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Nonlinear waveguides with two distinct domains of anomalous dispersion can support the formation of molecule-like two-color pulse compounds. They consist of two tightly bound subpulses with frequency loci separated by a vast frequency gap. Perturbing such a two-color pulse compound triggers periodic amplitude and width variations, reminiscent of molecular vibrations. With increasing strength of perturbation, the dynamics of the pulse compound changes from harmonic to nonlinear oscillations. The periodic amplitude variations enable coupling of the pulse compound to dispersive waves, resulting in the resonant emission of multi-frequency radiation. We demonstrate that the location of the resonances can be precisely predicted by phase-matching conditions. If the pulse compound consists of a pair of identical subpulses, inherent symmetries lead to degeneracies in the resonance spectrum. Weak perturbations lift existing degeneracies and cause a splitting of the resonance lines into multiple lines. Strong perturbations result in more complex emission spectra, characterized by well separated spectral bands caused by resonant Cherenkov radiation and additional four-wave mixing processes. [ABSTRACT FROM AUTHOR]

We present a detailed overview of the physics of two-color soliton molecules in nonlinear waveguides, i.e. bound states of localized optical pulses which are held together due to an incoherent interaction mechanism. The mutual confinement, or trapping, of the subpulses, which leads to a stable propagation of the pulse compound, is enabled by the nonlinear Kerr effect. Special attention is paid to the description of the binding mechanism in terms of attractive potential wells, induced by the refractive index changes of the subpulses, exerted on one another through cross-phase modulation. Specifically, we discuss nonlinear-photonics meta atoms, given by pulse compounds consisting of a strong trapping pulse and a weak trapped pulse, for which trapped states of low intensity are determined by a Schrödinger-type eigenproblem. We discuss the rich dynamical behavior of such meta-atoms, demonstrating that an increase of the group-velocity mismatch of both subpulses leads to an ionization-like trapping-to-escape transition. We further demonstrate that if both constituent pulses are of similar amplitude, molecule-like bound-states are formed. We show that z -periodic amplitude variations permit a coupling of these pulse compound to dispersive waves, resulting in the resonant emission of Kushi-comb-like multi-frequency radiation. [ABSTRACT FROM AUTHOR]

In this work we consider information-theoretic observables to analyze short symbolic sequences, comprising time series that represent the orientation of a single spin in a two-dimensional (2D) Ising ferromagnet on a square lattice of size L² = 128² for different system temperatures T. The latter were chosen from an interval enclosing the critical point Tc of the model. At small temperatures the sequences are thus very regular; at high temperatures they are maximally random. In the vicinity of the critical point, nontrivial, long-range correlations appear. Here we implement estimators for the entropy rate, excess entropy (i.e., "complexity"), and multi-information. First, we implement a Lempel-Ziv string-parsing scheme, providing seemingly elaborate entropy rate and multi-information estimates and an approximate estimator for the excess entropy. Furthermore, we apply easy-to-use black-box data-compression utilities, providing approximate estimators only. For comparison and to yield results for benchmarking purposes, we implement the information-theoretic observables also based on the well-established M-block Shannon entropy, which is more tedious to apply compared to the first two "algorithmic" entropy estimation procedures. To test how well one can exploit the potential of such data-compression techniques, we aim at detecting the critical point of the 2D Ising ferromagnet. Among the above observables, the multi-information, which is known to exhibit an isolated peak at the critical point, is very easy to replicate by means of both efficient algorithmic entropy estimation procedures. Finally, we assess how good the various algorithmic entropy estimates compare to the more conventional block entropy estimates and illustrate a simple modification that yields enhanced results. [ABSTRACT FROM AUTHOR]

The main characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here the disorder allows for negative edge weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter ρ that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. The random walks are "greedy" in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight (associated with a net gain of "energy" for the walker). Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of ρ for different bias strengths B is put under scrutiny. Upon tuning ρ, the probability to find such a feasible lattice walk increases from zero to 1. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point ρc, resulting from numerically exact and "static" simulations in terms of the NWP model, can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems. [ABSTRACT FROM AUTHOR]

