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

24 E. DelRe, M. Segev, D. Christodoulides, B. Crosignani, and G. Salamo
Fig. 17. Observed transverse intensity distribution for (1+1)D self-trapping in InP,
from [78].
6.3 Diffusion-driven self-action
In a conventional noncentrosymmetric crystalline phase, such as that characterizing
SBN or BaTiO3 at room temperature, charge diffusion leads to an
asymmetric index profile, which translates into a transverse phase chirp that
produces self-bending. As discussed in section 3.1 in conjunction with Eq.(5),
diffusion is typically merely a correction for screening soliton studies.
Consider now a situation where no external field is applied. On the basis
of Eq.(1) with g = 0 (null current), E = − kbT 1 dI
q I+Ib dx . Higher order corrections
due to saturation in this case are even less important, such that for a 10
µm beam, they represent a relative import of the order of ɛr ·10−6 , where ɛr is
the relative dielectric constant. For a sample heated above the ferroelectricparaelectric
phase-transition, manifesting a quadratic electro-optic response,
the resulting nonlinearity leads to a symmetric lensing effect, of the type
1 dI
∆n(I) ∝ ( I+Id dx )2 . Although in most conditions, such self-action is negligi-
ble, in the very proximity of the phase-transition, where ɛr attains values of
the order of 10 4 , self-focusing, the precursor of soliton formation, has been
observed [77, 87]. The resulting nonlinear equation, which can be extended
also to the full (2+1)D case, represents the singular situation in which a
nonlocal nonlinearity (involving a spatial derivative) allows for the explicit
analytical prediction of both the observed nonlinear diffraction, along with
such novel effects as ellipticity recovery (see Fig.(18)), and the prediction of
a full family of solitons, which, however, requiring extremely pure samples
and precise thermal conditions, and have not been observed.
6.4 Fixing the photorefractive soliton: Self-trapping by altering
the crystalline structure
Solitons in photorefractives are typically supported by the linear polarization
response to the local space-charge field, P = ɛE. However, optical beams can
also self-trap in photorefractiue media by altering the crystalline structure