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We show that a III-V semiconductor Vertical External-Cavity Surface-Emitting Lasers (VECSELs) can be engineered to generate light with a customizable spatio-temporal structure. The temporal control is achieved through the emission of Temporal Localized Structures (TLSs), a particular mode-locking regime that allows the individual addressing of the pulses traveling back and forth in the cavity. The spatial profile control relies on a degenerate external cavity and it is implemented thanks to an absorptive mask deposited onto the gain mirror that limits the positive net gain within two circular spots in the transverse section of the VECSEL. We show that each spot emits spatially uncorrelated TLS. Hence, the spatio-temporal structure of the light emitted can be shaped by individually addressing the pulses emitted by each spot. Because the maximum number of pulses circulating in the cavity and the number of positive net-gain spots in the VECSEL can be increased straightforwardly, this result is a proof of concept of a laser platform capable of handling light states of scalable complexity. We discuss applications to three dimensional all-optical buffer and to multiplexing of frequency combs that share the same laser cavity.

Localized structures (LS) in lasers have been actively sought for all-optical information processing. So far, two distinct approaches have been developed for achieving LS: one leading to addressable stationary peaks of light in the transverse section of the resonator, the other leading to addressable mode-locked pulses having a fundamental mode spatial profile. Here we show that temporal localized patterns appear in nearly self-imaging Vertical External-Cavity Surface-Emitting Lasers (VECSELs) with an intracavity saturable absorber. The observed patterns consist of a combination of an axial plane-wave with a set of tilted waves having a hexagonal arrangement in the Fourier space. In the time domain these patterns are individually addressable mode-locked pulses having a duration of about ten picoseconds. The theoretical analysis shows that the emergence of these pulsating patterns is a signature of a Turing instability whose critical wave vector depends on spherical aberrations of the optical elements. Our result shows that large aspect-ratio VECSELs offer unique opportunities for studying spatio-temporal phenomena and it paves the way to the generation of spatio-temporal LS.

Degenerate laser cavity have been used for second-harmonic generation [1] , [2] and spatially incoherent laser emission using solid-state gain medium and monolithic VCSEL with large area of excitation [3] , [4] . In this work we investigate cw spatial coherent states of a degenerate laser cavity using specially design 1/2-VCSEL based on III-V semiconductor technology, and high numerical aperture optical system, in order to be used in spatio-temporal localization of light also know as Light Bullets [5] . The external cavities implemented are made up two(four) lenses in 4-(-8)f self-imaging configurations. A Zeemax and optical physics study was carried out to design the optimized system of lenses to ensure high numerical aperture and high resolution down to wavelength scale with minimal aberrations for off axis operation. The Semiconductor Gain Mirror (1/2-VCSEL) have been designed based on GaAs materials at 1060nm wavelength and for efficient optical pumping at 800nm using commercial diode laser. The high reflectivity mirror is designed with an GaAs/AlAs bragg mirror and the optical gain is provided through a multi-quantum-well strained-balanced InGaAs/GaAsP active region. The 1/2-VCSEL was designed with the intent to minimize all waveguiding effect such as the thermal lens and strong self-guiding through gain saturation.

