Time-varying propagation model and dynamic-feedback-phase correction for multiplexed orbital angular momentum beams in atmospheric turbulence.

Freespace optical (FSO) communication in an outdoor setting is complicated by atmospheric turbulence (AT). A time-varying (TV) multiplexed orbital angular momentum (OAM) propagation model to consider AT under transverse-wind conditions is formulated for the first time, and optimized dynamic correction periods for various TV AT situations are found to improve the transmission efficiency. The TV nature of AT has until now been neglected from modeling of OAM propagation models, but it is shown to be important. First, according to the Taylor frozen-turbulence hypothesis, a series of AT phase screens influenced by transverse wind are introduced into the conventional angular-spectrum propagation analysis method to model both the temporal and spatial propagation characteristics of multiplexed OAM beams. Our model shows that while in weak TV AT, the power standard deviation of lower-order modes is usually smaller than that of higher-order modes, the phenomena in strong TV AT are qualitatively different. Moreover, after analyzing the effective time of each OAM phase correction, optimized dynamic correction periods for a dynamic feedback communication link are obtained. An optimized result shows that, under the moderate TV AT, both a system BER within the forward-error-correction limit and a low iterative computation volume with 6% of the real-time correction could be achieved with a correction period of 0.18 s. The research emphasizes the significance of establishing a TV propagation model for exploring the effect of TV AT on multiplexed OAM beams and proposing an optimized phase-correction mechanism to mitigate performance degradation caused by TV AT, ultimately enhancing overall transmission efficiency.

Resonant properties of the memory capacity of a laser-based reservoir computer with filtered optoelectronic feedback.

We provide a comprehensive analysis of the resonant properties of the memory capacity of a reservoir computer based on a semiconductor laser subjected to time-delayed filtered optoelectronic feedback. Our analysis reveals first how the memory capacity decreases sharply when the input-data clock cycle is slightly time-shifted from the time delay or its multiples. We attribute this effect to the inertial properties of the laser. We also report on the damping of the memory-capacity drop at resonance with a decrease of the virtual-node density and its broadening with the filtering properties of the optoelectronic feedback. These results are interpretated using the eigenspectrum of the reservoir obtained from a linear stability analysis. Then, we unveil an invariance in the minimum value of the memory capacity at resonance with respect to a variation of the number of nodes if the number is big enough and quantify how the filtering properties impact the system memory in and out of resonance.

Impact of filtering on photonic time-delay reservoir computing.

We analyze the modification of the computational properties of a time-delay photonic reservoir computer with a change in its feedback bandwidth. For a reservoir computing configuration based on a semiconductor laser subject to filtered optoelectronic feedback, we demonstrate that bandwidth selection can lead to a flat-topped eigenvalue spectrum for which a large number of system frequencies are weakly damped as a result of the attenuation of modulational instability by feedback filtering. This spectral configuration allows for the optimization of the reservoir in terms of its memory capacity, while its computational ability appears to be only weakly affected by the characteristics of the filter.

Revealing inscriptions obscured by time on an early-modern lead funerary cross using terahertz multispectral imaging.

The presence of a corrosion layer on lead art and archæological objects can severely impede the interpretation of inscriptions, thus hampering our overall understanding of the object and its context. While the oxidation of lead that dominates corrosion may be chemically reversible via reduction, potentially providing some access to inscriptions otherwise obscured by time, corrosion damage is overall neither entirely reversible nor is the reduction process in all cases easy or feasible to carry out. In this study, by taking advantage of the unique penetration ability of terahertz radiation and the abundant frequency bands covered by a single-cycle terahertz pulse, we perform nondestructive terahertz multispectral imaging to look under the corrosion on a sixteenth century lead funerary cross (croix d'absolution) from Remiremont in Lorraine, France. The multispectral images obtained from various terahertz frequency bands are fed into a judiciously designed post-processing chain for image restoration and enhancement, thus allowing us for the first time to read obscured inscriptions that might have otherwise been lost. Our approach, which brings together in a new way the THz properties of the constituent materials and advanced signal- and image-processing techniques, opens up new perspectives for multi-resolution analysis at terahertz frequencies as a technique in archæometry and will ultimately provide unprecedented information for digital acquisition and documentation, character extraction, classification, and recognition in archæological studies.

