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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in: Tarigo, J. [et al.]. Basin entropy as an indicator of a bifurcation in a time-delayed system. "Chaos", Maig 2024, vol. 34, núm. 5, article 053113 and may be found at https://doi.org/10.1063/5.0201932, The basin entropy is a measure that quantifies, in a system that has two or more attractors, the predictability of a final state, as a function of the initial conditions. While the basin entropy has been demonstrated on a variety of multistable dynamical systems, to the best of our knowledge, it has not yet been tested in systems with a time delay, whose phase space is infinite dimensional because the initial conditions are functions defined in a time interval [-t,0], where t is the delay time. Here we consider a simple time delayed system consisting of a bistable system with a linear delayed feedback term. We show that the basin entropy captures relevant properties of the basins of attraction of the two coexisting attractors. Moreover, we show that the basin entropy can give an indication of the proximity of a Hopf bifurcation, but fails to capture the proximity of a pitchfork bifurcation. The Hopf bifurcation is detected because before the fixed points become unstable, a oscillatory, limit-cycle behavior appears that coexists with the fixed points. The new limit cycle modifies the structure of the basins of attraction, and this change is captured by basin entropy that reaches a maximum before the Hopf bifurcation. In contrast, the pitchfork bifurcation is not detected because the basins of attraction do not change as the bifurcation is approached. Our results suggest that the basin entropy can yield useful insights into the long-term predictability of time delayed systems, which often have coexisting attractors., J.P.T., C.S., and A.C.M. acknowledge support of PEDECIBA (MEC-Udelar, Uruguay); C.M. acknowledges support of ICREA ACADEMIA, AGAUR (2021 SGR 00606), and Ministerio de Ciencia e Innovación Spain (Project No. PID2021-123994NB-C21). The numerical experiments were performed at the ClusterUY (https://cluster.uy), Peer Reviewed, Postprint (author's final draft)

We demonstrate all-optical spatial mode-cleaning in non-Hermitian waveguides. The effect is accounted by a unidirectional coupling among the modes resulting from a simultaneous modulation of the refractive index and the gain/loss along graded index multimodal waveguides. Depending on the spatial delay between the real and imaginary part of the potential modulation, higher or lower order modes are favored, which in latter case eventually leads to an nearly-monomode propagation. In this way, for any arbitrary initial field distribution an antisymmetric non-Hermitian modulation results in an effective mode-cleaning. The effect is demonstrated analytically, based on coupled mode theory in 1D waveguides, and numerically proven by solving the wave propagation equation with the antisymmetric non-Hermitian potential. The proposal is also generalized to the more involved case of 2D waveguides, leading to a significant reduction of the beam quality factor and improvement of beam spatial quality., This work has received funding from Horizon 2020 program project MEFISTA (Project No. 861152), from Spanish Ministry of Science, Innovation and Universities (MICINN) under the projects PID2019-109175GB-C2, and PID2022-138321NB-C21., Peer Reviewed, Postprint (published version)

Understanding the coupling structure of interacting systems is an important open problem, and many methods have been proposed to reconstruct a network from observed data. Most require continuous observation of the nodes’ dynamics; however, in many situations, we can only monitor the times when some events occur (e.g., in neural systems, spike times). Here, we propose a method for network reconstruction based on the analysis of event times at the network’s nodes. First, from the event times, we generate phase time series. Then, we assimilate the phase time series to the Kuramoto model by using the unscented Kalman filter (UKF) that returns the inferred coupling coefficients. Finally, we use a clustering algorithm to discriminate the coupling coefficients into two groups that we associate with existing and non-existing links. We demonstrate the method with synthetic data from small networks of Izhikevich neurons, where we analyze the spike times, and with experimental data from a larger network of chaotic electronic circuits, where the events are voltage threshold-crossings. We also compare the UKF with the performance of the cross-correlation (CC), and the mutual information (MI). We show that, for neural network reconstruction, UKF often outperforms CC and MI, while for electronic network reconstruction, UKF shows similar performance to MI, and both methods outperform CC. Altogether, our results suggest that when event times are the only information available, the UKF can give a good reconstruction of small networks. However, as the network size increases, the method becomes computationally demanding., R.P.A. acknowledges financial support from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior–Brasil (CAPES), Finance Code 001. H.A.C. thanks ICTP-SAIFR and FAPESP, Brazil grants 2021/14335-0 and 2021/11754-2. G.T. and C.M. acknowledge the support of ICREA ACADEMIA, AGAUR, Spain (2021 SGR 00606) and Ministerio de Ciencia e Innovación, Spain (Project No. PID2021-123994NB-C21)., Peer Reviewed, Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructura, Postprint (author's final draft)

Developing reliable methodologies to decode brain state information from electroencephalogram (EEG) signals is an open challenge, crucial to implementing EEG-based brain–computer interfaces (BCIs). For example, signal processing methods that identify brain states could allow motor-impaired patients to communicate via non-invasive, EEG-based BCIs. In this work, we focus on the problem of distinguishing between the states of eyes closed (EC) and eyes open (EO), employing quantities based on permutation entropy (PE). An advantage of PE analysis is that it uses symbols (ordinal patterns) defined by the ordering of the data points (disregarding the actual values), hence providing robustness to noise and outliers due to motion artifacts. However, we show that for the analysis of multichannel EEG recordings, the performance of PE in discriminating the EO and EC states depends on the symbols’ definition and how their probabilities are estimated. Here, we study the performance of PE-based features for EC/EO state classification in a dataset of subjects with one-minute 64-channel EEG recordings in each state. We analyze features obtained from patterns encoding temporal or spatial information, and we compare different approaches to estimate their probabilities (by averaging over time, over channels, or by “pooling”). We find that some PE-based features provide about 75% classification accuracy, comparable to the performance of features extracted with other statistical analysis techniques. Our work highlights the limitations of PE methods in distinguishing the eyes’ state, but, at the same time, it points to the possibility that subject-specific training could overcome these limitations., We acknowledge the support of ICREA ACADEMIA,AGAUR (2021 SGR 00606 and FI scholarship) and Ministerio de Ciencia e Innovación (Project No. PID2021-123994NB-C21), Peer Reviewed, Objectius de Desenvolupament Sostenible::3 - Salut i Benestar, Postprint (published version)

