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.

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.

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.

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.

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.

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.

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.

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.

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.

Experimental bifurcation-cascade diagram of an external-cavity semiconductor laser.

This Letter is the first to report experimental bifurcation diagrams of an external-cavity semiconductor laser (ECSL) in the low-to-moderate current injection regime and long-cavity case. Based on the bifurcation cascade behavior which was unveiled by Hohl and Gavrielides [Phys. Rev. Lett. 82, 1148-1151 (1999)], we present a detailed experimental investigation of the nonlinear dynamics of ECSLs and of the robustness of the cascade to changes in the current and cavity length. Also, we report for the first time a well resolved experimental Hopf bifurcation in an ECSL. Based on the Lang and Kobayashi model, we identify the dynamical regimes and the instabilities involved in the cascade, as well as the influence of the current and cavity length on the cascade.

Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser.

This paper reports the experimental investigation of two different approaches to random bit generation based on the chaotic dynamics of a semiconductor laser with optical feedback. By computing high-order finite differences of the chaotic laser intensity time series, we obtain time series with symmetric statistical distributions that are more conducive to ultrafast random bit generation. The first approach is guided by information-theoretic considerations and could potentially reach random bit generation rates as high as 160 Gb/s by extracting 4 bits per sample. The second approach is based on pragmatic considerations and could lead to rates of 2.2 Tb/s by extracting 55 bits per sample. The randomness of the bit sequences obtained from the two approaches is tested against three standard randomness tests (ENT, Diehard, and NIST tests), as well as by calculating the statistical bias and the serial correlation coefficients on longer sequences of random bits than those used in the standard tests.

Detection and compensation of basis deviation in satellite-to-ground quantum communications.

Basis deviation is the reference-frame deviation between a sender and receiver caused by satellite motion in satellite-to-ground quantum communications. It increases the quantum-bit error ratio of the system and must be compensated for to guarantee reliable quantum communications. We present a new scheme for compensating for basis deviation that employs a BB84 decoding module to detect basis deviation and half-wave plate to provide compensation. Based on this detection scheme, we design a basis-deviation compensation approach and test its feasibility in a voyage experiment. Unlike other polarization-correction schemes, this compensation scheme is simple, convenient, and can be easily implemented in satellite-to-ground quantum communications without increased burden to the satellite.

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.

Statistics of the optical intensity of a chaotic external-cavity DFB laser.

We study experimentally and theoretically the first- and second-order statistics of the optical intensity of a chaotic external-cavity semiconductor DFB laser in fully developed coherence-collapse. The second-order statistic is characterized by the autocorrelation, where we achieve consistent experimental and theoretical results over the entire parameter range considered. For the first-order statistic, we find that the experimental probability-density function is significantly more concentrated around the mean optical power and robust to parameter changes than theory predicts.

The vector reflector.

A linearly polarized Bessel beam, whose spatial frequencies correspond to the Brewster angle, impinging at normal incidence on a higher refractive-index interface is shown to lead to a reflected field that can be used to produce an azimuthally polarized optical vector beam.

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.