Optical square-wave generation in a semiconductor laser with optoelectronic feedback.

We report self-sustained optical square-wave (SW) generation in a semiconductor laser diode subjected to delayed optoelectronic feedback on its injection current (J). This optoelectronic oscillator relies on nonlinear effects present in both the laser diode and in the optoelectronic feedback loop through amplifier saturation. The repetition rate of the SW is an integer multiple of the inverse of the loop delay, while the duty cycle can be tuned with J.

Complete two-dimensional photonic bandgap in refractive-index ratio 2.1 photonic crystals due to high-order bands.

We find that in a suitably designed photonic crystal (PC) certain high-order photonic bands are less affected by the refractive-index ratio (RIR) than low-order bands, enabling the realization of a robust and complete two-dimensional (2D) photonic bandgap in a moderate refractive-index-ratio PC. A detailed theoretical investigation of low- and high-order bandgaps in a series of PCs with different configurations is performed that shows that high-order bands may favor substantial complete photonic bandgaps (CPBGs) for systems with a moderate RIR. Furthermore, the importance of the geometry and structural parameters on achieving a high-order CPBG is found. Specifically, a hexagonal lattice PC of annular-hole-peripheral connecting rods is proposed, which can support a CPBG with a refractive-index ratio (RIR) as low as nhigh:nlow=2.1; to the best of our knowledge, this is the lowest RIR used to obtain a 2D CPBG in a PC.

Scanning acoustic microscopy investigation of weld lines in injection-molded parts manufactured from industrial thermoplastic polymer.

Scanning acoustic microscopy (SAM) is used to characterize welds in a thermoplastic polymer (ABS) manufactured by injection-molding, particularly at the locations of weld-lines known to form as unavoidable significant defects. Acoustic micrographs obtained at 420 MHz clearly resolve the weld lines with morphological deformations and microelastic heterogenity. This is also where terahertz (THz) measurements, carried out in support of the SAM study, reveal enhanced birefringence corresponding to the location of these lines enabling verification of the SAM results. Rayleigh surface acoustic waves (RSAW), quantified by V(z) curves (with defocusing distance of 85 µm), are found to propagate slower in regions close to the weld lines than in regions distant from these lines. The discrepancy of about 100 m/s in the velocity of RSAW indicates a large variation in the micro-elastic properties between areas close to and distant from the weld lines. The spatial variations in velocity (VR) of RSAWs indicate anisotropic propagation of the differently polarized ultrasonic waves.

Characterization of nanoporous Al2O3 films at terahertz frequencies.

Terahertz birefringence in nanoporous Al2O3 films grown on Al substrates is characterized nondestructively by polarization-resolved terahertz spectroscopy. Sparse deconvolution is used to find the film thicknesses from the data, showing good agreement with the values measured directly by destructive cross-sectional field-emission scanning electron microscopy.

Resonances between fundamental frequencies for lasers with large delayed feedbacks.

High-order frequency locking phenomena were recently observed using semiconductor lasers subject to large delayed feedbacks. Specifically, the relaxation oscillation (RO) frequency and a harmonic of the feedback-loop round-trip frequency coincided with the ratios 1:5 to 1:11. By analyzing the rate equations for the dynamical degrees of freedom in a laser subject to a delayed optoelectronic feedback, we show that the onset of a two-frequency train of pulses occurs through two successive bifurcations. While the first bifurcation is a primary Hopf bifurcation to the ROs, a secondary Hopf bifurcation leads to a two-frequency regime where a low frequency, proportional to the inverse of the delay, is resonant with the RO frequency. We derive an amplitude equation, valid near the first Hopf bifurcation point, and numerically observe the frequency locking. We mathematically explain this phenomenon by formulating a closed system of ordinary differential equations from our amplitude equation. Our findings motivate experiments with particular attention to the first two bifurcations. We observe experimentally (1) the frequency locking phenomenon as we pass the secondary bifurcation point and (2) the nearly constant slow period as the two-frequency oscillations grow in amplitude. Our results analytically confirm previous observations of frequency locking phenomena for lasers subject to a delayed optical feedback.

