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Optoelectronic feedback on a laser diode is demonstrated to generate two distinct modes of periodic pulse-train formation depending on the injection current $J$ of the laser leading to microwave combs in two distinct regimes. For $J$ close to the threshold current $J_{th}$ , the pulse repetition rate $f_{\mathrm{ rep}}$ is the inverse of the loop delay. This behavior is attributed to feedback-induced gain-switching and leads to comb spacings in the tens of MHz range. In contrast, for $J \simeq 2J_{th}$ , the repetition rate $f_{\mathrm{ rep}}$ is observed to be related to the relaxation-oscillation frequency $f_{\mathrm{ RO}}$ . The potential to generate pulse trains and associated microwave combs may find use in metrology, optical communications, optical sampling, and spectroscopy.

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 .

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 n h i g h : n l o w = 2.1 ; to the best of our knowledge, this is the lowest RIR used to obtain a 2D CPBG in a PC.

Terahertz (THz) time-of-flight tomography (TOFT), a nondestructive-evaluation technique for the stratigraphic characterization of structures with layers on the micron-to-millimeter scales, has proven to be challenging to apply to samples containing both micron-scale and millimeter-scale layers. In THz TOFT, echoes reflected from distant interfaces and defects are often obscured as they may be immersed in a noisy background as such features in the reflected signal may be weak due to attenuation and dispersion, leading to the loss of valuable information. Moreover, overlapping echoes from any optically thin layers, such as thin coatings on thick specimens, are likely to be mistaken for a single interface in reconstructing the stratigraphy. Thus, layered structures containing both thick and thin layers have proven problematic for THz TOFT characterization. In this paper, a sparse-deconvolution (SD) technique, based on an interior-point method, and including a propagation model accounting for dispersion is demonstrated. The method is shown to be successful in extracting the impulse response of samples that combine the challenges of both thick and thin layers. The robustness and effectiveness of this method are verified numerically and experimentally. While the proposed SD approach does not perform as well as cross-correlation (CC) techniques in terms of the maximum thickness, it can provide a clearer and more accurate reconstruction of moderately thick samples incorporating thin layers.

International audience; The structure as well as morphology of nanoporous alumina (NP Al2O3) films on Al substrates are investigated by terahertz (THz) reflectometry and scattering imaging. An inhomogeneous area is identified in THz C-scan results off specular conditions at various angles. The thickness of NP Al2O3 films calculated based on THz results is in excellent agreement with destructive cross-sectional field emission scanning electron microscopy (FE-SEM) measurements.

Terahertz (THz) reflective imaging and scanning acoustic microscopy (SAM) were utilized for material characterization as well as quality control of an injection-molded thermoplastic electrical receptacle plate. V-notched weld lines that degrade the mechanical strength of injection-molded products significantly, are observed in both SAM and THz results. The dimension of V-shaped morphological feature of the weld line is ~ 400 μm in width and ~ 10 μm in depth. Position resolved THz birefringence also locates the weld line.

International audience; SD based on interior point method is used to extract structural information of a sample incorporating both optically thick and thin layers. Pulse spreading is taken into consideration as the THz signal propagates through the thick layers. Compared with both cross-correlation (CC) and frequency wavelet-domain deconvolution (FWDD), the proposed SD algorithm succeeds in resolving the structure of the sample clearly, demonstrating that SD-based approaches might be the preferred option in the presence of both the thick and thin layers.

Optical frequency combs (OFCs) and microwave frequency combs (MFCs) are of intense interest in fields ranging from metrology to multifrequency light sources. MFCs in particular have attracted interest for applications in microwave photonics. Timing jitter is a key limiting factor of the quality of OFCs and MFCs, and despite the central importance of timing jitter, a clear generic account of its effect on OFCs and MFCs that provides a connection between the two is lacking. We consider the power spectral density (PSD) of the OFCs and MFCs produced by active and hybrid active-passive mode-locked lasers in which the active mode locking is effected by a high-spectral-purity oscillator, but with timing noise originating in both the active locking and the mode-locked oscillators. Based on an analytically tractable theoretical treatment, we account quantitatively for the characteristic comb line shape consisting of a narrow central peak lying atop a broad pedestal. The theory provides a quantitative comparison between characteristic OFC and MFC line shapes and identifies the origin of the difference.

