Fifty years after the invention of the laser diode, and forty years after the butterfly effect signified the unpredictability of deterministic chaos, it is commonly believed that a laser diode ...behaves like a damped nonlinear oscillator and cannot be driven into chaotic operation without additional forcing or parameter modulation. Here, we counter that belief and report the first example of a free-running laser diode generating chaos. The underlying physics comprises a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time series and show, theoretically, the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles noise-driven mode hopping, but shows opposite statistical properties. Our findings open up new research areas for the creation of controllable and integrated sources of optical chaos.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
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.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
We consider an integrated electro-absorption modulator within a coupled-cavity VCSEL structure (EAM-VCSEL). We derive expressions for the modulation transfer function (MTF) of the EAM-VCSEL for ...small-signal modulation of either VCSEL injection current or EAM losses. For current modulation, the cut-off frequency remains limited by relaxation oscillation frequency. For EAM loss modulation, the MTF curve is much flatter and its shape around the relaxation oscillation frequency displays either a well-pronounced maximum, both a maximum and a minimum or a sharp minimum only depending on the bias point of the EAM losses. Such features have been found experimentally in Marigo-Lombart et al., J. Physiscs: Photonics, 1, 2019, but remained unexplained hitherto. Furthermore, the cut-off frequency remains beyond 100 GHz for moderate and week coupling between the VCSEL and EAM cavities. Such ultrahigh bandwidth modulation is due to the fact that the changes of EAM impact much less the optical power distribution along the EAM-VCSEL and, consequently, the confinement factor and photon density in the VCSEL cavity. The three cases of strong, intermediate and weak coupling are also considered when carrying out the large-signal modulation response of the EAM-VCSEL and a clear open-eye diagram is demonstrated at 100 Gbs for an optimal EAM cavity length.
We study spectral and polarization threshold characteristics of coupled-cavity Vertical-Surface-Emitting Lasers (CC-VCSEL) on the base of a simple matrix approach. We show that strong wavelength ...discrimination can be achieved in CC-VCSELs by slightly detuning the cavities. However, polarization discrimination is not provided by the coupled-cavity design. We also consider the case of reverse-biasing one of the cavities, i.e. using it as a modulator via linear and/or quadratic electrooptic effect. Such a CC-VCSEL can act as a voltage-controlled polarization or wavelength switching device that is decoupled from the laser design and can be optimized for high modulation speed. We also show that using QD stack instead of quantum wells in the top cavity would lead to significant reduction of the driving electrical field.
Optical frequency comb technologies have received intense attention due to their numerous promising applications ranging from optical communications to optical comb spectroscopy. In this study, we ...experimentally demonstrate a new approach of broadband comb generation based on the polarization mode competition in single-mode VCSELs. More specifically, we analyze nonlinear dynamics and polarization properties in VCSELs when subject of optical injection from a frequency comb. When varying injection parameters (injection strength and detuning frequency) and comb properties (comb spacing), we unveil several bifurcation sequences enabling the excitation of free-running depressed polarization mode. Interestingly, for some injection parameters, the polarization mode competition induces a single or a two polarization comb with controllable properties (repetition rate and power per line). We also show that the performance of the two polarization combs depends crucially on the injection current and on the injected comb spacing. We explain our experimental findings by utilizing the spin-flip VCSEL model (SFM) supplemented with terms for parallel optical injection of frequency comb. We provide a comparison between parallel and orthogonal optical injection in the VCSEL when varying injection parameters and SFM parameters. We show that orthogonal comb dynamics can be observed in a wide range of parameters, as for example dichroism linear dichroism (γa=−0.1 ns−1 to γa=−0.8 ns−1), injection current (μ=2.29 to μ=5.29) and spin-flip relaxation rate (γs=50 ns−1 to γs=2300 ns−1).
We suggest a new construction of spin-VCSEL with an embedded nematic liquid crystal (LC) in a second cavity. We design such a coupled-cavity LC-VCSEL and develop a procedure for calculating its ...LC-voltage dependent polarization resolved resonant longitudinal modes and their quantum-well confinement factors. Using these characteristics, we are able to slightly modify the spin-flip VCSEL model to include the voltage dependent birefringence and anisotropy. Then, we show that such an LC-VCSEL can reach small signal modulation response with a 3dB cut off frequency of several hundreds of GHz.
We consider the paradigmatic Brusselator model for the study of dissipative structures in far from equilibrium systems. In two dimensions, we show the occurrence of a self-replication phenomenon ...leading to the fragmentation of a single localized spot into four daughter spots. This instability affects the new spots and leads to splitting behavior until the system reaches a hexagonal stationary pattern. This phenomenon occurs in the absence of delay feedback. In addition, we incorporate a time-delayed feedback loop in the Brusselator model. In one dimension, we show that the delay feedback induces extreme events in a chemical reaction diffusion system. We characterize their formation by computing the probability distribution of the pulse height. The long-tailed statistical distribution, which is often considered as a signature of the presence of rogue waves, appears for sufficiently strong feedback intensity. The generality of our analysis suggests that the feedback-induced instability leading to the spontaneous formation of rogue waves in a controllable way is a universal phenomenon.
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We carry out a theoretical study of a Fabry–Perot resonator with a central layer of nematic liquid crystal as a nonlinear polarization rotation (NPR) device for passive Q-switching and mode locking. ...We develop a self-consistent procedure for calculating the device dynamical response as a function of the input light intensity and polarization. We show how a positive feedback effect for the optical reorientation of the liquid crystal director makes the resonator abruptly switch to high-reflectivity state. We demonstrate that the time-delay between the pulse initiation and the resonator switch can be avoided by tilted liquid crystal molequles at the resonator boundaries. We show that such a NPR optical device is suitable for Q-switching operation with μs pulses and hundreds of kHz repetition rates. Further decrease of pulse duration and increase of the pulse repetition rate is possible by either increasing the pulse power or by increasing the Fabry–Perot resonator finesse. Finally, we show that the same Fabry–Perot resonator can be used for Q-switching and mode locking at tens of MHz repetition rates and ns pulse durations by using an electro-optic uniaxial–biaxial transition as an alternative to NPR in order to reduce pulse duration and increase repetition rate.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The Kerr nonlinearity in two-dimensional (2D) nanomaterials is emerging as an appealing and intriguing research area due to their prominent light processing, modulation, and manipulation abilities. ...In this contribution, 2D black arsenic-phosphorus (B-AsP) nanosheets (NSs) were applied in nonlinear photonic devices based on spatial self-phase modula-tion (SSPM) method. By applying the Kerr nonlinearity in 2D B-AsP, an all-optical phase-modulated system is proposed to realize the functions of "on" and "off" in all-optical switching. By using the same all-optical phase-modulated system, another optical logic gate is proposed, and the logical "or" function is obtained based on the 2D B-AsP NSs dispersions. Moreover, by using the SSPM method, a 2D B-AsP/SnS2 hybrid structure is fabricated, and the result illustrates that the hybrid structure possesses the ability of the unidirectional nonlinear excitation, which helps in obtaining the function of spatial asymmetric light propagation. This function is considered an important prerequisite for the realization of diode functionalization, which is believed to be a factor in important basis for the design of isolators as well. The initial investig-ations indicate that 2D B-AsP is applicable for designing optical logical devices, which can be considered as an import-ant development in all-optical information processing.
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