We model the performance of an optoelectronic phase-chaos system operating with telecom components to generate random bits. The key component of the system is differential delay, namely the system is subject to two delay times which differ in an amount much larger than the autocorrelation time. This is implemented by a delay loop and an imbalanced Mach-Zhender modulator. We show that after suitable digitalization of the chaotic signal the generated bits pass all the NIST test for randomness. We also show that the system can be extended to have several chains in parallel each with a Mach-Zhender modulator, each chain being used to produce a sequence of random bits. If the differential delays of the Mach-Zhenders differ by an amount larger than the autocorrelation time of the chaotic dynamics, the output of the different chains is uncorrelated and therefore can be used for parallel generation of statistically independent random bit-streams. In addition, we also find that a sequence constructed by interleaving the parallel bit-streams also pass all the NIST tests for randomness. Based on the least significant bits which can be included in the sequence and the number of the parallel branches which can be implemented, we show that bit rates up to Tb/s can be achieved.
We propose a simple physical mechanism to explain observed instabilities in the dynamics of passively phased fiber amplifier arrays that arises from two properties: First that a weak phase disturbance of the output field of the array is converted into a strong intensity disturbance through the mode-selective feedback mechanism. Second, that this intensity fluctuation regenerates a phase fluctuation due to the nonlinear properties of the amplifying media. At sufficiently high operating power levels this cyclic disturbance continues to grow upon each cavity round trip, creating instability. This simple picture is supported by the results of a linear stability analysis of the set of propagation and population rate equations, which are in good agreement with observed critical power levels. A third level of quantitative confirmation was obtained by comparison to the results of numerical integration of the original set of nonlinear equations. This predicted instability is entirely a property of passively phased arrays of more than one element.
We performed a linearized stability analysis and preliminary simulations of passive phasing in a CW operating ring-geometry fiber laser array coupled in an external cavity with a single-mode feedback fiber that functions as spatial filter. A two-element array with path length error is predicted to have a dynamically stable stationary operating state at the compputer operating wavelength.
We analyze a rate equation model in the Langevin formulation for the two modes of the electric field and the
carrier density, modelling the spontaneous emission noise in a semiconductor ring laser biased in the bidirectional
regime. We analytically investigate the influence of complex backscattering coefficient when the two modes
are reinterpreted in terms of mode-intensity sum (I-Spectrum) and difference (D-spectrum). The D-spectrum
represents the energy exchange between the two counterpropagating modes and it is shaped by the noisy precursor
of a Hopf bifurcation influenced mainly by the conservative backscattering. The I-Spectrum reflects the energy
exchange between the total field and the medium and behaves similarly to the standard relative intensity noise
for single-mode semiconductor lasers. Good agreement between analytical approximation and numerical results
is found.
Cavity solitons are controllable two-dimensional transverse Localized Structures (LS) in dissipative optical cavities.
Such LS have been suggested for use in optical data storage and information processing. Typically,
diffraction constrains the size of these light spots to be of the order of the square root of the diffraction coefficient of the system. Due to recent advances in the development of metamaterials, the diffraction strength in a
cavity could be controlled by adding a left-handed material layer in a Fabry-Perot resonator together with a traditional
nonlinear material. This system thus potentially allows for LS beyond the size limit imposed by natural
diffraction. However, when the diffraction strength becomes smaller, the non-local response of the left-handed
metamaterial starts to dominate the nonlinear spatiotemporal dynamics. Considering a typical linear non-local
response, we develop a mean-field model describing the spatiotemporal evolution of LS. First, the influence of this
non-local response on the minimal attainable width of the LS is studied [Gelens et al., Phys. Rev. A 75, 063812
(2007)]. Secondly, we elaborate on the different possible mechanisms that can destabilize the LS, leading to
stable oscillations, expanding patterns, or making the LS disappear. Furthermore, we also show multiple routes
towards excitability present in the system. We demonstrate that these different regions admitting stationary,
oscillating or excitable LS unfold from two Takens-Bogdanov codimension-2 points [Gelens et al., Phys. Rev. A
77 (2008)].