International audience; Terahertz (THz) spectroscopy is used to measure permittivity (100 GHz-2.5 THz) of ZnO and CuO powders with low fill factor pressed into pellets in a polyethylene binder. We show that porosity (air) of such pressed pellets has a large effect on effective pellet permittivity (~10 %) and on the extracted permittivity of the oxide constituent (~150 %). We explore a twostep analysis based on sequential application of different effective medium models (EMMs), first to account for the air, and subsequently to extract the oxide's dielectric properties. We show that the combination of the Vegard's law and the Maxwell Garnett is the best to account, respectively, for the air and the oxides. In this regard, the capacity that this approach has to adapt to each phase's physical characteristics by using multiple EMMs is an advantage. The resulting oxide permittivities are significantly larger than previously reported for such pellets as a consequence of the porosity. We find for the real relative permittivities of CuO and ZnO ~12.1 and ~8.9, respectively, in the THz range.

International audience; Ordered nanoporous (NP) alumina (Al2O3) films were grown on Al substrates through a two-step electrochemical anodization process. The morphology as well as the roughness are characterized by terahertz (THz) reflectometry and scattering imaging. In particular, we show that before the second anodization, irregular surface morphology of the NP Al2O3 films leads to significant THz scattering, whereas the far more homogeneous films following the second anodization show far less scattering. The regularity of the surface morphology is not readily ascertained using visible-light optical microscopy. The THz results are corroborated by field-emission scanning electron microscopy (SEM) and atomic-force microscopy (AFM), both of which are time-consuming, not easy to operate, and can only provide the local characterization of NP Al2O3 films on Al substrate. THz-based techniques allow for the nondestructive characterization of the surface morphology of the entire NP Al2O3 films on the 10–100 μm length scale important for a range of applications while providing information over macroscopic scan areas, and obviate the need for sample preparation required by other common surface-morphology characterization techniques.

The thickness of 2, 4, 6, 8, 10, and 12 mm thick polycarbonate (PC) and poly-methyl methacrylate (PMMA) sheets were characterized nondestructively by terahertz time-of-flight tomography in reflection. Due to terahertz attenuation and dispersion in the material, first characterized in transmission, features in the reflected signal associated with structure deep in the sample (i.e., the back interface) may be difficult to identify, and therefore signal processing is employed, namely frequency-wavelet domain deconvolution and a cross-correlation approach in which we account for dispersion. The refractive indices are found to be n ( ν ) = 1.67 − 0.0096 v for PC and n ( ν ) = 1.61 − 0.0085 v for PMMA, while the absorption coefficients, which follow the form of the universal dielectric response, are α ( ν ) = 0.628 + 4.64 v − . 675 for PC and α ( ν ) = 0.388 + 13.15 v 1.777 for PMMA, where ν is measured in THz and the absorption coefficient is in units of cm−1. We show that straightforward analysis techniques that neglect dispersion are limited to measuring layer thicknesses in these materials of less than ∼17 mm, while accounting for dispersion results in a factor-of-two improvement, allowing us to measure samples as thick as ∼36 mm.

International audience; Amphorae frequently have a whitish skin that has been mistaken for a slip or painted layer over the otherwise pinkish ceramic. This skin is due to the simultaneous presence of calcite and NaCl in the clay, leading to depletion of red iron oxides near the surface. We demonstrate that terahertz time-of-flight tomography can provide a nondestructive, contactless means to measure the skin thickness on amphora sherds, finding a thickness of ~50 μm.

We study delay-based photonic reservoir computing using a semiconductor laser with an optoelectronic feedback. We investigate the connection between the bifurcation landscape of this system with the computational performance of the reservoir. Specifically, there are multiple Hopf bifurcation branches possessing the parity asymmetry with relation to the feedback sign. We observe the corresponding difference in the normalized means square error (NMSE) values using the prediction on the chaotic Santa-Fe time series as a benchmark.

Graphical abstract Scanning acoustic microscopy (SAM) and Terahertz imaging analysis of weld lines in thermoplastic polymer (ABS) manufactured by injection-molding., Highlights • Two techniques to investigate plastic welds, Ultrasonic Microscopy and Terahertz Imaging • Weld lines, inevitable draw backs of melds, of unpredictable locations and of weaker mechanical properties • Micro-elastic visualization of weld lines by Scanning acoustic microscopy • Micro-elastic heterogeneity and acoustic anisotropy • Birefringence at weld lines, 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.

International audience; The optical constants (complex dielectric function) of isotropically distributed CuO and ZnO particles in polyethylene pellets are measured by terahertz time-domain spectroscopy. The determination of the dielectric properties of these materials is of interest for energy-storage applications. Maxwell-Garnett theory is used to extract the contribution to the frequency-dependent optical constants of the oxide powders. The validity of the assumptions of Maxwell-Garnett theory are experimentally verified and self-consistency of the results of the model confirmed. On this basis, experimental complex permittivity values for isotropic CuO and ZnO oxide powders are reported in the 100 GHz-3 THz range.

