J. P. Toomey

Mapping the dynamic complexity of a semiconductor laser with optical feedback using permutation entropy

A semiconductor laser with delayed optical feedback is an experimental implementation of a nominally infinite dimensional dynamical system. As such, time series analysis of the output power from this laser system is an excellent test of complexity analysis tools, as applied to experimental data. Additionally, the systematic characterization of the range and variation in complexity that can be obtained in the output power from the system, which is available to be used in applications like secure communication, is of interest. Output power time series from a semiconductor laser system, as a function of the optical feedback level and the laser injection current, have been analyzed for complexity using permutation entropy. High resolution maps of permutation entropy as a function of optical feedback level and injection current have been achieved for the first time. This confirms prior research that identifies a coherence collapse region which is found to be uninterrupted with respect to any embedded islands with different dynamics. The results also show new observations of low optical feedback dynamics which occur in a region below that for coherence collapse. The map of the complexity shows a strong dependence on the delay time used in the permutation entropy calculation. Short delay times, which sample information at the complete measurement bandwidth, produce maps with drastically different systematic variation in complexity throughout the coherence collapse region, compared to maps generated with a delay time that matches the optical feedback delay. Evaluating the complexity with a permutation entropy delay equal to the external cavity delay produces results consistent with the notion of weak/strong chaos, as well as categorizing the dynamics as being of high complexity where the external cavity delay time is harder to identify. These are both desirable features for secure communication applications. The results also show permutation entropy as a function of delay time can be used to detect key frequencies driving the dynamics, including any that may exist due to, or arise from, technicalities of device fabrication and/or noise. A more complete insight into complexity as measured by permutation entropy is gained by considering multiple delay times.

Correlation dimension signature of wideband chaos synchronization of semiconductor lasers

Chaos data analysis has been performed on the chaotic output power time series data from a synchronized transmitter-receiver pair of semiconductor lasers. The system uses an asymmetric, bidirectional coupling configuration between the master (transmitter), which is a laser diode with optical feedback, and a stand-alone slave semiconductor laser. The correlation dimension of the chaotic time series has a minimum value of 4, which was obtained from high-bandwidth measurements. The correlation dimensions for both the master and the synchronized slave are identical when the cross-correlation coefficient of the synchronized chaos is above 0.9. These results establish correlation dimension analysis as an effective tool for the determination of the quality of wideband chaos synchronization.

Nonlinear dynamics of semiconductor lasers with feedback and modulation

The nonlinear dynamics of two semiconductor laser systems: (i) with optical feedback, and (ii) with optical feedback and direct current modulation are evaluated from multi-GHz-bandwidth output power time-series. Animations of compilations of the RF spectrum (from the FFT of the time-series) as a function of optical feedback level, injection current and modulation signal strength is demonstrated as a new tool to give insight into the dynamics. The results are contrasted with prior art and new observations include fine structure in the RF spectrum at low levels of optical feedback and non-stationary switching between periodic and chaotic dynamics for some sets of laser system parameters. Correlation dimension analysis successfully identifies periodic dynamics but most of the dynamical states are too complex to be extracted using standard algorithms.

Automated correlation dimension analysis of optically injected solid state lasers

Nonlinear lasers are excellent systems from which to obtain high signal-to-noise experimental data of nonlinear dynamical variables to be used to develop and demonstrate robust nonlinear dynamics analysis techniques. Here we investigate the dynamical complexity of such a system: an optically injected Nd:YVO(4) solid state laser. We show that a map of the correlation dimension as a function of the injection strength and frequency detuning, extracted from the laser output power time-series data, is an excellent mirror of the dynamics map generated from a theoretical model of the system. An automated computational protocol has been designed and implemented to achieve this. The correlation dimension map is also contrasted with prior research that mapped the peak intensity of the output power as an experimentally accessible measurand reflecting the dynamical state of the system [Valling et al., Phys. Rev. A 72, 033810 (2005)].

Complexity in pulsed nonlinear laser systems interrogated by permutation entropy

Permutation entropy (PE) has a growing significance as a relative measure of complexity in nonlinear systems. It has been applied successfully to measuring complexity in nonlinear laser systems. Here, PE and weighted permutation entropy (WPE) are discovered to show an unexpected inversion to higher values, when characterizing the complexity at the characteristic frequencies of nonlinear drivers in laser systems, for output power sequences which are pulsed. The cause of this inversion is explained and its presence can be used to identify when irregular dynamics transform into a fairly regular pulsed signal (with amplitude and timing jitter). When WPE is calculated from experimental output power time series from various nonlinear laser systems as a function of delay time, both the minimum value of WPE, and the width of the peak in the WPE plot are shown to be indicative of the level of amplitude variation and timing jitter present in the pulsed output. Links are made with analysis using simulated time series data with systematic variation in timing jitter and/or amplitude variations.

