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In this work, we experimentally and theoretically report on optical comb dynamics in VCSELs induced by optical injection. We show that injection of a narrow comb with parallel, orthogonal or arbitrary polarization can sustain two polarization comb dynamics in single-mode VCSELs. More specifically, we show that the two polarization comb dynamics can be observed whatever the injected comb's polarization. The appearance of the comb can be controlled with the linewidth enhancement factor for fixed injected comb spacing and detuning frequency. Also, we show that the harmonics comb in the two orthogonal polarization modes can be suppressed with the linewidth enhancement factor in the cases of parallel and orthogonal optical injection.

Two VCSELs placed facing each other with one biased chip while the second chip is unbiased is shown as a promising alternative to the popularly used conventional SESAM mode-locked VECSEL to generate mode-locked pulses. We propose a theoretical model using time-delay differential rate equations and numerically show that the proposed dual-laser configuration functions as a typical gain-absorber system. Parameter space defined by laser facet reflectivities and current are used to show general trends in the exhibited nonlinear dynamics and pulsed solutions.

We investigate experimentally polarization dynamics of passively mode-locked VECSEL. We demonstrate that the normalized Stokes parameters and degree of polarization are functions of time reaching extreme values at the pulse peaks. Our experiments show that light has vertical, 45° polarization components, and a small amount of circular polarization.

We report the existence of stable dissipative light bullets in Kerr cavities. These three-dimensional (3D) localized structures consist of either an isolated light bullet (LB), bound together, or could occur in clusters forming well-defined 3D patterns. They can be seen as stationary states in the reference frame moving with the group velocity of light within the cavity. The number of LBs and their distribution in 3D settings are determined by the initial conditions, while their maximum peak power remains constant for a fixed value of the system parameters. Their bifurcation diagram allows us to explain this phenomenon as a manifestation of homoclinic snaking for dissipative light bullets. However, when the strength of the injected beam is increased, LBs lose their stability and the cavity field exhibits giant, short-living 3D pulses. The statistical characterization of pulse amplitude reveals a long tail probability distribution, indicating the occurrence of extreme events, often called rogue waves.

We investigate the destabilization mechanisms of dissipative solitons in inhomogeneous nonlinear res-onators subjected to injection and to time-delayed feedback. We consider the paradigmatic Lugiato-Lefever model describing inhomogeneous driven nonlinear optical resonator. We analyze the pinning-depinning transition of dissipative solitons by introducing a potential induced by the inhomogeneity. Fur-ther, we identify conditions under which these structures are destabilized and describe different bifurca-tion scenarios. We show that the combined influence of inhomogeneities and delayed feedback induces an Andronov-Hopf-bifurcation that leads to oscillations of the dissipative soliton around the inhomogene-ity. Finally, we show that for large values of the feedback strength, the dissipative solitons escapes from the potential well and starts to drift. (c) 2021 Elsevier Ltd. All rights reserved.

Stable light bullets and clusters of them are presented in the monostable regime using the mean-field Lugiato-Lefever equation [Gopalakrishnan, Panajotov, Taki, and Tlidi, Phys. Rev. Lett. 126, 153902 (2021)]. It is shown that three-dimensional (3D) dissipative structures occur in a strongly nonlinear regime where modulational instability is subcritical. We provide a detailed analysis on the formation of optical 3D crys-tals in both the super-and sub-critical modulational instability regimes, and we highlight their link to the formation of light bullets in diffractive and dispersive Kerr resonators. We construct bifurcation diagrams associated with the formation of optical crystals in both monostable and bistable regimes. An analytical study has predicted the predominance of body-centered-cubic (bcc) crystals in the intracavity field over a large variety of other 3D solutions with less symmetry. These results have been obtained using a weakly nonlinear analysis but have never been checked numerically. We shownumerically that indeed the most robust structures over other self-organized crystals are the bcc crystals. Finally, we show that light-bullets and clusters of them can occur also in a bistable regime. (C) 2021 Elsevier Ltd. All rights reserved.