International audience; We present a time-of-flight tomography method for exceeding the naïve axial (i.e., depth) resolution limit of terahertz (THz) deconvolution by autoregressive spectral extrapolation (AR) based on the modified covariance method (AR/MCM). In contrast to Wiener filtering combined with wavelet denoising, AR/MCM does not discard any frequency components in the low signal-to-noise (SNR) regions of the measured data, and unlike the AR approach based on the Burg method (AR/BM), no peak splitting (single peaks in the impulse response function appearing as double peaks) as well as frequency bias (spectral peaks shifted with respect to their correct positions) is observed after deconvolution. After verifying the advantages of AR/MCM over Wiener filtering in conjunction with wavelet denoising as well as over AR/BM, using synthetic data, AR/MCM is employed to reconstruct a single layer of mill scale on a steel coupon from experimental THz time-of-flight tomography data. The reconstruction shows good agreement with the film thickness obtained from destructive cross-sectional measurements. In addition, unlike AR/BM, optimizing the parameters to obtain stable reconstruction is straightforward relying of Akaike’s information criterion suggesting that AR/MCM can be an easier to implement for THz nondestructive characterization of stratigraphy under noisy conditions, particularly when estimates of the stratigraphy may not a priori be available.

International audience; We measure in a nondestructive and noncontact fashion the thicknesses of three scale films with thicknesses 28.5 ± 1.4 μm, 13.4± 0.9 μm, and 5.1 ± 0.3 μm on steel substrates employing terahertz time-of-flight tomography combined with advanced signal-processing techniques. Wüstite is the dominant phase in the scale films, though magnetite and hematite are also present. Because wüstite is electrically insulating, the incident terahertz electromagnetic pulses largely penetrate into the scale film; however, the pulses are entirely reflected by the underlying electrically conductive steel substrate. Because the film layers are thin, in some cases optically thin, the distinct pulses reflected at the air/scale and scale/steel interfaces overlap in time and thus are not visually evident in the reflected terahertz signal, necessitating the use of deconvolution techniques to recover the sample structure. We compare the merits of three deconvolution techniques, one unsuccessful (frequency-wavelet domain deconvolution) and two successful (sparse deconvolution and autoregressive extrapolation), to characterize the thicknesses of these scale films.

International audience; A laser diode subjected to optoelectronic feedback in which some light is converted to photocurrent that is fed back into the laser injection terminals can display periodic oscillations in its optical intensity. We demonstrate experimental and numerical evidence that, as the feedback level is varied, a step-wise change in the relaxation oscillation frequency manifests itself in the output optical intensity. These transitions in the dynamics can either correspond to an abrupt jump between two limit cycles, associated with a subcritical torus bifurcation of a limit cycle, or to a progressive switching mediated by an intermediate quasiperiodic state. Finally, when ramping the feedback level down, hysteresis is observed in the sequence of switching events between the limit cycles. Such devices are of interest for photonic microwave sources for wavelength-division multiplexed radio-over-fiber systems.

International audience; 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 analyze the quantum dynamics of a two-level emitter in a resonant microcavity with optical feedback provided by a distant mirror (i.e., a half cavity) with a focus on stabilizing the emitter-microcavity subsystem. Our treatment is fully carried out in the framework of cavity quantum electrodynamics. Specifically, we focus on the dynamics of a perturbed subradiant state of the emitter-microcavity subsystem to ascertain its stability (existence of time oscillatory solutions around the candidate state) or lack thereof. In particular, we find conditions under which multiple feedback modes of the half cavity contribute to the stability, showing certain analogies with the Lang-Kobayashi equations, which describe a laser diode subject to classical optical feedback.

Terahertz birefringence in nanoporous A l 2 O 3 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.

Recently, terahertz time-of-flight tomography (THz TOFT) has attracted attention for the localization and quantitative characterization of internal defects in composite materials due to its superior time and spatial resolution and high penetration for various non-metallic materials. However, the dispersion in the THz optical constants and a lack of prior knowledge of defect types in a composite sample significantly degrade the temporal and spatial resolution in THz TOFT measurements, which hinders the super-resolution characterization of the defects internal the material. Here, a sparse Bayesian learning-based (SBL) spectrum-graph integration method is proposed to enable super-resolution characterization of multi-ply glass fiber reinforced polymer (GFRP) composites with delamination defects. The core of this strategy includes spectrum localization and graph quantification. The spectrum-localization process is first implemented to accurately obtain the depth location of delamination defects by SBL, in which dispersion compensation based on double parametric dictionaries is performed to address the dispersion and overlapping issues of the dispersive THz echoes reflected from various interfaces within the sample. Then, based on the estimated depth information for each delamination defect, the graph-quantification process is carried out to characterize the transverse location and size of each delamination defect by the local peak-to-peak stratified imaging method. The estimated size accuracy for the delamination defects can reach more than 95%. Overall, the proposed strategy can quantitatively and simultaneously characterize the axial and transverse information of delamination defects internal GFRP composites with high resolution.