There is an increasing interest toward disclosing and explaining confinement effects on liquids, such as water or aqueous solutions, in slit pore setups. Particularly puzzling are the changes of physical and chemical properties in the nanoconfinement regime where no bulk-like water phase exists between the two interfacial water layers such that the density profile across the slit pore becomes highly stratified, ultimately leading to bilayer and monolayer water. These changes must be quantified with respect to some meaningful reference state of water, the most natural one being bulk water at the same pressure and temperature conditions. However, bulk water is a homogeneous liquid with isotropic properties, whereas water confined in slit pores is inhomogeneous, implying anisotropic properties as described by the perpendicular and parallel components of the respective tensors. In the case of pressure, the inhomogeneous nature of the setup results in a well-defined difference between the perpendicular and parallel pressure tensor components that is uniquely determined by the interfacial tension being a thermodynamic property. For bilayer water constrained in graphene slit pores that are only about 1 nm wide, we demonstrate that there exists a thermodynamic point where the pressure tensor of the inhomogeneous fluid, nanoconfined water, is effectively isotopic and the pressure is thus scalar as in the homogeneous fluid, bulk water. This specific point of vanishing effective interfacial tension is proposed to serve as a well-defined reference state to compare the properties of nanoconfined liquids to those of the corresponding bulk liquid at the same (isotropic) pressure and temperature conditions. In future work, this idea could be applied to assess confinement effects on chemical reactivity in aqueous solutions as well as to other nanoconfined liquids in other pores such as layered minerals., We are particularly grateful to Daniel Mun˜oz-Santiburcio for insightful discussions. Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy– EXC 2033– 390677874– RESOLV as well as by the individual DFG grant MA 1547/11–2 to DM. Computing resources have been provided by Leibniz-Rechenzentrum Mu¨nchen (SuperMUC and SuperMUC– NG), HPC@ZEMOS, HPC– RESOLV, and BOVILAB@RUB., Peer Reviewed, Postprint (author's final draft)

The 2021 Nobel Prize in Physics recognized the fundamental role of complex systems in the natural sciences. In order to celebrate this milestone, this editorial presents the point of view of the editorial board of JPhys Complexity on the achievements, challenges, and future prospects of the field. To distinguish the voice and the opinion of each editor, this editorial consists of a series of editor perspectives and reflections on few selected themes. A comprehensive and multi-faceted view of the field of complexity science emerges. We hope and trust that this open discussion will be of inspiration for future research on complex systems., The authors acknowledge their funding sources, including: Royal Society (IEC\NSFC\191147 (G Bianconi); NSF Grants CCF-1839232, PHY-1806372, DGE-2125899, PHY-2210566 (L.C.); NRF, Grant No. NRF-2014R1A3A2069005 and the KENTECH Research Grant (KRG2021-01-007) (B Kahng); EU H2020 ICT48 project ‘Humane AI Net’ under Contract #952026 and EU Horizon 2020—ERC Synergy Grant 810115 ‘Dynasnet’ (J Kertesz); ICREA Academia Award, Catalan Institution for Research and Advanced Studies (C Masoller); National Science Foundation Award No. DMS-1647351 (A E Motter); Slovenian Research Agency (Grant Nos. P1-0403 and J1-2457) (M Perc); PID2019-106811GB-C31 from MCIN/AEI/10.13039/501100011033 (M Sales Pardo); PACSS (RTI2018-093732-B-C21) and MDM-2017-0711 from MCIN/AEI/10.13039/501100011033, Spain (M San Miguel). FR acknowledges support by the Army Research Office (W911NF-21-1-0194) and by the Air Force Office of Scientific Research (FA9550-21-1-0446)., Peer Reviewed, Article signat per 19 autors/es : Ginestra Bianconi, Alex Arenas, Jacob Biamonte, Lincoln D Carr, Byungnam Kahng, Janos Kertesz, Jürgen Kurths, Linyuan Lu, Cristina Masoller, Adilson E Motter Matjaz Perc, Filippo Radicchi, Ramakrishna Ramaswamy, Francisco A Rodrigues, Marta Sales-Pardo, Maxi San Miguel, Stefan Thurner and Taha Yasseri., Postprint (published version)

Understanding diffusive processes in networks is a significant challenge in complexity science. Networks possess a diffusive potential that depends on their topological configuration, but diffusion also relies on the process and initial conditions. This article presents Diffusion Capacity, a concept that measures a node’s potential to diffuse information based on a distance distribution that considers both geodesic and weighted shortest paths and dynamical features of the diffusion process. Diffusion Capacity thoroughly describes the role of individual nodes during a diffusion process and can identify structural modifications that may improve diffusion mechanisms. The article defines Diffusion Capacity for interconnected networks and introduces Relative Gain, which compares the performance of a node in a single structure versus an interconnected one. The method applies to a global climate network constructed from surface air temperature data, revealing a significant change in diffusion capacity around the year 2000, suggesting a loss of the planet’s diffusion capacity that could contribute to the emergence of more frequent climatic events., Research partially supported by Brazilian agencies FAPEMIG, CAPES, and CNPq. P.M.P. acknowledges support from the “Paul and Heidi Brown Preeminent Professorship in ISE, University of Florida”, and RSF 14-41- 00039, Humboldt Research Award (Germany) and LATNA, Higher School of Economics, RF. C.M. acknowledges partial support from Spanish MINECO (PID2021-123994NB-C21) and ICREA ACADEMIA. A.D.- G. knowledges support from the Spanish grants PGC2018-094754-BC22 and PID2021-128005NB-C22, funded by MCIN/AEI/ 10.13039/ 501100011033 and “ERDF A way of making Europe”; and from Generalitat de Catalunya (2021SGR00856). M.G.R acknowledges partial support from FUNDEP., Peer Reviewed, Postprint (published version)

Non-Hermitian systems offer new platforms for unusual physical properties that can be flexibly manipulated by redistribution of the real and imaginary parts of refractive indices, whose presence breaks conventional wave propagation symmetries, leading to asymmetric reflection and symmetric transmission with respect to the wave propagation direction. Here, we use supervised and unsupervised learning techniques for knowledge acquisition in non-Hermitian systems which accelerate the inverse design process. In particular, we construct a deep learning model that relates the transmission and asymmetric reflection in non-conservative settings and propose sub-manifold learning to recognize non-Hermitian features from transmission spectra. The developed deep learning framework determines the feasibility of a desired spectral response for a given structure and uncovers the role of effective gain-loss parameters to tailor the spectral response. These findings offer a route for intelligent inverse design and contribute to the understanding of physical mechanism in general non-Hermitian systems., Postprint (published version)

