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

6 E. DelRe, M. Segev, D. Christodoulides, B. Crosignani, and G. Salamo
Imaging
Lens
CCD
CCD
Photorefractive
Sample
Spherical
Lens
Polarizer BS
V
c
Beam
Expander
Fig. 3. Scheme used to stabilize screening solitons, as described in [17] and [19].
Now the diffracting launch beam is accompanied by an ordinary unfocused wave
appropriately extracted from the single laser.
since termed a screening soliton, and constitutes the most commonly studied
type of photorefractive soliton. Its explanation requires a treatment which
goes beyond the small modulation depth treatment, and for which single
mode description, such as the involved in two-wave mixing, is unsatisfactory.
Photorefractive solitons have since been observed in SBN, BSO, BGO,
BTO, BaTiO3, LiNbO3, InP, CdZnTe, KLTN, KNbO3, polymers and organic
glass.
3 A saturable nonlinearity
The formulation of a descriptive and predictive theory for photorefractive
solitons involves some profoundly different aspects and theoretical tools than
those employed in traditional wave-mixing theories. First, no periodic structure
is present, and second, in most configurations, all the physical variables
vary across the beam profile by a large fraction (e.g., from peak to zero intensity)
such that the modulation cannot be treated as a small perturbation.
However, steady-state photorefractive solitons have two intrinsic symmetries
which reduce the problem: they are evidently time-independent, and their
intensity I is independent of the propagation coordinate z. Yet the heart of
complexity is nonlinearity, and even for a z-invariant photoionizing intensity I
there is still a wide range of parameters, of which only a small subset can support
solitons. In order to formulate a semi-analytic theory, a one-dimensional
reduction must be implemented: the beam should be such that no y-dynamics
emerge, the soliton intensity being solely x-dependent [I(x)]. Experimentally,
this was achieved by launching a beam focused down through a cylindrical
lens, and quite similarly this has led to quasi-steady-state self-trapping in the
absence of background [9], and to steady-state screening solitons for appropriate
values of E0 (see Fig.(4)) [19].
In fact, in many aspects these one-dimensional (stripe) waves, generally
termed one-plus-one dimensional screening solitons [(1+1D)], share with
z
y
PBS
x
Laser