Nanometric sensing with laser feedback interferometry.

We demonstrate a nanometric sensor based on feedback interferometry in a distributed feedback (DFB) laser by using a measurement of either the optical frequency or laser voltage. We find that in an optimal range of optical feedback, the sensor operates reliably down to an extrapolated 12 nm; for the sensor demonstrated here at ∼1550 nm, this provides a minimum detectible displacement of λ/130.

Multistate intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity.

We observe experimentally two regimes of intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity as the feedback level is increased. The first regime encountered corresponds to multistate intermittency involving two or three states composed of several combinations of periodic, quasiperiodic, and subharmonic dynamics. The second regime is observed for larger feedback levels and involves intermittency between period-doubled and chaotic regimes. This latter type of intermittency displays statistical properties similar to those of on-off intermittency.

Global mapping of stratigraphy of an old-master painting using sparsity-based terahertz reflectometry.

The process by which art paintings are produced typically involves the successive applications of preparatory and paint layers to a canvas or other support; however, there is an absence of nondestructive modalities to provide a global mapping of the stratigraphy, information that is crucial for evaluation of its authenticity and attribution, for insights into historical or artist-specific techniques, as well as for conservation. We demonstrate sparsity-based terahertz reflectometry can be applied to extract a detailed 3D mapping of the layer structure of the 17th century easel painting Madonna in Preghiera by the workshop of Giovanni Battista Salvi da Sassoferrato, in which the structure of the canvas support, the ground, imprimatura, underpainting, pictorial, and varnish layers are identified quantitatively. In addition, a hitherto unidentified restoration of the varnish has been found. Our approach unlocks the full promise of terahertz reflectometry to provide a global and detailed account of an easel painting's stratigraphy by exploiting the sparse deconvolution, without which terahertz reflectometry in the past has only provided a meager tool for the characterization of paintings with paint-layer thicknesses smaller than 50 µm. The proposed modality can also be employed across a broad range of applications in nondestructive testing and biomedical imaging.

Depth resolution enhancement of terahertz deconvolution by autoregressive spectral extrapolation.

This Letter presents a method for enhancing the depth resolution of terahertz deconvolution based on autoregressive (AR) spectral extrapolation. The terahertz frequency components with a high signal-to-noise ratio (SNR) are modeled with an AR process, and the missing frequency components in the regions with low SNRs are extrapolated based on the AR model. In this way, the entire terahertz frequency spectrum of the impulse response function, corresponding to the material structure, is recovered. This method, which is verified numerically and experimentally, is able to provide a "quasi-ideal" impulse response function and, therefore, greatly enhances the depth resolution for characterizing optically thin layers in the terahertz regime.

Compressive Sensing with Optical Chaos.

Compressive sensing (CS) is a technique to sample a sparse signal below the Nyquist-Shannon limit, yet still enabling its reconstruction. As such, CS permits an extremely parsimonious way to store and transmit large and important classes of signals and images that would be far more data intensive should they be sampled following the prescription of the Nyquist-Shannon theorem. CS has found applications as diverse as seismology and biomedical imaging. In this work, we use actual optical signals generated from temporal intensity chaos from external-cavity semiconductor lasers (ECSL) to construct the sensing matrix that is employed to compress a sparse signal. The chaotic time series produced having their relevant dynamics on the 100 ps timescale, our results open the way to ultrahigh-speed compression of sparse signals.

Terahertz frequency-wavelet domain deconvolution for stratigraphic and subsurface investigation of art painting.