We report experimental observations and numerical simulations of second and third harmonic generation from a gold nanograting, which exhibits a plasmonic resonance in the near infrared. The resonance is tunable, with a spectral position that depends on the angle of incidence. All things being equal, the enhancement of nonlinear optical processes produced by the field localization in the nanograting when compared with a flat gold mirror manifests itself dramatically from the ultraviolet to the visible range: second harmonic generation conversion efficiencies increase by more than three orders of magnitude, while we report a third harmonic generation conversion efficiency enhancement factor of 3200, both in excellent agreement with our theoretical predictions. The clear inferences one may draw from our results are that our model describes the dynamics with unprecedented accuracy and that much remains to be revealed in the development of nonlinear optics of metals at the nanoscale., L.R.-S., J.T., and C.C. acknowledge the Spanish Agencia Estatal de Investigación (Project No. PID2019-105089GB-I00/AEI/10.130397501100011033) and the U.S. Army Research Laboratory Cooperative Agreement No. W911NF1920279 issued by the U.S. ARMY ACC-APG-RTP., Peer Reviewed, Postprint (published version)

© 2023 Optica Publishing Group. 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., Optical feedback can reduce the linewidth of a semiconductor laser by several orders of magnitude, but it can also cause line broadening. Although these effects on the temporal coherence of the laser are well known, a good understanding of the effects of feedback on the spatial coherence is still lacking. Here we present an experimental technique that allows discriminating the effects of feedback on temporal and spatial coherence of the laser beam. We analyze the output of a commercial edge-emitting laser diode, comparing the contrast of speckle images recorded using a multimode (MM) or single mode (SM) fiber and an optical diffuser, and also, comparing the optical spectra at the end of the MM or SM fiber. Optical spectra reveal feedback-induced line broadening, while speckle analyses reveal reduced spatial coherence due to feedback-excited spatial modes. These modes reduce the speckle contrast (SC) up to 50% when speckle images are recorded using the MM fiber, but do not affect the SC when the images are recorded using the SM fiber and diffuser, because the spatial modes that are excited by the feedback are filtered out by the SM fiber. This technique is generic and can be used to discriminate spatial and temporal coherence of other types of lasers and under other operating conditions that can induce a chaotic output., Institució Catalana de Recerca i Estudis Avançats (Academia); Agència de Gestió d’Ajuts Universitaris i de Recerca (2021 SGR 00606, FI Scholarship); Ministerio de Ciencia, Innovación y Universidades (PID2021-123994NBC21)., Peer Reviewed, Postprint (published version)

Synchronization phenomena is ubiquitous in nature, and in spite of having been studied for decades, it still attracts a lot of attention as is still challenging to detect and quantify, directly from the analysis of noisy signals. Semiconductor lasers are ideal for performing experiments because they are stochastic, nonlinear, and inexpensive and display different synchronization regimes that can be controlled by tuning the lasers’ parameters. Here, we analyze experiments done with two mutually optically coupled lasers. Due to the delay in the coupling (due to the finite time the light takes to travel between the lasers), the lasers synchronize with a lag: the intensity time traces show well-defined spikes, and a spike in the intensity of one laser may occur shortly before (or shortly after) a spike in the intensity of the other laser. Measures that quantify the degree of synchronization of the lasers from the analysis of the intensity signals do not fully quantify the synchronicity of the spikes because they also take into account the synchronization of fast irregular fluctuations that occur between spikes. By analyzing only the coincidence of the spike times, we show that event synchronization measures quantify spike synchronization remarkably well. We show that these measures allow us to quantify the degree of synchronization and, also, to identify the leading laser and the lagging one., C.M. acknowledges the support of Ministerio de Ciencia, Innovación y Universidades (No. PID2021-123994NB-C21) and Institució Catalana de Recerca i Estudis Avançats (Academia)., Peer Reviewed, Postprint (author's final draft)

© 2023 Optica Publishing Group. 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., Nonlinear silicon photonics offers unique abilities to generate, manipulate and detect optical signals in nano-devices, with applications based on field localization and large third order nonlinearity. However, at the nanoscale, inefficient nonlinear processes, absorption, and the lack of realistic models limit the nano-engineering of silicon. Here we report measurements of second and third harmonic generation from undoped silicon membranes. Using experimental results and simulations we identify the effective mass of valence electrons, which determines second harmonic generation efficiency, and oscillator parameters that control third order processes. We can then accurately predict the nonlinear optical properties of complex structures, without introducing and artificially separating the effective ¿(2) into surface and volume contributions, and by simultaneously including effects of linear and nonlinear dispersions. Our results suggest that judicious exploitation of the nonlinear dispersion of ordinary semiconductors can provide reasonable nonlinear efficiencies and transformational device physics well into the UV range., The authors thank Zack Coppens and Dana Dement for useful discussions and help with the sample. LRS, JT, and CC acknowledge to US Army Research Laboratory Cooperative Agreement N° W911NF1920279 issued by US ARMY ACC-APG-RTP and Spanish Agencia Estatal de Investigación (project no. PID2019-105089GBI00/AEI/10.130397501100011033). MAV was partially sponsored by the Army Research Laboratory under Cooperative Agreement N° W911NF2020078., Peer Reviewed, Postprint (published version)

We analyze the transverse modes in flat-flat mirror microchip-laser resonators, which occur due to the gain guiding and the thermal lensing. We rigorously calculate the transverse-mode functions, their eigenfrequencies, and their generation-threshold conditions. We apply a plausible assumption that the mode amplitudes in multi-transverse-mode emission are proportional to the individual gain factors of each mode, and we estimate the beam quality factor for the multi-transverse-mode emission. This simple and intuitive approach leads to the beam quality estimations corresponding well to the experimental measurements performed here., Postprint (published version)

Resonantly enhanced x-ray difference-frequency generation (re-XDFG) is a second-order nonlinear effect that involves illuminating a molecule with two-color x-ray pulses with photon energies O1 and O2. The energy difference $\Omega_1-\Omega_2$ is tuned to match an x-ray absorption edge of an atom in the molecule. We have numerically studied the re-XDFG effect considering different individual molecules in the gas phase using density functional theory calculations and have verified the non-centrosymmetric character of the target transitions. Two-level molecular systems with permanent dipoles are evaluated for the description of re-XDFG taking into account different two-color input pulse geometries. This innovative nonlinear x-ray methodology offers a means to measure the K-edge NEXAFS spectrum of light elements, such as carbon, nitrogen, or oxygen, in dense media using non-resonant x-rays. It can also be used to investigate chemical material dynamics that are inaccessible by linear spectroscopy. These findings enable the combination of atomic-scale structure with chemical specificity and the selective and local access to x-ray excitations using hard x-ray pulses., Peer Reviewed, Postprint (author's final draft)

