We numerically analyze a delay differential equation model of a short-cavity semiconductor laser with an intracavity frequency swept filter and reveal a complex bifurcation structure responsible for the asymmetry of the output characteristics of this laser. We show that depending on the direction of the frequency sweep of a narrowband filter, there exist two bursting cycles determined by different parts of a continuous-wave solutions branch.
We theoretically investigate the influence of optical feedback onto the dynamics of a semiconductor swept source laser. In particular, we show that optical feedback can be used to lock the phase of the successive lasing modes of a multi-section semiconductor laser commonly used for Optical Coherence Tomography (OCT) applications. We also identify two different regimes called sliding frequency self-mixing and sliding frequency mode-locking. The second regime demonstrates sub-nanosecond sliding frequency pulses for non-linear optics applications.
Full-field swept-source optical coherence tomography (FF-SS-OCT) and laser Doppler holography (LDH) are two holographic imaging techniques presenting unique capabilities for ophthalmology. We report on interlaced FF-SS-OCT and LDH imaging with a single instrument. Effectively, retinal blood flow and pulsation could be quasi-simultaneously monitored. This instrument holds potential for a wide scope of ophthalmic applications.
It has been known for quite some time that spinning polygon, and similar, swept lasers used in OCT favor the short to long wavelength sweep direction because of four wave mixing in the gain medium. Here we have reformulated the problem in the time domain and show experimentally and through numerical simulation that these lasers are pulsed. The emitted pulses modulate the gain medium refractive index to red shift the light. Instead of new wavelengths being built up slowly from spontaneous emission, each pulse hops to a longer wavelength by nonlinear means, tracking the tunable filter. This allo…
Light detection and ranging (lidar) has long been used in various applications. Solid-state beam steering mechanisms are needed for robust lidar systems. Here we propose and demonstrate a lidar scheme called "Swept Source Lidar" that allows us to perform frequency-modulated continuous-wave (FMCW) ranging and nonmechanical beam steering simultaneously. Wavelength dispersive elements provide angular beam steering, while a laser frequency is continuously swept by a wideband swept source over its whole tuning bandwidth. Employing a tunable vertical-cavity surface-emitting laser and a 1-axis mechan…
We present a theoretical model and its efficient numerical implementation for the simulation of wavelength-swept waveform propagation in fiber systems such as Fourier domain mode-locked (FDML) lasers, fully accounting for the polarization dynamics in fiber spools and further polarization dependent optical components in the setup. This approach enables us to perform long-time simulations of the FDML laser dynamics over more than 100000 cavity roundtrips, as required for some FDML configurations to ensure convergence to the steady state operating regime. The model is validated against experiment…
We demonstrate an ultrahigh-speed optical coherence tomography (OCT) based on a 100 MHz swept source (SS). An all polarization-maintaining figure-9 mode-locked fiber laser is used as the seed laser. After nonlinear spectral expansion in an Erbium-doped fiber amplifier, a flat top spectrum with respectively 1-dB and 10-dB bandwidths of 73.7 nm and 106 nm is obtained. The broadband femtosecond pulse is time stretched to a swept signal in a section of dispersion compensation fiber with a total dispersion of -84 ps/nm. With the swept source, the axial resolution of the SS-OCT is measured to be 21 …
Collision refers to a striking nonlinear interaction in dissipative systems, revealing the particle-like properties of solitons. In dual-wavelength mode-locked fiber lasers, collisions are inherent and periodic. However, how collisions influence the dynamical transitions in the dual-wavelength mode-locked state has still not been explored. In our research, dispersion management triggers the complex interactions between solitons in the cavity. We reveal the smooth or reversible Hopf-type bifurcation transitions of dual-color soliton molecules (SMs) during collision by real-time spectral measure…
We report on the experimental observation of period-doubling bifurcation of dissipative-soliton-resonance (DSR) pulses in a fiber laser passively mode-locked by using the nonlinear optical loop mirror. Increasing the pump power of the fiber laser, we show that temporally a stable, uniform DSR pulse train could be transformed into a period-doubling state, exhibiting two sets of pulse parameters between the adjacent cavity roundtrip. It is found that DSR pulses in the period-doubling state could maintain the typical feature of DSR pulse: fixed pulse peak power and linear variation in pulse width…
Mode-locked fiber lasers are rich dynamical systems that may present several different types of pulsed operating modes, depending on external control parameters such as pump power. A systematic experimental characterization of such regimes is a challenging problem. Here single pulse regimes of ytterbium mode-locked fiber laser are explored and related to the nonlinear amplitude modulation affecting the pulses inside the laser cavity. To understand the full dynamics of this system, average power measurements (slow time scale) have been performed and compared to simultaneous time-resolved measur…
