Azimuthons in weakly nonlinear waveguides of different symmetries

We show that weakly guiding nonlinear waveguides support stable propagation of rotating spatial solitons (azimuthons). We investigate the role of waveguide symmetry on the soliton rotation. We find that azimuthons in circular waveguides always rotate rigidly during propagation and the analytically predicted rotation frequency is in excellent agreement with numerical simulations. On the other hand, azimuthons in square waveguides may experience spatial deformation during propagation. Moreover, we show that there is a critical value for the modulation depth of azimuthons above which solitons just wobble back and forth, and below which they rotate continuously. We explain these dynamics using the concept of energy difference between different orientations of the azimuthon.Comment: 12 pages, 8 figure

Shaping the longitudinal electric field component of light

International audienceThis paper illustrates examples of shaping the longitudinal electric field component of light which is relevant for tightly focused beams. Given that the latter is not directly accessible via conventional beam shaping techniques we elaborate on the interplay between the transverse polarization and longitudinal electric field components. A Helmholtz decomposition of the transverse electric field components in the transverse plane permits on the one hand to draw insightful analogies with electro-and magnetostatics and with fluid dynamics. On the other hand, it allows to clearly isolate the remaining degree of freedom in the transverse electric field components for a given longitudinal electric field component and with that to generalize the concepts of radial and azimuthal polarization. We discuss degrees of freedom and show how one can exploit the findings to generate novel customized vector beams. Furthermore, we present a thought experiment to study beams containing evanescent waves

Threaded Rings that Swim in Excitable Media

Cardiac tissue and the Belousov-Zhabotinsky reaction provide two notable examples of excitable media that support scroll waves, in which a filament core is the source of spiral waves of excitation. Here we consider a novel topological configuration in which a closed filament loop, known as a scroll ring, is threaded by a pair of counterrotating filaments that are perpendicular to the plane of the ring and end on the boundary of a thin medium. We simulate the dynamics of this threaded ring (thring) in the photosensitive Belousov-Zhabotinsky excitable medium, using the modified Oregonator reaction-diffusion equations. These computations reveal that the threading topology induces an exotic motion in which the thring swims in the plane of the ring. We propose a light templating protocol to create a thring in the photosensitive Belousov-Zhabotinsky medium and provide experimental confirmation that this protocol indeed yields a thrin

Length of excitable knots

In this paper, we present extensive numerical simulations of an excitable medium to study the long-term dynamics of knotted vortex strings for all torus knots up to crossing number 11. We demonstrate that FitzHugh-Nagumo evolution preserves the knot topology for all the examples presented, thereby providing a field theory approach to the study of knots. Furthermore, the evolution yields a well-defined minimal length for each knot that is comparable to the ropelength of ideal knots. We highlight the role of the medium boundary in stabilizing the length of the knot and discuss the implications beyond torus knots. We also show that there is not a unique attractor within a given knot topology

Rings on strings in excitable media

We study the dynamics and interaction of coaxial vortex rings in the FitzHugh–Nagumo excitable medium. We find that threading vortex rings with a vortex string results in significant qualitative differences in their evolution and interaction. In particular, threading prevents the annihilation of rings in a head-on collision, allows generic ring overtaking, and can even reverse the direction of motion of a ring. We identify that an important mechanism for producing this new behaviour is that threaded vortex rings interact indirectly via induced twisting of the threading vortex string