In the present article, statistical properties regarding the topology and standard percolation on relative neighborhood graphs (RNGS) for planar sets of points, considering the Euclidean metric, are put under scrutiny. RNGs belong to the family of "proximity graphs"; i.e., their edgeset encodes proximity information regarding the close neighbors for the terminal nodes of a given edge. Therefore they are, e.g., discussed in the context of the construction of backbones for wireless ad hoc networks that guarantee connectedness of all underlying nodes. Here, by means of numerical simulations, we determine the asymptotic degree and diameter of RNGs and we estimate their bond and site percolation thresholds, which were previously conjectured to be nontrivial. We compare the results to regular 2D graphs for which the degree is close to that of the RNG. Finally, we deduce the common percolation critical exponents from the RNG data to verify that the associated universality class is that of standard 2D percolation. [ABSTRACT FROM AUTHOR]

We study numerically the geometrical properties of minimally weighted paths that appear in the minimally weighted path (MWP) model on two-dimensional lattices assuming a combination of periodic and free boundary conditions (BCs). Each realization of the disorder consists of a random fraction (1 - p) of bonds with unit strength and a fraction p of bond strengths drawn from a Gaussian distribution with zero mean and unit width. For each such sample, a path is forced to span the lattice along the direction with the free BCs. The path and a set of negatively weighted loops form a ground state. A ground state on such a lattice can be determined performing a nontrivial transformation of the original graph and applying sophisticated matching algorithms. Here we examine whether the geometrical properties of the paths are in accordance with the predictions of the Schramm-Loewner evolution (SLE). Measuring the fractal dimension, considering the winding angle statistics, and reviewing Schramm's left passage formula indicate that the paths cannot be described in terms of SLE. [ABSTRACT FROM AUTHOR]

We consider the "Touch and Stop" cluster growth percolation (CGP) model on the two-dimensional square lattice. A key parameter in the model is the fraction p of occupied "seed" sites that act as nucleation centers from which a particular cluster growth procedure is started. Here, we consider two growth styles: rhombic and disk-shaped cluster growth. For intermediate values of p the final state, attained by the growth procedure, exhibits a cluster of occupied sites that span the entire lattice. Using numerical simulations we investigate the percolation probability and the order parameter and perform a finite-size scaling analysis for lattices of side length up to L = 1024 in order to carefully determine the critical exponents that govern the respective transition. In contrast to previous studies, reported in Tsakiris et al. [Phys. Rev. E 82, 041108 (2010)], we find strong numerical evidence that the CGP model is in the standard percolation universality class. [ABSTRACT FROM AUTHOR]

The information-theoretic observables entropy (a measure of disorder), excess entropy (a measure of complexity), and multi-information are used to analyze ground-state spin configurations for disordered and frustrated model systems in two and three dimensions. For both model systems, ground-state spin configurations can be obtained in polynomial time via exact combinatorial optimization algorithms, which allowed us to study large systems with high numerical accuracy. Both model systems exhibit a continuous transition from an ordered to a disordered ground state as a model parameter is varied. By using the above information-theoretic observables it is possible to detect changes in the spatial structure of the ground states as the critical point is approached. It is further possible to quantify the scaling behavior of the information-theoretic observables in the vicinity of the critical point. For both model systems considered, the estimates of critical properties for the ground-state phase transitions are in good agreement with existing results reported in the literature. [ABSTRACT FROM AUTHOR]

The direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three-dimensional (3D) wave equation for an initial acoustic stress profile. In contrast, the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider an effectively 1D approach, based on the assumption of a Gaussian transverse irradiation source profile and plane acoustic waves, in which the effects of acoustic diffraction are described in terms of a linear integral equation. The respective inverse problem along the beam axis can be cast into a Volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity as well as the limits of the inversion scheme via numerical experiments, with parameters geared toward actual optoacoustic problem instances. The considered inversion input consists of synthetic data, obtained in terms of the effectively 1D approach, and, more generally, a solution of the 3D optoacoustic wave equation. Finally, we also analyze the effect of noise and different detector-to-sample distances on the optoacoustic signal and the reconstructed pressure profiles. [ABSTRACT FROM AUTHOR]

The pivotal quality of proximity graphs is connectivity, i.e., all nodes in the graph are connected to one another either directly or via intermediate nodes. These types of graphs are often robust, i.e., they are able to function well even if they are subject to limited removal of elementary building blocks, as may occur for random failures or targeted attacks. Here, we study how the structure of these graphs is affected when nodes get removed successively until an extensive fraction is removed such that the graphs fragment. We study different types of proximity graphs for various node-removal strategies. We use different types of observables to monitor the fragmentation process, simple ones like the number and sizes of connected components and more complex ones like the hop diameter and the backup capacity, which is needed to make a network N-1 resilient. The actual fragmentation turns out to be described by a second-order phase transition. Using finite-size scaling analyses we numerically assess the threshold fraction of removed nodes, which is characteristic for the particular graph type and node deletion scheme; this suffices to decompose the underlying graphs. [ABSTRACT FROM AUTHOR]

We estimate the critical thresholds of bond and site percolation on nonplanar, effectively two-dimensional graphs with chimeralike topology. The building blocks of these graphs are complete and symmetric bipartite subgraphs of size 2n, referred to as Kn,n graphs. For the numerical simulations we use an efficient union-find-based algorithm and employ a finite-size scaling analysis to obtain the critical properties for both bond and site percolation. We report the respective percolation thresholds for different sizes of the bipartite subgraph and verify that the associated universality class is that of standard two-dimensional percolation. For the canonical chimera graph used in the D-Wave Systems Inc. quantum annealer (n = 4), we discuss device failure in terms of network vulnerability, i.e., we determine the critical fraction of qubits and couplers that can be absent due to random failures prior to losing large-scale connectivity throughout the device. [ABSTRACT FROM AUTHOR]

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from d = 2 to the upper critical dimension d = 6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in the full ensemble of loops with negative weight, i.e., nontrivial (system spanning) loops as well as topologically trivial ("small") loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize-using this extensive and exhaustive numerical study-the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations, we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics. [ABSTRACT FROM AUTHOR]

We investigate the impact of collisions with two-frequency photonic molecules aiming to observe internal dynamic behavior and challenge their strong robustness. Versatile interaction scenarios show intriguing state changes expressed through modifications of the resulting state such as temporal compression and unknown collision-induced spectral tunneling. These processes show potential for efficient coherent supercontinuum generation and all-optical manipulation.

We study incoherently coupled two-frequency pulse compounds in waveguides with single zero-dispersion and zero-nonlinearity points. In such waveguides, supported by a negative nonlinearity, soliton dynamics can be obtained even in domains of normal dispersion. We demonstrate trapping of weak pulses by solitary-wave wells, forming nonlinear-photonics meta-atoms, and molecule-like bound-states of pulses. We study the impact of the Raman effect on these pulse compounds, finding that, depending on the precise subpulse configuration, they decelerate, accelerate, or are completely unaffected. Our results extend the range of systems in which two-frequency pulse compounds can be expected to exist and demonstrate further unique and unexpected behavior.

This publisher's note contains corrections to Opt. Lett.46, 5603 (2021)OPLEDP0146-959210.1364/OL.440567.

We reveal the crucial role played by the frequency dependence of the nonlinear parameter on the evolution of femtosecond solitons inside photonic crystal fibers (PCFs). We show that the conventional approach based on the self-steepening effect is not appropriate when such fibers have two zero-dispersion wavelengths, and several higher-order nonlinear terms must be included for realistic modeling of the nonlinear phenomena in PCFs. These terms affect not only the Raman-induced wavelength shift of a soliton but also impact its shedding of dispersive radiation.

