Three - University of Arkansas Physics Department

476 / CLE0'99 / THURSDAY AFTERNOON
CLEO '99. Conference on Lasers and Electro-Optics, p 476-791999
mhS6 Fig. 1. Maximum instability for different
grating strength ratios, y and negative$
Plotted here is growth rate versus phase mismat&,
p, and intensity. Dimensionlcrs parameters
usedare ru = 1, f = - 1, (a) y = 10; (b) y 4.
Note that all axes are scaled differently.
where r, = $)/vy) is the ratio of group velocity
of the fundaments! (FH) and the second
harmonic (SH), p = r,&k,/~, is a normalized
phasemismatch and y = ~ .K~/K, is theratioof
the grating strengths to SH and FH.
The continuous wave (CW) solutions can
be written as:
where aj, are amplitudes, is the frequency
and Q is the wavenumber of the CW solution.
a
af
a,- = -
Qlf = -$q'
fi'
a,, = -fZ Q - $1,a2-= -f-'- Q-$1,
(3)
where f is a parameter that indicates the position
of the solution w.r.t. the FH band-gap.
Choosing f and as free parameters, we find
that Q is given by: AQ~
A = 2r,V2 - 1)
+ BQ + C = 0 where
B = (1 f2)(y - p - 2a) - 2r.
x (1 -'y-~p
-.f3n)/f
C = (- 1 k fl)(p(l 2 f' t f a) + R(2
5 2f2 t zn)))/f. (4)
Once Q has been determined, we obtain an
equation for a, which reads, a' = (2n f p 2
y)(ff-'t 2n)'2rUQ(-f-Cf-Ik2Q).
Following standard procedure, we add
small perturbations to the CW solutions and
study their wolution. This leads to an 8 X 8
matrix, the largest imaginary part of the eigenvalues
of this matrix correspond to the instability
growth rate of the CW solution. The
main difficulty is that there are five degrees of
freedom in choosing the parameters: r,,J y, p
and $1.
We can narrow our search range by dixussing
the physical significance of the five parameters:
(1) r,, the ratio of material goup velocities
at the FH and the SH. For most nonlinear
optical materials, this ratio is usually around
unity. Three values, r, = 0.5; 1.0, 2.0 were
chosen to represent a large range of pouible
situations. (2) f gives the position of a CW
solution with respect to the fundamental
band-gap. Typical values off are f = 20.1,
t0.5, 1.0. Note that f and l/fare equivalent.
the only difference being the direction of
propagation.' (3) y represents the relative
strength of the gratings at the FH and the SH.
The following values y = 0.1,0.5,1,2,10 cover
a large range of possible physical configurations
( ty lead to the same results). We treat
the two remaining parameters, p and R, as
"free," and scan p, and space for MI at a
given set of the other parameters.
In general, most CW solutions are unstable.
Stable areas are found in the nonlinear Schrddiiger
limit, and if the grating strength of the
SH is significantly larger than that of the FH.
Here we present examples of the latter with, y
= 10.4, and f = - 1. The fundamental excitation
is now just above the band-gap, giving
anomalous dispersion. However, the sign of
the coupling constant indicates that the nonlinear
coupling is predominantly to secondharmonic
modes below the bandgap, which
have normal dispersion. Therefore, the quasimodes
that are coupled have opposite signs of
dispersion, a necessary condition for stabity
in the EMA limit. Note from Figs. 1 that the
sign of the phase mismatch is also important.
*Department of Physics, University of Queencland,
QLD 4072, Australia
**Department of Interdisciplinary Studies, Faculty
of Engineering, Tel Aviv University, Tel
Aviv 69978, Israel
I. B. J. Eggleton, C. M. de Sterke, R. Slusher,
and J. Sipe, Electron. Lett. 32,2341 (1996).
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F. Lederer, and B. A. Malomed,
Phys. Rev. E 55,4730 (1997); C. Conti, S.
Trillo, and G. Assanto. Phys. Rev. Lett. 12,
2341 (1997).
3. C. M. de Sterke, J. Opt. Soc. Am. B (1998),
in press.
4. H. He, P. D. Drummond, and B. A.
Malorned, Opt. Commun. 123, 395
(1996); S. Trillo and P. Ferro, Opt. Len. 20,
438 (1995); A. V. Buryakand Y. S. Kivshar,
Phys. Rev. A 51, R41 (1995).
. . CCD Camera
Optical circuitry In photorefractive
strontium barlum nlobate
Matthew Klotz, Mike Crosser.
Gregory J. Salarno. Mordechai Segev,' Physics
Department, University ofArkansas,
Fayetteville, Arizona 72701 USA; E-mail:
mklotz@comp.uark.edu
Optical spatial solitons' in photorefractive
crystals2 have shown potential to form optical
circuitry by forming graded index waveguides
which can guide other beams.'+ A soliton
forms when a photoinduced index change in
the material exactly compensates for the diffraction
of the beam; i.e. the beam creates its
own waveguide. In photoreffactivematerials, a
screening soliton is formed by applying an external
electric field that within the incident
light beam is screened by photoinduced
charges.5 The external field then lowers the
refractive index around the screened area, via
the Pockels effect, creating a waveguide. However,
these induced waveguides disappear if the
applied field is removed from the material. In
this paper we report on the use of soliton formation
to create permanent waveguides by selectively
reorienting ferroelectric domains
within the incident light beam.
For the experiment, the output of an argonion
laser is collimated and focused to a spot
size of 12 pm on the front face of a 1 cm cubic
SBN:75 crystal. When a 3 kV/cm electric field
is applied to the crystal along the direction of
the spontaneous polarization, the beam self
focuses to its input diameter. Theexternal field
is then removed and a uniform background
beam that fills the crystal is switched on. The
space charge field due'to photoinducedscreening
charges is larger than the coercive field of
the ferroelectric domains and causes the domains
in the area of the incident beam to reverse
their orientation. At equilibrium, a new
space charge field, due to the bound charge at
the domain boundaries is locked in place. This
new field increases the index of refraction in
only the area of the original soliton, so that a
waveguide is formed. The waveguides are observed
to have the same size as the original
soliton, exhibit single mode behavior and last
indefinitely.
In addition to fixing a single soliton, a co-
, Delay Arm
CrhS7 Fig. 1. Experimental apparatus for fixing of optical circuitry.