A laser consisting of two independently-pumped resonators can exhibit mode bifurcations that evolve out of the exceptional points (EPs) of the linear system at threshold. The EPs are non-Hermitian degeneracies occurring at the parity/time-reversal ($\mathcal{PT}$) symmetry breaking points of the threshold system. Above threshold, the EPs become bifurcations of the nonlinear zero-detuned laser modes, which can be most easily observed by making the gain saturation intensities in the two resonators substantially different. Small pump variations can then switch abruptly between different laser beh…
High-order frequency locking phenomena were recently observed using semiconductor lasers subject to large delayed feedbacks [B. Tykalewicz, et al., Opt. Express 24, 4239 (2016); B. Kelleher, et al., Chaos 27, 114325 (2017)]. Specifically, the relaxation oscillation (RO) frequency and a harmonic of the feedback-loop round-trip frequency coincided with the ratios 1:5 to 1:11. By analyzing the rate equations for the dynamical degrees of freedom in a laser subject to a delayed optoelectronic feedback, we show that the onset of a two-frequency train of pulses occurs through two successive bifurcati…
A Robust Hertz-Linewidth Quantum-Dot Coherent Swept Source with Adaptive Self-Linearization
State Key Laboratory for Extreme Photonics and Instrumentation, Zhejiang Key Laboratory of Optoelectronic Information Technology, College of Optical Science and Engineering, International Research Center for Advanced Photonics, Zhejiang University（浙江大学）；State Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology, Sun Yat-Sen University（中山大学）；China Jiliang University（中国计量大学）；Intelligent Optics and Photonics Research Center, Jiaxing Research Institute, Zhejiang University（浙江大学嘉兴研究院）
Period-doubling bifurcation is a universal dynamic of nonlinear systems, which has been extensively investigated in laser systems with a single transverse mode. This study presents an experimental observation and theoretical investigation of the period-doubling bifurcation in spatiotemporal mode-locked (STML) multimode fiber lasers. In the period-doubling state, it is observed that the pulse train modulation varies with the transverse-mode, and the output beam profile fluctuates rapidly and periodically. The numerical simulations conducted in this study are in good agreement with the experimen…
Topological lasers are of growing interest as a way to achieve disorder-robust single mode lasing using arrays of coupled resonators. We study lasing in a two-dimensional coupled resonator lattice exhibiting transitions between trivial and topological phases, which allows us to systematically characterize the lasing modes throughout a topological phase. We show that, unlike conventional topological robustness that requires a sufficiently large bulk band gap, bifurcations in topological edge mode lasing can occur even when the band gap is maximized. We show that linear mode bifurcations from si…
Optical coherence tomography (OCT) applications like ultra-widefield and full eye-length imaging are of high interest for various diagnostic purposes. In swept-source OCT these techniques require a swept light source, which is coherent over the whole imaging depth. We present a zero roll-off 1060 nm Fourier Domain Mode Locked-Laser (FDML-Laser) for retinal OCT imaging at 1.7 MHz A-scan rate and first long-range imaging results with it. Several steps such as improved dispersion compensation and frequency regulation were performed and will be discussed. Besides virtually no loss in OCT signal ov…
Local bifurcation control is a topic of fundamental importance in the field of nonlinear dynamical systems. We discuss an original example within the context of storage-ring free-electron laser physics by presenting a new model that enables analytical insight into the system dynamics. The transition between the stable and the unstable regimes, depending on the temporal overlapping between the light stored in the optical cavity and the electrons circulating into the ring, is found to be a Hopf bifurcation. A feedback procedure is implemented and shown to provide an effective stabilization of th…
Semiconductor lasers exhibit a wealth of dynamics, from emission of a constant beam of light, to periodic oscillations and excitability. Self-pulsing regimes, where the laser periodically releases a short pulse of light, are particularly interesting for many applications, from material science to telecommunications. Self-pulsing regimes need to produce pulses very regularly and, as such, they are also known to be particularly sensitive to perturbations, such as noise or light injection. We investigate the effect of delayed optical feedback on the dynamics of a self-pulsing semiconductor laser …
We report on the mid-infrared nonlinear photothermal spectrum of the neat liquid crystal 4-Octyl-4'-Cyanobiphenyl (8CB) using a tunable Quantum Cascade Laser (QCL). The nonequilibrium steady state characterized by the nonlinear photothermal infrared response undergoes a supercritical pitchfork bifurcation. The bifurcation, observed in heterodyne two-color pump-probe detection, leads to ultrasharp nonlinear infrared spectra similar to those reported in the visible region. A systematic study of the peak splitting as function of absorbed infrared power shows the bifurcation has a critical exponen…