Hybrid electronic/optical synchronized chaos communication system

A hybrid electronic/optical system for synchronizing a chaotic receiver to a chaotic transmitter has been demonstrated. The chaotic signal is generated electronically and injected, in addition to a constant bias current, to a semiconductor laser to produce an optical carrier for transmission. The optical chaotic carrier is photodetected to regenerate an electronic signal for synchronization in a matched electronic receiver The system has been successfully used for the transmission and recovery of a chaos masked message that is added to the chaotic optical carrier. Past demonstrations of synchronized chaos based, secure communication systems have used either an electronic chaotic carrier or an optical chaotic carrier (such as the chaotic output of various nonlinear laser systems). This is the first electronic/optical hybrid system to be demonstrated. We call this generation of a chaotic optical carrier by electronic injection.

Time-Scale Independent Permutation Entropy of a Photonic Integrated Device

A new measure of complexity, time-scale independent permutation entropy, has been developed and applied to fully characterize the relative complexity of the emission of a four-section photonic integration chip (PIC) laser. The new technique allows the relative complexity of dynamics with different characteristic time scales to be compared. The analysis reveals the range of possible outputs the PIC device can produce over a three-dimensional operating parameter space. From the perspective of using such devices as synchronized transmitter and receiver pairs in chaos-based secure communication applications, a region of uninterrupted, highly complex, unpredictable dynamics has been identified for the device. Regions surrounding this desired complex state show intermittency, pulse packages, and limit-cycle oscillations. The effect of varying the lasers biasing current, feedback strength, and feedback phase reveals the extent of the short-cavity regime and provides insight to the fundamental physics driving the integrated device dynamics.

High Accuracy Measurement of Relaxation Oscillation Frequency in Heavily Damped Quantum Well Lasers

The frequency of relaxation oscillations in a heavily damped quantum well laser, as a function of injection current, have been measured with an accuracy as good as 0.3% using a new method involving averaging of many, real-time, individual, relaxation oscillation events. This accuracy represents at least a six fold improvement compared to that obtained by the standard RF spectral analysis method applied to the same system. This accuracy enables critical comparison of experimental results with standard theory and suggests systematic variation of the experimental values from expected theory. This motivates further developments in the theory of relaxation oscillations in quantum well semiconductor lasers.

Variable pulse repetition frequency output from an optically injected solid state laser

An optically injected solid state laser (OISSL) system is known to generate complex nonlinear dynamics within the parameter space of varying the injection strength of the master laser and the frequency detuning between the master and slave lasers. Here we show that within these complex nonlinear dynamics, a system which can be operated as a source of laser pulses with a pulse repetition frequency (prf) that can be continuously varied by a single control, is embedded. Generation of pulse repetition frequencies ranging from 200 kHz up to 4 MHz is shown to be achievable for an optically injected Nd:YVO4 solid state laser system from analysis of prior experimental and simulation results. Generalizing this to other optically injected solid state laser systems, the upper bound on the repetition frequency is of order the relaxation oscillation frequency for the lasers. The system is discussed in the context of prf versatile laser systems more generally. Proposals are made for the next generation of OISSLs that will increase understanding of the variable pulse repetition frequency operation, and determine its practical limitations. Such variable prf laser systems; both low powered, and, higher powered systems achieved using one or more optical power amplifier stages; have many potential applications from interrogating resonance behaviors in microscale structures, through sensing and diagnostics, to laser processing.

Precision Threshold Current Measurement for Semiconductor Lasers Based on Relaxation Oscillation Frequency

The soft turn-on of semiconductor lasers leads to uncertainty in defining and measuring the laser threshold injection current, I th. Previously, practical calculation algorithms have been developed to achieve high-accuracy measurement of a clearly defined and reproducible quantity which is called I th. We demonstrate a new and higher accuracy measurement of I th using the dependency of the relaxation oscillation frequency on injection current, as compared to the existing standardized approaches. Further, if it is accepted that relaxation oscillations do not occur below laser threshold, this may be regarded as a more fundamentally based definition and measurement method to determine the laser threshold injection current in a semiconductor laser. The method may also be applicable to other types of lasers.