Subdiffractive discrete cavity solitons

We describe what we believe to be novel types of discrete cavity solitons in nonlinear waveguide arrays that are driven by an external holding beam. We demonstrate that a holding beam with a definite inclination drives the system in a subdiffractive regime and allows the formation of stable discrete cavity solitons. We predict the existence of both bright and dark moving midband discrete cavity solitons for an identical set of system parameters for both focusing and defocusing Kerr nonlinearities.     

Evaluation of Redox Activity of Human Myocardium‐derived Mesenchymal Stem Cells by Scanning Electrochemical Microscopy

In this study the redox activity of human myocardium‐derived mesenchymal stem cells (hmMSC) were investigated by redox‐competition (RC‐SECM) and generation‐collection (GC‐SECM) modes of scanning electrochemical microscopy (SECM), using 2‐methylnaphthalene‐1,4‐dione (menadione, MD) as a redox mediator. The redox activity of human healthy and dilated hmMSCs was evaluated by measuring reduction of MD. Measurements were performed by approaching and retracting the UME from the surface of growing hmMSC cells. The current study shows that the RC‐SECM mode can be applied to investigate integrity of cell membranes, whereas the most promising results were observed by using the GC‐SECM mode and applying the Hill's equation for the calculation/fitting of dependencies of electrical current vs menadione concentration. The calculated apparent Michaelis constant (K_M) for the production of menadiol (MDH₂) in the pathological hmMSC cells was 14.4 folds higher compared to that of the healthy hmMSC revealing the lover redox activity of pathological cells. Moreover, the calculated Hill's coefficient n shows a negative cooperative binding between MD and healthy hmMSC and positive cooperative binding between MD and pathological hmMSC. It means that healthy hmMSC is of lower affinity to MD, which is also related to the better membrane integrity of healthy cells. Data of this study demonstrate that SECM can be applied to investigate intracellular redox and membrane changes ongoing in human dilated myocardium‐derived hmMSC in order to improve their functioning and further regenerative potential.     

Cooperative frequency locking and tristability in a class-B laser

The locking and unlocking phenomena of the modes of the transverse familyq=1 in a CO₂ laser are investigated. The experimental results show three characteristic regions: a bistability between two helical waves of opposite handedness, a tristability among the two helicities of opposite handedness and an unlocked state, and the unlocked state. Near the locking threshold, oscillations which can be interpreted as due to the oscillations of the modal amplitudes and relative phase are also observed. These results are found to be consistent with solutions of the two-mode Maxwell-Bloch equations for class-B lasers.     

Broad angle phase matching in subdiffractive photonic crystals

We show that photonic crystals made of materials with normal dispersion allow broad angular range phase matching in nonlinear wave mixing processes if tuned to the subdiffractive (or equivalently self-collimated) beam propagation regimes for the frequencies of both interacting waves. This allows efficient parametric mixing of narrow beams. We demonstrate this idea by numerical simulation of the second harmonic generation in two-dimensional photonic crystal in particular nonlinear material (AlGaAs) in planar waveguide geometry.     

Self-collimation and self-imaging effects in modulated waveguide arrays

Self-collimation and self-imaging are comparatively investigated for discretized light in engineered modulated arrays of optical waveguides. It is shown that self-imaging is a rather extraordinary effect related to a fortuitous band collapse and it is thus rather distinct from self-collimation.     

Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals

We predict a novel type of cavity solitons, Bloch cavity solitons, existing in nonlinear resonators with the refractive index modulated in both longitudinal and transverse directions and for both focusing (at normal diffraction) and defocusing (at anomalous diffraction) nonlinearities. We develop a modified mean-field theory and analyze the properties of these novel cavity solitons demonstrating, in particular, their substantial narrowing in the zero-diffraction regime.     

Computation of phase response curves via a direct method adapted to infinitesimal perturbations

A new numerical algorithm for computation of phase response curves of stable limit cycle oscillators is proposed. The idea of the algorithm originates from a direct method that is based on computation of the oscillator response to short finite pulses delivered at different phases of oscillations. Here we adapt the direct method to the case of infinitesimal perturbations and compare our algorithm with the standard algorithm based on the backward integration of the adjoint equations. In contrast to the standard algorithm, our algorithm does not require any backward integration and it is easier to program since a necessity of numerical interpolation for the Jacobian matrix is avoided. In addition, we demonstrate by examples that our algorithm is faster than the standard algorithm and this advantage is especially notable for weakly stable limit cycle oscillators.     

High-directional wave propagation in periodic loss modulated materials

Amplification/attenuation of light waves in artificial materials can become sensitive to the propagation direction by spatially modulating the gain/loss response of the medium on the wavelength scale. We give a numerical proof of the high anisotropy of the gain/loss in two dimensional periodic structures with square and rhombic lattice symmetry by solving the full set of Maxwell's equations using the finite difference time domain method. Anisotropy of amplification/attenuation leads to the narrowing of the angular spectrum of propagating radiation with wavevectors close to the edges of the first Brillouin Zone. The effect provides a novel and useful method to filter out high spatial harmonics from noisy beams.