We investigate experimentally the polarization dynamics of a vertical external-cavity surface-emitting laser with a saturable absorber mirror in the cavity. We demonstrate that the normalized Stokes parameters and degree of polarization are functions of time reaching extreme values around the pulse peaks. Our experiments show that light is elliptically polarized, being able to have a circular right-handed or left-handed component, depending on the orientation of the saturable absorber mirror.

We consider arrays of coupled nonlinear optical cavities subject to coherent optical injection. These devices are described by the discrete generalized Lugiato-Lefever equation. We predict that stable three-dimensional localized structures, often called discrete light bullets, and clusters of them may form in the output of the coupled optical resonators. We consider both anomalous and normal dispersion and show that it results in the generation of, respectively, bright and dark discrete light bullets., SCOPUS: ar.j, info:eu-repo/semantics/published

Atomically monolayer 2D material was predicted thermal dynamically unstable, until the ground-breakthrough reports of the isolation of graphene in 2004, which was shortly recognized by the Nobel Prize in 2010. Monoelemental graphene inherits the merits of simple stoichiometry and crystal structure, which offers the possibilities for basic physics scenarios demonstrations and a great deal of functional devices explorations. The recent decades have witnessed the unprecedented enthusiasm of investigations and fruitful achievements on the nano-platform of graphene. Recently, the family of monoelemental 2D materials has embraced the birth of multiple members, including silicene, germanene, phosphorene, and so forth. Moreover, heterostructures and superlattices of monoelemental 2D materials have opened a new realm in materials science, offering unlimited possibilities. In this special issue, we collected 6 original articles, 3 comprehensive reviews, and 2 research news from the leading research groups, and we are grateful to have received such warm feedback and support.

Tunable vertical-cavity surface-emitting lasers (VCSEL) provide broad wavelength tuning range at very high modulation speed, but usually employ micro electromechanical systems, which are sensitive to vibrations. In this paper we propose a tunable 1550 nm VCSEL design with enclosed intra-cavity liquid-crystal (LC) cell. The laser is electrically pumped and the wavelength selectivity is obtained by varying LC’s refractive index through electro-optical tuning of the LC director. By performing one-dimensional transfer-matrix optical calculations, supplemented with a fully-vectorial three-dimensional self-consistent modeling of thermal, electrical and optical phenomena, we optimize the design and show the dependency of the emitted wavelength on LC cell thickness and the LC director orientation. The analysis is concluded with a possibility of achieving 68.5 nm tuning range in a continuous-wave operation regime and without polarization or transverse mode switching.

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International audience; We propose a new approach of broad frequency comb generation by exploiting the polarization dynamics in a VCSEL induced by parallel frequency comb injection. Polarization mode competition leads to two tunable combs with orthogonal polarization.

Recent works have shown the possibility to control through optical injection frequency combs generated by gain switching in Vertical-Cavity Surface-Emitting Lasers (VCSELs) [1] . The opposite situation, in which VCSEL is subject to injection of an optical frequency comb (OFC) deserves close attention and has not been addressed so far. In this work, we analyze the nonlinear polarization dynamics of a single-mode VCSEL with optical injection. Here, we select and reveal several bifurcations scenarios leading to generation of a two polarization OFC.

We investigate experimentally the nonlinear polarization dynamics of a VCSEL subject to optical injection of a frequency comb. By tuning the polarization of the injected comb to be orthogonal to that of the VCSEL, we demonstrate the generation of either a single polarization or a dual polarization frequency comb. The injection parameters (injected power and detuning frequency) are then used either to generate harmonics of the initial comb spacing or to increase the number of total output frequency lines up to 15 times the number of injected comb lines. Optimisation of the injection parameters yields a comb extending over 60 GHz for a comb spacing of 2 GHz with a carrier to noise ratio (CNR) of up to 60 dB. Our technique allows us to separately control the comb spacing, comb bandwidth, CNR and polarization. Our finding can be used for spectroscopy measurement and also for polarization division multiplexing in optical data communications. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Coupled-cavity VCSELs typically support two fundamental longitudinal modes. Their wavelengths as a function of the difference of the optical lengths of the two cavities display avoided wavelength crossing (or anticrosing). In this article, we numerically solve the set of Maxwell equations for a coupled-cavity VCSEL. We show that when brought closer spectrally higher transverse-order modes of different orders display not only wavelength crossing (as anticipated by the Helmholtz equation) but also avoided crossing.

