Stable solitons in elliptical photonic lattices

Abstract

We introduce the basic properties of solitons in elliptical photonic lattices induced optically by a superposition of Mathieu beams. Owing to the modulation of the intensity along its elliptical rings, these lattices allow novel dynamics of propagation, being possible, for the first time to our knowledge, to propagate solitons in an elliptic motion with varying rotation rate.

Soliton dynamics in modulated Bessel photonic lattices

“…The addition of the initial transverse momentum leads immediately to the observation in the MBL of the three regimes of soliton motion which were reported previously for the EPL [15]: (i) oscillatory motion, which occurs when solitons oscillate around an intensity maximum, see Fig. 4(a); (ii) rotational motion, which takes place when solitons rotate in a closed trajectory confined in a light ring, displayed in Fig.…”

“…This result shows that specific conditions between the lattice topology and the initial tilt are necessary to produce a transition motion. This explains why this type of dynamics was not previously observed in the case of the EPL [15] when the lattice modulation was fixed. It is important to note that we have used in our simulations a propagation distance of z = 80, which corresponds to several diffraction lengths.…”

“…More recently, Ruelas et al [15] analyzed the stable propagation of solitons in elliptical photonic lattices (EPLs), generated by a superposition of Mathieu beams. It was found that the EPLs exhibit three basic regimes of soliton motion: oscillatory, rotating, and unbounded or escape motion.…”

A particle-like model for soliton propagation in optical lattices

“…Photonic lattices can be thought as steady optical patterns imposed into a spatial region that modifies the effective refractive index experimented by the solitons, offering thus new dynamics in optical soliton propagation [2][3][4]. For example, the soliton intensity profile can be affected by the lattice topology producing novel localized nonlinear structures and in a similar way, the photonic lattice intensity profile can modify the transverse velocity of the soliton, allowing diverse soliton-based blocking and routing schemes [5][6][7][8]. This work proposes a simplified model that can be useful to describe the dynamics of motion of solitons propagating through optical lattices.…”

Quasi-one-dimensional optical lattices for soliton manipulation

“…Group theory demonstrates there are only four coordinate systems where the Helmholtz equation can be separable into their longitudinal and transversal components [13], allowing invariant solutions along the ξ axis: plane waves in Cartesian coordinates, Bessel beams in circular cylindrical coordinates [8], Mathieu beams in elliptic cylindrical coordinates [9], and parabolic beams in parabolic cylindrical coordinates [10]. Several studies of soliton propagation in the four nondiffracting beam families have been done using these families of nondiffracting beams [14][15][16][17][18][19]. An alternative form to express a nondiffracting beam is via the Whittaker integral Rη; ς; ξ…”