Localized waves in optical systems with periodic dispersion and nonlinearity management

We overview our recent developments in the theory of dispersion-managed (DM) solitons within the context of optical applications. First, we present a class of localized solutions with a period multiple to that of the standard DM soliton in the nonlinear Schrödinger equation with periodic variations of the dispersion. In the framework of a reduced ordinary differential equation-based model, we discuss the key features of these structures, such as a smaller energy compared to traditional DM solitons with the same temporal width. Next, we present new results on dissipative DM solitons, which occur in the context of mode-locked lasers. By means of numerical simulations and a reduced variational model of the complex Ginzburg-Landau equation, we analyze the influence of the different dissipative processes that take place in a laser.

Stabilization of standing waves through time-delay feedback

Standing waves are studied as solutions of a complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms. The onset is described as an instability of the uniform oscillations with respect to spatially periodic perturbations. The solution of the standing wave pattern is given analytically and studied through simulations. © 2013 American Physical Society.

Nonlinear Waves: An Introduction

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, we propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks), existence and uniqueness results, etc. The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding -shocks are also considered. As it concerns numerical methods we apply the CNN approach. The book is addressed to a broader audience including graduate students, Ph.D. students, mathematicians, physicist, engineers and specialists in the domain of PDE.

Phase noise tolerance study in coherent optical circular QAM transmissions with Viterbi- Viterbi carrier phase estimation

We present a performance evaluation of a non-conventional approach to implement phase noise tolerant optical systems with multilevel modulation formats. The performance of normalized Viterbi-Viterbi carrier phase estimation (V-V CPE) is investigated in detail for circular m-level quadrature amplitude modulation (C-mQAM) signals. The intrinsic property of C-mQAM constellation points with a uniform phase separation allows a straightforward employment of V-V CPE without the need to adapt constellation. Compared with conventional feed-forward CPE for square QAM signals, the simulated results show an enhanced tolerance of linewidth symbol duration product (ΔvTs) at a low sensitivity penalty by using feed-forward CPE structure with C-mQAM. This scheme can be easily upgraded to higher order modulations without inducing considerable complexity.

Multi-band carrier-less amplitude and phase modulation for bandlimited visible light communications systems

Visible light communications is a technology with enormous potential for a wide range of applications within next generation transmission and broadcasting technologies. VLC offers simultaneous illumination and data communications by intensity modulating the optical power emitted by LEDs operating in the visible range of the electromagnetic spectrum (~370-780 nm). The major challenge in VLC systems to date has been in improving transmission speeds, considering the low bandwidths available with commercial LED devices. Thus, to improve the spectral usage, the research community has increasingly turned to advanced modulation formats such as orthogonal frequency-division multiplexing. In this article we introduce a new modulation scheme into the VLC domain; multiband carrier-less amplitude and phase modulation (m-CAP) and describe in detail its performance within the context of bandlimited systems.

Simultaneous multichannel carrier-suppressed return-to-zero to non-return-to-zero format conversion using a fiber Bragg grating

A novel multichannel carrier-suppressed return-to-zero (CSRZ) to non-return-to-zero (NRZ) format conversion scheme based on a single custom-designed fiber Bragg grating (FBG) with comb spectra is proposed. The spectral response of each channel is designed according to the algebraic difference between the CSRZ and NRZ spectra outlines. The tailored group delays are introduced to minimize the maximum refractive index modulation. Numerical results show that four-channel 200-GHz-spaced CSRZ signals at 40 Gbits/s can be converted into NRZ signals with high Q-factor and wide-range robustness. It is shown that our proposed FBG is robust to deviations of bandwidth and central wavelength detuning. Another important merit of this scheme is that the pattern effects are efficiently reduced owing to the well-designed spectra response.

Global Waves with Non-Positive Energy in General Relativity

2000 Mathematics Subject Classification: 35Lxx, 35Pxx, 81Uxx, 83Cxx.

Mitigation of EEPN in long-haul n-PSK coherent transmission system using modified optical pilot carrier

We present the compensation of the equalization enhanced phase noise (EEPN) in the long-haul n-level phase shift keying (n-PSK) coherent optical transmission system, by employing a scheme of phase modulated optical pilot carrier. © OSA 2013.