International audience; Despite predictions of the paperless office, global demand for printing and writing paper remains strong, and paper appears to be here to stay for some time. Not only firms, but also governments, libraries, and archives are in possession of large collections of legacy documents that still must be sorted and scanned. In this study, terahertz-based techniques are demonstrated to address several routine tasks related to the automated paper handling of unsorted legacy documents. Specifically, we demonstrate terahertz-based counting of the number of sheets in unconsolidated paper stacks, as well as locating stapled documents buried in paper stacks.

We carry out a nondestructive study of injection-mold weld lines in an acrylonitrile butadiene styrene (ABS) thermoplastic electrical receptacle plate. Terahertz techniques show morphological features at the weld lines and reveal terahertz birefringence properties localized around the welds, indicating frozen-in molecular orientation and stress proximate to the welds. Surface acoustic microscopy corroborates the morphological features at the welds shown by terahertz imaging and also reveals anomalous mechanical properties at the weld lines. These results indicate that THz-based techniques provide nondestructive reliability assessment and quality control for injection-molded thermoplastic products.

Opening the terahertz electromagnetic band to a wealth of applications still requires the development of new devices. For example, effective means to filter, modulate, and route terahertz beams are still required for terahertz communications, spectroscopy, and sensing to achieve their promise. In particular, metasurfaces are widely discussed for future 6G wireless communications systems. These applications, however, will also require new functionality, such as the ability to design structures enabling a more complex spectral response. Here we outline systematic design principles to realize the polarization-independent electromagnetically induced transparency-like effect in a class of planar terahertz metamaterials that can be fabricated using commonly available processes and whose structural parameters can be flexibly varied to provide wide tuning of the transparency windows within the broader absorption band. We also show how the basic concept can be used to achieve dual transparency bands.

International audience; Terahertz imaging is a relatively new technique for nondestructive evaluation. Compared with the destructive micro-cut technique that provides information along the line of cut only, THz imaging nondestructively provides a global mapping of a sample. Hence, this technique has been applied to characterize coated materials and composite laminates. In this work, we characterize optically thin wüstite layers on steel leveraging signal-processing techniques.

High-order frequency locking phenomena were recently observed using semiconductor lasers subject to large delayed feedbacks [B. Tykalewicz, et al., Opt. Express 24, 4239 (2016); B. Kelleher, et al., Chaos 27, 114325 (2017)]. 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 new 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., 13 pages, 10 figures

In laser feedback interferometry (LFI), a laser diode is shone onto a target and the reflection from that target is injected back into the laser cavity. It has been demonstrated that changes in the laser dynamics induced by the fed back light can be exploited to measure target displacement, absolute position, or velocity [1,2]. In particular, displacement sensors have been demonstrated to reach minimum detectible displacements (MDD) as small as a few nanometers. However, such small MDD levels require post-processing of the measured signals and/or to modify, and thus increase the complexity of, the LFI setup [3,4].

International audience; Semiconductor lasers subject to optoelectronic (OE) feedback have been the focus of research for the last decades, but have recently attracted attention as a possible source of microwave generation when operated in limit-cycle (i.e., periodic) regime. Due to the importance of these systems for a number of emerging applications, understanding their fundamental aspects remains a challenge. In this work, we explore experimentally and theoretically the dynamics of a DFB quantum well laser subject to OE feedback with an emphasis on the impact of high-pass electronic filtering on the complex emerging bifurcations, which is of interest for microwave photonics applications of these devices. The laser is characterized with high damping of side modes in the absence of OE feedback. The feedback loop includes an optical path with a polarizer and a rotating waveplate to control the feedback rate.

The consequences of a four-point bending test, up to 12 mm, are examined by emitting 1 MHz ultrasonic guided waves in woven carbon fiber reinforced polymer specimens, using coda wave interferometry (CWI), revealing a potential use for nondestructive evaluation. It is known that CWI is more sensitive to realistic damage than the conventional method based on the first arriving time of flight in geophysical, or in civil engineering applications such as concrete structures. However, in composite materials CWI is not well established because of the involved structural complexity. In this paper, CWI is investigated for monitoring the occurrence of realistic defects such as micro-cracks in a woven carbon fiber composite plate. The micro-cracks are generated by a four-point bending test. The damage state is stepwise enhanced by gradually increasing the load level, until failure initiation. The damage is monitored, after each loading, using ultrasound. It is demonstrated that CWI is a powerful tool to detect damage, even low levels, in the sample. Two damage indicators based on CWI, i.e. signals correlation coefficient and relative velocity change, are investigated and appear to be complimentary. Under significant loading levels, the normalized cross-correlation coefficient between the waveforms recorded in the damaged and in the healthy sample (reference at 0 mm), decreases sharply; this first indicator is therefore useful for severe damage detection. It is also demonstrated, by means of a second indicator, that the relative velocity change between a baseline signal taken at zero loading, and the signals taken at various loadings, is linear as a function of the loading, until a critical level is reached; therefore this second indicator, is useful for low damage level detection. The obtained evolution of the relative velocity measurement is supported by relative comparison to the evolution of the bending modulus in function of displacement. The relative velocity change exhibits the same evolution as the bending modulus with loading. It could be used to indicate when the material stiffness has decreased significantly. The research is done in the framework of composite manufacturing quality control and appears to be a promising inspection technique. This work is supported by the Région Grand Est.

