Lucas Illing

Synchronization and communication using semiconductor lasers with optoelectronic feedback

Semiconductor lasers provide an excellent opportunity for communication using chaotic waveforms. We discuss the characteristics and the synchronization of two semiconductor lasers with optoelectronic feedback. The systems exhibit broadband chaotic intensity oscillations whose dynamical dimension generally increases with the time delay in the feedback loop. We explore the robustness of this synchronization with parameter mismatch in the lasers, with mismatch in the optoelectronic feedback delay, and with the strength of the coupling between the systems. Synchronization is robust to mismatches between the intrinsic parameters of the lasers, but it is sensitive to mismatches of the time delay in the transmitter and receiver feedback loops. An open-loop receiver configuration is suggested, eliminating feedback delay mismatch issues. Communication strategies for arbitrary amplitude of modulation onto the chaotic signals are discussed, and the bit-error rate for one such scheme is evaluated as a function of noise in the optical channel.

Broadband Chaos Generated by an Optoelectronic Oscillator

We study an optoelectronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. We derive approximate mappings that do an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultrawide-band sensor networks.

Shaping current waveforms for direct modulation of semiconductor lasers

We demonstrate a technique for shaping current inputs for the direct modulation of a semiconductor laser for digital communication. The introduction of shaped current inputs allows for the suppression of relaxation oscillations and the avoidance of dynamical memory in the physical laser device, i.e., the output will not be influenced by previously communicated information. For the example of time-optimized bits, the possible performance enhancement for high data rate communications is shown numerically.

High-speed chaos in an optical feedback system with flexible timescales

We describe a new optoelectronic device with time-delayed feedback that uses a Mach-Zehnder interferometer as passive nonlinearity and a semiconductor laser as a current-to-optical-frequency converter. Band-limited feedback allows tuning of the characteristic time scales of both the periodic and high dimensional chaotic oscillations that can be generated with the device. Our implementation of the device produces oscillations in the frequency range of tens to hundreds of megahertz. We develop a model and use it to explore the experimentally observed Andronov-Hopf bifurcation of the steady state and to estimate the dimension of the chaotic attractor.

Controlling Optical Chaos, Spatio-Temporal Dynamics, and Patterns

Abstract We describe how small perturbations applied to optical systems can be used to suppress or control optical chaos, spatio-temporal dynamics, and patterns. This research highlights the fact that complex behavior, such as chaos, has a beautiful and orderly underlying structure. We demonstrate that this orderly structure can be exploited for a variety of applications, such as stabilizing laser behavior in a regime where the device would normally produce erratic behavior, communicating information masked in a seemingly noise-like chaotic carrier, and improving the sensitivity of ultra-low-light level optical switches.

Ultra-high-frequency chaos in a time-delay electronic device with band-limited feedback

We report an experimental study of ultra-high-frequency chaotic dynamics generated in a delay-dynamical electronic device. It consists of a transistor-based nonlinearity, commercially-available amplifiers, and a transmission-line for feedback. The feedback is band-limited, allowing tuning of the characteristic time-scales of both the periodic and high-dimensional chaotic oscillations that can be generated with the device. As an example, periodic oscillations ranging from 48 to 913 MHz are demonstrated. We develop a model and use it to compare the experimentally observed Hopf bifurcation of the steady-state to existing theory [Illing and Gauthier, Physica D 210, 180 (2005)]. We find good quantitative agreement of the predicted and the measured bifurcation threshold, bifurcation type and oscillation frequency. Numerical integration of the model yields quasiperiodic and high dimensional chaotic solutions (Lyapunov dimension approximately 13), which match qualitatively the observed device dynamics.

Exactly solvable chaos in an electromechanical oscillator.

A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that include a linear second order ordinary differential equation with negative damping and a discrete switching condition that controls the oscillatory fixed point. The system produces provably chaotic oscillations with a topological structure similar to either the Lorenz butterfly or Rösslers folded-band oscillator depending on the configuration. Exact solutions are written as a linear convolution of a fixed basis pulse and a sequence of discrete symbols. We find close agreement between the exact analytical solutions and the physical oscillations. Waveform return maps for both configurations show equivalence to either a shift map or tent map, proving the chaotic nature of the oscillations.

Observation of ultra-low-light-level all-optical switching

Photonic circuits require elements that can control optical signals with other optical signals. Ultra-low-light-level operation of all-optical switches opens the possibility of photonic devices that operate in the single-quantum regime, a prerequisite for quantum-photonic devices. We describe a new type of all-optical switch that exploits the extreme sensitivity to small perturbations displayed by instability-generated dissipative optical patterns. Such patterns, when controlled by applied perturbations, enable control of microwatt-power-level output beams by an input beam that is over 600 times weaker. In comparison, essentially all experimental realizations of light-by-light switching have been limited to controlling weak beams with beams of either comparable or higher power, thus limiting their implementation in cascaded switching networks or computation machines. Furthermore, current research suggests that the energy density required to actuate an all-optical switch is of the order of one photon per optical cross section. Our measured switching energy density of ~4.4 × 10-2 photons per cross section suggests that our device can operate at the single-photon level with modest system improvement.

Digital Communication Using Self-Synchronizing Chaotic Pulse Position Modulation

We review a new approach to communication with chaotic signals based upon chaotic signals in the form of pulse trains where intervals between the pulses are determined by chaotic dynamics of a pulse nary information is modulated onto this carrier by the pulse position modulation method, such that each pulse is either left unchanged or delayed by a certain time, depending on whether 0 or 1 is transmitted. By synchronizing the receiver to the chaotic-pulse train we can anticipate the timing of pulses corresponding to 0 and 1 and thus can decode the transmitted information. Based on the results of theoretical and experimental studies we discuss the basic design principles for the chaotic-pulse generator, its synchronization, and the performance of the chaotic-pulse communication scheme in the presence of channel noise and filtering.