Three - University of Arkansas Physics Department

220 / QELS'96 / THURSDAY ACTERN(
ION
QELS - Technic :a1 Digest Series v 10, p 220,1996
quasiequilibrium Bose-Einstein condensate
cannot build up in the presence of
the exponential LO-phonon-assisted optical
decay of the para-x's, Our scenario
explains the cotresponding experimental
observations1" in which the BEC seemed
to be approached only asymptotically.
We also present some approximations
for the thermodyfiamic relationships of a
degenerate Bose gas of para-x's. In particular,
along the equilibrium phase diagram
the change of the chemical potential
Ap ce -AT for T >> T, md Ap. a
-(AT)' for T C* T, (see Fig. 3).
This work has been supported by the
Volkswagen Stlftung.
1. D. W. Snoke, J. P. Wolfe, A. Mysyrowicz,
Phys. Rev. Lett. 59,827
(1987); Phys. Rev. B 41, 11171 (1990).
2. D. FrOhlich, A. Kulik, B. Uebbing,
A. Mysyrowicz, V. Langer, H. Stolz,
W. von der Osten, Phys. Rev. Lett.
67, 2343 (1991).
3. J. L. Lin, J. P. Wolfe, Phys. Rev. Lett.
71, 1222 (1993).
QThK
Spatial Solitons, Patterns and
Instabilities
4:30 pm
Room 82
Mordechai Segev, Princeton Uniwsity,
Presider
QThKl (Invited)
430 pm
Self-induced trapping of optical beams in
semiconductors
M. Chauvet. S. A. Hawkins. G. I. Salamo.
. " .
Mordechai kgev,* D. F. Bliss,** G.
Bryant," Physics Department, Uniwrsity of
Arkansas, Fayetteville, Arkmrsas 72701
Spatial solitons in photorefractive mate-
-rials have been a subject of recent interest.'
When compared with Kerr spatial
solitons, their most distinctive features is
that they are observed at low light htensities
and trapping occurs in both transverse
dimensions. Photorefractive spatial
solitons have been observed in the hulgsten
bronze ferroelectric oxidesz and in
the nonferroelectric sillenite oxides In
this paper we report self-induced trapping
in one dimension in the semi-mulating
compound semiconductor InP:Fe.
In particular, we observe that for milliwatt
laser beams diffraction is exactlv
balanced by the photorefractively k-
duced index change. Our observation is
made under steady-state conditions that
were similar to that used for the observation
of photorefractive solitons in
strontium barium niobate (SBN).'
The semi-insulating compound semiconductor,
InP:Fe, is an interesting photorefractive
material. It is attractive
because of its compatiiility with semiconductor
lasers and optical commmication
applications. It is unusual because
the observed photorefractive effect is
markedly intemity dependent. Jn fact,
QThKl Fig. 1 Theoretical TWM space
charge field amplitude and phase shift
as a function of intensity in 1nP:Pe. The
grating modulation is 0.1, Ti, = 10 KV/
em, and other parameters are taken
from Ref. 4.
QThKl Fig. 2 Beam profiles taken at
the input face (left), at the output face
after diffraction (center), and at the
output face with diffraction
compensated by the photorefractive
effect (right).
both the two-wave-mixing gain and the
relative phase between the intemity spatial
pattern and the induced index pattern
are intensity dependent. In parbcula,
the gain exhibits an intensity-dependent
resonance while the phase varies
from 0 to w, taking on ~ /2, at the resonant
intensity. Although the behavior deviates
substantial from traditional photorefractive
phenomena it is beautifully
predicted using a two-carrier5 tramport
model developed by Picoli, Ozkul, and
View:
A qualitative example of the behavior
of the gain and relative phase for InP using
this model is shown in Fig. 1. The
figure clearly shows the intensity-dependent
resonance in two-wave-mixing gain
and the intensity-dependent phase. Another
way to picture this behavior is to
look at the in-phase and out-of-phase
components of the induced space=charge
field. The in-phase component results in
an index change while the out-of-~hase
component proYduces energy exchan'ge. In
our experiment, self-induced focusinn
and difocusing effects peak with th;
magnitude of the in-phase component of
the space-charge field while an observed
beam deflection peaked with the magnitude
of the out-of-phase component.
The apparatus for our experiment is
similar to that used in Ref. 4. A continuous
wave Ti:sapphire laser, tumble between
0.9 arrd 1.1 micro119 was tuned
away from the InP band edge to about 1
miaon, to avoid significant absorption.
The output beam fmm the laser was
about 2 mm in diameter and was focused
into the InP eample along the (110) direction
uhg a cylindrical lens of cm focal
length. The input and output beam diameters
were measured by imaging them
onto a CCD beam profil~ system. The incident
beam diameter was 47 miaons
while the diffracted output beam dhe-
ter was 80 microns. A voltage of about 5
KV was applied along the 5 mm, (001),
direction. Trapping occurred for an input
laser beam power of about 100 rniaowatts.
The trapped output beam diameter
was 45 miaons. These beam profiles
ate shown in Fig. 2.
We have observed self-trapping of optical
beams in semiconductore using the
photorefractive effect. The major advantage
of using photorefractive semiconductors
as opposed to the tungsten
bronze or sellenite insulators is that their
response times are several orders of magnitude
shorter, leading to improved pob
sibilities for application.
*Electrical Engineering Dept. and Advanced
Center for Photonics and Optoelectronic
Materials (POEM), Princeton University,
Princeton, New Jersy 08544
"Rome Laboratory, U.S.A.F., Hanscorn AFB,
Mnssachusefts 01731
1. M. Segev, B. Crosignani, A. Yariv, B.
Fisher, Phys. Rev. Lett. 68,923
(1992); M. Morin, G. Duree, G. Salamo,
M. Segev, Opt. Lett. 20,2066
(1995) and ref. therein.
2. G. Duree, J. L. Shultz, G. Salamo, M.
Segev, A. Yariv, B. Crosignani, P.
DiPortb, E. Sharp, R. Neurgaonkar,
Phys. Rev. Lett. n, 533 (1993).
3. Observations of steady-state self focusing
effects were presented by M.
D. Iturbe-Castillo, P. A. Marquez-
Aguilar, J. J. Sanchez-Mondragon, S.
Stepanov, V. Vysloukh, Appl. Phys.
Lett. 64,408 (1994).
4. M. Shih, M. Segev, G. C. Valley, G.
Salanto, B. Crosignani, and DiPorto,
Electron Lett. 31, 826 (1995).
5. M. B. Klein, G. C. Vdey, J. Appl.
Phys. 57, 4901 (1985).
6. G. Picoli, P. Gravey, C. Ozkul, V.
View, J. Appl. Phys. 66, 3798 (1989).
Steady-state dark screening sotitons and
soliton-induced waveguides formed in a
bulk photorefractive medium
Zhigang Chen, Matthew Mitchell, Mingfeng
Shih, Mordechai Segw, Mark H.
Garrett,, George C. Valley* Electrical
Enfirwering Deuartmolt and Colter for
~Gtonics &d bptoelectronic ~ntehls
(POEM), Princeton Uniwrsitq, Princeton,
Steady-state dark photorefractive screening-eolitons,
as predicted recently,' are
observed when a laser beam containing a
dark notch propagates through a buk
strontium barium niobate crystal biased
by an electric field. The photorefractive
dark solitons induce waveguides in the
bulk of a photorefractive crystal that