Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in ...studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose-Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics.
Abstract
Understanding dynamical complexity is one of the most important challenges in science. Significant progress has recently been made in optics through the study of dissipative soliton laser ...systems, where dynamics are governed by a complex balance between nonlinearity, dispersion, and energy exchange. A particularly complex regime of such systems is associated with noise-like pulse multiscale instabilities, where sub-picosecond pulses with random characteristics evolve chaotically underneath a much longer envelope. However, although observed for decades in experiments, the physics of this regime remains poorly understood, especially for highly-nonlinear cavities generating broadband spectra. Here, we address this question directly with a combined numerical and experimental study that reveals the physical origin of instability as nonlinear soliton dynamics and supercontinuum turbulence. Real-time characterisation reveals intracavity extreme events satisfying statistical rogue wave criteria, and both real-time and time-averaged measurements are in quantitative agreement with modelling.
With the advent of quantum key distribution (QKD) systems, perfect (i.e., information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar ...protocols use classical error-correcting codes for both error correction (for the honest parties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model that corresponds to such a setting is the wire tap channel introduced by Wyner in 1975. In this correspondence, we study fundamental limits and coding methods for wire tap channels. We provide an alternative view of the proof for secrecy capacity of wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide security at rates below secrecy capacity. For the special case of a noiseless main channel and binary erasure channel, we consider encoder and decoder design for codes achieving secrecy on the wiretap channel; we show that it is possible to construct linear-time decodable secrecy codes based on low-density parity-check (LDPC) codes that achieve secrecy.
Dissipative solitons are remarkably localized states of a physical system that arise from the dynamical balance between nonlinearity, dispersion and environmental energy exchange. They are the most ...universal form of soliton that can exist, and are seen in far-from-equilibrium systems in many fields, including chemistry, biology and physics. There has been particular interest in studying their properties in mode-locked lasers, but experiments have been limited by the inability to track the dynamical soliton evolution in real time. Here, we use simultaneous dispersive Fourier transform and time-lens measurements to completely characterize the spectral and temporal evolution of ultrashort dissipative solitons as their dynamics pass through a transient unstable regime with complex break-up and collisions before stabilization. Further insight is obtained from reconstruction of the soliton amplitude and phase and calculation of the corresponding complex-valued eigenvalue spectrum. These findings show how real-time measurements provide new insights into ultrafast transient dynamics in optics.
Colloidal quantum dots (CQDs) have drawn strong interest in the past for their high prospects in scientific, medical, and industrial applications. However, the full characterization of these quantum ...emitters is currently restricted to the visible wavelengths, and it remains a key challenge to optically probe single CQDs operating in the infrared spectral domain, which is targeted by a growing number of applications. Here, we report the first experimental detection and imaging at room temperature of single infrared CQDs operating at telecommunication wavelengths. Imaging was done with a doubly resonant bowtie nanoaperture antenna (BNA) written at the end of a fiber nanoprobe, whose resonances spectrally fit the CQD absorption and emission wavelengths. Direct near-field characterization of PbS CQDs reveal individual nanocrystals with a spatial resolution of 75 nm (λ/20) together with their intrinsic 2D dipolar free-space emission properties and exciton dynamics (blinking phenomenon). Because the doubly resonant BNA is strongly transmissive at both the CQD absorption and the emission wavelengths, we are able to perform all-fiber nanoimaging with a standard 20% efficiency InGaAs avalanche photodiode (APD). The detection efficiency is predicted to be 3000 fold larger than with a conventional circular aperture tip of the same transmission area. Double resonance BNA fiber probes thus offer the possibility of exploring extreme light–matter interaction in low band gap CQDs with current plug-and-play detection techniques, opening up new avenues in the fields of infrared light-emitting devices, photodetectors, telecommunications, bioimaging, and quantum information technology.
We report on a theoretical study and experimental characterization of coherent-population-trapping (CPT) resonances in buffer-gas-filled vapor cells with push-pull optical pumping (PPOP) on Cs D1 ...line. We point out that the push-pull interaction scheme is identical to the so-called lin ⊥ lin polarization scheme. Expressions of the relevant dark states, as well as of absorption, are reported. The experimental setup is based on the combination of a distributed feedback diode laser, a pigtailed intensity Mach-Zehnder electro-optic modulator (MZ EOM) for optical sideband generation and a Michelson-like interferometer. A microwave technique to stabilize the transfer function operating point of theMZ EOM is implemented for proper operation. A CPT resonance contrast as high as 78% is reported in a cm-scale cell for the magnetic-field-insensitive clock transition. The impact of the laser intensity on the CPT-clock signal key parameters (linewidth, contrast, linewidth/contrast ratio) is reported for three different cells with various dimensions and buffer-gas contents. The potential of the PPOP technique for the development of high-performance atomic vapor-cell clocks is discussed.
During the last 4 years, chaotic waveforms for random number generation found a deep interest within the community of analogue broadband chaotic optical systems. Earlier investigations on chaos-based ...RNG were proposed in the 90s and early 2000, however mainly based on piecewise linear (PL) 1D map, with bit rate determined by analog electronic processing capabilities to provide the PL nonlinear function of concern. Optical chaos came with promises for much higher bit rate, and entropy sources based on high complexity (high dimensional) continuous time (differential) dynamics. More specifically in 2009, Reidler published a paper entitled "An optical ultrafast random bit generator", in which they presented a physical system for a random number generator based on a chaotic semiconductor laser. This generator is claimed to reach potentially the extremely high rate of 300 Gb/s. We report on analysis and experiments of their method, which leads to the discussion about the actual origin of the obtained randomness. Through standard signal theory arguments, we show that the actual binary randomness quality obtained from this method, can be interpreted as a complex mixing operated on the initial analogue entropy source. Our analysis suggests an explanation about the already reported issue that this method does not necessarily require any specific deterministic property (i.e., chaos) from the physical signal used as the source of entropy. The bit stream randomness quality is found to result from "aliasing" phenomena performed by the post-processing method, both for the sampling and the quantization operations. As an illustration, such random bit sequences extracted from different entropy sources are investigated. Optoelectronic noise is used as a non deterministic entropy source. Electro-optic phase chaotic signal, as well as simulations of its deterministic model, are used as deterministic entropy sources. In all cases, the extracted bit sequence reveals excellent randomness.
The Eckhaus instability is a secondary instability of nonlinearspatiotemporal patterns in which high-wave-number periodicsolutions become unstable against small-wave-number perturbations.Here we show ...that this instability can take place in Kerr combscorresponding to subcritical Turing patterns upon changes in thelaser detuning. The development of the Eckhaus instability leads tothe cracking of patterns and a long-lived transient where the peaksof the pattern rearrange in space due to spatial interactions. Inthe spectral domain, this results in a metastable Kerr combdynamics with timescales that can be larger than 1 min. Thistime is, at least, seven orders of magnitude larger than theintracavity photon lifetime and is in sharp contrast with all thetransient behaviors reported so far in cavity nonlinear optics thatare typically only a few photon lifetimes long (i.e., in thepicosecond to the microsecond range). This phenomenology, studiedtheoretically in the Lugiato-Lefever model and the observeddynamics is compatible with experimental observations in Kerr combsgenerated in ultra-high-<span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" style="font-size: 107%;"><span id="MJXc-Node-1" class="mjx-math"><span id="MJXc-Node-2" class="mjx-mrow"><span id="MJXc-Node-3" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"style="padding-top: 0.471em; padding-bottom: 0.471em;">Q</span></span></span></span></span>whispering-gallery mode resonators.
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