Nonlinear Bloch modes in two-dimensional photonic lattices

Abstract

Abstract:We generate experimentally different types of two-dimensional Bloch waves of a square photonic lattice by employing the phase imprinting technique. We probe the local dispersion of the Bloch modes in the photonic lattice by analyzing the linear diffraction of beams associated with the highsymmetry points of the Brillouin zone, and also distinguish the regimes of normal, anomalous, and anisotropic diffraction through observations of nonlinear self-action effects.

Self-trapping of optical vortices in waveguide lattices with a self-defocusing nonlinearity

“…3. Furthermore, our numerical simulations to longer propagation distance also indicate that the tails of the self-trapped m=2 vortex have wave properties typical to Bloch modes located in the vicinity of the first-band M point (being out-of-phase between adjacent sites along directions of the lattice principal axes [25]). This is consistent with the k-space power spectrum that settles onto four M points, indicating that the m=2 vortex evolves into a gap quadrupole soliton bifurcated from the edge of the first Bloch band.…”

“…Again, dramatic differences between m=1 and m=2 vortices can be seen in these k-space spectra, indicating quite different physical pictures for self-trapping. For the m=1 vortex, most of the power is located alongside the first BZ, but it would not concentrate just to the four corner points (corresponding to four highsymmetry M points) which mark the edge of the first Bloch band and where the diffraction is anomalous [6,25]. For the m=2 vortex, however, the nonlinear spectrum reshaping makes the power spectrum settle into the M-points quickly, similar to those of the fundamental gap solitons and gap soliton trains [12].…”

Geometric stabilization of extendedS=2vortices in two-dimensional photonic lattices: Theoretical analysis, numerical computation, and experimental results

“…Indeed, the theoretical proposal [5] of such lattice solitons was followed quickly by their experimental realization in 2D induced lattices [9,10], subsequently leading to the observation of a host of novel solitons in this setting, including dipole [11], multipole [12], necklace [13], and rotary [14] solitons as well as discrete [15,16] and gap [17] vortices. In addition to lattice solitons, photonic lattices have enabled observations of other intriguing phenomena such as higher order Bloch modes [18], Zener tunneling [19], and localized modes in honeycomb [20], hexagonal [21] and quasi-crystalline [22] lattices, and Anderson localization [23] (see, e.g., the recent review [24] for additional examples). In parallel, experimental development in the area of BECs closely follows, with prominent recent results including the observation of bright, dark and gap solitons in quasi-onedimensional settings [25], with the generation of similar structures in higher dimensions being experimentally feasible for BECs trapped in optical lattices [26,27].…”

Observation of dipole-like gap solitons in self-defocusing waveguide lattices

“…We visualize the phase structure of the dipole nonlinear output by taking its interference pattern with a tilted broad beam. The initial IP structure of the dipole is preserved in the central two peaks, while the tails along the dipole direction show signs of the OOP relation between adjacent peaks as the fringes tend to break and shift, as if to match the Bloch modes at the M points of the first band (OOP along the dipole direction [13]). …”

“…It can be clearly seen that the dipole has an OOP or "staggered" phase structure not only for the central two peaks but also for any two adjacent peaks in the tails along the dipole direction [ Fig. 2(d), bottom], characteristic to Bloch modes at M points of the first band [13].…”