We consider self-pulsing in lasers with a gain section and an absorber section via a mechanism known as Q-switching, as described mathematically by the Yamada ordinary differential equation model for the gain, the absorber and the laser intensity. More specifically, we are interested in the case that gain and absorber decay on different time scales. We present the overall bifurcation structure by showing how the two-parameter bifurcation diagram in the plane of pump strength versus decay rate of the gain changes with the ratio between the two decay rates. In total, there are ten cases BI to BX…
Period doubling is a universal bifurcation of central importance in all disciplines of nonlinear science, which generally signals the existence of chaotic dynamics in the vicinity of the system parameters. Although observed in diverse ultrafast laser configurations, there is still no consensus on its physical origin. The observations also include other types of pulsating dissipative solitons, with either short or long periods. Real time spectral characterization allows to investigate optical spectral oscillations, whose features reveal the intracavity dynamics leading to instabilities. Followi…
Bifurcation structure of soliton self-injection locking in microresonators
Emergent Complexity in Physical Systems Laboratory (ECPS), Swiss Federal Institute of Technology Lausanne (EPFL)（复杂物理系统实验室，洛桑联邦理工学院）；Laboratoire Temps-Fréquence, Université de Neuchâtel（时间频率实验室，纳沙泰尔大学）
The concept of broken symmetry is used to study bifurcations of equilibria and dynamical instabilities in dynamic model of one-mode laser (nonresonant complex Lorenz model) on the basis of modified Hopf theory. It is shown that an invariant set of stationary points bifurcates into an invariant torus (doubly-periodic branching solution). Influence of the symmetry breaking on stability of branching solutions is investigated as a function of detuning. The invariant torus is found to be stable under the detuning exceeds its critical value, so that dynamically broken symmetry results in the apprear…
A detailed experimental study of antiphase dynamics in a two-mode semiconductor laser with optical injection is presented. The device is a specially designed Fabry-Perot laser that supports two primary modes with a THz frequency spacing. Injection in one of the primary modes of the device leads to a rich variety of single and two-mode dynamical scenarios, which are reproduced with remarkable accuracy by a four dimensional rate equation model. Numerical bifurcation analysis reveals the importance of torus bifurcations in mediating transitions to antiphase dynamics and of saddle-node of limit cy…
A homogeneously broadened unidirectonal ring laser can emit in several longitudinal modes for large enough pump and cavity length because of Rabi splitting induced gain. This is the so called Risken-Nummedal-Graham-Haken (RNGH) instability. We investigate numerically the properties of the multi-mode solution. We show that this solution can coexist with the single-mode one, and its stability domain can extend to pump values smaller than the critical pump of the RNGH instability. Morevoer, we show that the multi-mode solution for large pump values is affected by two different instabilities: a pi…
Bifurcation of laser-dressed band extrema in solids under intense low-frequency fields
Voronezh State University（沃罗涅日国立大学）；Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences（中国科学院西安光学精密机械研究所）；Peking University（北京大学）；A.V. Gaponov-Grekhov Institute of Applied Physics, Russian Academy of Sciences（俄罗斯科学院阿·瓦·加波诺夫-格列霍夫应用物理研究所）
In numerous applications, Fourier-domain optical coherence tomography (FD-OCT) suffers from a limited imaging depth due to signal roll-off, a limited focal range, and autocorrelation noise. Here, we propose a parallel full-field FD-OCT imaging method that uses a swept laser source and an area camera in combination with an off-axis reference, which is incident on the camera at a small angle. As in digital off-axis holography, this angle separates autocorrelation signals and the complex conjugated mirror image from the actual signal in Fourier space. We demonstrate that by reconstructing the sig…
FDML lasers provide sweep rates in the MHz range at wide optical bandwidths, making them ideal sources for high speed OCT. Recently, at lower speed, ultralong-range swept-source OCT has been demonstrated1, 2 using a tunable vertical cavity surface emitting laser (VCSEL) and also using a Vernier-tunable laser. These sources provide relatively high sweep rates and meter range coherence lengths. In order to achieve similar coherence, we developed an extremely well dispersion compensated Fourier Domain Mode Locked (FDML) laser, running at 3.2 MHz sweep rate and 120 nm spectral bandwidth. We demons…
We consider a delay differential equation (DDE) model for mode-locked operation in class-A semiconductor lasers containing both gain and absorber sections. The material processes are adiabatically eliminated as these are considered fast in comparison to the delay time for a long cavity device. We determine the steady states and analyze their bifurcations using DDE-BIFTOOL [K. Engelborghs, T. Luzyanina, and D. Roose, ACM Trans. Math. Softw. 28, 1 (2002)]. Multiple forms of coexistence, transformation and hysteretic behavior of stable steady states and fundamental periodic regimes are discussed …