International audience; Terahertz time-domain spectroscopy has been attracted numerous attention due to its nondestructively, non-ironically and high penetration toward non- or semi-conductive material. In this project, reflection spectra as well as advanced signal-post processing techniques have been applied to characterization the thickness of plastic sheets. Moreover, the nature of frequency-dependent dispersion is also discussed based on transmission spectra.

International audience; 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.

International audience; ime-domain terahertz reflectometry has long been of interest to obtain three-dimensional information about objects transparent in the 100 GHz-3 THz frequency range. The application of such techniques has been limited by the conductivity of the materials and by conventional axial resolution criteria. Specifically, I discuss work on detecting subsurface damage in carbon fiber composites and in measuring paint-layer thicknesses down to ~20 microns. We employ a typical commercial broadband time-domain source with bandwidth from ~100 GHz to ~3 THz. Yet terahertz imaging faces two important limitations. (1) The first is that in materials with a significant conductivity, the attenuation of incident terahertz electromagnetic waves is very rapid, limiting the penetration into the object. (2) The second limitation can best be illustrated by a stratified medium. Due to the Fresnel coefficients associated with the variation of the refractive index across material interfaces, one expects a reflected signal that is composed of various echoes associated with the interfaces (as well as multiple reflections which in practice are often weak). If the layers are sufficiently thin, then the echoes from successive layers will overlap, and thus multiple echoes will not be visually evident in the reflected signal. In this talk I discuss my group’s recent work to circumvent these limitations. The approaches rely upon applying advanced signal-processing techniques to extract the maximum information from the detected signals. Specifically, I provide case studies of coatings on metals, fiber composite laminates, and an oil painting on canvas with multiple paint layers.

International audience; We demonstrate a nanometric sensor based on feedback interferometry in a 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. Nanodisplacement sensors have been demonstrated based on a variety of physical effects and for a range of applications [1, 2]. The laser feedback interferometry (LFI) or self-mixing interferometry sensor [3, 4] we demonstrate is a noncontact sensor, and therefore we set aside discussion of most MEMS-based approaches. As for noncontact nanodisplacement sensors, there are a number of approaches, including those based on capacitance, eddy currents, and atomic-force microscopy [5, 6]. These approaches, while in some cases sensitive to atomic-scale displacements can be complex, costly, and sensitive to quite small displacement ranges (small dynamic range). LFI is based on light, reflected back into the active region, which in turn affects the laser diode (LD) operation in a fashion dependent on the phase of the reflected light [7, 8]. LFI itself provides sensitivity at least on the scale of the emission wavelength λ, though below we show that the minimum detectible displacement (MDD) can be λ. A LD with optical feedback is generally known as an external-cavity semiconductor laser (ECL). Heuristically, when the target distance L is varied by ∆L, the properties of an ECL (frequency ν, linewidth, and threshold gain) undergo periodic variation, which is broadly understood on the basis of the Lang and Kobayashi (LK) equations [9]. The feedback-phase sensitivity of the LFI sensor depends on the change of frequency ν with L, which in turn is also manifested in the optical output power P PD measured by a photodiode (PD) and change of carrier concentration measured by the LD terminal voltage V LD (under constant injection current J). We demonstrate LFI sensors enabling unprecedentedly high sensitivity providing a linear sawtooth dependence on L of the sensing parameter, here focusing on V LD. LFI has been exploited for imaging [10, 11], biomedical sensing [12] and measuring absolute distance [13, 14], displacement [15-17], reflective index [18], velocity [19, 20], and flow [21]. Recently, Keeley et al. [22] investigated the emission spectrum of a THz QCL by measuring ν and V LD as functions of the displacement ∆L and showed that LFI can achieve a similar spectral resolution as Fourier-transform infrared spectroscopy. LFI displacement sensors have been demonstrated usually using a moving target, e.g. a harmonic piezo-actuator or loudspeaker that sweeps several µm , combined with high sampling rates to measure fringes of the LFI signals. Their MDDs are from a few to hundreds of nm but require post-processing of the LFI signals and/or substantial modifications of the basic LFI setup [23-28], laser feedback grating (< 10 nm) [26], Fourier transform (λ/50) [27], phase shifting (λ/12) [28-30]. In contrast, our approach requires neither modification of the basic LFI setup nor any signal processing, but relies on the direct physical measurement of the LFI signals in parameter ranges leading to high linearity and signal-to-noise ratio (SNR). Specifically, we demonstrate a LFI sensor with a MDD of λ/130, assuming the feedback level can be adjusted in an optimal range. Since the LFI sensing mechanism is based on the feedback phase, such a sensor can also be used as a gas or liquid sensor using refractive index change. For the MDD and geometry we focus upon, this translates into the ability to sense refractive-index changes in the optical feedback loop of ∆n min ∼ 10 −8. In this Letter, because of the key rôle played by ν in LFI, we start with its dependence on L before proceeding to focus on V LD. We first review important theoretical points that describe the variation in ν and consequently in V LD with L.The theory of LFI is discussed in Refs. [7, 31]. Briefly, the excess-phase equation derived from the LK model relates ∆L to ∆ν = ν − ν 0 as a periodic function where ν is the output frequency of the ECL and ν 0 is the frequency of the free-running LD (i.e., in the absence of optical feedback). When ∆L changes, ∆ν obeys ∆ν(∆L) = mF(∆L) with m the optical-feedback modulation index that defines the signal slope with respect to ∆L, F(∆L) a periodic function with period λ 0 where λ 0 = c/ν 0 with c the speed of light in vacuo. Qualitatively, the dependence of ν on ∆L tends to be sinusoidal for weak feedback. The shape can become close to a piecewise linear function

