi si illustrano i principi di funzionamento ed il progetto per un nuovo dispositivo, diverso da quelli fino ad ora realizzati, che sfrutti il decadimento spontaneo di atomi di rubidio eccitati tramite due fasci laser opportunamente incrociati. Nel punto di incrocio si produce luce visibile a 420 nm. Con un opportuno sistema di specchi che muovono velocemente il punto di intersezione tra i due fasci è possibile realizzare un vero ologramma tridimensionale visibile da quasi ogni angolazione.

Quantification of MgO surface excess on the SnO(2) nanoparticles and relationship with nanostability and growth

In this work, we experimentally showed that the spontaneous segregation of MgO as surface excess in MgO doped SnO(2) nanoparticles plays an important role in the system`s energetics and stability. Using Xray fluorescence in specially treated samples, we quantitatively determined the fraction of MgO forming surface excess when doping SnO(2) with several different concentrations and established a relationship between this amount and the surface energy of the nanoparticles using the Gibbs approach. We concluded that the amount of Mg ions on the surface was directly related to the nanoparticles total free energy, in a sense that the dopant will always spontaneously distribute itself to minimize it if enough diffusion is provided. Because we were dealing with nanosized particles, the effect of MgO on the surface was particularly important and has a direct effect on the equilibrium particle size (nanoparticle stability), such that the lower the surface energy is, the smaller the particle sizes are, evidencing and quantifying the thermodynamic basis of using additives to control SnO(2) nanoparticles stability. (C) 2010 Elsevier B.V. All rights reserved.

Parity violation in Aharonov-Bohm systems: The spontaneous Hall effect

We show how macroscopic manifestations of P (and T) symmetry breaking can arise in a simple system subject to Aharonov-Bohm interactions. Specifically, we study the conductivity of a gas of charged particles moving through a dilute array of flux tubes. The interaction of the electrons with the flux tubes is taken to be of a purely Aharonov-Bohm type. We find that the system exhibits a nonzero transverse conductivity, i.e., a spontaneous Hall effect. This is in contrast to the fact that the cross sections for both scattering and bremsstrahlung (soft-photon emission) of a single electron from a flux tube are invariant under reflections. We argue that the asymmetry in the conductivity coefficients arises from many-body effects. On the other hand, the transverse conductivity has the same dependence on universal constants that appears in the quantum Hall effect, a result that we relate to the validity of the mean-field approximation.