Stability control in laser is still an emerging field of research. In this paper the dynamics of External cavity semiconductor lasers (ECSLs) is widely studied applying the methods of chaos physics. The stability is analyzed through plotting the Lyapunov exponent spectra, bifurcation diagrams and time series. The oscillation of the electric field E has been reported to be either periodic (P1,P2,..) or chaotic. The results of the study show that the rich nonlinear dynamics of the electric field |E|^2 includes saddle node bifurcations, quasi-periodicity and regular pulse packages. The issue of f…
The time-delayed Adler equation is arguably the simplest model for an injected semiconductor laser with coherent injection and optical feedback. It is able to reproduce the existence of topological localized structures (LSs) and their rich interactions. In this paper we perform the first extended bifurcation analysis of this model and we explore the mechanisms by which LSs emerge. We also derive the effective equations governing the motion of distant LSs and we stress how the lack of parity in time-delayed systems leads to exotic, non-reciprocal, interactions between topological localized stat…
The ray dynamics of optical cavities exhibits bifurcation points: special geometries at which ray trajectories switch abruptly between stable and unstable. A prominent example is the Fabry-Perot cavity with two planar mirrors, which is widely employed for broad-area semiconductor lasers. Such cavities support lasing in a relatively small number of transverse modes, and the laser is highly susceptible to filamentation and irregular pulsations. Here we demonstrate experimentally that a slight deviation from this bifurcation point (planar cavity) dramatically changes the laser performance. In a n…
In this paper, we analyze the effect of optical feedback on the dynamics of a passively mode-locked ring laser operating in the regime of temporal localized structures. This laser system is modeled by a system of delay differential equations, which include delay terms associated with the laser cavity and the feedback loop. Using a combination of direct numerical simulations and path-continuation techniques, we show that the feedback loop creates echos of the main pulse whose position and size strongly depend on the feedback parameters. We demonstrate that in the long-cavity regime, these echos…
In this paper, we analyze the formation and dynamical properties of discrete light bullets (dLBs) in an array of passively mode-locked lasers coupled via evanescent fields in a ring geometry. Using a generic model based upon a system of nearest-neighbor coupled Haus master equations we show numerically the existence of dLBs for different coupling strengths. In order to reduce the complexity of the analysis, we approximate the full problem by a reduced set of discrete equations governing the dynamics of the transverse profile of the dLBs. This effective theory allows us to perform a detailed bi…
We study the emergence and the stability of temporal localized structures in the output of a semiconductor laser passively mode-locked by a saturable absorber in the long cavity regime. For large yet realistic values of the linewidth enhancement factor, we disclose the existence of secondary dynamical instabilities where the pulses develop regular and subsequent irregular temporal oscil- lations. By a detailed bifurcation analysis we show that additional solution branches that consist in multi-pulse (molecules) solutions exist. We demonstrate that the various solution curves for the single and…
In this paper we study the formation and dynamics of self-propelled cavity solitons (CSs) in a model for vertical cavity surface-emitting lasers (VCSELs) subjected to external frequency selective feedback (FSF), and build their bifurcation diagram for the case where carrier dynamics is eliminated. For low pump currents, we find that they emerge from the modulational instability point of the trivial solution, where traveling waves with a critical wavenumber are formed. For large currents, the branch of self-propelled solitons merges with the branch of resting solitons via a pitchfork bifurcatio…
We analyze the dynamics of passively mode-locked integrated external-cavity surface-emitting Lasers (MIXSELs) using a first-principle dynamical model based upon delay algebraic equations. We show that the third order dispersion stemming from the lasing micro-cavity induces a train of decaying satellites on the leading edge of the pulse. Due to the nonlinear interaction with carriers, these satellites may get amplified thereby destabilizing the mode-locked states. In the long cavity regime, the localized structures that exist below the lasing threshold are found to be deeply affected by this in…
In this paper, we analyze the dynamics and formation mechanisms of bound states (BSs) of light bullets in the output of a laser coupled to a distant saturable absorber. First we approximate the full three-dimensional set of Haus master equations by a reduced equation governing the dynamics of the transverse profile. This effective theory allows us to perform a detailed multiparameter bifurcation study and to identify the different mechanisms of instability of BSs. In addition, our analysis reveals a non-intuitive dependence of the stability region as a function of the linewidth enhancement fac…
