Photorefractive Solitons (Chapter in Springer book ... - Tripod

14 E. DelRe, M. Segev, D. Christodoulides, B. Crosignani, and G. Salamo
that can only find its explanation in the full expression of Eq.(5). It appears
that, even though these nonlocal terms produce a parabolic trajectory, they
do not greatly influence the existence curve. From a different perspective,
we note that self-bending becomes an important issue when experiments are
carried in highly solitonic regimes, characterized by a large ratio between selftrapped
propagation distance and linear diffraction length Lz/Ld: to increase
Lz/Ld we can either use a longer sample, this increasing nonlinearly the
lateral shift, or use tighter launch beams, this increasing η.
4 Two-dimensional solitons
The (1+1)D screening solitons represent the firm experimental and theoretical
foothold on which a large part of research rests, especially because of the
appealing nature of the saturable nonlinearity which gives rise to numerous
(fascinating) soliton interactions not present with Kerr-type solitons. However,
the most ground-breaking achievement, both from the physical and from
the applicative point of view, is the self-trapping of (2+1)D solitons. As their
lower-dimensional counterparts, needles form both in the transient regime
- as quasi-steady-state self-trapping [7] - and in temporal steady state as
(2+1)D screening solitons [17, 18]. Such needle-like solitons were originally
documented in SBN, and have been replicated in most soliton-supporting
photorefractive media, such as other ferroelectrics [34], semiconductors [35],
paraelectrics [36], sillenites [37], and indeed for most types of self-trapping:
bright, photovoltaic [38], multimode [39, 40, 41], and incoherent [42, 43], to
name a few. Furthermore, even (2+1)D dark solitons were observed in photorefractives,
in quasi-steady-state [44] and in steady-state [45] under a bias
field, as well as photovoltaic [46] and incoherent [47] dark ”vortex” solitons.
An example of a dark vortex screening soliton is shown in Fig.(12). Twoplus-one
dimensional solitons form when a circularly symmetric beam is focused
down onto the input face of the sample, and the initially diffracting
beam collapses into a non-diffracting 2D beam having an almost ideally
circularly-symmetric shape (see Fig.(9)). These studies, which constitute
one of the rare possibilities of observing (2+1)D solitons, have greatly
contributed to the understanding of the physics associated with higher-thanone-dimensional
nonlinear waves. The observation of soliton spiraling in full
3D [48], as well as fusion, fission, birth and annihilation of (2+1)D solitons
[49, 50, 51], have extended the very concept of soliton-particle behavior.
The description and understanding of the mechanisms that support
(2+1)D solitons are, to some extent even today, still incomplete. This is
because the propagation involves a nontrivial three-dimensional, anisotropic,
and spatially nonlocal nonlinear problem [52, 53, 54, 55, 56, 57]. The fact
that photorefractives can support self-trapped needles of (almost ideally)
circularly-symmetric shape seems very surprising right from the outset. More