We consider theoretically the power spectral density S E ( ν ) of an otherwise periodic optical pulse train with optical field E ( t ) , i.e., the optical frequency comb, in the presence of noise in the pulse-to-pulse carrier-envelope phase slip in carrier-envelope-stabilized optical pulse trains. The spectrum is a frequency comb where the comb line shape is Gaussian. To obtain these results, we implement a heuristic theory based on an Adler equation for the carrier-envelope frequency noise that for weak noise leads to fluctuation statistics described by an Ornstein–Uhlenbeck process.

Terahertz time-of-flight tomography is employed to characterize the individual layers in a multilayer coating on steel substrates. The multilayers, containing up to three layers, consist first of a cataphoretic layer, sealer, and varnish progressing upward from the steel substrate. The individual layer thicknesses were reconstructed from the experimental data using autoregressive spectral extrapolation based on the modified covariance method (AR/MCM), which extrapolates the frequency components of the transfer function into the low signal-to-noise-ratio (SNR) regions from the high SNR regions. Due to the high sensitivity of AR/MCM to the presence of noises, wavelet denoising, in some cases, was needed to precondition the data prior to application of AR/MCM. The method is verified numerically and experimentally, showing that it can reconstruct individual layers in the 10-μm range, and good agreement is found between the thicknesses of individual layers extracted by AR/MCM and characterized by eddy-current measurements.

Slow light in square-lattice chalcogenide photonic-crystal (PC) holey fibers with uniform longitude geometry are proposed and theoretically investigated. By using the planewave-expansion method, a largest normalized complete 2-D photonic bandgap (CPBG) width of about 7.4% is found in an optimized connected-rod square-lattice chalcogenide PC, and the CPBG remains open with a refractive-index contrast as low as 2.48:1. We then consider the PCs as cladding layers to form holey fibers, and group indices up to several hundreds are predicted.

A novel polarization beam splitter based on a silicon photonic crystal (PC) heterostructure operating in the optical-telecommunications band is envisaged and is configured for planar integration with other PC or waveguide structures. The small 9 μm × 9.4 μm footprint polarization beam splitter is investigated by the plane-wave expansion and finite-difference time-domain methods. Due to the combined effects of self-collimation and the photonic band gap, self-collimation transmission and 90° beam splitting for the two orthogonal polarizations are achieved. The transmissivity exceeds 60% (78%) for TE (TM) polarization covering a 115-nm bandwidth, and it is also observed that the polarization extinction ratios of the device are higher than 13 and 31 dB, respectively. Moreover, at the wavelength of 1550 nm, TE (TM) polarization has high transmissivity 94.9% (88%) with high polarization extinction ratio of 17 dB (41 dB). A compact and efficient polarization beam splitter is successfully designed for applications in optical communications.

