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

20 E. DelRe, M. Segev, D. Christodoulides, B. Crosignani, and G. Salamo
Y = e −τQ (1 + 1
Q (eτQ − 1)), (13)
where Q is an appropriate time average. Whereas this approach can be
meaningful and useful for conditions in which a soliton (i.e., the beam I)
is steady, such as for steady-state incoherent solitons which we will describe
below, it can say nothing as to beam transients. It has been speculated that
Eq.(13) could be valid when a negligible amount of diffraction is involved
[65, 66, 67, 68, 69].
Delaying the discussion of incoherent self-trapping, a consequence of cumulative
inertial response, to section 10, we add a mention to the wealth of
transient phenomenologies that occur for higher-dimensional needles [70], and
those associated to a time-dependent external bias E0 [11, 71, 72, 73]. Lastly,
we should mention the study of single pulse propagation and space-charge
build-up [74, 75].
6 Various photorefractive mechanisms supporting
self-trapping
One of the nicest features of self-trapping of optical beams in photorefractives
is the diversity of mechanisms that can support solitons. Apart from
the solitons described in the previous section, which relied on an externallyapplied
bias field, self-trapping in photorefractives can also arise from photovoltaic
effects [76], or from diffusion-driven effects [77], or from resonantlyenhanced
effects caused by the excitation of both electrons and holes [78]. In
several cases, combinations of two of these effects can also lead to solitons
[e.g., solitons supported by the photovoltaic and the screening nonlinearities
simultaneously]. Furthermore, in some cases, self-trapping can arise from
semi-permanent changes in the crystalline structure, either though clustering
of ferroelectric domains [79], or through re-poling of macroscopic regions
[80, 81], both being driven by the local space charge field. Such permanent
changes are in fact ”fixed” (soliton-induced) waveguides, acting as microstructure
optical circuits ”impressed” into the volume of the bulk nonlinear crystal.
To this date, this is one of the very few techniques to create intricate 3D optical
circuitry. In this section, we briefly review these additional mechanisms
supporting self-trapping of optical beams in photorefractive media.
6.1 Photovoltaic solitons
Soliton-supporting mechanisms appear in photorefractives also in the absence
of electric fields, the major example being photovoltaic solitons [76, 82]. Here,
in open-circuit conditions and for the (1+1)D geometry, the non-uniform optical
excitation translates into a non-uniform photoinduced current. This, at