Introduction to the Issue on Physics and Applications of Laser Dynamics (IS-PALD 2017).

In this paper, we introduce the Optics Express feature issue of the 7th International Symposium on Physics and Applications of Laser Dynamics (IS-PALD). This issue consists of expanded papers related to oral and poster presentations. Selected papers represent the best of IS-PALD 2017.

Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback.

We demonstrate numerically that a semiconductor laser subjected to phase-conjugate feedback (PCF) can exhibit an enhancement in the complexity of chaos by comparison to conventional optical feedback. Using quantifiers from spectral analysis and information theory, we demonstrate that under similar parametric conditions, PCF exhibits a larger chaotic bandwidth and higher spectral flatness and statistical complexity. These properties are of utmost importance for applications in secure communications and random number generation.

Aflibercept in persistent neovascular AMD: comparison of different treatment strategies in switching therapy.

PurposeTo evaluate the effects of aflibercept administered according to a pro re nata (PRN) or Fixed Regimen to patients with neovascular AMD and persistent intraretinal/subretinal fluid (IRF/SRF) despite three consecutive ranibizumab injections.MethodsPatients were switched to aflibercept injection (IVA) administered according to a PRN or to a fixed regimen for 1 year in two different retina centers. At baseline each patient underwent a complete ophthalmologic evaluation, including best-corrected visual acuity assessment (BCVA ETDRS chart), fluorescein, and indocyanine green angiography and OCT.ResultsEach group included 36 eyes. After 1 year the PRN group showed BCVA stabilization (63 vs 60 letters, P=0.33), whereas fixed regimen group showed significant BCVA improvement (68 vs 71, P=0.008). The median central retinal thickness decreased by 94 µm in the PRN (P=0.002) and by 148 µm in the fixed regimen group (P≤0.001). Complete IRF/SRF reabsorption was found in 58% of eyes in the PRN and in 42% of eyes in the fixed regimen group. At 1-year visit, the percentage of eyes with pigment epithelium detachment did not significantly decrease, but a height reduction was recorded in both groups. The median number of IVA was 3.5 in the PRN and 7 in the fixed regimen group.ConclusionThe switch to aflibercept with both treatment strategies enabled improvement in morphological parameters and stabilization of visual acuity. BCVA improvement and reduction in vision loss with reduction in retinal thickness, fluid and PED height was achieved with the fixed regimen in previously treated nAMD after 1 year.

Physical random bit generation from chaotic solitary laser diode.

We demonstrate the physical generation of random bits at high bit rates (> 100 Gb/s) using optical chaos from a solitary laser diode and therefore without the complex addition of either external optical feedback or injection. This striking result is obtained despite the low dimension and relatively small bandwidth of the laser chaos, i.e. two characteristics that have been so far considered as limiting the performances of optical chaos-based applications. We unambiguously attribute the successful randomness at high speed to the physics of the laser chaotic polarization dynamics and the resulting growth rate of the dynamical entropy.

Spatial rogue waves in a photorefractive pattern-forming system.

We have experimentally analyzed pattern formation in an optical system composed of a bulk photorefractive crystal subjected to a single optical feedback. In a highly nonlinear regime far above the modulational instability threshold, we are reporting on turbulent spatiotemporal dynamics that leads to rare, intense localized optical peaks. We have proven that the statistics and features of those peaks correspond to the signatures of two-dimensional spatial rogue events. These optical rogue waves occur erratically in space and time and live typically the same amount of time as the response time of the photorefractive material.

Bistability of time-periodic polarization dynamics in a free-running VCSEL.

We report experimentally a bistability between two limit cycles (i.e. time-periodic dynamics) in a free-running vertical-cavity surface-emitting laser. The two limit cycles originate from a bifurcation on two elliptically polarized states which exhibit a small frequency difference and whose main axes are symmetrical with respect to the linear polarization eigenaxes at threshold. We demonstrate theoretically that this peculiar behavior can be explained in the framework of the spin-flip model model by taking into account a small misalignment between the phase and amplitude anisotropies.

Two-parameter study of square-wave switching dynamics in orthogonally delay-coupled semiconductor lasers.