New resonant emission of dispersive waves by oscillating solitary structures in optical fiber cavities is considered analytically and numerically. The pulse propagation is described in the framework of the Lugiato-Lefever equation when a Hopf-bifurcation can result in the formation of oscillating dissipative solitons. The resonance condition for the radiation of the dissipative oscillating solitons is derived and it is demonstrated that the predicted resonances match the spectral lines observed in numerical simulations perfectly. The complex recoil of the radiation on the soliton dynamics is discussed. The reported effect can have importance for the generation of frequency combs in nonlinear microring resonators.

We study localized dissipative structures in a generalized Lugiato-Lefever equation, exhibiting normal group-velocity dispersion and anomalous quartic group-velocity dispersion. In the conservative system, this parameter-regime has proven to enable generalized dispersion Kerr solitons. Here, we demonstrate via numerical simulations that our dissipative system also exhibits equivalent localized states, including special molecule-like two-color bound states recently reported. We investigate their generation, characterize the observed steady-state solution, and analyze their propagation dynamics under perturbations.

The realization of optical interconnects between multimode (MM) optical fibers and waveguides based on a self-writing process in photopolymer media represents an efficient approach for fast and easy-to-implement connection of light-guiding elements. When light propagates through photopolymer media, it modulates the material properties of the media and confines the spreading of the light beam to create a waveguide along the beam propagation direction. This self-writing process can be realized with a single photopolymer medium and is also suited to connect optical fibers or waveguides with active elements such as light sources and detectors. Numerical simulations of the underlying light-induced polymerization process is carried out by using a diffusion based material model which takes account both monomer diffusion and its conversion to polymer chains in regions exposed to light fields. In this work experimental results obtained from a one-polymer approach are validated with theoretical predictions from the diffusion model. The study involved the demonstration of temporal dynamics and transmittance from self-written waveguide (SWW) couplers during the self-writing process. The measured attenuation coefficient from experiment α experiment  = (8.43 ± 0.3) × 10 -5 dB/µm showed good agreement with the theoretically predicted attenuation coefficient α simulation  = 7.93 × 10 -5 dB/µm, thus demonstrating a successful application of the diffusion model to epoxy based acrylate SWWs. For comparison, attenuation measurements between optical fibers with SWWs as interconnects and one without SWW, i.e. with an air gap in between, were performed. The obtained results reveal that the theoretical approach correctly describes the waveguide formation process so that in the next step the studies can be extended towards including further relevant parameters such as temperature.

We demonstrate a peculiar mechanism for the formation of bound states of light pulses of substantially different optical frequencies, in which pulses are strongly bound across a vast frequency gap. This is enabled by a propagation constant with two separate regions of anomalous dispersion. The resulting soliton compound exhibits moleculelike binding energy, vibration, and radiation and can be understood as a mutual trapping providing a striking analogy to quantum mechanics. The phenomenon constitutes an intriguing case of two light waves mutually affecting and controlling each other.

In this article, we present a simple and intuitive approach to create a handheld optoacoustic setup for near field measurements. A single piezoelectric transducer glued in between two sheets of polymethyl methacrylate (PMMA) facilitates nearfield depth profiling of layered media. The detector electrodes are made of indium tin oxide (ITO) which is both electrically conducting as well as optically transparent, enabling an on-axis illumination through the detector. By mapping the active detector area, we show that it matches the design form precisely. We also present a straightforward approach to determine the instrument response function, which allows to obtain the original pressure profile arriving at the detector. To demonstrate the validity of this approach, the measurement on a simple test sample is deconvolved with the instrument response function and compared to simulation results. Except for the sputter instrumentation, all required materials and instruments as well as the tools needed to create such a setup are available to standard scientific laboratories.