International audience; The stabilization of a relatively simple microwave oscillator tunable across the full X-band based on a laser subjected to optical feedback is achieved. Specifically, a resonance effect based on locking the two inherent dynamic frequencies of the system, as well as, optoelectronic feedback are utilized to achieve a sub-ps jitter and typical phase noise in the range of −107 dBc/Hz at 10 kHz offset from an oscillation frequency that can be tuned from 5.5 to 12.1 GHz. Further, the microwave signal is extracted from the laser-diode injection terminals and eliminates the need for multiple lasers, radio-frequency filters, and external RF sources. This architecture, therefore, realizes a compact and low-cost tunable microwave photonic oscillator.

International audience; The chaotic terminal voltage dynamics of a semiconductor laser subjected to external optical feedback are utilized to directly generate electronic random number streams with minimal post-processing at rates of 40-120 Gb/s, thus obviating the need for optical-to-electrical conversion and facilitating integration with high-speed computers and devices. Further, a comparison of the terminal voltage to the optical intensity being utilized as entropy sources is performed. It is shown that the voltage dynamics have an inherently larger entropy, a reduction in delay signature, and a more suitable distribution for generating random bit streams. Random bit sequences are commonly utilized in cryptography , machine learning, and simulations. But, due to the need for fast rates and ease of generation most random bit sequences are generated using deterministic algorithms and not truly random entropy sources. Therefore , fast physical random bit generators that can be easily integrated into computers or electronic systems are of interest for these applications. In this paper, we point the way to such a device by utilizing the chaotic terminal voltage of a laser diode. Specifically, laser diodes undergo a profound modification to their dynamical variables , i.e., carrier density, photon number, and optical phase, when subjected to optical self-feedback. It is well-known that these systems can display chaotic dynamics and have been utilized as an archetypical testbed for non-linear dynamics [1] and for high-speed information processing applications [2]. In the latter context, the first use of sampled chaotic optical intensity fluctuations as an entropy source utilized for high-speed random number generation was demonstrated by Uchida et al. [3]. The generated bit streams were an order of magnitude faster than any other previously utilized physical source. Since then, various realizations and improvements utilizing optical chaos have been demonstrated allowing for faster generation rates up to Tb/s. Various methods based on creating symmetric distributions without bias through post-processing techniques have been proposed, for example, using derivatives [4-6] and finite differences [7]. To further improve the paradigm, other novel chaotic laser sources and schemes have been demonstrated, such as, through bandwidth enhancement [8], in photonic integrated circuits [9], ring lasers [10, 11], heterodyning [12], terahertz optical asymmetric demultiplexers [13], chaotic solitary vertical-cavity surface-emitting lasers [14], polarization rotated feedback [15], as well as, long on-chip optical feedback [16]. Additionally, fast rates have been demonstrated utilizing parallel significant bits [17] and * alocquet@georgiatech-metz.fr parallel-laser schemes [18]. The bit streams in most of the previously cited works are post-processed offline. Interestingly in some cases, real-time implementations have been demonstrated, using delayed feedback lasers [19] and photonic integrated circuits [20]. Recently, an interesting concept, physical white chaos, has been proposed and the enhanced chaos leads to random number generation at 320 Gb/s [21]. While there have been many improvements and schemes demonstrated in the field of random number generators based on chaotic lasers, in almost all cases advanced post-processing, complex experimental schemes, optical to electronic conversion, and/or exotic components are required for passing the standard randomness tests and for achieving ultrafast bit rates. In this Letter, we demonstrate that the chaotic laser terminal voltage V (t), as a surrogate for carrier density n(t) in the gain medium [22-25], can be used as a novel, fully electronic, entropy source for random number generation at rates of 40-120 GS/s, where only simple post-processing is required when compared to utilizing the optical intensity I(t). In order to understand the reason behind this improvement, we compare the voltage entropy source with the commonly utilized optical intensity which was measured simultaneously from the same chaotic laser. Specifically, the entropy sources are compared utilizing distributions, delay-correlation, and permutation entropy analysis. It is shown that the simple physical measurement of V (t) is an inherently superior entropy source compared to the optical intensity, I(t). Further, our approach has the benefit of simplicity, while still generating random bit streams at tens to hundreds of Gb/s. Specifically, the system, for the first time, offers a fast electronic entropy source that can be used to generate Gb/s streams without any optical-to-electrical conversion, thus facilitating the use of this entropy source for high-speed computing. In the experiment, an unpackaged multi-quantum well DFB laser was utilized [25, 26] operating at 1550 nm. The laser was subjected to delayed feedback from a mirror placed at a distance L resulting in a delay time of τ. The sub-nanosecond AC component of V (t) was

International audience; In this paper, we investigate the possibility of using optical injection to efficiently suppress the time-delay (TD) signatures of chaotic signals in a large experimentally accessible parameter range of semiconductor ring lasers (SRLs). We also study how this optical injection can improve the signal bandwidths. The injection signal is obtained from a master SRL with either optical self-or cross-feedback. For optical self-feedback configurations, it is found that the suppression of TD signatures is similar to what has been found in injected Fabry-Perot semiconductor lasers, i.e., narrow range of parameters with respect to the detuning and injection strengths. For cross-feedback configurations, however, the TD signatures can be suppressed in a wide range of parameters meanwhile the bandwidths are significantly improved for the same range of parameters. This is particularly useful for the security in chaos-based communications and also for generating random bits with improved properties.