The design and development of advanced devices based on metamaterials to control the transmission of acoustic waves is a hot topic. An important class of these metamaterials is based on phononic crystals with Locally Resonant Structure, included in those commonly known as Locally Resonant Sonic Materials. In these metamaterials, wave control is basically performed by two mechanisms: internal (or local) resonances in the scatterers that form the phononic crystal, and Bragg bandgaps due to structural periodicity. Their main control feature is the resonance peaks forming additional stop-bands away from the Bragg frequency, mainly in the low frequency regime. For some applications, coupling of the two phenomena is necessary to create a broad transmission gap. However, when both are located in close frequency ranges, some destructive interferences can occur. In this paper, the authors develop a comprehensive numerical model of periodic arrays of Hemholtz resonators, which explains in detail the physical mechanisms of this destructive interference and, simultaneously, allows the reproduction of the consequences of the interference. The numerical results are supported by experimental tests., Postprint (published version)

While generating high harmonics in long media of helium gas, at certain laser intensities and chirp, the spectral shift and split of the harmonic lines were experimentally observed, sometimes exceeding one harmonic order. Beyond reporting these results, numerical simulations were performed to understand the phenomenon. A 3D propagation model was solved under the strong field approximation. According to the simulations, the distortion of the laser beam profile during propagation and the consequently accused change in the conditions of phase matching are responsible for the observations. The observed phenomena can be an excellent tool to produce tunable narrow band harmonic sources covering a broad range around 13.5 nm for spectroscopy and for seeding X-ray lasers, and to understand non-desired detuning of the seed wavelength., This research was funded by Japan Society for the Promotion of Science, KAKENHI, JP20H00141, JP19K15402, and JP21H03750; JKA and its promotion funds from KEIRIN RACE; and the transmittance calibration of Zr thin films was performed at BL11D of the Photon Factory, KEK Japan (Proposal Nos. 2019G547 and 2021G525). This study was also funded by the Horizon 2020 Framework Programme (856415); European Metrology Program for Innovation and Research (20FUN01 TSCAC); Österreichische Nationalstiftung für Forschung (AQUnet)., Peer Reviewed, Postprint (published version)

In semiarid regions, vegetated ecosystems can display abrupt and unexpected changes, i.e., transitions to different states, due to drifting or time-varying parameters, with severe consequences for the ecosystem and the communities depending on it. Despite intensive research, the early identification of an approaching critical point from observations is still an open challenge. Many data analysis techniques have been proposed, but their performance depends on the system and on the characteristics of the observed data (the resolution, the level of noise, the existence of unobserved variables, etc.). Here, we propose an entropy-based approach to identify an upcoming transition in spatiotemporal data. We apply this approach to observational vegetation data and simulations from two models of vegetation dynamics to infer the arrival of an abrupt shift to an arid state. We show that the permutation entropy (PE) computed from the probabilities of two-dimensional ordinal patterns may provide an early warning indicator of an approaching tipping point, as it may display a maximum (or minimum) before decreasing (or increasing) as the transition approaches. Like other spatial early warning indicators, the spatial permutation entropy does not need a time series of the system dynamics, and it is suited for spatially extended systems evolving on long time scales, like vegetation plots. We quantify its performance and show that, depending on the system and data, the performance can be better, similar or worse than the spatial correlation. Hence, we propose the spatial PE as an additional indicator to try to anticipate regime shifts in vegetated ecosystems., Peer Reviewed, Postprint (published version)

We present an experimental study of the effect of continuous-wave optical injection (OI) from a vertical-cavity surface-emitting laser (VCSEL) on the timing jitter of a gain-switched discrete-mode semiconductor laser (DML). Timing jitter was analyzed over a wide range of temperatures of the DML, which allowed tuning the detuning between the lasers emissions, and it was compared with the inter-pulse timing jitter. We have found that there is a range of detunings in which OI diminishes the jitter by 70% with respect to the jitter of the solitary DML. However, within this region, there are some detunings for which OI significantly increases the jitter., This work was supported by AGAUR (2021 SGR 00606 and FI scholarship), ICREA Academia, Ministerio de Ciencia e Innovación (PID2021-123994NB-C21 and PID2021-12345OB-C22 MCIN/AEI/FEDER UE), and Beatriz Galindo program (Ministerio de Ciencia, Innovación y Universidades)., Peer Reviewed, Postprint (published version)

Copyright 2023 Society of Photo‑Optical Instrumentation Engineers (SPIE). One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this publication for a fee or for commercial purposes, and modification of the contents of the publication are prohibited., We propose a new light management mechanism in graded index (GRIN) multimode fibers (MMFs) that allow to control the spectral mode distribution of the propagated beam. The effect is achieved through longitudinal non-Hermitian modulations of the complex refractive index, i.e. the refraction index (for instance, a modulation of the core radius) and a periodic gain/loss profile. The applied potential holding a longitudinal spatial period close to the intermodal beat frequency of the parabolic index profile, to strongly influence the transverse mode dynamics. The non-Hermitian potential introduces a unidirectional and controllable coupling between the transverse modes. In turn, the spatial shift between the real and imaginary components of the modulation controls the unidirectional coupling either to higher or lower order modes. The effect is simultaneously demonstrated by solving a (2+1) D Linear Schrodinger Equation (two transverse plus one longitudinal spatial coordinates) as well as it is predicted by a simplified model for an oscillating Gaussian beam ansatz, leading to a system of ordinary differential equations. We demonstrate, both analytically and numerically, a mode cleaning effect, i.e. the improvement of the spatial structure of light in its propagation along the modulated MMFs; in an ideal case resulting in single-mode spatially coherent output. On the contrary, when inducing the coupling towards higher order modes, pulsing is enhanced, which may eventually contribute to super-continuum generation. The proposed scheme could lead to actual applications as it could be experimentally realized within the current nanofabrication technologies., Peer Reviewed, Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructura, Postprint (author's final draft)

