Friedemann Kaiser

Self-bending of photorefractive solitons

Self-bending of photorefractive solitons is caused by diffusion in photorefractive crystals and becomes an important effect when the beam size is in the range of the charge carriers diffusion length. In this paper we present an experimental and numerical examination of the beam bending dependence on relevant parameters such as the applied electric field and the beam intensity. We demonstrate that the bending dependence on the electric field in the low saturation regime has the form of a square function at low values of the field and becomes linear for higher values. For stronger saturation the curve gets the form of a square root function. The bending dependence on the beam intensity has a maximum at defined intensity. The experimental data are compared with numerical simulations, giving a good qualitative agreement.

Transverse modulational instabilities of counterpropagating solitons in photorefractive crystals

We study numerically the counterpropagating vector solitons in SBN:60 photorefractive crystals. A simple theory is provided for explaining the symmetry-breaking transverse instability of these solitons. Phase diagram is produced that depicts the transition from stable counterpropagating solitons to bidirectional waveguides to unstable optical structures. Numerical simulations are performed that predict novel dynamical beam structures, such as the standing-wave and rotating multipole vector solitonic clusters. For larger coupling strengths and/or thicker crystals the beams form unstable self-trapped optical structures that have no counterparts in the copropagating geometry.

Spatiotemporal effects in double phase conjugation

Spatial and temporal effects arising in photorefractive crystals during the process of double phase conjugation are analyzed numerically with a novel beam-propagation method. Slowly varying envelope wave equations in the paraxial approximation are solved under the appropriate boundary conditions. Our analysis includes dynamical effects caused by the buildup of diffraction gratings in the crystal and the turn-on of phase-conjugate beams as well as spatial effects caused by the finite transverse spread of beams and by the propagation directions of the beams. Various phenomena are observed, such as self-bending of phase-conjugate beams, convective flow of energy out of the interaction region, mode oscillations, critical slowing down at the oscillation threshold, and irregular spatial pattern formation. For a real beam-coupling constant and constructive interaction of interference fringes in the crystal we find steady or periodic behavior. For a complex coupling constant and/or induced phase mismatch in the grating a transition to spatiotemporal chaos is observed. We believe that under stable operating conditions the transverse double phase-conjugate mirror in the paraxial approximation is a convective oscillator, rather than an amplifier. Improved agreement with experimental results is obtained.

Anisotropic waveguides induced by photorefractive (2+1)D solitons

We present theoretical and experimental investigations of the anisotropic character of the refractive-index modulation that is induced by a light beam propagating in a photorefractive strontium barium niobate crystal. Such a structure creates a so-called spatial screening soliton that is able to carry a second wave of a different wavelength and therefore can act as a waveguide. We show in numerical simulations as well as in experimental investigations the anisotropic property of refractive-index modulation. Furthermore, the noncircular shape of the induced waveguide is justified by the excitation of higher-order modes, which were found to be asymmetric in both transverse directions. Whereas in the direction perpendicular to the applied electric field the TEM01 and TEM02 modes can easily be excited, excitement of the TEM10 mode in the direction of the applied field is rather difficult. This effect can be explained by the constricted extension of the waveguide in this direction.

TIME-DELAYED FEEDBACK IN A NET OF NEURAL ELEMENTS: TRANSITION FROM OSCILLATORY TO EXCITABLE DYNAMICS

The influence of time-delayed feedback on the dynamics of a net of oscillatory FitzHugh-Nagumo elements is investigated. We show that the global oscillation of the net can be suppressed (amplitude death) via time-delayed feedback for properly chosen delay time and feedback strength. The result of a linear stability analysis fits very well to the simulations. In the amplitude death regime, weak additive noise can induce excitation waves (noise-induced pattern formation), a fingerprint of excitable network dynamics.

Anisotropic interaction of three-dimensional spatial screening solitons

A theory based on the paraxial propagation of laser beams in nonlinear media and on the Kukhtarev material equations is developed to explain the interaction of bright spatial screening solitons in photorefractive crystals. A numerical study in three dimensions is performed to reveal qualitative and quantitative agreement with experiment. Screening solitons display a variety of propagation effects, such as inelastic scattering, attraction and repulsion, and oscillation and spiraling. In particular, we investigate the influence of initial separation and launching directions on the propagation of incoherent solitons.

Multicomponent dipole-mode spatial solitons

We study (2+1) -dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents and demonstrate that these solitary waves exhibit a symmetry-breaking instability, provided their total topological charge is nonzero. We describe a novel type of stable multicomponent dipole-mode solitons with intriguing swinging dynamics.

Identification of rhythmic subsystems in the circadian cycle of Crassulacean acid metabolism under thermoperiodic perturbations

Abstract Leaves of the Crassulacean acid metabolism (CAM) plant Kalanchoë daigremontiana Hamet et Perrier de la Bâthie show overt circadian rhythms in net CO2 uptake, leaf conductance to water and intercellular CO2 concentration, which are entrained by periodic temperature cycles. To probe their sensitivity to thermoperiodic perturbations, intact leaves were exposed to continuous light intensity and temperature cycles with a period of 16 h, applying a set of different baseline temperatures and thermodriver amplitudes. All three overt rhythms were analyzed with respect to their frequency spectra and their phase relations with the thermodriver. For most stimulation protocols, stomatal conductance and net CO2 change were fully or partially entrained by the temperature pulses, while the internal CO2 concentration remained dominated by oscillations in the circadian range. Prolonged time series recorded for up to 22 d in continuous light underline the robustness of these circadian oscillations. This suggests that the overt circadian rhythm of net CO2 uptake in CAM results from the interaction of two coupled original systems: (i) an endogenous cycle of CO2 fixation in the mesophyll, showing very robust periodic activity, and (ii) stomatal movements that respond to environmental stimuli independently of rhythmic processes in the mesophyll, and thus modulate the gas exchange amplitude.

Transverse instabilities in photorefractive counterpropagating two-wave mixing.

Threshold analysis for transverse instabilities in photorefractive counterpropagating two-wave mixing through reflection gratings is performed. A numerical algorithm for the treatment of wave equations in this geometry is developed, displaying the emergence of running transverse waves. They appear above a threshold in the applied electric field, and their transverse wave number and oscillation frequency agree well with the values predicted by stability analysis.

Counterpropagating self-trapped beams in photorefractive crystals

A time-dependent model for the formation of self-trapped optical beams in photorefractive media by counterpropagating laser beams is analysed. It is shown that dynamically the beams may form stable steady-state structures or display periodic and irregular temporal behaviour. Steady-state solutions of non-uniform cross section are found, representing a general class of self-trapped waveguides, that include counterpropagating spatial vector solitons as a particular case. Two critical curves are identified in the plane of parameters, the first one separating vector solitons from the stable bidirectional waveguides and the second one separating stable waveguides from the unstable ones. Dynamically stable rotating beam structures are discovered that have no analogues in the usual steady-state theory of spatial solitons.