International audience; We experimentally and theoretically demonstrate the variety of the nonlinear dynamics exhibited by a single frequency semiconductor laser subjected to optical injection from a frequency comb. The injection parameters (the detuning and the injection strength) and the comb properties (comb spacing and the amplitude of the injected comb lines) are varied to unveil several dynamics such as injection locking, wave-mixing, chaotic dynamics, and unlocked time-periodic dynamics corresponding to new comb solutions. The asymmetry of the injected comb is shown to modify the size of the injection locking region in the parameter space, as well as the common properties between the new comb solutions observed and the injected comb.

We investigate and review the formation of two-dimensional dissipative rogue waves in cavity nonlinear optics with transverse effects. Two spatially extended systems are considered for this purpose: the driven Kerr optical cavities subjected to optical injection and the broad-area surface-emitting lasers with a saturable absorber. We also consider a quasi-two-dimensional system (the two dimensions being space and time) of a fiber laser describing the complex cubic-quintic Ginzburg-Landau equation. We show that rogue waves are controllable by means of time-delayed feedback and optical injection. We show that without delayed feedback, transverse structures are stationary or oscillating. However, when the strength of the delayed feedback is increased, all the systems generate giant two-dimensional pulses that appear with low probability and suddenly appear and disappear. We characterize their formation by computing the probability distribution, which shows a long tail. Besides, we have computed the significant wave height, which measures the mean wave height of the highest third of the waves. We show that for all systems, the distribution tails expand beyond two times the significant wave height. Furthermore, we also show that optical injection may suppress the rogue wave formation in a semiconductor laser with a saturable absorber., SCOPUS: ar.j, info:eu-repo/semantics/published

International audience; This work reports on numerical analysis of the nonlinear dynamics of a semiconductor laser subject to an optical injection with a frequency comb. We identified the fundamental difference between the single mode injection and frequency comb injection. By varying the injection parameters (detuning and injection ratio), the results show that the slave laser is able to reproduce the injected frequency comb (new comb) in different parameters regions. The appearance of the new comb depends on the number of injected comb lines for fixed comb properties.

We report on random lasing observed with 5-m-long Er-doped fiber comprising an array of weak fiber Bragg gratings (FBGs) inscribed in the fiber core and uniformly distributed over the whole fiber length. The laser design ensures domination of dynamical population inversion grating over the FBGs in total distributed feedback enabling laser stabilization and nonlinear laser line filtering of the natural laser Lorentzian linewidth down to sub-300-Hz range, both observed in the experiment.

Spectrally pure lasers are the heart of precision high-end scientific and commercial applications. Self-injection locking of a DFB laser through an external feedback is one of the most promising mechanisms for the laser line narrowing. To provide the effect, a part of the optical radiation emitted by the laser is returned back into the laser cavity. This relatively simple technique allows to design cost-effective narrow-band laser sources based on standard laser diodes making them an attractive solution in comparison with conventional laser systems based on an active feedback. Recently, we have demonstrated significant line narrowing (similar to 1000 times) of a conventional low-cost DFB laser locked to an external fiber optic ring resonator. Once locking, any slow change of resonator mode frequency (due to temperature fluctuations, for example) leads to a simultaneous change of the laser generation frequency. However, in real conditions, in the presence of environment noise the stable laser operation in a single longitudinal mode occurs within a time interval limited to several seconds. These intervals are interrupted by short-time jumps in the lasing intensity caused by laser mode-hopping. Here, we report on linewidth narrowing and stabilization of semiconductor DFB laser implementing the self-injection locking in conjugation with an active optoelectronic feedback controlled by the simplest low-cost USB-DAQ card. In this assemble, the principle laser linewidth narrowing is provided by the self-injection-locking mechanism, whereas the applied active feedback helps to maintain this passive stabilization regime. Therefore, in terms of the feedback bandwidth, complexity, and allocated memory the proposed combined solution is much less consuming than active stabilization schemes based on the Pound-Drever-Hall (PDH) and Hansch-Couillaud methods commonly used with fiber lasers. Moreover, we will show that the active optoelectronic feedback which is initially implemented for better laser stabilization plays a second role granting control and tunability to laser linewidth.