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Aristides, R. [et al.]. Parameter and coupling estimation in small networks of Izhikevich's neurons. "Chaos", 12 Abril 2023, vol. 33, núm. 4, article 043123 and may be found at https://doi.org/10.1063/5.0144499., Nowadays, experimental techniques allow scientists to have access to large amounts of data. In order to obtain reliable information from the complex systems that produce these data, appropriate analysis tools are needed. The Kalman filter is a frequently used technique to infer, assuming a model of the system, the parameters of the model from uncertain observations. A well-known implementation of the Kalman filter, the unscented Kalman filter (UKF), was recently shown to be able to infer the connectivity of a set of coupled chaotic oscillators. In this work, we test whether the UKF can also reconstruct the connectivity of small groups of coupled neurons when their links are either electrical or chemical synapses. In particular, we consider Izhikevich neurons and aim to infer which neurons influence each other, considering simulated spike trains as the experimental observations used by the UKF. First, we verify that the UKF can recover the parameters of a single neuron, even when the parameters vary in time. Second, we analyze small neural ensembles and demonstrate that the UKF allows inferring the connectivity between the neurons, even for heterogeneous, directed, and temporally evolving networks. Our results show that time-dependent parameter and coupling estimation is possible in this nonlinearly coupled system., R.P.A. acknowledges financial support from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior–Brasil (CAPES), Finance Code 001. H.A.C. thanks ICTP-SAIFR and FAPESP grant 2021/14335-0. G.T. and C.M. acknowledge the support of the ICREA ACADEMIA program of Generalitat de Catalunya and Ministerio de Ciencia e Innovación, Spain (Project No. PID2021- 123994NB-C21)., Peer Reviewed, Objectius de Desenvolupament Sostenible::3 - Salut i Benestar, Objectius de Desenvolupament Sostenible::4 - Educació de Qualitat, Postprint (published version)

Taming the instabilities inherent to many nonlinear optical phenomena is of paramount importance for modern photonics. In particular, the so-called snake instability is universally known to severely distort localized wave stripes, leading to the occurrence of transient, short-lived dynamical states that eventually decay. This phenomenon is ubiquitous in nonlinear science—from river meandering to superfluids—and so far it apparently remains uncontrollable; however, here we show that optical snake instabilities can be harnessed by a process that leads to the formation of stationary and robust two-dimensional zigzag states. We find that such a new type of nonlinear waves exists in the hyperbolic regime of cylindrical microresonators, and that it naturally corresponds to two-dimensional frequency combs featuring spectral heterogeneity and intrinsic synchronization. We uncover the conditions of the existence of such spatiotemporal photonic snakes and confirm their remarkable robustness against perturbations. Our findings represent a new paradigm for frequency comb generation, thus opening the door to a whole range of applications in communications, metrology and spectroscopy., Peer Reviewed, Postprint (author's final draft)

Zero incidence angle spatial filters of a compact design can be very useful, among others, for intracavity spatial filtering in high-power micro-lasers. Typically, micro-lasers, especially in high-power operation regimes, emit beams of low spatial quality due to the large aspect ratio of the laser resonator. A promising proposal for compact spatial filtering is the integration of the Photonic Crystals structures into the micro-resonator of the laser. Here, we report efficient spatial filters with desired filtering properties engineered by the inverse design. Such filters can be designed not only separately for both polarizations of the incident radiation but also simultaneously for both S and P polarizations. Moreover, we fabricate the inverse-designed structure by physical vapor deposition and highlight good correspondence of the angle-wavelength transmission map to the target one., Postprint (published version)

Semiconductor lasers are very sensitive to optical feedback. Although it is well known that coherent feedback lowers the threshold of the laser, the characteristics of the transition from low-coherence radiation—dominated by spontaneous emission—below threshold to high-coherence radiation—dominated by stimulated emission—above threshold have not yet been investigated. Here we show experimentally that, in contrast to the transition that occurs in the solitary laser, in the laser with feedback the transition to high-coherence emission can occur abruptly. We use the speckle technique to show that the transition varies from smooth to abrupt as the amount of light fed back to the laser increases., Peer Reviewed, Postprint (published version)

We uncover new families of stable periodic solutions by the introduction of non-Hermitian potentials in the universal complex Ginzburg–Landau equation. We perform a comprehensive analysis on the dynamics and stability of the system by determining and following these new solutions for a one-dimensional system, and demonstrate that the results hold for higher spatial dimensions and for the corresponding complex Ginzburg–Landau fractional order equation. We prove the robustness of the stabilisation within a broad range in parameter space. The universality of the CGLE allows extending these results to different actual systems described by other specific models. In particular, we provide results on the stabilisation for Vertical Cavity Surface Emitting Lasers., Peer Reviewed, Postprint (author's final draft)

We evaluate causal dependencies between thirteen indices that represent large-scale climate patterns (El Nino/Southern Oscillation, the North Atlantic Oscillation, the Pacifc Decadal Oscillation, etc.) using a recently proposed approach based on a linear approximation of the transfer entropy. We demonstrate that this methodology identifes causal relations that are well-known, as well as it uncovers some relations which, to the best of our knowledge, have not yet been reported in the literature. We also identify signifcant changes in causal dependencies that have occurred in the last three decades., Open Access funding provided thanks to the CRUECSIC agreement with Springer Nature. This work received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No 813844. C.M. also acknowledges funding by the ICREA ACADEMIA program of Generalitat de Catalunya and Ministerio de Ciencia e Innovacion, Spain, project PID2021-123994NB-C21., Peer Reviewed, Postprint (published version)

When confined between walls at nanometer distances, water exhibits surprisingly different properties with reference to bare interfacial water. Based on computer simulations, we demonstrate how vibrational sum frequency generation (VSFG) spectroscopy can be used–even with very mild symmetry breaking–to discriminate multilayer water in wide slit pores from both bilayer and monolayer water confined within molecularly narrow pores. Applying the technique, the VSFG lineshapes of monolayer, bilayer, and multilayer water are found to differ in characteristic ways, which is explained by their distinct density stratifications giving rise to different H-bonding patterns in the respective solvation layers., Peer Reviewed, Postprint (published version)

We have found a way for penetrating the space of the dynamical systems towards systems of arbitrary dimension exhibiting the nonlinear mixing of a large number of oscillation modes through which extraordinarily complex time evolutions may arise. The system design is based on assuring the occurrence of a number of Hopf bifurcations in a set of fixed points of a relatively generic system of ordinary differential equations, in which the main peculiarity is that the nonlinearities appear through functions of a linear combination of the system variables. The paper outlines the design procedure and presents a selection of numerical simulations with a variety of designed systems whose dynamical behaviors are really rich and full of unknown features. For concreteness, the presentation is focused to illustrating the oscillatory mixing effects on the periodic orbits, through which the harmonic oscillation born in a Hopf bifurcation becomes successively enriched with the intermittent incorporation of other oscillation modes of higher frequencies while the orbit remains periodic and without necessity of bifurcating instabilities. Even in the absence of a proper mathematical theory covering the nonlinear mixing mechanisms we find enough evidence to expect that the oscillatory scenario be truly scalable concerning the phase space dimension, the multiplicity of involved fixed points and the range of time scales, so that extremely complex but ordered dynamical behaviors could be sustained through it., Peer Reviewed, Postprint (author's final draft)

