The linear perspective [23] was first to reveal that the axis
of the
polarization ellipse rotates as the classical spatial soliton propagates
in the usual Kerr medium which exhibits induced birefringence, unless the
soliton is linearly
polarized or unless linear birefringence is present to compensate for the
rotation. More importantly, it also shows that the spatial profile of
the two vector components comprising the soliton field can differ
significantly from one another. One can approximate the usual sech
function, while the other is (sech)
, where s depends on the induced
birefringence of the nonlinear material. This has important
ramifications for light guiding light, because the waveguide seen by a small signal can differ enormously from that induced by the classical sech soliton.
It is well known that the effective refractive index of a Kerr cubic
nonlinearity is circularly birefringent to elliptically polarized light,
but isotropic for linearly polarized light, [28]. A soliton
propagating in this medium will induce a linear waveguide that is
circularly birefringent. The field 
of such a linear waveguide
can be decomposed into circularly polarized modes, whose vector field
components
are 
.
Each
component `sees' a different induced waveguide, 
, where 
and B are
constants set by the nonlinear material [28].
The spatial soliton has the dynamic character of (2),
taking `a' and `b' to be the (+), 
components respectively, where
are each fundamental (no node) modal field amplitudes of the
induced waveguide. These fields are found by solving (6), with
, 
.
Consider a one-dimensional soliton, with 
.
Then (6) describes the motion of a unit mass in a conservative
potential of two dimensional space. The fact that identical equations
have been solved in other physical contexts, e.g. [31],
proves the
existence of elliptically polarized, dynamic solitons.
The solution of (6) has implications for light guiding
light. If the soliton, say, is (+) polarized then it has the classical
sech form [2]. This strong `pump' beam induces a sech profile
(linear) isotropic waveguide which is single moded [18,32]
(also Sec. 4.1 below).
Next, use
this induced waveguide to propagate a small (`signal') beam at the same
wavelength as the pump, but orthogonally 
polarized. In other words,
and so 
while 
, where 
is the sech
profile. The
pump and signal
both `see' a sech
waveguide, but the signal `sees' one with 
larger
by 
. From linear waveguide theory [18,32], the
signal `sees'
a waveguide characterized by 
with a modal
field of the form 
. Here the parameter 
is that of the
classical soliton, 
,
and 
, 
are respectively the
maximum and minimum induced refractive index.