International audience; We analyze the nonlinear dynamics of a semiconductor laser with optical injection from a frequency comb. When varying both the injection parameters (detuning and injection ratio) and the comb properties (number of comb lines and comb spacing), we identify and select several dynamics, including (1) injection locking with selective amplification of the comb line that shows the smallest detuning from the injected laser, (2) unlocked time-periodic dynamics that correspond to a new frequency comb with a broadened optical spectrum, thereby sharpening the pulse generated at the injected laser output, and (3) unlocked chaotic dynamics.

We report the existence of vectorial dark dissipative solitons in optical cavities subject to a coherently injected beam. We assume that the resonator is operating in a normal dispersion regime far from any modulational instability. We show that the vectorial front locking mechanism allows for the stabilisation of dark dissipative structures. These structures differ by their temporal duration and their state of polarization. We characterize them by constructing their heteroclinic snaking bifurcation diagram showing evidence of multistability within a finite range of the control parameter., Comment: \copyright 2021 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved

Rogue waves (RWs) are rare, extreme amplitude, localized wave packets, which have received much interest recently in different areas of physics. Fiber lasers with their abundant nonlinear dynamics provide an ideal platform to observe optical RW formation. We review recent research progress on rogue waves in fiber lasers. Basic concepts of RWs and the mechanisms of RW generation in fiber lasers are discussed, along with representative experimental and theoretical results. The measurement methods for RW identification in fiber lasers are presented and analyzed. Finally, prospects for future RW research in fiber lasers are summarized.

We introduce a spin-flip model for a vertical-externalcavity surface-emitting laser (VECSEL) with a saturable absorber. We demonstrate the possibility, due to the spin-flip dynamics, to generate two orthogonally linearly polarized frequency combs in the mode-locked regime. The two combs are shifted in wavelength due tothe birefringence in the VECSEL gain and/or saturable absorption mirror. We show that the polarization degree of freedom may also lead to several pulses being generated per roundtrip in the two orthogonal linear polarizations and to more complicated dynamics with both linear polarizations excited., SCOPUS: ar.j, info:eu-repo/semantics/published

We propose a model for the oscillation of a single-frequency feedback semiconductor laser based on a ring fibre interferometer. It is shown that at a certain level of feedback, the semiconductor laser generation frequency is locked by the transmission peak of the fibre interferometer. The effect is accompanied by the narrowing of the spectral line and the reduction of noises. The described results are in qualitative agreement with the experimental data.

Physical curiosity at the beginning, optical chaos is now attracting increasing interest in various technological areas such as detection and ranging or secure communications, to name but a few. However, the complexity of optical chaos generators still significantly hinders their development. In this context, the generation of chaotic polarization fluctuations in a single laser diode has proven to be a significant step forward, despite being observed solely for quantum-dot vertical-cavity surface-emitting lasers (VCSELs). Here, we demonstrate experimentally that a similar polarization dynamics can be consistently obtained in quantum-well VCSELs. Indeed, by introducing anisotropic strain in the laser cavity, we successfully triggered the desired chaotic dynamics. The simplicity of the proposed approach, based on low-cost and easily available components including off-the-shelf VCSELs, paves the way to the wide spread use of solitary VCSELs for chaos-based applications.

