We study delay-based photonic reservoir computing using a semiconductor laser with an optoelectronic feedback. A rate-equation model for a laser with an optoelectronic filtered feedback is used. The filter allows only high-frequency signals to pass through the feedback loop. The delay-differential equation model consists of three equations for the normalized electric field intensity I(t), the carrier density N(t); and the filtered intensity signal IF (t). The stability boundaries which correspond to the Hopf bifurcation condition are determined analytically, showing multiple Hopf bifurcation branches in the dynamics, and the parity asymmetry with relation to the feedback sign.
We use the Santa Fe time-series prediction task to evaluate the performance of reservoir computing. Our objective is to determine location of the optimal operating point defined as corresponding to minimal normalized means square error (NMSE) and relate it to the stability properties of the system. We use 3000 points for training and 1000 for testing, number of virtual nodes is chosen in regard to the relaxation oscillation frequency. Single-point prediction of the chaotic data is performed. Input signal is determined by the chaotic waveform
having n sampling points, and three cases are investigated: prediction of n + 1 ,n + 2 or n + 3 sampling point. The best NMSE value order of 10^7 for n + 1 point prediction task is obtained in the absence of feedback and the rapid increase in NMSE is observed in the vicinity of Hopf bifurcation without regard to the feedback sign. On the contrary, the minimum values of NMSE for n + 2 and n + 3 point prediction task correspond to the Hopf bifurcation, and only for the positive feedback. We discuss whether the parity asymmetry can explain strongly asymmetric reservoir computing results.
We explore experimentally and theoretically the dynamics of a DFB quantum well laser subject to external optical feedback from a mirror. With increasing feedback, the system exhibits the following dynamical scenario: an extremely small limit cycle appears first and is followed by a quasi-periodic regime, and then by three subsequent limit cycles with different repetition rates. This sequence of limit cycles can be associated with the change of phase of the reflected field which reveals translational symmetry and the fact of periodic solutions coexistence which we confirm numerically. The results can be useful for applications in reservoir computing with phase space of coexisting limit cycles acting as a nonlinear reservoir as well as for other applications.
A relatively simple and stable microwave oscillator tunable across the full X-band is achieved. The microwave oscillations are self-generated limit-cycles produced by a laser diode subjected to optical feedback from a mirror. Further, the oscillations are stabilized utilizing two techniques in tandem, the first being a resonance effect based on locking the two inherent timescales of the laser, and the second being optoelectronic feedback. The resulting stable oscillations are fully tunable across the X-band from 5.5 to 12.1 GHz with typical phase noise performance of -107 dBc/Hz at 10 kHz offset. Further, the system is relatively simple by not requiring multiple lasers, radio-frequency filters, external RF sources, or any specialized equipment, thus, enabling a compact and low-cost microwave oscillator for applications in radar, radio over fiber, and telecommunications.
Terahertz pulsed imaging has attracted considerable interest for revealing the stratigraphy and hidden features of art paintings. The reconstruction of the stratigraphy is based on the precise extraction of THz echo parameters from the reflected signals. Several historical panel paintings and wall paintings have been well studied by THz reflective imaging, in which the detailed stratigraphy has been successfully revealed. To our knowledge, however, the stratigraphy of oil paintings has not been clearly uncovered by THz imaging, since the paint layers in an oil painting on canvas, especially for the 16th and 17th century art works, are usually very thin (~10 μm) in the THz regime. Therefore, in order to improve the performance of THz imaging, advanced signal-processing techniques with higher depth-resolution are still needed. In this study, THz reflective imaging is employed to reveal for the first time the detailed stratigraphy of a 17th century Italian oil painting on canvas. The paint layers on the supporting canvas are very thin in the THz regime, as the THz echoes corresponding to the stratigraphy totally overlap in the first cycle of the reflected THz signal. THz sparse deconvolution based on an iterative shrinkage algorithm is utilized to resolve the overlapping echoes. Based on the deconvolved signals, the detailed stratigraphy of this oil painting on canvas, including the varnish, pictorial, underdrawing, and ground layers, is successfully revealed. The THz C- and B-scans based on the THz deconvolved signals also enable us to reveal the features of each layer. Our results thus enhance the capability of terahertz imaging to perform detailed analysis and diagnostics of historical oil paintings on canvas with foreseen applications for the study of the artist’s technique and for authentication.