International audience; Semiconductor lasers subjected to optical feedback have been intensively used as archetypical testbeds for high-speed (sub-ns) and high-dimensional nonlinear dynamics. By simultaneously extracting all the dynamical variables, we demonstrate that for larger current, the commonly named "quasiperiodic" route is in fact based on mixed external-cavity solutions that lock the oscillation frequency of the intensity, voltage, and separation in optical frequency through a mechanism involving successive rejections along the unstable manifold of an antimode. We show that chaos emerges from a crisis resulting from the inability to maintain locking as the unstable manifold becomes inaccessible.

Polarization-sensitive terahertz imaging is applied to characterize subsurface damage in woven carbon fiber-reinforced composite laminates in this study. Terahertz subsurface spectral imaging based on terahertz deconvolution is tailored and applied to detect, in a nondestructive fashion, the subsurface damage within the first ply of the laminate caused by a four-point bending test. Subsurface damage types, including matrix cracking, fiber distortion/fracture, as well as intra-ply delamination, are successfully characterized. Our results show that, although the conductivity of carbon fibers rapidly attenuates terahertz propagation with depth, the imaging capability of terahertz radiation on woven carbon fiber-reinforced composites can nonetheless be significantly enhanced by taking advantage of the terahertz polarization and terahertz deconvolution. The method demonstrated in this study is capable of extracting and visualizing a number of fine details of the subsurface damage in woven carbon fiber-reinforced composites, and the results achieved are confirmed by comparative studies with X-ray tomography. The authors gratefully acknowledge the financial support of the Conseil Régional du Grand Est of the Fonds Européen de Développement Régional (FEDER), and of the Institut Carnot ARTS.

International audience; 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.

International audience; Periodic arrays of proximate but noncontacting noble metal nanoparticles provide the ability to electromagnetically couple the surface plasmons on various nanoparticles to produce collective delocalized surface-plasmon-polariton modes with well characterized mode structure. Such structures provide intrinsic interest as well as provides an attractive concept for optical sensing in potentially open structures permitting gas or liquid to percolate through the structure. In this talk, I review our work on modeling the surface-plasmon-polariton modes of various nanoparticle arrays. I discuss one-dimensional chains and two-dimensional nanoparticle slabs. Ways of dealing with losses will be discussed. Provided the ratio of nanoparticle spacing to nanoparticle diameter (for spherical nanoparticles) exceeds a critical value, the electromagnetic interactions between nanoparticles are dominated by dynamic dipole-dipole coupling. In other words, one nanoparticle acts on the others (and on itself) by means of the retarded electromagnetic dipole-dipole interactions between all nanoparticles. The resulting collective modes delocalized over the structure are surface-plasmon polaritons. We consider various structures including infinite and finite chains, ring-shaped arrangements of nanoparticles, and two-dimensional slab arrays. Given the dispersion of surface-plasmon polaritons, we can then obtain the linear optical properties (e.g., reflection and transmission spectra, angle-dependence of reflectivity and transmittivity), which in turn provide important information on the design of nanoparticle-array-based devices. Surface-plasmon polaritons are strongly attenuated by homogeneous and inhomogenous broadening as well as by intrinsic radiative loss. We discuss strategies for mitigating these losses.

International audience; 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. Published by AIP Publishing. https://doi.org/10.1063/1.5013332 Irregular switching between dynamical regimes, or, intermittency, is a ubiquitous phenomenon observed in many nonlinear systems when a parameter of the system approaches a critical point. External-cavity lasers (ECLs) exploit an external mirror to provide time-delayed optical feedback into the laser diode. Their dynamics can be high-dimensional and highly multistable; thus, ECLs are interesting testbeds to observe and understand transitions between attractors and the involved timescales. Despite the existence of several reports on intermittency in ECLs, there is still a lack of knowledge in the important case in which the laser is biased well above its threshold. We observe in this case two distinct intermit-tency regimes on the route to chaos, as the feedback strength is increased. The first regime corresponds to multistate intermittency involving two or three states composed of several combinations of periodic, quasiperi-odic, and subharmonic dynamics. The second regime is observed for larger feedback levels and involves intermit-tency between period-doubled and chaotic regimes.