By utilizing a fully-vectorial three-dimensional cold-cavity optical simulation, we analyze the spectral, polarization, and modal-losses behavior of a vertical-cavity surface-emitting laser with a nematic liquid-crystal (LC) overlay. We identify phenomena responsible for mode and polarization selectivities and show how they can be controlled by varying design geometry parameters, such as LC thickness and oxide aperture diameter, or by electrooptically tuning the LC director. We present possibility of achieving voltage-controlled polarization switching of a fundamental mode or transverse mode switching within the same polarization. Furthermore, we show that it is theoretically possible to obtain improved single-mode operation by means of increased higher order transverse mode discrimination. Finally, we point out a way to destabilize the diode by equalizing the modal losses of all the analyzed modes.

We investigate the dynamics of a ring cavity made of photonic crystal fiber and driven by a coherent beam working near to the resonant frequency of the cavity. By means of a multiple-scale reduction of the Lugiato-Lefever equation with high-order dispersion, we show that the dynamics of this optical device, when operating close to the critical point associated with bistability, is captured by a real order parameter equation in the form of a generalized Swift-Hohenberg equation. A Swift-Hohenberg equation has been derived for several areas of nonlinear science such as chemistry, biology, ecology, optics, and laser physics. However, the peculiarity of the obtained generalized Swift-Hohenberg equation for photonic crystal fiber resonators is that it possesses a third-order dispersion. Based on a weakly nonlinear analysis in the vicinity of the modulational instability threshold, we characterize the motion of dissipative structures by estimating their propagation speed. Finally, we numerically investigate the formation of moving temporal localized structures often called cavity solitons.

International audience; Vertical-cavity surface-emitting lasers with vertically integrated electro-absorption modulators (EAM-VCSELs) potentially can reach higher modulation bandwidths than directly current-modulated VCSELs. The aforementioned device modulation capabilities are, however, currently restricted by their electrical contact parasitics. It, thus, becomes critical to optimize their access line to improve performance. In this paper, we numerically and experimentally demonstrate that a microstrip (MS) access line using a planarized benzocyclobutene (BCB) layer exhibits improved high-frequency characteristics compared to the coplanar waveguide (CPW) access line used to-date, since it reduces the losses induced by the doped substrates. We also use this opportunity to introduce an innovative technique for BCB layer planarization, which is not only compatible with the EAM-VCSEL double-mesa structure, but is also independent of the device pitch. The resulting BCB layer dielectric permittivity and losses are measured up to 100 GHz, and a side-by-side comparison of the electrical response of three-electrodes MS and CPW access lines is subsequently carried out. Finally, using the measured pad and access line RF responses and the EAM modulation characteristics, the devices with MS access are shown to be no longer limited by their electrode parasitics, but by the modulator internal impedance.

We consider the formation of temporal localized structures or Kerr-comb generation in a microresonator with inhomogeneities. We show that the introduction of even a small inhomogeneity in the injected beam widens the stability region of localized solutions. The homoclinic snaking bifurcation associated with the formation of localized structures and clusters of them with decaying oscillatory tails is constructed. Furthermore, the inhomogeneity allows us to not only control the position of localized solutions, but strongly affects their stability domains. In particular, a new stability domain of a single peak localized structure appears outside of the region of multistability between multiple peaks of localized states. We identify a regime of larger detuning, where localized structures do not exhibit a snaking behavior. In this regime, the effect of inhomogeneities on localized solutions is far more complex: They can act either attracting or repelling. We identify the pitchfork bifurcation responsible for this transition. Finally, we use a potential well approach to determine the force exerted by the inhomogeneity and summarize with a full analysis of the parameter regime, where localized structures and therefore Kerr-comb generation exist, and analyze how this regime changes in the presence of an inhomogeneity., SCOPUS: ar.j, info:eu-repo/semantics/published