The stabilization of a relatively simple optoelectronic oscillator tunable across the X-band based on a laser subjected to optical feedback is achieved. Specifically, a resonance effect based on locking the two inherent frequencies of the system, as well as, self-modulation were utilized to achieve a sub-ps phase jitter.
In the last ten years terahertz techniques have become increasingly common laboratory and industrial tools. This progress has been made possible by over thirty years of concentrated effort. In this talk we discuss our recent work combining time-domain terahertz imaging with advanced signal-processing to obtain unprecedented depth information in a nondestructive fashion about subsurface damage in both glass and carbon fiber composites and in coatings on metals. In addition, we present an example characterizing the stratigraphy of an art painting to illustrate the technique to measure thicknesses in a multilayer coating. Other optically opaque materials, including polymers, glass, textiles, paper, and ceramics, are transparent to terahertz radiation, and thus terahertz imaging may access information in these materials below the surface.
Signal processing techniques are needed to unleash the power of terahertz imaging to measure thin layers of thickness on the order of 10 microns. These approaches permit us to gain information about thin layers that are obscured in the raw signals. That is, when the time duration of the terahertz pulses is longer than the optical delay to traverse a given layer, the terahertz echoes associated with reflections off the various interfaces may temporally overlap. Specifically, we have successfully employed frequency-wavelet domain deconvolution, sparse deconvolution, and autoregressive deconvolution for a range of problems.
We explore both experimentally and numerically the dynamics of semiconductor lasers subject to delayed optical feedback and show that the external cavity repetition rate can be resonant with the relaxation oscillations leading to a discretisation of the relaxation oscillation frequency which evolves in a series of discrete steps, remaining almost constant along each step. Numerically, the steps are found to result from different Hopf bifurcation branches.
Terahertz (THz) reflective imaging is applied to the stratigraphic and subsurface investigation of oil paintings, with a focus on the mid-20th century Italian painting, ‘After Fishing’, by Ausonio Tanda. THz frequency-wavelet domain deconvolution, which is an enhanced deconvolution technique combining frequency-domain filtering and stationary wavelet shrinkage, is utilized to resolve the optically thin paint layers or brush strokes. Based on the deconvolved terahertz data, the stratigraphy of the painting including the paint layers is reconstructed and subsurface features are clearly revealed. Specifically, THz C-scans and B-scans are analyzed based on different types of deconvolved signals to investigate the subsurface features of the painting, including the identification of regions with more than one paint layer, the refractive-index difference between paint layers, and the distribution of the paint-layer thickness. In addition, THz images are compared with X-ray images. The THz image of the thickness distribution of the paint exhibits a high degree of correlation with the X-ray transmission image, but THz images also reveal defects in the paperboard that cannot be identified in the X-ray image. Therefore, our results demonstrate that THz imaging can be considered as an effective tool for the stratigraphic and subsurface investigation of art paintings. They also open up the way for the use of non-ionizing THz imaging as a potential substitute for ionizing X-ray analysis in nondestructive evaluation of art paintings.
We use a laser diode from a commercial CD/DVD-ROM drive to detect changes in the surface of a diffraction grating without a photodiode. Specifically, we exploit the changing terminal voltage in the laser-diode due to changing feedback strength as the laser is rastered across the grating's surface.
We demonstrate experimentally that optical chaos generated by a laser diode with optical feedback is suitable for compressive sensing of sparse signals. Specifically, we find that the coherence collapse regime guarantees that the generation of a sensing matrix, necessary for sparse reconstruction, has a comparable level of performance to those constructed with Gaussian random sequences. Our result opens new avenues for the use of optical chaotic devices for signal processing applications at ultra-high speed.
We report experimental bifurcation diagrams (BDs) of an external-cavity semiconductor laser (ECSL). We have focused on the case of the ECSL biased just above threshold to moderate and subjected to feedback from a distant reflector and observed a sequence of bifurcations involving bifurcation cascade as well as intermittency between multiple coexisting attractors. More importantly, we reiterate: the results map out, for the first time to our knowledge, detailed BDs of the ECSL as a function of feedback strength for various external cavity lengths and currents, thus covering a significant portion of parameter space. We have grounded our discussion in extensive theoretical studies based on the Lang-Kobayashi equations and simulated BDs in accordance with our experimental results.
Random bit generation (RBG) with chaotic semiconductor lasers has been extensively studied because of its potential applications in secure communications and high-speed numerical simulations. Researchers in this field have mainly focused on the improvement of the generation rate and the compactness of the random bit generators. In this paper, we experimentally demonstrate the existence of two regimes of fast RBG using a single chaotic laser subjected to delayed optical feedback: the first one is based on the extraction of all min-entropy contained in each random sample, and the second one is to demonstrate a possibility of increasing the generation rate by extracting 55 bits from each variable.
