Self-trapped modes in highly nonlocal nonlinear media

Exact analytical solutions describing spatially localized self-trapped modes in highly nonlocal nonlinear media are presented. We formulate the model in a coordinate-free form and show that it allows us to obtain useful closed-form expressions for a large variety of mode structures and their interactions in a highly nonlocal nonlinear medium.

Figure 1

(Color online) (a) Propagation and interaction of three solitons launched in parallel into a HNN medium with $a=1$. (b) Helical trajectories of the three solitons launched with the appropriate skew.

Figure 2

(Color online) Quasi-invariant (a) dipole and (b) quadrupole vortex self-trapped HzG beam. (c) Rotating propagation of an elliptic vortex self-trapped HzG beam constructed with a helical Mathieu beam.

Figure 3

(Color online) Propagation dynamics of an elliptic vortex self-trapped HzG beam in a nonlocal nonlinear medium. (a), (b) High nonlocality (the Gaussian width nonlocal response is three times larger than the maximum beam width). Here the beam remains self-trapped and many periods of rotation can be observed. The maximum value of the normalized intensity oscillates but remains within a finite range. (c) Intensity and phase profiles for low nonlocality (the Gaussian width nonlocal response is equal to the maximum beam width). (d) The beam diffracts decreasing its maximum normalized intensity and there is not significant intensity rotation.