We analyze both theoretically and experimentally the impact of optical feedback on the dynamics of external-cavity mode-locked semiconductor lasers (VECSELs) operated in the long cavity regime [1]. In particular, by choosing certain ratios between the cavity round-trip time and the feedback delay, we show that feedback acts as a solution discriminator that either reinforces or hinders the appearance of one of the multiple harmonic arrangements of temporal localized structures. For the theoretical modeling, the delayed differential equation model [2] is extended by a term describing the optical feedback. Denoting by A the amplitude of the optical field, G the gain, and Q the saturable losses, the model reads\begin{align*} & \frac{{\dot A}}{\gamma } = \sqrt \kappa \exp \left[ {\frac{{1 - i{\alpha _g}}}{2}G\left( {t - {\tau _c}} \right) - \frac{{1 - i{\alpha _a}}}{2}Q\left( {t - {\tau _c}} \right)} \right]A\left( {t - {\tau _c}} \right) - A(t) + \eta {e^{i{{\Omega }}}}A\left( {t - {\tau _f}} \right),\tag{1} \\ & \dot G = {g_0} - {{\Gamma }}G - {e^{ - Q}}\left( {{e^G} - 1} \right)|A{|^2},\quad \dot Q = {q_0} - Q - s\left( {1 - {e^{ - Q}}} \right)|A{|^2}\tag{2}\end{align*}where time has been normalized to the SA recovery time, α g and α a are the linewidth enhancement factors of the gain and absorber sections, respectively, κ the fraction of the power remaining in the cavity after each round- trip, g 0 the pumping rate, Γ the gain recovery rate, q 0 is the value of the unsaturated losses which determines the modulation depth of the SA, τ c the round-trip time in the cavity, s the ratio of the saturation energy of the SA and of the gain sections and γ is the bandwidth of the spectral filter, η is the feedback rate, Ω is the feedback phase and τ f the round-trip time in the feedback loop. For the experimental realization, the gain medium consisting in 6 quantum wells embedded between a bottom totally reflective Bragg mirror and a top partially reflective Bragg mirror (½VCSEL) was considered; the ½VCSEL was then placed in an external cavity that was closed by a fast semiconductor saturable absorber mirror (SESAM) to operate the laser in the passive mode-locked regime (see fig. 1). In the absence of the optical feedback such a laser can generate so-called harmonic mode-locked solutions denoted by HML n where n is the number of equally spaced pulses per round-trip. The optical feedback induces that each pulse is followed by a train of small copies of itself. The size and position of this echo can be controlled via the feedback rate and the delay time, respectively. When an echo is placed close to the leading edge of another pulse, the pulse experiences less amplification by the gain medium as it is already depleted by the echo. This interaction can lead to the destruction of the main pulse. In consequence, the system settles on a solution where pulses and echos are well-separated and thus, do not interact. This mechanism is visualized in fig. 2 where a HML 4 and HML 2 are exposed to optical feedback and therefor, the output changes to a HML 3 and fundamental mode-locked solution, respectively. This behaviour was also observed in the experiment. In the further steps, a detailed bifurcation analysis is conducted where the influence of the position of the echo is investigated.

Spatial and temporal localized structures in optical cavities, also called Dissipative Solitons, have attracted a great deal of attention in the last two decades [1] , [2] . Beyond their fundamental interest, these structures can be used to code and process information bits in optical resonators. In general, two conditions appear to be necessary for a system to exhibit LSs: i) to have a large aspect-ratio and ii) to feature a multistable response. We have recently shown that an optically pumped passively mode-locked Vertical External Cavity Surface Emitting Laser (VECSEL) can be operated in a regime where mode-locked pulses becomes localized, i.e. they are individually addressable [3] , [4] . This regime requires long external cavity, i.e. cavity roundtrip time be significantly larger than gain recovery time, τ c >> τ g . Both the gain section and the saturable absorber mirrors needs to be properly engineered to provide multistability between different PML solutions with different number of pulses per roundtrip. Moreover, VECSEL geometry is very interesting because the external cavity can be designed in a self-imaging configuration which allow for reaching high-Fresnel number, hence paving the way also to spatial LSs [5] .

A huge amount of research is devoted today to determine good indicators applicable on time series obtained from real systems that may anticipate a change in its behaviour [1] , [2] . A well-established indicator is the so-called "critical slowing down" (CSD). CSD is the asymptotic growth of the of the relaxation time of a kicked dynamical system when it is approaching a bifurcation [3] . In this contribution, we address the question whether CSD is always a good indicator of an incoming bifurcation in a system where a parameter is linearly changing in time. We answer by presenting a laser system with a time swept pump where CSD appears only after the bifurcation has already occurred, hence when it is too late to reverse its behavioural change. Furthermore, we show experimentally that a perturbation in the accessible control parameter is unable to provide any indication, nor on the occurrence of CSD nor on the bifurcation crossing.

This paper aims to characterise, both experimentally and theoretically, the dynamics which occur during the turn on transient of a long cavity semiconductor laser. The laser comprised of a semiconductor optical amplifier (SOA), centered around 1300nm, a tuneable narrow bandwidth filter, for wavelength selectivity, a polarisation controller, an output coupler and multiple single mode fibre isolators to ensure the unidirectional propagation of light within the ring cavity. The bias current driven to the SOA was periodically switched on and off in order to examine the laser dynamics within each cavity round trip. It is observed that the laser intensity builds up in a step-wise manner, with each step corresponding to one cavity round trip. By examining the space-time diagrams of the lasers intensity during the turn on, it is seen that the laser will initially randomly oscillate before transitioning into a semi-stationary state. After a certain amount of round trips the laser may develop one or more localised structures, characterised by their short and fast drops of intensity. In this paper we also aim to not only explain the formation of these localised structures but also expand on their development by examining the phase evolution of their electric field.