Optical chaos-based cryptosystems hide an information-bearing message within the chaotic dynamics of a laser system.
On-off phase-shift keying (OOPSK) is considered to be a particularly efficient encryption technique. It is based on the
modulation of the feedback phase of a chaotic external-cavity emitter laser at the rhythm of a digital message. At the
receiving end, message values are decrypted by observing the synchronization and de-synchronization of an external-cavity
receiver which has a constant feedback phase. This cryptosystem is popular because so far it has been thought to
be impossible to find the message by analyzing the chaotic optical field transmitted from the emitter to the receiver laser,
thus, it is hitherto thought, providing high security. We demonstrate that the phase modulation produces a displacement
of the chaotic attractor which is detectable by analyzing low-dimensional projections or sections of the high-dimensional
attractor. This leads to the successful decryption of the message value based on an analysis of the chaotic optical field
sent to the receiver only. We show that the bit-error-rate (BER) of the decrypted message varies with the modulation
depth and speed. Though small depths and large bit rates lead to an increase of the BER, we find it possible to extract the
message for most operating conditions of an on/off phase- shift keying-based cryptosystem.
We present an architecture tailored for the multiplexing of multiple optical chaotic carriers generated by semiconductor
lasers with external optical cavities. Our setup can discriminate multiple chaotic signals with high spectral overlap. The
various emitters are mutually globally coupled thanks to a shared optical feedback, which creates a multiplexed optical
field. This field is then coherently and unidirectionally injected in the decoupled receivers, and allows each of them to
synchronize on their respective emitter. Using this setup, it would be possible to transmit several messages and make a
better use of the wide chaotic spectrum. In this paper, we demonstrate theoretically and numerically the possibility to
synchronize two optical chaotic fields as a premise for the transmission of two messages. We also study the robustness of
synchronization to parameter mismatch and noise, which are important issues in real field experiments.
We investigate theoretically the identification of the
external-cavity roundtrip time of an external-cavity semiconductor
laser (ECSL). The time-delay identification is performed by analyzing the laser-intensity time series with conventional
techniques based on the autocorrelation function or mutual information. We find that a weak feedback rate and a time-delay
close to the laser's intrinsic relaxation-oscillation period are two conditions leading to difficult delay identification.
This arduous time-delay identification is of particular interest for the security improvement of chaos-based
communications schemes using ECSLs.
We study the identification of the delays of several chaotic optical cryptosystems subjected to one or two delayed feedbacks. We show that the delay of a single-delay system can be identified, even if highly complex chaos is used. For certain types of systems with two delays, the same identification techniques that work for single-delay systems also work for multiple-delay systems. These systems thus do not provide a significant increase of the security level. A careful choice of the architecture of multiple-delay system can, however, make these techniques fail. We propose some higher-dimensional techniques that lead to the identification of the delays for these architectures too. The increased complexity of these techniques means, however, that it takes a significantly longer time to identify the delays.
We study numerically the synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers. Depending on the operating conditions, the receiver laser intensity, IR(t), synchronizes with the intensity of the optically injected field, IT(t-tc), where tc is the flight time from the transmitter laser to the receiver laser, or synchronizes with IT(t-tc+t), where t is the is the external-cavity round-trip time. In the latter case, the intensity produced by the receiver anticipates the injected intensity IT(t-tc) by an anticipation time equal to t. We find that synchronization with a lag time tc-t is much more sensitive to frequency detuning and noise than synchronization with a lag time tc. Moreover, we also find that though synchronization with a lag time tc can be obtained using either an external-cavity or an open-loop receiver, the synchronization quality is always better when an external-cavity receiver is used.
We demonstrate numerically a secure communication scheme based on the synchronization of two chaotic laser diodes that are respectively subjected to incoherent optical feedback and incoherent optical injection. In this scheme, the optical fields emitted by the two lasers and the fields that are fed back and injected into these two lasers have orthogonal polarizations. Consequently, the external fields do not coherently interact with the lasing fields but only act on the population inversions. Synchronization of both lasers does not require fine tuning of their optical frequencies neither accurate control of the external cavity lengths contrary to the cryptographic systems based on conventional optical feedback. The message encoding/decoding is achieved by chaos shift keying.