Vortex Emission Accompanies the Advection of Optical Localized Structures

We show that the advection of optical localized structures is accompanied by the emission of vortices, with phase singularities appearing in the wake of the drifting structure. Localized structures are obtained in a light-valve experiment and made to drift by a mirror tilt in the feedback loop. Pairs of oppositely charged vortices are detected for small drifts, whereas for large drifts a vortex array develops. Observations are supported by numerical simulations and linear stability analysis of the system equations and are expected to be generic for a large class of translated optical patterns.

Figure 1

(a) Successive experimental snapshots (time separation 1.07 s) of an optical localized structure drifting along the $x$ direction; the advection occurs after tilting the mirror $M$ at the entrance of the feedback loop; the first three snapshots realize the process of symmetry breaking whereas the last four account for the propagative phenomenon; the dotted line is the velocity acquired after the initial acceleration; (b) experimental setup: FB optical fiber bundle, $L$ lenses, PC polarizing cube splitter; the other cubes deflect part of the beam to the CCD camera for detection; a reference beam (dashed line) is used to realize a Mach-Zehnder interferometer through mirrors m; the half-wave plate, $\lambda /2$, and the neutral density filter, NF, adjust the polarization, respectively, the intensity of the reference beam.

Figure 2

(a) Experimental snapshot with inverted intensity levels and digitized fringe maxima showing a localized structure moving along the arrow direction; oppositely charged phase singularities, marked by + and -, appear as dislocations; (b) corresponding one-dimensional profile.

Figure 3

Numerical intensity profiles of a drifting localized structure, (a) $\Delta x=0$, (b) $\Delta x=126\mu \mathrm{m}$, (c) $\Delta x=182\mu \mathrm{m}$; on the right, corresponding one-dimensional profiles along the advection direction $x$; on the left, null lines of the electric field; dark (blue online), light (red online) lines corresponds to real, respectively, imaginary part of the field; phase singularities are nucleated at the intersections.

Figure 4

(a) Numerically calculated advection velocity $v_d$ vs the translation $\Delta x$; $L=-16\mathrm{cm}$. (b)–(d) Chains of localized structure: (b) experimental interference pattern; (c) numerical intensity pattern for $\Delta x=253\mu \mathrm{m}$ with superimposed null lines of the electric field; dark (blue), light (red) lines corresponds to real, respectively, imaginary part of the field; (d) corresponding phase pattern, where dark (blue), light (red) intensity maps a phase change from $-\pi$ to $\pi$.

Figure 5

Dispersion relation $\Re (\sigma )$ vs $q_x$, $q_y$ for a $\Delta x$ of (a) 0, (b) 50, (c) 100, (d) 150, (e) 200, (f) $250\mu \mathrm{m}$.