We present here a combined theoretical and experimental study to investigate the influence of external optical feedback in a semiconductor swept-source laser. The applied feedback is shown to transfer the coherence between the subsequent modes and retain it along the full sweep. As a result, the technique can act as a solution to the de-coherence during the mode-hops observed in this kind of swept-source lasers thus noticeable increasing the image quality of Optical Coherence Tomography systems.

In this paper, we experimentally and theoretically analyse the formation and interaction of dark solitons in a long laser. The laser includes a semiconductor optical amplifier (SOA), centred around 1300nm, an intracavity filter and a fibre cavity whose length can vary from 20m to 20km. Near the lasing threshold the laser exhibits slowly evolving power dropouts the circulate the cavity. These dropouts are associated with the formation of Nozaki-Bekki Holes (NBH), also referred to as dark solitons. We observe both experimentally and numerically that the core of these holes exhibit chaotic dynamics and emit short light pulses. These pulses are found to be blue shifted with respect to the frequency of the dark solitons and therefore travel with a faster group velocity. These pulses are strongly damped, as they are detuned with respect to the filter transmission, but they may lead to the creation of new dark solitons. These pulses also play a major role in the development of optical turbulence when the filter is set at a frequency above 1310nm. In this case, the laser displays numerous dark solitons per round trip and the fast travelling pulses act as an interaction between the solitons, which can lead to the development of defect mediated turbulence.

We present the study on the dynamics of a semiconductor laser with a tunable Fabry-Perot filter and a ring single-mode fiber based long cavity. Theoretically and experimentally, we analyse dynamical regimes of the laser in various operation regimes, including stable and chaotic dynamics and the formation of coherent structures. The laser coherence build up is studied during the turn on, as well as different scenarios of coherence deterioration in such lasers are examined.

Zero modes are symmetry protected ones whose energy eigenvalues have zero real parts. In Hermitian arrays, they arise as a consequence of the sublattice symmetry, implying that they are dark modes. In non-Hermitian systems that naturally emerge in gain/loss optical cavities, particle-hole symmetry prevails instead; the resulting zero modes are no longer dark but feature π / 2 phase jumps between adjacent cavities. Here, we report on the direct observation of zero modes in a non-Hermitian three coupled photonic crystal nanocavities array containing quantum wells. Unlike the Hermitian counterparts, the observation of non-Hermitian zero modes upon single pump spot illumination requires vanishing sublattice detuning, and they can be identified through far-field imaging and spectral filtering of the photoluminescence at selected pump locations. We explain the zero-mode coalescence as a parity-time phase transition for small coupling. These zero modes are robust against coupling disorder and can be used for laser mode engineering and photonic computing.

We study a two-dimensional low-dissipation nonautonomous dynamical system, with a control parameter that is swept linearly in time across a transcritical bifurcation. We investigate the relaxation time of a perturbation applied to a variable of the system and we show that critical slowing down may occur at a parameter value well above the bifurcation point. We test experimentally the occurrence of critical slowing down by applying a perturbation to the accessible control parameter and we find that this perturbation leaves the system behavior unaltered, thus providing no useful information on the occurrence of critical slowing down. The theoretical analysis reveals the reasons why these tests fail in predicting an incoming bifurcation. JRT thanks the program ECOS-Sud A14E03 Evénements extr^emes en dynamique non linéaire for granting support to this research. MG and MM acknowledge ANR Blason (ANR-18-CE24-0002). CM acknowledges partial support from Spanish MINECO (PGC2018-099443-B-I00) and from the program ICREA ACADEMIA of Generalitat de Catalunya.

Time-delayed dynamical systems materialize in situations where distant, point-wise, nonlinear nodes exchange information that propagates at a finite speed. However, they are considered devoid of dispersive effects, which are known to play a leading role in pattern formation and wave dynamics. We show how dispersion may appear naturally in delayed systems and we exemplify our result by studying theoretically and experimentally the influence of third order dispersion in a system composed of coupled optical micro-cavities. Dispersion induced pulse satellites emerge asymmetrically and destabilize the mode-locking regime.

We show theoretically that optical feedback can be used to phase lock the successive modes of multi-section frequency-swept source lasers as a means to increase the coherence length. The time-gated feedback technique can be applied to transfer the coherence between the subsequent modes to retain the coherence along the full sweep or to synchronise two independent swept sources. In analogy with CW lasers, we derive an Adler equation describing the locking conditions. When the constant feedback is applied, the laser can operate in a self-mixing, mode-locking or chaotic regime, depending on the sweeping speed. In order to verify the theoretical results, we have developed an experimental set up and performed initial measurements with optical feedback.

In this paper we study, both experimentally and theoretically, the turn on transient dynamics observed in a long (20m) cavity laser. The laser consists of a ring cavity based on a single mode fiber with unidirectional propagation of light. The gain is provided by a semiconductor optical amplifier (SOA) centered around 1300nm and wavelength selection is provided by a tunable narrow transmission bandwidth Fabry-Perot filter. At high bias current and when the filter transmission sets the laser to operate in an anomalous dispersion regime, the laser exhibits only chaotic oscillations, while in a normal dispersion regime, the laser can exhibit stable operation. At a bias current close to the threshold the laser always exhibits multiple dropouts. In order to record the lasing build up dynamics, the bias current driven to the SOA is periodically switched from the off-state to a high current level. The lasing build up occurs at each roundtrip via a step-wise increase of the laser intensity. The laser intensity is widely oscillating during the first steps and approaches a stationary state after a large number of roundtrips. Recording of the phase evolution of the electric field during each step demonstrates the linewidth narrowing at each subsequent roundtrip. Theoretically, we describe the system by a set of delay differential equations and observe similar behavior. While typically a semiconductor laser exhibits relaxation oscillations before reaching the stable lasing regime, which is associated with class B lasers, our study shows that the long cavity laser demonstrates a different mechanism of lasing build up.

Spatially Localized States are individually addressable structures that may appear in large aspect-ratio optical resonators. They can be used as bits of information for all-optical buffering. We design and operate a modeless laser cavity based on a 1/2 VCSEL coupled to a distant mirror in self-imaging condition. Our study indicates how a VeCSEL can be specially designed to provide a robust system potentially capable of emitting Spatially Localized States and paves the way towards the observation of three dimensional - in space and time - confined states, the so-called light bullets.

We present the detailed phase-locking analysis of a telecom hybrid III-V-on-silicon passively mode-locked laser with a ring cavity and quantum wells as active region. We use a stepped-heterodyne measurement to quantify the modal phase chirp and reconstruct the pulse envelop. With this technique we are able to identify regimes of transform-limited operation and we assess the degradation of the phase-locking when saturable absorber bias voltage is changed.

We present the detailed characterization of the phase dynamics of a telecom hybrid III-V-on-silicon passively mode-locked laser with a ring cavity. We explore the various regimes of operation as a function of gain current and saturable absorber bias voltage. We use a stepped-heterodyne measurement to quantify the spectral chirp and reconstruct the pulse envelop. With this technique we are able to identify regimes of near-transform-limited operation and we assess the degradation of mode-locking in the comb phase relationship when saturable absorber bias voltage is changed. Finally, we present a preliminary study of the phase-locking in hybrid mode-locked operation and demonstrate transform-limited pulses., Comment: 6 pages, 5 figures

Speckle is a wave interference phenomenon that has been studied in various fields, including optics, hydrodynamics, and acoustics. Speckle patterns contain spectral information of the interfering waves and of the scattering medium that generates the pattern. Here, we study experimentally the speckle patterns generated by the light emitted by two types of semiconductor lasers: conventional laser diodes, where we induce low-coherence emission by optical feedback or by pump current modulation, and coupled nanolasers. In both cases, we analyze the intensity statistics of the respective speckle patterns to inspect the degree of coherence of the light. We show that the speckle analysis provides a non-spectral way to assess the coherence of semiconductor laser light.

We report on the first experimental observation of mirror symmetry breaking in coherently driven-dissipative coupled nanocavities. Our results pave the way to the experimental study of symmetry breaking at low photon number.

Two coupled semiconductor nanolasers exhibit a mode switching transition, theoretically characterized by limit cycle $-$or mode-beating$-$ oscillations. Their decay rate is vanishingly small in the thermodynamic limit, i.e. when the spontaneous emission noise $\beta$-factor tends to zero. We provide experimental evidence of mesoscopic limit cycles $-$with $\sim 10^3$ intracavity photons$-$ through photon statistics measurements. We first show that the order parameter quantifying the limit cycle amplitude can be reconstructed from the mode intensity statistics. As a main result we observe a maximum of the averaged amplitude at the mode switching, accounting for limit cycle oscillations. We finally relate this maximum to a dip of mode cross-correlations, reaching a minimum of $g_{ij}^{(2)}=2/3$, which we show to be a mesoscopic limit. Coupled nanolasers are thus an appealing testbed for the investigation of spontaneous breaking of time-translation symmetry in presence of strong quantum fluctuations.

Time-delayed dynamical systems materialize in situations where distant, pointwise, nonlinear nodes exchange information that propagates at a finite speed. However, they are considered devoid of dispersive effects, which are known to play a leading role in pattern formation and wave dynamics. We show how dispersion may appear naturally in delayed systems and we exemplify our result by studying theoretically and experimentally the influence of third order dispersion in a system composed of coupled optical microcavities. Dispersion-induced pulse satellites emerge asymmetrically and destabilize the mode-locking regime.

Delayed dynamical systems (DDSs) describe a large number of phenomena in nature and they exhibit a wealth of dynamical regimes such as localized structures (LSs) [1], fronts and chimera states. A fertile perspective lies in their interpretation as spatially extended diffusive systems which holds in the limit of long delays [2]. A strong limitation of DDSs for this aim comes from the difficulty of taking into consideration chromatic dispersion. As such, DDSs description of wave propagation is limited to low dispersive media and/or narrow-spectrum signals. Nevertheless, chromatic dispersion plays a leading role in many phenomena occurring during wave evolution [3]. Beyond second order dispersion (SOD), third order dispersion (TOD) is the lowest order non-trivial parity symmetry breaking effect, which leads to convective instabilities [4] and drifts.

We show experimentally and theoretically that localized pulses can be generated from an electrically biased 200 μm multitransverse-mode vertical-cavity surface-emitting laser. The device is passively mode-locked using optical feedback from a distant resonant saturable absorber mirror and is operated below its threshold. We observe multistability between the nonlasing (off) solution and a large variety of pulsating solutions which have a different number and arrangement of pulses per round trip, thus indicating that the mode-locked pulses are localized, i.e., mutually independent. We show that modulation of the bias current allows control of the number and the location of the pulses traveling within the cavity, thus suggesting that our system can be operated as an arbitrary pattern generator of mode-locked pulses.

Temporal Localized Structures are short pulses travelling back and forth in a nonlinear cavity which can be individually addressed and manipulated. Hence, they can be used as fundamental information bits, thus enabling data buffering and processing. They can also be used for generating arbitrary patterns of picosecond laser pulses at arbitrary low rate. In this contribution we review the results obtained in Vertical Cavity Surface-Emitting Lasers coupled to an external Saturable Absorber Mirror.

Microscale and nanoscale lasers inherently exhibit rich photon statistics due to complex light-matter interaction in a strong spontaneous emission noise background. It is well known that they may display superthermal fluctuations—photon superbunching—in specific situations due to either gain competition, leading to mode-switching instabilities, or carrier-carrier coupling in superradiant microcavities. Here we show a generic route to superbunching in bimodal nanolasers by preparing the system far from equilibrium through a parameter quench. We demonstrate, both theoretically and experimentally, that transient dynamics after a short-pump-pulse-induced quench leads to heavy-tailed superthermal statistics when projected onto the weak mode. We implement a simple experimental technique to access the probability density functions that further enables quantifying the distance from thermal equilibrium via the thermodynamic entropy. The universality of this mechanism relies on the far-from-equilibrium dynamical scenario, which can be mapped to a fast cooling process of a suspension of Brownian particles in a liquid. Our results open up new avenues to mold photon statistics in multimode optical systems and may constitute a test bed to investigate out-of-equilibrium thermodynamics using micro or nanocavity arrays.