Spin glasses are prototypical random systems modelling magnetic alloys. One important way to investigate spin glass models is to study domain walls. For two dimensions, this can be algorithmically understood as the calculation of a shortest path, which allows for negative distances or weights. This led to the creation of the negative weight percolation (NWP) model, which is presented here along with all necessary basics from spin glasses, graph theory and corresponding algorithms. The algorithmic approach involves a mapping to the classical matching problem for graphs. In addition, a summary of results is given, which were obtained during the past decade. This includes the study of percolation transitions in dimension from d = 2 up to and beyond the upper critical dimension d u = 6 , also for random graphs. It is shown that NWP is in a different universality class than standard percolation. Furthermore, the question of whether NWP exhibits properties of Stochastic-Loewner Evolution is addressed and recent results for directed NWP are presented.

We investigate both analytically and numerically the ensemble of minimum-weight loops in the negative-weight percolation model on random graphs with fixed connectivity and bimodal weight distribution. This allows us to study the mean-field behavior of this model. The analytical study is based on a conjectured equivalence with the problem of self-avoiding walks in a random medium. The numerical study is based on a mapping to a standard minimum-weight matching problem for which fast algorithms exist. Both approaches yield results that are in agreement on the location of the phase transition, on the value of critical exponents, and on the absence of any sizable indications of a glass phase. By these results, the previously conjectured upper critical dimension of d(u)=6 is confirmed.

By means of numerical simulations, we investigate the geometric properties of loops on hypercubic lattice graphs in dimensions d=2 through 7, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of system-spanning loops of total negative weight. The resulting negative-weight percolation (NWP) problem is fundamentally different from conventional percolation, as we have seen in previous studies of this model for the two-dimensional case. Here, we characterize the transition for hypercubic systems, where the aim of the present study is to get a grip on the upper critical dimension d u of the NWP problem. For the numerical simulations, we employ a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. We characterize the loops via observables similar to those in percolation theory and perform finite-size scaling analyses, e.g., three-dimensional hypercubic systems with side length up to L=56 sites, in order to estimate the critical properties of the NWP phenomenon. We find our numerical results consistent with an upper critical dimension d u=6 for the NWP problem.

Sequence alignment is a tool in bioinformatics that is used to find homological relationships in large molecular databases. It can be mapped on the physical model of directed polymers in random media. We consider the finite-temperature version of local sequence alignment for proteins and study the transition between the linear phase and the biologically relevant logarithmic phase, where the free energy grows linearly or logarithmically with the sequence length. By means of numerical simulations and finite-size-scaling analysis, we determine the phase diagram in the plane that is spanned by the gap costs and the temperature. We use the most frequently used parameter set for protein alignment. The critical exponents that describe the parameter-driven transition are found to be explicitly temperature dependent. Furthermore, we study the shape of the (free-) energy distribution close to the transition by rare-event simulations down to probabilities on the order 10(-64). It is well known that in the logarithmic region, the optimal score distribution (T=0) is described by a modified Gumbel distribution. We confirm that this also applies for the free-energy distribution (T>0). However, in the linear phase, the distribution crosses over to a modified Gaussian distribution.

We investigate the geometric properties of loops on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of spanning loops of total negative weight. The resulting percolation problem is fundamentally different from conventional percolation, as we have seen in a previous study of this model for the undiluted case. Here, we investigate how the percolation transition is affected by additional dilution. We consider two types of dilution: either a certain fraction of edges exhibits zero weight, or a fraction of edges is even absent. We study these systems numerically using exact combinatorial optimization techniques based on suitable transformations of the graphs and applying matching algorithms. We perform a finite-size scaling analysis to obtain the phase diagram and determine the critical properties of the phase boundary. We find that the first type of dilution does not change the universality class compared to the undiluted case whereas the second type of dilution leads to a change in the universality class.