We perform a detailed numerical analysis of square-wave (SW) polarization switching in two semiconductor lasers with time-delayed, orthogonal mutual coupling. An in-depth mapping of the dynamics in the two-parameter plane coupling strength versus frequency detuning shows that stable SWs occur in narrow parameter regions that are localized close to the boundary of stability of the pure-mode solution. In this steady state, the two coupled lasers emit orthogonal polarizations. We also show that there are various types of SW forms and that stable switching does not need the inclusion of noise or nonlinear gain in the model. As these narrow regions of deterministic and stable SWs occur for quite different combinations of parameters, they could potentially explain the waveforms that have been observed experimentally. However, on the other hand, these regions are narrow enough to be in fact considered as experimentally unreachable. Therefore, our results indicate that further experimental statistical studies are needed in order to distinguish deterministic and stationary square waveforms from long transients because of noise.

Nonlocal effect on vortex-induced pattern dynamics.

We show experimentally and theoretically that the interplay between a vortex-induced pattern rotation and an optical feedback nonlocality-induced pattern drift leads to new dynamics and geometries of optical pattern formation. First, the vortex-induced pattern rotation and the nonlocality-induced drift can annihilate each other, resulting in the formation of static zones in the near field of the otherwise drifting pattern. Second, increasing the external mirror tilt leads to new pattern solutions that are composed of wave vectors of different amplitudes and directions, resulting in a multistriped pattern geometry.

Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers.

Using advanced continuation techniques for dynamical systems, we elucidate the bifurcations leading to asymptotically stable square-wave pulsing and polarization mode switching in semiconductor lasers with mutual time-delayed and polarization rotating coupling. We find that the increase of coupling strength leads to a cascade of Hopf bifurcations on a mixed-mode steady state up to a transcritical bifurcation on a so-called pure-mode steady state where both lasers emit with the injected polarization state. From these successive Hopf bifurcations emerge time-periodic solutions that have a period close to the laser relaxation oscillation for weak coupling but a period close to twice the time delay for large coupling strength. The wave form of the time-periodic solutions also evolves from harmonic pulsing up to square-wave pulsing as has been observed recently in experiments.

Vortex induced rotation dynamics of optical patterns.

We demonstrate that modulation instability leading to optical pattern formation can arise by using nonconventional counterpropagating beams carrying an orbital angular momentum (optical vortices). Such a vortex beam is injected into a nonlinear single feedback system. We evidence different complex patterns with peculiar phase singularities and rotating dynamics. We prove that the dynamics is induced by the vortex angular momentum and the rotation velocity depends nonlinearly on both the vortex topological charge and the intensity of the input beam.

Generation of orthogonal codes with chaotic optical systems.

We propose to use an electro-optic oscillator based on two Mach-Zehnder modulators in two different delayed feedback loops to generate two orthogonal chaotic spreading sequences (codes). We numerically demonstrate, for such codes, spectrally efficient multiplexing and demultiplexing of two digital data streams at multi-Gb/s rates using chaos synchronization and covariance-based detection.

Spectrally efficient multiplexing of chaotic light.

We numerically demonstrate multiplexing and demultiplexing of two distinct chaotic optical signals with strongly overlapped spectra, which are generated by mutually coupled external-cavity semiconductor lasers. Demultiplexing is performed by complete chaos synchronization, while the lasers at the receiving end are optically injected with the same multiplexed signal that couples the emitters together. Such a configuration could lead to spectrally efficient chaos-based optical encryption and decryption of multiple data streams.

Mapping of two-polarization-mode dynamics in vertical-cavity surface-emitting lasers with optical injection.

We report theoretically on the interplay between polarization switching and bifurcations to nonlinear dynamics in a vertical-cavity surface-emitting laser (VCSEL) subject to orthogonal optical injection. Qualitatively different bifurcation scenarios leading to polarization switching are found and mapped out in the plane of the injection parameters, i.e., the frequency detuning vs injection strength plane. A Hopf bifurcation mechanism on the two-polarization-mode solution determines the injection-locking boundaries and influences polarization switching induced by optical injection. We furthermore report on a torus bifurcation emerging from a two-linearly polarized (LP) mode time-periodic dynamics before polarization switching and injection locking appear. It corresponds to an interesting combination of relaxation oscillation dynamics in the x -LP mode together with wave mixing dynamics in the injected y -LP mode. In agreement with recent experiments, we unveil a period-doubling route to chaos that involves both VCSEL orthogonal LP modes. The corresponding region of chaotic dynamics coincides with abrupt changes in the polarization switching boundaries in the plane of the injection parameters.

Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks.

We propose an efficient and fast bit-multiplexed encryption scheme exploiting hyperchaotic regimes of a single nonlinear oscillator with multiple time-delay feedback loops. Each data stream is encrypted by digitally modulating the values of the various time delays and decrypted using chaos synchronization and cross-correlation measurements. We have numerically applied our approach to an optoelectronic chaotic oscillator based on standard semiconductor lasers subjected to multiple feedbacks and have demonstrated successful data transmission and recovery between multiple users at several Gbits/s on a single communication channel.

Experimental control of pattern formation by photonic lattices.

We study the control of modulational instability and pattern formation in a nonlinear dissipative feedback system with a periodic modulation of the material refractive index. We use a one-dimensional photonic lattice in a single-mirror feedback configuration and identify three mechanisms for pattern control: bandgap suppression of instability modes, periodicity induced pattern modes, and orientational pattern control.

Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation.

In this paper we report on a theoretical investigation of the nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers (VCSELs) under current modulation. Special attention is given to the comparison with a previously studied case of single-transverse mode VCSEL emitting in two orthogonal polarizations. The consideration of spatial effects in VCSEL modifies the polarization dynamics that accompanies the period doubling route to chaos for large modulation amplitudes. Depending on the modulation parameters, the excitation of a higher order transverse mode may either induce chaotic pulsing in an otherwise regularly pulsating VCSEL, or induce a time-periodic pulsing dynamics in an otherwise chaotic VCSEL. Bifurcation diagrams obtained for different modulation frequencies, several values of the dichroism, and different transverse mode characteristics allow us to identify the different scenarios of polarization dynamics in a directly modulated VCSEL. Temporal analysis of carrier number radial profile reveals considerable changes for the multitransverse mode case only constituting the physical origin of the reported changes in the temporal and polarization dynamics.

Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback.

We investigate theoretically the possibility of retrieving the value of the time delay of a semiconductor laser with an external optical feedback from the analysis of its intensity time series. When the feedback rate is moderate and the injection current set such that the laser relaxation-oscillation period is close to the delay, then the time-delay identification becomes extremely difficult, thus improving the security of chaos-based communications using external-cavity lasers.

Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection.

We analyze theoretically the polarization dynamics in unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs). The master VCSEL is subject to an isotropic optical feedback. The slave VCSEL is subject to an orthogonal optical injection from the master VCSEL, i.e., only the linearly polarized mode orthogonal to the dominant linearly polarized mode of the free-running slave VCSEL is injected into the slave VCSEL. This laser configuration may lead the slave VCSEL polarization to switch to that of the injected master laser field. The injected power required for polarization switching depends on the frequency detuning. We identify in the plane of the injection parameters two regions of enhanced synchronization between the injected LP mode and the corresponding slave LP mode. In the so-called region II the slave VCSEL exhibits anticorrelated dynamics in its two LP modes while in the so-called region I the slave VCSEL exhibits dynamics in only one LP mode, which corresponds to the polarization of the injected field. The two regions exhibit different synchronization properties in both the LP mode dynamics and total intensity dynamics. We furthermore analyze the dependency of the synchronization quality on the parameter mismatch between master and slave VCSELs and on the polarization switching properties of each VCSEL.

Two-mode injection locking in vertical-cavity surface-emitting lasers.

We report on the dynamics that accompany polarization switching induced by orthogonal optical injection in a vertical-cavity surface-emitting laser (VCSEL). As the injection strength increases, the VCSEL bifurcates to injection-locked steady states and time-periodic and possibly chaotic dynamics. Of particular interest is a two-mode injection-locking solution, i.e., locking of the two VCSEL polarization modes. A detailed stability analysis unveils new bistability mechanisms in optical injection problems.