We study the output of a semiconductor laser with optical feedback operated in the lowfrequency fluctuations (LFFs) regime and subject to weak sinusoidal current modulation. In the LFF regime, the laser intensity exhibits abrupt drops, after which it recovers gradually. Without modulation, the drops occur at irregular times, while, with weak modulation, they can lock to the external modulation and they can occur, depending on the parameters, every two or every three modulation cycles. Here, we characterize experimentally the locking regions and use the wellknown Lang–Kobayashi model to simulate the intensity dynamics. We analyze the effects of several parameters and find that the simulations are in good qualitative agreement with the experimental observations., This research was funded by the Spanish Ministerio de Ciencia, Innovacion y Universidades (PGC2018-099443-B-I00) and the ICREA ACADEMIA program of Generalitat de Catalunya., Postprint (published version)

We present acoustic drill beams, structured sound beams exhibiting a dynamic intensity distribution that matches the shape of a helix. The intensity distribution rotates along the beam axis with controlled direction and angular frequency, resembling in this way the shape of a mechanical drill bit. Acoustic drill beams emerge as the spatiotemporal interference of two confocal, detuned vortex beams. The beam parameters are fully tuneable. The detuned frequency, the detuned wavenumber and the detuned topological charge of the composing beams can be tuned to control the drill parameters such as the number of drill arms, the winding period, the rotational speed, and their direction. We show that elongated drill beams are obtained using two confocal high-order Bessel beams, allowing analytical solutions for optimal overlap. In addition, drill beams can also be synthesised using focused ultrasound vortices. Analytical, numerical, and experimental results are shown in the ultrasound regime using a low-cost device based on two 1-MHz confocal piezoelectric transducers and 3D printed acoustic holograms. This exotic structured wavefront opens new avenues for wave-matter interaction, such as contactless particle manipulation, matter processing or biomedical applications., Postprint (published version)

Reliable anomaly/outlier detection algorithms have practical applications in many fields. For instance, anomaly detection allows to filter and clean the data used to train machine learning algorithms, improving their performance. However, outlier mining is challenging when the data is high-dimensional, and different approaches have been proposed for different types of data (temporal, spatial, network, etc). Here we propose a methodology to mine outliers in generic datasets in which it is possible to define a meaningful distance between elements of the dataset. The methodology is based on defining a fully connected, undirected graph, where the nodes are the elements of the dataset and the links have weights that are the distances between the nodes. Outlier scores are defined by analyzing the structure of the graph, in particular, by using the Jensen–Shannon (JS) divergence to compare the distributions of weights of different nodes. We demonstrate the method using a publicly available database of credit-card transactions, where some of the transactions are labeled as frauds. We compare with the performance obtained when using Euclidean distances and graph percolation, and show that the JS divergence leads to performance improvement, but increases the computational cost., Peer Reviewed, Postprint (published version)

We propose and explore a stabilization mechanism of a semiconductor laser array based on asymmetric coupling between neighboring lasers. The stabilization scheme takes advantage of the symmetry breaking of non-Hermitian potentials. We perform a comprehensive numerical analysis in terms of the design parameters, namely the distance between lasers and spatial shift between the individual laser stripe and corresponding electrode. In turn, a mirrorsymmetric architecture is intended to lead to a light redistribution within the array which is expected to facilitate direct coupling efficiency to optical fibers., Postprint (author's final draft)

We report a critical narrowing of resonances of a driven potential well, when their eigenfrequencies approach the edge of the continuum. The resonances also obtain unusual sharp-peak shapes at the continuum boundary. The situation can be realized for the electromagnetic wave propagating across the dielectric thin films with a periodically modulated interface(s). We show the general phenomenon semi-analytically on a simplified model of a driven quantum potential well, also by rigorous numerical analysis of Maxwell equations for the wave propagation across the thin film with a modulated interface(s). We justify the phenomenon experimentally, by the measurements of light reflection from the dielectric thin film deposited on a periodically modulated surface. The narrow and sharp-peak resonances can be used for an efficient narrow-band frequency- and spatial filtering of light., Postprint (author's final draft)

Among other possible designs, metamaterials constructed from ensembles of meta-dipoles emerged as a flexible platform to redirect wave fields. We present an acoustic PT-dipole constructed from two Helmholtz resonators with different losses for such acoustic metamaterials. We explore dipole ensembles in a two dimensional space to either concentrate the field in a predefined area or create a silent area. Numerical simulations agree with experimental results and confirm the sound directivity created by the PT-dipole ensembles., Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructura, Postprint (published version)

In this work we show the prospect of using periodic refractive index modulation – photonic crystals – to control the spatial dispersion curvature in a way that could potentially counteract the Kerr effect, thus suppressing filamentation. Numerical simulations by beam propagation method indicate that fine control of the spatial dispersion can be achieved by tuning the photonic crystal geometry and projecting to the appropriate Bloch mode by chirping the longitudinal period. Fabrication of such photonic crystals poses some unique challenges due to the small feature size and large-scale requirement. Bessel beam writing is shown to be a valid method for the fabrication of such photonic crystals., Postprint (author's final draft)

We report contrasted experimental and theoretical results on second and third harmonic generation from an amorphous silicon nanolayer. We perform this study by analysing the harmonic optical signals generated when fs and ps pulses tuned at 800nm and 1064nm, respectively, interact with the material. We measure second and third harmonic efficiencies as functions of angle of incidence and compare with numerical simulations based on a microscopic hydrodynamic model that accounts for different possible contributions to the nonlinear polarization. We measure and estimate the efficiencies of the nonlinear signals using no assumptions about effective surface or volume nonlinearities, enabling proper explanations about the microscopic origins of SH and TH signals arising from the amorphous silicon nanolayer., Peer Reviewed, Postprint (published version)

We show an efficient mechanism to control optical turbulence in systems with different dispersion laws, including parabolic, sub-diffractive, hyper-diffractive or general fractional dispersion. The method is based on the modification of the energy cascade through spatial scales leading to turbulence: a non-Hermitian spatio-temporal periodic potential allows unidirectional coupling between modes in the excitation process. We prove a significant increase and reduction of the energy flow in turbulent states, by either condensing the excitation towards small wave-numbers or affecting the energy transfer towards large wave-number. The study is based on the complex Fractional Ginzburg–Landau equation, a universal model for pattern formation and turbulence in a wide range of systems. The enhancement or reduction of turbulence is indeed dependent on the imposed direction of the energy flow, controlled by the phase shift between the real and imaginary parts of the temporal oscillation of the non-Hermitian potential., Peer Reviewed, Postprint (published version)

