Topological signature of deterministic chaos in short nonstationary signals from an optical parametric oscillator

Although deterministic chaos has been predicted to occur in the triply resonant optical parametric oscillator (TROPO) fifteen years ago, experimental evidence of chaotic behavior in this system has been lacking so far, in marked contrast with most nonlinear systems, where chaos has been actively tracked and found. This situation is probably linked to the high sensitivity of the TROPO to perturbations, which adversely affects stationary operation at high power. We report the experimental observation in this system of a burst of irregular behavior of duration 80 microseconds. Although the system is highly nonstationary over this time interval, a topological analysis allows us to extract a clearcut signature of deterministic chaos from a time series segment of only 9 base cycles (3 microseconds). This result suggests that nonstationarity is not necessarily an obstacle to the characterization of chaos

Multi-soliton interactions underlying the dynamics of breather rogue waves

We consider the most famous one-breather solutions of the focusing one-dimensional nonlinear Schrodinger equation which are used in the theory of rogue waves -- the Peregrine, Akhmediev and Kuznetsov-Ma breathers, as well as the general case of drifting Tajiri-Watanabe breather. In terms of the inverse scattering transform (IST) theory, it is known that these breathers are constructed by "dressing" a plane wave solution with a single soliton. In this construction, we replace the plane wave with an exact $N$-soliton solution which converges asymptotically to the plane wave at large number of solitons $N$. As a result, we obtain exact $(N+1)$-soliton solutions practically indistinguishable from the Peregrine, Akhmediev, Kuznetsov-Ma and Tajiri-Watanabe breathers in a relatively wide region of space and time. The constructed solutions are localized in space with characteristic width proportional to $N$ and approximate the breathers with accuracy improving as $N$ grows. Our method makes it possible to build solitonic models with the same dynamical properties for the higher-order rational and super-regular breathers, and can be generalized straightforwardly to multi-breather solutions, breathers on a nontrivial background (e.g., cnoidal waves) and other integrable systems.Comment: 16 pages, 9 figure

Statistics of extreme events in integrable turbulence

We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schr\"odinger equation (fNLSE). This is done by invoking a stochastic interpretation of the inverse scattering transform for fNLSE and analytically evaluating the kurtosis of the emerging random nonlinear wave field in terms of the spectral density of states of the corresponding soliton gas. We then apply the general result to two fundamental scenarios of the generation of integrable turbulence: (i) the asymptotic development of the spontaneous (noise induced) modulational instability of a plane wave, and (ii) the long-time evolution of strongly nonlinear, partially coherent waves. In both cases, involving the bound state soliton gas dynamics, the analytically obtained values of the kurtosis are in perfect agreement with those inferred from direct numerical simulations of the the fNLSE, providing the long-awaited theoretical explanation of the respective rogue wave statistics. Additionally, the evolution of a particular non-bound state gas is considered providing important insights related to the validity of the so-called virial theorem.Comment: 11 pages, 5 figure

Cooperative oscillation of non-degenerate transverse modes in an optical system: multimode operation in parametric oscillators

We show experimentally that parametric interaction can induce a cooperative oscillation of non simultaneously resonant transverse modes in an optical parametric oscillator. More generally, this effect is expected to occur in any spatially extended system subjected to boundary conditions where nonlinear wave mixing of two nonresonant spatial modes can generate a resonant oscillation

British Torture in the 'War on Terror'

Despite longstanding allegations of UK involvement in prisoner abuse during counterterrorism operations as part of the US-led ‘war on terror’, a consistent narrative emanating from British government officials is that Britain neither uses, condones nor facilitates torture or other cruel, inhuman, degrading treatment and punishment. We argue that such denials are untenable. We have established beyond reasonable doubt that Britain has been deeply involved in post-9/11 prisoner abuse, and we can now provide the most detailed account to date of the depth of this involvement. We argue that it is possible to identify a peculiarly British approach to torture in the ‘war on terror’, which is particularly well-suited to sustaining a narrative of denial. To explain the nature of UK involvement, we argue that it can be best understood within the context of how law and sovereign power have come to operate during the ‘war on terror’. We turn here to the work of Judith Butler, and explore the role of Britain as a ‘petty sovereign’, operating under the state of exception established by the US Executive. UK authorities have not themselves suspended the rule of law so overtly, and indeed have repeatedly insisted on their commitment to it. They have nevertheless been able to construct a rhetorical, legal and policy ‘scaffold’ that has enabled them to demonstrate at least procedural adherence to human rights norms, while at the same time allowing UK officials to acquiesce in the arbitrary exercise of sovereignty over individuals who are denied any access to appropriate representation or redress in compliance with the rule of law

'The Germans are Hydrophobes': Germany and the Germans in the Shaping of French Identity

This article addresses issues of national identity and nationalism in the age of the French Revolution by looking at French attitudes towards the Germans. It engages with theories of nationalism while presenting empirical evidence gleaned from archival research. This material, sometimes grimly, sometimes rather amusingly, reveals much about French ideas and prejudices about the Germans and how it reflected back on the revolutionary and Napoleonic sense of what it meant to be French

Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers

Formation of coherent structures and patterns from unstable uniform state or noise is a fundamental physical phenomenon that occurs in various areas of science ranging from biology to astrophysics. Understanding of the underlying mechanisms of such processes can both improve our general interdisciplinary knowledge about complex nonlinear systems and lead to new practical engineering techniques. Modern optics with its high precision measurements offers excellent test-beds for studying complex nonlinear dynamics, though capturing transient rapid formation of optical solitons is technically challenging. Here we unveil the build-up of dissipative soliton in mode-locked fibre lasers using dispersive Fourier transform to measure spectral dynamics and employing autocorrelation analysis to investigate temporal evolution. Numerical simulations corroborate experimental observations, and indicate an underlying universality in the pulse formation. Statistical analysis identifies correlations and dependencies during the build-up phase. Our study may open up possibilities for real-time observation of various nonlinear structures in photonic systems

Analysis of laser radiation using the Nonlinear Fourier transform

Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions