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We propose and analyze numerically new approaches to force the laser emission from VCSELs in a well-defined linear polarization independent of the existing phase and amplitude anisotropies by using dielectric columnar thin-film (CTF) layers in the distributed Bragg reflector (DBR). In one approach, we have demonstrated CTF-VCSELs with top DBR consisting of two alternating CTF layers grown in orthogonally oriented planes and with high and low refractive index for one linear polarization while having the same value of the refractive index value for the orthogonal linear polarization. Such CTF-VCSELs have large dichroism of the mirror losses for two orthogonal linear polarizations. We have also shown DBR designs with parallel columnar orientations of the two CTF dielectric materials. In a second approach, we implement only one CTF layer in the dielectric DBR chosen in such a way that only one linearly polarized longitudinal mode is resonant in the CTF-VCSEL while light with the orthogonally oriented linear polarization is out of resonance and thus cannot lase. Simple estimation of the polarization mode suppression ratio for the different exemplary designs of CTF-VCSELs based on TiO2 and TaO2 dielectric CTFs results in values as high as 80 dB, which compares favorably to the existing alternative approaches.

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 modulation (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 investigations indicate that 2D B-AsP is applicable for designing optical logical devices, which can be considered as an important development in all-optical information processing.

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.

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 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.

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 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.

The pioneering paper ‘Optical rogue waves’ by Solli et al (2007 Nature450 1054) started the new subfield in optics. This work launched a great deal of activity on this novel subject. As a result, the initial concept has expanded and has been enriched by new ideas. Various approaches have been suggested since then. A fresh look at the older results and new discoveries has been undertaken, stimulated by the concept of ‘optical rogue waves’. Presently, there may not by a unique view on how this new scientific term should be used and developed. There is nothing surprising when the opinion of the experts diverge in any new field of research. After all, rogue waves may appear for a multiplicity of reasons and not necessarily only in optical fibers and not only in the process of supercontinuum generation. We know by now that rogue waves may be generated by lasers, appear in wide aperture cavities, in plasmas and in a variety of other optical systems. Theorists, in turn, have suggested many other situations when rogue waves may be observed. The strict definition of a rogue wave is still an open question. For example, it has been suggested that it is defined as ‘an optical pulse whose amplitude or intensity is much higher than that of the surrounding pulses’. This definition (as suggested by a peer reviewer) is clear at the intuitive level and can be easily extended to the case of spatial beams although additional clarifications are still needed. An extended definition has been presented earlier by N Akhmediev and E Pelinovsky (2010 Eur. Phys. J. Spec. Top.185 1–4). Discussions along these lines are always useful and all new approaches stimulate research and encourage discoveries of new phenomena. Despite the potentially existing disagreements, the scientific terms ‘optical rogue waves’ and ‘extreme events’ do exist. Therefore coordination of our efforts in either unifying the concept or in introducing alternative definitions must be continued. From this point of view, a number of the scientists who work in this area of research have come together to present their research in a single review article that will greatly benefit all interested parties of this research direction. Whether the authors of this ‘roadmap’ have similar views or different from the original concept, the potential reader of the review will enrich their knowledge by encountering most of the existing views on the subject. Previously, a special issue on optical rogue waves (2013 J. Opt.15 060201) was successful in achieving this goal but over two years have passed and more material has been published in this quickly emerging subject. Thus, it is time for a roadmap that may stimulate and encourage further research. [ABSTRACT FROM AUTHOR]