Effect of spatial inhomogeneity of charge carrier mobility on current-voltage characteristics in organic field-effect transistors

A semi-quantitative model is put forward elucidating the role of spatial inhomogeneity of charge carrier mobility in organic field-effect transistors. The model, based on electrostatic arguments, allows estimating the effective thickness of the conducting channel and its changes in function of source-drain and gate voltages. Local mobility gradients in the direction perpendicular to the insulator/semiconductor interface translate into voltage dependences of the average carrier mobility in the channel, resulting in positive or negative deviations of current-voltage characteristics from their expected shapes. The proposed effect supplements those described in the literature, i.e., density-dependent mobility of charge carriers, short-channel effects, and contribution of contact resistance.

Impact of the carrier relaxation paths on two-state operation in quantum dot lasers

We study InGaAs QD laser operating simultaneously at ground (GS) and excited (ES) states under 30ns pulsed-pumping and distinguish three regimes of operation depending on the pump current and the carrier relaxation pathways. An increased current leads to an increase in ES intensity and to a decrease in GS intensity (or saturation) for low pump range, as typical for the cascade-like pathway. Both the GS and ES intensities are steadily increased for high current ranges, which prove the dominance of the direct capture pathway. The relaxation oscillations are not pronounced for these ranges. For the mediate currents, the interplay between the both pathways leads to the damped large amplitude relaxation oscillations with significant deviation of the relaxation oscillation frequency from the initial value during the pulse.

Analysis of carrier phase extraction methods in 112-Gbit/s NRZ-PDM-QPSK coherent transmission system

We present a comparative analysis on three carrier phase extraction approaches, including a one-tap normalized least mean square method, a block-average method, and a Viterbi-Viterbi method, in coherent transmission system considering equalization enhanced phase noise. © OSA 2012.

Practical and cost-effective high-fidelity optical carrier dissemination using coherent communication techniques

We report a unidirectional frequency dissemination scheme for high-fidelity optical carriers deployable over telecommunication networks. For the first time, a 10 Gb/s Binary Phase Shift Keying (BPSK) signal from an ultra-narrow linewidth laser was transmitted through a field-installed optical fibre with round-trip length of 124 km between Cork City and town of Clonakilty, without inline optical amplification. At the receiver, using coherent communication techniques and optical injection-locking the carrier was recovered with noise suppression. The beat signal between the original carrier at the transmitter and recovered carrier at the receiver shows a linewidth of 2.8 kHz. Long term stability measurements revealed fractional instabilities (True Allan deviation) of 3.3 × 10-14 for 1 s averaging time, prior to phase noise cancellation.

Optical rogue waves in telecommunication data streams

Large broadening of short optical pulses due to fiber dispersion leads to a strong overlap in information data streams resulting in statistical deviations of the local power from its average. We present a theoretical analysis of rare events of high-intensity fluctuations-optical freak waves-that occur in fiber communication links using bit-overlapping transmission. Although the nature of the large fluctuations examined here is completely linear, as compared to commonly studied freak waves generated by nonlinear effects, the considered deviations inherit from rogue waves the key features of practical interest-random appearance of localized high-intensity pulses. We use the term "rogue wave" in an unusual context mostly to attract attention to both the possibility of purely linear statistical generation of huge amplitude waves and to the fact that in optics the occurrence of such pulses might be observable even with the standard Gaussian or even rarer-than-Gaussian statistics, without imposing the condition of an increased probability of extreme value events. © 2011 American Physical Society.

Reply to "comment on 'Optical rogue waves in telecommunication data streams'"

We feel that the main claim made in the abstract of the preceding Comment is wrong. Using results obtained in our paper, we prove that rogue waves with amplitudes much larger than the average level can be observed during a short period of time in purely linear propagation regimes in optical fiber systems. © 2011 American Physical Society.