International audience; The increase in modulation bandwidth of a vertical-cavity surface-emitting laser (VCSEL) can be achieved through the vertical integration of a modulator onto the laser. This approach has already been proposed and demonstrated to be competitive [1-3]. In this specific case, a double mesa structure with three contacts is needed to apply a high-frequency voltage signal to the modulator section and inject a CW current into the underlying VCSEL section. The middle contact serves as a shared ground. Indeed, splitting the emitting and the modulating parts circumvents the carrier dynamics limitation of the modulation bandwidth encountered in direct current-modulated VCSELs. However, the parasitic capacitances of the access line and contact pad play a significant role in the high-frequency limit of such a device. In this paper, we present the design, fabrication and modulation characteristics of an electro-absorption modulator (EAM) vertically-integrated onto an 850-nm VCSEL that is compatible with high-frequency operation. The two optical cavities are such that their mutual optical coupling is small to improve the modulation properties at high frequencies. This EAM-VCSEL device has been successfully fabricated by molecular beam epitaxy, followed by an original technological process [4]. In particular, planarized BCB layers and microstrip access lines have been implemented to optimize the high-frequency signal injection. Thanks to the optimized wavelength detuning between the cavities resonances of the EAM and the VCSEL and respectively to the quantum well absorption tail of the modulator, the EAM modulator exhibits a modulation depth of more than 40% within a 4V span. This vertically integrated EAM-VCSEL approach enables also to minimize the wavelength chirp during the modulation, which in our case is lower than 80 pm. Finally, 3-dB frequency bandwidths up to 29 GHz were measured on both stand-alone vertical EAM devices and vertically-integrated EAM-VCSELs. (a) (b)Fig. 1 (a) Schematics of the EAM-VCSEL structure under study with planarized BCB and (b) high-frequency modulation response of the EAM-VCSEL device with different DC bias voltages applied to the EAM.

The control of linear and nonlinear properties of Photonic Crystal Fibers (PCF) has led to several applications in optoelectronics, sensing, and laser science [1]. In particular, driven optical microcavities are widely used for the generation of optical frequency combs. They can be modeled by the Lugiato-Lefever equation that possesses solutions in the form of localized structures (LSs) [2]. Optical frequency-combs generated in high-Q Kerr resonators [3] are in fact the spectral content of the stable temporal pattern occurring in the cavity.

Driven Kerr resonators support temporal cavity solitons (CS) in the form of short optical pulses propagating along the cavity. They are also called localized structures and have been theoretically predicted in [1] and experimentally observed in [2]. They are often generated in the sub-critical modulation instability regime. The generation of CSs and their connections to optical comb generation have been recently reviewed [3]. They possess potential applications as bits in all-optical buffers and coherent optical frequency combs.

A cavity soliton (CS) consists of one or more regions in one state surrounded by a region of a qualitatively different state. Such patterns may be stationary or oscillatory, static or moving and they are important in a wide variety of fields [1, 2]. They are potentially interesting for all-optical control of light. To this end, a delayed feedback can be used to control these CSs [3, 4]. Indeed, slowly moving spots subject to delay appear in various other fields. For example, spreading depolarization waves responsible for both migraine and strokes have been described as reaction-diffusion waves subject to delay [5]. Of particular interest are time delayed feedback control (TDEC) schemes. TDFC is based on the use of the difference between systems variables at the current moment of time and their values at some time in the past. They are smooth controls because the steady states of the unperturbed problem are solutions of the delayed feedback problem. More recently, we have investigated the combined influence of an inhomogeneity of the pumping and delayed feedback and shown that it induces oscillations and drift of localized structures in the Swift-Hohenberg equation describing pattern formation in the transverse plane of an optical cavity [6].

A simple, versatile model for the dynamics of electrically and optically pumped vertical-external-cavity surface-emitting lasers, which are mode locked by a semiconductor saturable-absorber mirror, is presented. The difference between the laser operation in the linear and folded cavity, as well as the potential for a colliding pulse operation, are studied.

We present in this paper the vertical integration of an electro-absorption modulator (EAM) onto a vertical-cavity surface-emitting laser (VCSEL). We discuss the design, fabrication, and measured characteristics of the combined VCSEL and EAM. We previously demonstrated a standalone EAM with an optical bandwidth around 30 GHz. In this paper we present for the first time an optical bandwidth of 30 GHz for an EAM integrated onto a VCSEL. This device exhibits single-mode operation and a very low chirp, below 0.1 nm, even with a modulation depth of 70% which makes this device very competitive for high-speed communications in data centers.

SCOPUS: ed.j, info:eu-repo/semantics/published