Mechanically interlocked molecules represent chemical architectures whose composing elements are linked because of their topology instead of covalent bonds [1]. Among them, the catenanes are analogous to an ensemble of interlaced rings, globally locked yet locally independent. We disclose in this work the equivalent of such exotic molecules in the realm of nonlinear Photonics. They appear as interlocked bound states of localized structures (LSs) found in the temporal output of a Vertical-Cavity Surface-Emitting Laser (VCSEL) in presence of a point-wise nonlocality.

We show that the pumping current is a convenient parameter for manipulating the temporal Localized Structures (LSs), also called localized pulses, found in passively mode-locked Vertical-Cavity Surface-Emitting Lasers. While short electrical pulses can be used for writing and erasing individual LSs, we demonstrate that a current modulation introduces a temporally evolving parameter landscape allowing to control the position and the dynamics of LSs. We show that the localized pulses drifting speed in this landscape depends almost exclusively on the local parameter value instead of depending on the landscape gradient, as shown in quasi-instantaneous media. This experimental observation is theoretically explained by the causal response time of the semiconductor carriers that occurs on an finite timescale and breaks the parity invariance along the cavity, thus leading to a new paradigm for temporal tweezing of localized pulses. Different modulation waveforms are applied for describing exhaustively this paradigm. Starting from a generic model of passive mode-locking based upon delay differential equations, we deduce the effective equations of motion for these LSs in a time-dependent current landscape., Comment: 13 pages and 12 figures, submitted to Phys. Rev. A

In semiconductor-coupled micro and nano-cavities, the combination between tight light confinement and high optical nonlinearities open up new routes for the study of light-matter interaction in non-equilibrium driven dissipative systems. Even at the semiclassical level, coupled cavities may display a wide range of rich nonlinear dynamical phenomena such as instabilities and bifurcations [1]. Mode competition is at the heart of multimode laser dynamics, and may occur when different modes share the same gain medium. Mode switching (MS) and bistability have been observed in standard microcavity systems, such as vertical-cavity surface-emitting lasers (VCSELs) [2], micropillar lasers [3], semiconductor ring lasers [4]. These mechanisms usually rely on symmetric cross-gain saturation effects [4]. However, mode interaction in semiconductor cavities may also be asymmetric, resulting from stimulated scattering due to a dynamic carrier population grating in the gain medium, which oscillates at the beat note frequency between adjacent cavity modes. Such an asymmetric interaction enables energy transfer from the laser mode at the blue side of the spectrum to the mode at the red side [5].

Dissipative solitons often behave as quasiparticles, and they may form molecules characterized by well-defined bond distances. We show that pointwise nonlocality may lead to a new kind of molecule where bonds are not rigid. The elements of this molecule can shift mutually one with respect to the others while remaining linked together, in a manner similar to interlaced rings in a chain. We report experimental observations of these chains of nested dissipative solitons in a time-delayed laser system.

In this contribution we describe recent results on the generation and control of temporal localized structures in a passively mode-locked Vertical-Cavity Surface-Emitting Laser mounted in an external cavity closed by a resonant saturable absorber mirror. When the cavity roundtrip is much larger than the medium timescales, this system exhibits a temporal aspect-ratio large enough to host pulses which can be individually addressed. These localized pulses have been proposed as information bits and the possibility of their manipulation opens interesting perspectives for information processing. We will show that a modulation of the pumping current leads to control the position and the speed of the localized pulses within the cavity. In addition to pin the pulses at well-defined positions, which enables clocking the bit flow, the pulses can be driven to collide one against the other, thus unveiling the purely repulsive mutual interaction.

In this contribution we describe recent results on the generation and control of temporal localized structures in a passively mode-locked Vertical-Cavity Surface-Emitting Laser mounted in an external cavity closed by a resonant saturable absorber mirror. When the cavity roundtrip is much larger than the medium timescales, this system exhibits a temporal aspect-ratio large enough to host pulses which can be individually addressed. These localized pulses have been proposed as information bits and the possibility of their manipulation opens interesting perspectives for information processing. We will show that a modulation of the pumping current leads to control the position and the speed of the localized pulses within the cavity. In addition to pin the pulses at well-defined positions, which enables clocking the bit flow, the pulses can be driven to collide one against the other, thus unveiling the purely repulsive mutual interaction.