Terahertz frequency-wavelet deconvolution is utilized specifically for the stratigraphic and subsurface investigation of art paintings with terahertz reflective imaging. In order to resolve the optically thin paint layers, a deconvolution technique is enhanced by the combination of frequency-domain filtering and stationary wavelet shrinkage, and applied to investigate a mid-20th century Italian oil painting on paperboard, After Fishing, by Ausonio Tanda. Based on the deconvolved terahertz data, the stratigraphy of the painting including the paint layers is reconstructed and subsurface features are clearly revealed, demonstrating that terahertz frequency-wavelet deconvolution can be an effective tool to characterize stratified systems with optically thin layers.

Half-disordered photonic crystal slabs.

Optical transmission spectra of finite-thickness slabs of two-dimensional triangular-lattice photonic crystals of air holes in a dielectric matrix with various concentrations of randomly located vacancies (absent air holes) are studied. We focus on structures in which only one half of the structure-the incidence or transmission side-is disordered. We find vacancy-induced scattering gives rise to a strong difference in the two cases; for light incident on the disordered side, high transmission within the photonic pseudogap at normal incidence is predicted, in strong contrast to the opposite case, where low transmission is predicted throughout the pseudogap, as is observed in the case of an ideal structure with no defects.

Low-frequency fluctuations in an external-cavity laser leading to extreme events.

We experimentally investigate the dynamical regimes of a laser diode subject to external optical feedback in light of extreme-event (EE) analysis. We observe EEs in the low-frequency fluctuations (LFFs) regime. This number decreases to negligible values when the laser transitions towards fully developed coherence collapse as the injection current is increased. Moreover, we show that EEs observed in the LFF regime are linked to high-frequency pulsing events observed after a power dropout. Finally, we prove experimentally that the observation of EEs in the LFF regimes is robust to changes in operational parameters.

Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection.

The concealment of the time-delay signature (TDS) of chaotic external-cavity lasers is necessary to ensure the security of optical chaos-based cryptosystems. We show that this signature can be removed simply by optically injecting an external-cavity laser with a large linewidth-enhancement factor into a second, noninjection-locked, semiconductor laser. Concealment is ensured both in the amplitude and in the phase of the optical field, satisfying a sought-after property of optical chaos-based communications. Meanwhile, enhancement of the dynamical complexity, characterized by permutation entropy, coincides with strong TDS suppression over a wide range of parameters, the area for which depends sensitively on the linewidth-enhancement factor.

Vacancy-induced transmission in three-dimensional photonic crystal slabs.

The transmission spectra of finite-thickness slabs of three-dimensional (3D) diamond-lattice photonic crystals of air spheres in a dielectric background in which various concentrations of randomly located vacancies are present are studied. We find that resonant modes associated with isolated defects couple to form an extended defect band, leading to a significant increase in transmission for frequencies inside the 3D photonic bandgap. Outside the 3D gap, vacancies induce scattering from evanescent to propagating modes, leading to an increase in transmission near the pseudo-gap edges within the gap. The local defect density of states for several concentrations of vacancies is computed; thus, it is shown that the total number of defect states and the range of supported frequencies increase due to increasing vacancy density.

Mapping the nonlinear dynamics of a laser diode via its terminal voltage.

We show that the bifurcations between dynamical states originating in the nonlinear dynamics of an external-cavity semiconductor laser at constant current can be detected by its terminal voltage V. We experimentally vary the intensity fed back into the gain medium by the external cavity and show that the dc component V(dc) of V tracks the optical intensity-based bifurcation diagram. It is shown using computational results based upon the Lang-Kobayashi model that whereas optical intensity accesses the dynamical-state variable |E|, V is related to population-inversion carrier density N. The change in feedback strength affects N and thereby the quasi-Fermi energy level difference at the p-i-n junction band-gap of the gain medium. The change in the quasi-Fermi energy-level thereby changes the terminal voltage V. Thus V is shown to provide information on the change in the dynamical-state variable N, which complements the more conventionally probed optical intensity.