We consider a wide-aperture surface-emitting laser with a saturable absorber section subjected to time-delayed feedback. We adopt the mean-field approach assuming a single longitudinal mode operation of the solitary VCSEL. We investigate cavity soliton dynamics under the effect of time- delayed feedback in a self-imaging configuration where diffraction in the external cavity is negligible. Using bifurcation analysis, direct numerical simulations and numerical path continuation methods, we identify the possible bifurcations and map them in a plane of feedback parameters. We show that for both t…
Quantum cascade laser (QCL) frequency combs have revolutionized mid-infrared (MIR) spectroscopy by their high brightness and fast temporal resolution, and are a promising technology for fully-integrated and cost-effective sensors. As for other integrated comb sources such as micro-combs and interband cascade laser, QCLs have a comb spacing of several GHz, which is adequate for measurements of wide absorbing structures, typically found in liquid or solid samples. However, high-resolution gas-phase spectra require spectral interleaving and frequency calibration. We developed a frequency calibrat…
Understanding the dynamics of Fourier domain mode-locked (FDML) lasers is crucial for determining physical coherence limits, and for finding new superior methods for experimental realization. In addition, the rich interplay of linear and nonlinear effects in a laser ring system is of great theoretical interest. Here we investigate the dynamics of a highly dispersion-compensated setup, where over a bandwidth of more than 100 nm, a highly coherent output with nearly shot-noise-limited intensity fluctuations was experimentally demonstrated. This output is called the sweet-spot. We show by numeric…
Lasers can exhibit nonlinear and chaotic dynamics driven by the interaction of multiple lasing modes, and investigating the different scenarios of mode competition and bifurcations of their dynamics is of great interest on a fundamental level as well as in view of applications. We study the dynamics of a broad-area vertical-cavity surface-emitting laser (VCSEL) in solitary continuous-wave operation with a comprehensive investigation of its polarization state, lasing spectra, near-field distributions, and temporal dynamics. Fluctuations at the frequency of birefringence splitting and other freq…
Spectral hole burning reduces sodium laser guide star efficiency. Due to photon recoil, atoms that are initially resonant with the single-frequency laser get Doppler shifted out of resonance, which reduces the return flux. Frequency-chirped (also known as frequency-swept) continuous-wave lasers have the potential to mitigate the effect of spectral hole burning and even increase the laser guide star efficiency beyond the theoretical limit of a single-frequency laser. On-sky measurements of a frequency-chirped, single-frequency laser guide star are performed at the Roque de los Muchachos Observa…
We numerically investigate the effect of phase-amplitude coupling modulation on power spectra in semiconductor lasers subject to optical injection in a face to face configuration, when a non-negligible injection delay time is taken into account. We find that as phase-amplitude coupling factor alpha varies, the system goes through a sequence of phase transactions between In-phase locking states to anti-phase locking states via phase-flip bifurcation. Moreover, we observed the signature of frequency discretization (Frequency Island) and uncovered the physical mechanism for the existence of multi…
We investigate the various routes to spatiotemporal chaos in Kerr optical frequency combs obtained through pumping an ultra-high quality whispering-gallery mode resonator with a continuous-wave laser. The Lugiato-Lefever model is used to build bifurcation diagrams with regards to the parameters that are externally controllable, namely, the frequency and the power of the pumping laser. We show that the spatiotemporal chaos emerging from Turing patterns and solitons display distinctive dynamical features. Experimental spectra of chaotic Kerr combs are also presented for both cases, in excellent …
When a driven oscillator loses phase-locking to a master oscillator via a Hopf bifurcation, it enters a bounded-phase regime in which its average frequency is still equal to the master frequency, but its phase displays temporal oscillations. Here we characterize these two synchronization regimes in a laser experiment, by measuring the spectrum of the phase fluctuations across the bifurcation. We find experimentally, and confirm numerically, that the low frequency phase noise of the driven oscillator is strongly suppressed in both regimes in the same way. Thus the long-term phase stability of t…
We investigate the effect of tunable optical feedback on a commercial DFB laser edge coupled to a Silicon Photonics planar integrated circuit in which a tunable reflector has been implemented by means of a ring resonator based add-drop multiplexer. Controlled optical feedback allows for fine-tuning of the laser oscillation frequency. Under certain conditions it also allows suppression of bifurcation modes triggered by reflections occurring elsewhere on the chip. A semi-analytical model describing laser dynamics under combined optical feedback from the input facet of the edge coupler and from t…