We show spontaneous mirror-symmetry breaking in two coupled photonic crystal nanolasers. A pitchfork bifurcation has been observed with only 150 intracavity photons, which makes this system promising to investigate nonlinear dynamics with few photons

© 2015 Macmillan Publishers Limited. We show that the nonlinear polarization dynamics of a vertical-cavity surface-emitting laser placed in an external cavity lead to the emission of temporal dissipative solitons. These are vectorial solitons because they appear as localized pulses in the polarized output, but leave the total intensity constant. When the cavity roundtrip time is much longer than the soliton duration, several independent solitons as well as bound states (molecules) may be hosted in the cavity. All these solitons coexist together and with the background solution. The experimental results are well described by a theoretical model that can be reduced to a single delayed equation for the polarization orientation, which allows the vectorial solitons to be interpreted as polarization kinks. A Floquet analysis is used to confirm the mutual independence of the observed solitons., J.J. acknowledges financial support from the Ramon y Cajal fellowship. J.J. and S.B. acknowledge financial support from project RANGER (TEC2012-38864-C03-01). The INLN group acknowledges funding from Region Provence-Alpes Cote d'Azur with the >Projet Volet General 2011: Generation et Detection des Impulsions Ultra Rapides (GEDEPULSE)>, project ANR >OPTIROC> and project ANR - Jeunes Chercheurs >MOLOSSE>

We study theoretically the non linear polarization dynamics of Vertical-Cavity Surface-Emitting Lasers in the presence of an external cavity providing delayed optical feedback and cross polarization re-injection. We show that far from the laser threshold, the dynamics remains confined close to the equatorial plane of a Stokes sphere of a given radius and we reduce the dynamics to a dynamical system composed of two phases: the orientation phase of the quasi-linear polarization and the optical phase of the field. We explore the complex modal structure given by the double feedback configuration and recovers as particular cases the Lang-Kobayashi modes and the modes founds by Giudici et al. [1]. We also re-interpret the square waves switching dynamics as phase kinks.

We review the dynamics of VCSELs that experience both Polarization-Selective Feedback (PSF) and Crossed- Polarization Reinjection (XPR). Different regimes of regular pulsation were found. For strong enough XPR levels, the VCSEL emission in each of its linearly-polarized components displays a square-wave modulation which regularity is greatly enhanced by small levels of PSF. Such a square-wave is in antiphase for the two polarizations, and it turns out to be stable and robust over broad intervals of current. The frequency of the square-wave is determined by the length of the XPR arm. For weak levels of PSF and XPR, the VCSEL emits a regular train of short optical pulses arising from the locking of the modes in the PSF cavity. The frequency of the pulse train is stable on short time scales, but it wanders with a characteristic time scale of hundreds of roundtrips in the PSF cavity. The experimental results are successfully explained by an extension of the Spin-Flip Model that incorporates gain saturation and the effects of PSF and XPR.

© 2014 IEEE. We show experimentally and theoretically that an electrically biased 200μm multitransverse mode vertical-cavity surface-emitting laser can be passively mode-locked using optical feedback from a distant resonant saturable absorber mirror. This is achieved when one cavity is placed at the Fourier plane of the other. Such nonconventional optical feedback leads to the formation of two tilted plane waves traveling in the external cavity with opposite transverse components and alternating in time at every round-trip. Each of these plane waves gives birth to a train of mode-locked pulses separated by twice the external cavity round-trip, while the two trains are time shifted by a round-trip. A large portion of the transverse section of the device contributes to mode-locked emission leading to pulses of approximately 1-W peak power and 10-ps width. We discuss how inhomogeneities in the transverse section of the saturable absorber select the emitted tilted waves, thus leading to tunable emission over 4 nm.