We review three two-mode models for different semiconductor laser structures: Vertical-Cavity Surface-Emitting Lasers (VCSELs), Twin-Stripe Semiconductor-Lasers (TSSL), and Semiconductor Ring Lasers (SRL). The VCSELs model and TSSL model display rich dynamic behavior when a saturable absorber is embedded in the cavity. VCSELs with saturable absorber showed polarization chaos, which found applications in encoded communications; TSSLs with saturable absorber show coherent locked states as well as chaotic behavior; and SRLs show a complex two-mode dynamics giving rise to bidirectional operation, alternate oscillations and spontaneous symmetry breaking toward quasi-unidirectional bistable solutions, with potential applications to all-optical switching.
We have theoretically investigated the bifurcation scenario that leads to the emergence of a bistable regime in a two-mode model for a Semiconductor Ring Laser. The bistability takes place between two quasi-unidirectional solutions for the electric field, which are selected as stable solutions via gain-crossaturation, for well-above threshold operating conditions. Furthermore, we analyzed the switching properties of a single Semiconductor Ring Laser (SRL) operating in the bistable regime, under coherent optical pulse injection, in view of the possible implementation of a single SRL
an optically adressable memory element. The result is that the response time and the minimum switching energy respectively attain values the order of a few tenth of ps, and 1 fJ. Those values are espected to scale down with the device radius, due to the consequent decreasing of the cavity flight time. We have observed that the fast switching dynamic is due to an energy redistribution process between the two counterpropagating modes, that does not involve the (slow) carrier density through field-medium energy exchange processes. This allows to attain time scales much faster than the typical limit represented by the inverse of relaxation oscillation frequency.
Dissipative localized structures, also known as cavity solitons, arise in the transverse plane of several nonlinear optical devices. We present two general mechanisms for their formation and some scenarios for their instability. In situations of coexistence of a homogeneous and a pattern state, we characterize excitable behavior mediated by localized structures. In this scenario, excitability emerges directly from the spatial dependence since it is absent in the purely temporal dynamics. In situations of coexistence of two homogeneous states, we discuss localized structures either due to the interaction of front tails (dark ring cavity solitons) or due to a balance between curvature effects and modulational instabilities of front solutions (stable droplets).
We investigate the detrimental effect of chaotic noise on the performance of an optical chaos cryptosystem. Hyperchaos is generated in the emitter and receiver systems with Mach-Zehnder interferometers fed by semiconductor lasers and subjected to electro-optical feedback. In this optical chaos cryptosystem, (chaotic) noise originates from the mismatch in parameters between the emitter and the receiver. We therefore determine the amplitude of this noise as a fonction of the parameter mismatch, and we evaluate its effect on the bit error rate (BER) performance of the communication system. Analytical predictions are confirmed by numerical simulations and experimental results.
We characterize the chaotic dynamics of semiconductor lasers subject to either optical or electro-optical feedback modeled by Lang-Kobayashi and Ikeda equations, respectively. This characterization is relevant for secure optical communications based on chaos encryption. In particular, for each system we compute as function of tunable parameters the Lyapunov spectrum, Kaplan-Yorke dimension and Kolmogorov-Sinai entropy.
We numerically study the entrainment of two unidirectional coupled single-mode semiconductor lasers in a master-slave configuration. The emitter laser is an external-cavity laser subject to optical feedback that operates in a chaotic regime while the receiver has no optical feedback and consequently operates under CW when it is uncoupled (open loop scheme). We compare the performance of this scheme with the close loop one in which both emitter and receiver are subjected to optical feedback and operate in a chaotic state. We compute the degree of entrainment or synchronization of the two lasers as a function of the detuning, the emitter-receiver coupling constant and the feedback rate of the receiver. We find that the close loop scheme has, in general, a larger region of synchronization when compared with the open loop. We also study the possibility of message encoding and decoding in the both open and close loops and their robustness against parameters mismatch. Finally we compute the time it takes the system to recover the synchronization or entrainment state when the coupling between the two subsystems is lost. We find that this time is much larger in the close loop than in the open one.
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