One of the key trends in laser material processing is the usage of structured laser beams. Collimated and focused Gaussian beams are the most common tools; however, more exotic beams can be beneficial too. For instance, Bessel beams with elongated focal area and self-healing properties, or vortex beams with helical wave fronts and a dark area along the optical axis are being increasingly used. Here, we propose and experimentally demonstrate dynamical “optical drill” beams presenting nonstationary intensity distributions that resemble a spinning mechanical drill. Optical drills appear as the spatiotemporal interference of two Bessel-vortex beams of different topological charges and different carrier frequencies. By mixing a pair of high-order Bessel beams, synthesized using a liquid crystal spatial light modulator, optical drills of tuned helicities are experimentally observed, and the simplest cases of matter processing (fluorescence) with such beams are demonstrated. Optical drill beams are expected to be useful in material processing by light or in cell and particle manipulation in biomedical applications., Postprint (author's final draft)

We show that a non-Hermitian modulation of the potential along the nonlinear multimode fibers controls dynamics of propagating radiation. Specifically we consider simultaneous modulation of the refraction index and gain/loss profile. We observe that the non-Hermitian modulation introduces a unidirectional and controllable coupling towards the lower/higher order transverse modes, depending on the potential parameters. Such effect may enhance the beam self-cleaning phenomena. On the contrary, coupling towards higher order modes may enhance pulsing, turbulence and, eventually help in super-continuum generation., Peer Reviewed, Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructura, Postprint (published version)

We show that the simultaneous modulation of the propagation constant and of the gain/loss coefficient along the multimode fibers results in unidirectional coupling among the modes, which, depending on the modulation parameters, leads to the enhancement or reduction of the excitation of higher order transverse modes. In the latter case, effective mode-cleaning is predicted, in ideal case resulting in single-mode spatially coherent output. The effect is semi-analytically predicted on a simplified Gaussian beam approximation and numerically proven by solving the wave propagation equation introducing the modulated potential., Peer Reviewed, Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructura, Preprint

We present direct and inverse-design strategies to achieve ‘on demand’ dynamical manipulation of light by non-Hermitian potentials. The direct approach, based on a generalized Hilbert Transform, widens the concept of the Kramers Kronig relations in space. Yet, the inverse-design concept enables analyzing the underlying fundamental insights of the resulting permittivity distributions, bridging the gap between direct and inverse-design approaches to engineer non-Hermitian optical systems. Our findings may have to applications encompassing laser science., Postprint (published version)

In 2002, in a seminal article, Bandt and Pompe proposed a new methodology for the analysis of complex time series, now known as Ordinal Analysis. The ordinal methodology is based on the computation of symbols (known as ordinal patters) which are defined in terms of the temporal ordering of data points in a time series, and whose probabilities are known as ordinal probabilities. With the ordinal probabilities the Shannon entropy can be calculated, which is the permutation entropy. Since it was proposed, the ordinal method has found applications in fields as diverse as biomedicine and climatology. However, some properties of ordinal probabilities are still not fully understood, and how to combine the ordinal approach of feature extraction with machine learning techniques for model identification, time series classification or forecasting, remains a challenge. The objective of this perspective article is to present some recent advances and to discuss some open problems., The authors acknowledge hospitality of the Max Planck Institute for the Physics of Complex Systems, where a collaboration was established and this work started. C.M. acknowledges funding from the ICREA ACADEMIA pro- gram, Generalitat de Catalunya; M.Z. from the Euro- pean Research Council (ERC) under grant agreement No 851255; MZ and JHM. from the Spanish State Re- search Agency through Grant MDM-2017-0711 funded by MCIN/AEI/10.13039/501100011033; I.L. from the Spanish State Research Agency through Grant PID2020- 113737GB-I00. JHM acknowledges J. M. Buldú for valu- able comments and J. J. Ramasco for his assistance., Peer Reviewed, Postprint (author's final draft)

The Nobel Prize in Physics 2021 was awarded to Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi for their “groundbreaking contributions to our understanding of complex systems,” including major advances in the understanding of our climate and climate change. In this Perspective article, we review their key contributions and discuss their relevance in relation to the present understanding of our climate. We conclude by outlining some promising research directions and open questions in climate science., All authors received funding from the European Union’s Horizon 2020 research and innovation program under Marie Sklodowska Curie Grant Agreement No. 813844. C.M. also acknowledges funding from the Spanish Ministerio de Ciencia, Innovación y Universidades (No. PGC2018-099443-B-I00) and the ICREA ACADEMIA program of Generalitat de Catalunya. J.K. was supported by the Russian Ministry of Science and Education (Agreement No. 075-15-2020-808)., Peer Reviewed, Postprint (published version)

The Madden–Julian Oscillation (MJO) is a major source of predictability on the sub-seasonal (10 to 90 d) timescale. An improved forecast of the MJO may have important socioeconomic impacts due to the influence of MJO on both tropical and extratropical weather extremes. Although in the last decades state-of-the-art climate models have proved their capability for forecasting the MJO exceeding the 5-week prediction skill, there is still room for improving the prediction. In this study we use multiple linear regression (MLR) and a machine learning (ML) algorithm as post-processing methods to improve the forecast of the model that currently holds the best MJO forecasting performance, the European Centre for Medium-Range Weather Forecasts (ECMWF) model. We find that both MLR and ML improve the MJO prediction and that ML outperforms MLR. The largest improvement is in the prediction of the MJO geographical location and intensity., The authors thank Linus Magnusson for providing access to the data. This work received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska–Curie Actions agreement no. 813844. Cristina Masoller also acknowledges funding by the Spanish Ministerio de Ciencia, Innovacion y Universidades (PGC2018-099443- B-I00) and the ICREA ACADEMIA program of Generalitat de Catalunya. Sebastian Lerch acknowledges support by the Vector Stiftung through the Young Investigator Group “Artificial Intelligence for Probabilistic Weather Forecasting”., Peer Reviewed, Postprint (published version)

Recent advancements in nanolaser design and manufacturing open up unprecedented perspectives in terms of high integration densities and ultra-low power consumption, making these devices ideal for high-performance optical computing systems. In this work, we exploit the symmetry properties of the collective modes of a nanolaser array for a simple binary classification task of small digit images. The implementation is based on a 8 × 8 nanolaser array and relies on the activation of a collective optical mode of the array—the so-called “zero-mode”—under spatially modulated pump patterns., This work was supported by a public grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (Labex NanoSaclay, Reference No. ANR-10-LABX-0035) and by Grant No. ANR UNIQ DS078. G.T. and C.M. are supported, in part, by Ministerio de Ciencia, Innovación y Universidades (Grant No. PID2021-123994NA-C22); C.M. also acknowledges funding from Institució Catalana de Recerca i Estudis Avançats (Academia). K.J. acknowledges support from the China Scholarship Council (Grant No. 202006970015)., Peer Reviewed, Postprint (published version)