Vertical Cavity Surface-Emitting Laser (VCSEL) may exhibit bistability between two orthogonal polarization emissions [1]. Hysteresis has been reported in a narrow range of pumping current [2]. In this contribution we consider a VCSEL with negligible dichroism, where bistability is extended to the whole range of biasing current, from threshold to absolute maximum biasing rate. In practice two polarisation-resolved light-current curves coexist (Fig.1). The polarization emission state can be controlled by perturbing the VCSEL with crossed polarisation reinjection (XPR) pulses or feedback pulses. While an XPR pulse may induce a jump from situation depicted by Fig. 1, left panel, to situation depicted in Fig. 1, right panel, a feedback pulse can induce the reverse jump of the polarisation state. The temperature of the device can be used as a second parameter in order to vary the degree of stability of one component with respect to the other. We are not aware of any previous observation of such robust polarisation bistability.

We report experimental evidence of nonvolatile all-optical memory operation using the two linear polarization states emitted from a GaAs oxide-confined VCSEL. The two polarization states coexist in a large range of pumping currents and substrate temperatures, and they can be controlled all-optically by exposing the device to polarization selective feedback, to crossed polarization reinjection orby injecting external light pulses. The active polarization state is recovered after powering off and on the VCSEL, while memory is lost if the substrate temperature is varied.

In this presentation we will review the results recently obtained on Time-Localized Structures (TLS) in VCSELs coupled to an external cavity. We show that, when the cavity roundtrip is much larger than the medium timescales, this system exhibits a temporal aspect-ratio large enough to host TLS. Two configurations will be considered. In the first one the system is submitted to cross-polarization reinjection which leads to the formation of vectorial TLS. In the second one the external cavity is closed by a Resonant Saturable Absorber Mirror, a scheme conventionally used to obtain mode-locked pulses. Here we will show how TLS can be obtained from mode-locking.

A great variety of nonlinear dissipative systems are known to host structures having a correlation range much shorter than the size of the system. The dynamics of these Localized Structures (LSs) have been investigated so far in situations featuring parity symmetry. In this letter we extend this analysis to systems lacking of this property. We show that the LS drifting speed in a parameter varying landscape is not simply proportional to the parameter gradient, as found in parity preserving situations. The symmetry breaking implies a new contribution to the velocity field which is a function of the parameter value, thus leading to a new paradigm for LSs manipulation. We illustrate this general concept by studying the trajectories of the LSs found in a passively mode-locked laser operated in the localization regime. Moreover, the lack of parity affects significantly LSs interactions which are governed by asymmetrical repulsive forces., Comment: 6 pages, 4 figures, final version accepted in Physical Review Letters

We show existence of Localized Laser Structures (LLS) in two coupled semiconductor microresonators. LLS generate from spontaneous emission noise as independent lasers without any driving field. The phase invariance leads to exotic LLS, as localized vortices.

Nonlinear polarization dynamics of VCSELs with a long-delay external cavity lead to vectorial dissipative solitons. The large temporal aspect-ratio enables the observation of multiple -- independent and/or bound -- solitons within the same roundtrip.

In quantum optics, the statistical properties of the emitted photons define the nature of a light source. The black body is a well known example of source with large fluctuations and for which the statistics of the photon number is P(n) ≈ 1/〈 N 〉e−n/(n), if 〈n 〉 ≫ 1 with second order coherence g2 (0) = 2 (thermal light).

We investigate the relationship between passive mode-locking and the formation of temporal localized structures in the output of a laser, allowing for individual pulse addressing and arbitrary low repetition rates.

This contribution numerically and experimentally illustrates how regular and robust square wave emission can be obtained in Vertical Cavity Surface Emitting Lasers (VCSELs) using the polarisation degrees of freedom of these devices. The scheme propose is based on crossed-polarization re-injection (XPR). In such scheme, the emission from the laser is split into its two linearly polarized components, LP-x and LP-y, and only one of these components (LP-x, say) is fed back into the laser after being rotated into the orthogonal polarization direction (LP-y). In this way, cross-saturation of the polarization states modifies the photon density in each LP component and may eventually lead to square-wave modulation of the power emitted in each of the LP components with a period close to 2τr. When the dichroism in the device is strong enough and the emission occurs on a single polarization mode, XPR above a critical level leads to square-wave modulation which is stable over large ranges of bias currents. The emission dynamics for different levels and delays of XPR and PSF (polarization-selective optical feedback) were experimentally characterized. An asymmetry in the effects of PSF for the two polarizations is found. The experimental observations are satisfactorily explained within the Spin-Flip Model supplemented with appropriate terms describing XPR and PSF.