Identifying approaching bifurcations and regime transitions from observations is an important challenge in time series analysis with practical applications in many fields of science. Well-known indicators are the increase in spatial and temporal correlations. However, the performance of these indicators depends on the system under study and on the type of approaching bifurcation, and no indicator provides a reliable warning for any system and bifurcation. Here we propose an indicator that simultaneously takes into account information about spatial and temporal correlations. By performing a bivariate correlation analysis of signals recorded in pairs of adjacent spatial points, and analyzing the distribution of lag times that maximize the cross-correlation, we find that the variance of the lag distribution displays an extreme value that is a consistent early warning indicator of the approaching bifurcation. We demonstrate the reliability of this indicator using different types of models that present different types of bifurcations, including local bifurcations (transcritical, saddle-node, supercritical and subcritical Hopf), and global bifurcations., This work was funded by the Spanish Ministerio de Ciencia, Innovación y Universidades (PGC2018-099443-B-I00 ) and the ICREA ACADEMIA program of Generalitat de Catalunya., Peer Reviewed, Postprint (published version)

© 2222 Optica Publishing Group. 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., We study experimentally and numerically the dynamics of a semiconductor laser near threshold, subject to optical feedback and sinusoidal current modulation. The laser operates in the low frequency fluctuation (LFF) regime where, without modulation, the intensity shows sudden spikes at irregular times. Under particular modulation conditions the spikes lock to the modulation and their timing becomes highly regular. While the modulated LFF dynamics has received a lot of attention, an in-depth comparison with the predictions of the Lang-Kobayashi (LK) model has not yet been performed. Here we use the LK model to simulate the laser dynamics and use the Fano factor to quantify the regularity of the timing of the spikes. The Fano factor is calculated by counting the number of spikes in successive segments of the intensity time-series and keeps information about temporal order in the spike sequence that is lost when the analysis is based on the distribution of inter-spike intervals. Here we compare the spike timing regularity in experimental and in simulated spike sequences as a function of the modulation amplitude and frequency and find a good qualitative agreement. We find that in both experiments and simulation for appropriate conditions the spike timing can be highly regular, as revealed by very small values of the Fano factor., Institució Catalana de Recerca i Estudis Avançats (Academia); Ministerio de Ciencia, Innovación y Universidades (PGC2018-099443-B-I00)., Peer Reviewed, Postprint (published version)

This study was aimed to investigate the growth process of thin films on a pre-structured surface using different optically transparent materials and their optical properties. As results of conformal deposition of ion beam sputtered dense single layers on nano-modulated surfaces showed, replicability of surface modulation depends on the layer¶s material itself. Among investigated metal oxides, namely tantalum, niobium, hafnium, and silicon oxides, materials with higher molecular weight tend to better repeatability of the initial structure. As an example, the surface modulation depth of tantalum oxide single layer of a1 ¿m thickness has preserved almost 97 % of the initial structure, while the silica layer showed the most rapid smoothening of modulation since preserved only ~ 65 %. Considering that tantalum oxide single layers showed the best replicability results, its optical properties were investigated in a more detailed way. Optical characterization revealed the presence of Fano-like resonance phenomenon in such single-layer structure with high refractive index, surrounded by a lower refractive index media. Due to the coupling of thin film's waveguided modes with excited Fabry-Perot modes this phenomenon results in extremely low transmittance lines in the transmittance maps in a plane of the angle of incidence ¿ and wavelength ¿. Moreover, these resonance lines show sensitivity to the angle and the wavelength of the incident light, which can serve as a demonstration of spatial and spectral filtering properties in such compact photonic single-layer structures., Postprint (author's final draft)

One of the key trends in laser material processing is the usage of structured laser beams. One such example is the Bessel beam with an elongated focal area and self-healing properties. Higher-order Bessel beams can be formed by axicons, spiral phase plates, or equivalently by the phase masks (holograms). In this work, a demonstration of “optical drill” beams with dynamic intensity distributions resembling the spinning mechanical drill is shown. Bessel beam mixing of two different helicities is achieved by using a Spatial Light Modulator (SLM). Both Bessel beams are formed on the same optical component – the phase mask consisting of two parts. Each part consists of spirals with different winding numbers and different periods that correspond to different step plates and axicons. Such a mask forms the stationary optical drill beam. As the beam propagates the outer and inner parts start to overlap and form the resultant interfering beam. Now, to make it a true drill, it must rotate in time. In our experiment, that is achieved by rotating one part of the combined hologram. This induces an angular offset to the interference and as a result, the orientation of the helical intensity pattern starts to rotate in time. This continuous motion gives the impression of an optical drill. With the beams dynamic properties, it could become a new tool in laser material micromachining, as a mechanical drill was to construction., Postprint (author's final draft)

In this work, we introduce a spatial filtering mechanism that can be effectively utilized by photonic crystals. The phenomenon utterly expressed here is Rayleigh-Wood’s anomaly. Such a mechanism is realized and optimized via RCWA (Rigorous Coupled Wave Analysis) together with a global optimization algorithm for both s and p polarized inputs. The calculated transmission and reflection spectra of such mechanisms show that the Rayleigh anomaly provides the necessary sharp transmission profile near the critical wavelength from which the diffraction can occur., Postprint (author's final draft)

The transverse modes in microchip lasers (MCL) appear different from the classical mode theory, as the resonator consists of a set of plane mirrors (similar to semiconductor edge-emitting lasers and VCSELs). Then the parabolic potential is absent, and the electromagnetic radiation is confined in the transverse space of the resonator by other mechanisms, essentially by gain guiding. Thermal lensing also can play some role in confining the radiation. Laser engineers use several intuitive assumptions about the number of supported modes in the resonator, relating with the Fresnel number of the resonator. However, despite some attempts to calculate the modes in such resonators and investigate combined gain with index guiding, no clear and straightforward methods were provided to calculate the beam radiation profiles. We aim to fill this gap by providing analytical and numerical treatment of MCL modes in two dimensions. We analyze the transverse modes in microchip laser formed due to both gain guiding and thermal lensing. Analytical and numerical results are compared with the results of experimental measurements. Using the cylindrical pumping profile approach, we provide a simple 2D theory of the gain-guided and thermal-lens induced modes in such plane-mirror resonators. We estimate the mode beam quality factor dependency on pumping strength. The model is versatile and applicable to wider range of optical resonators consisting of plane mirrors with longitudinal pumping. Finally, we compare the experimental measurements of beam quality factor with our theoretical model., Postprint (author's final draft)