Summary form only given. Some of the novel quantified characteristics for double phase conjugate mirrors are analysed including the effects of the nonlinearity on the critical dynamics (approach to saturation) and on the spatial distribution of the grating (large scale distortion of the beams and conjugation fidelity) and sensitivity to noise (seeding). The approach used also clarifies the question of linear instability and predicts a new transition to an oscillatory regime

Cross, M. C.

Engin, D.

Segev, M.

Yariv, A.

English

Caltech Authors - Main

11 8 1 QELS'96 I WEDNESDAY AFTERNOON 
W-lP 
QWE4 Fig. 1 Temporal profile of 
optical pumping effect on DFWM 
intensity as a function of a delay time 
between pump pulse at 400 nm and 
two probe pulses 
at 800 run. 
pumping effect on DFWM intensity was 
independent of the polarization angle of 
pumping pulse at 400 run. These results 
suggest that the enhancement of DFWM 
intensity by optical pumping might be 
ascribed to the gain of the electronic 
third-order susceptibility. Exciton states 
were well known to be created in one- 
dimensional chain backbone of a conju- 
gated polymer by optical excitation? Ex- 
citon states possess an intense transition 
to higher excited states in a region from 
near IR to IR. That might be one of the 
mechanisms for the optical pumping en- 
hancement of DFWM intensity. 
1. H. Sakaguchi, T. Nagamura, T. Mat- 
suo, Jpn. J. Appl. Phys. 30(3A), UT7 
(1991). 
2. H. Sakaguchi, T. Nagamura, T. L. 
Penner, D. G. Whitten, Thin Solid 
Films 244, 947 (1994). 
D. C. Rodenberger, J. R. Helfin, A. E 
Garito, Nature 359, 309 (1992). 
D. C. Rodenberger, J. R. Helfin, A. E 
Garito, Phys. Rev. A, 51(4), 3234 
(1995). 
T. Kobayashi, M. Yoshizawa, U. 
Sta", M. Tdji, M. Hasegawa, J. 
Opt. Soc. Am. B 7(8), 1558 (1989). 
3. 
4. 
5. 
QWES 
Optical bistability in reflection-mode 
operation of a diode laser amplifier 
Donald M. Wood, Gautam Vemuri, Physics 
Department, Indiana University-Purdue 
University, Indianapolis, 402 N. Blackford 
Street, Indianapolis, Indiana 46202-3273 
A number of physical systems exhibit 
hysteresis and bistability, ranging from 
electronic devices like a Schmitt trigger, 
to quantum devices like the single-atom 
micromaser. Lasers, and laser diode am- 
plifiers (LDA) have been demonstrated to 
exhibit dynamical hysteresis, and the in- 
timate connection between this bistability 
and delayed bifurcations has been theo- 
retically and experimentally elucidated. 
Bistability and hysteresis in LDAs is es- 
pecially interesting for its potential ap- 
plication in developing optical switches 
and logic gates. For LDAs, Roy and co- 
workers' have demonstrated that the 
width of the hysteresis loop in the output 
of the amplifier, when an input signal is 
periodically modulated, increases with 
an increase in the frequency of modula- 
tion. These workers derived scaling laws 
for the width of the hysteresis versus fre- 
quency, for different bias conditions of 
the amplifier. Most previous experiments 
that examined hysteresis in amplifiers 
utilized the amplifier in a transmission 
mode, where the light transmitted 
through the amplifier was monitored. Re- 
flection mode operation of diode laser 
amplifiers has not been as thoroughly in- 
vestigated, though it is expected to be of 
relevance to some forms of logic gates, 
such as NAND and NOR gates. 
We report results of an experiment in 
which the output of a single-mode diode 
laser is injected into a diode laser ampli- 
fier operated close to its lasing threshold. 
The injected light is periodically modu- 
lated at frequencies very slow compared 
with the relevant relaxation frequencies 
within the amplifier. In contrast to most 
experiments, we operate the amplifier in 
a reflection mode instead of the trans- 
mission mode. Under the influence of the 
periodic modulation, the amplifier out- 
put exhibits several novel types of hys- 
teresis and associated bistable behavior. 
Specifically, we find that for some oper- 
ating conditions, determined by the am- 
plifier bias current and temperature, one 
obtains a reversal in the direction of the 
hysteresis, where the output of the am- 
plifier switches from the conventional 
positive hysteresis, to negative hysteresis. 
Our measurements follow the route 
taken by the hysteresis as it switches di- 
rections, which indicates that an X- 
shaped hysteresis is the intermediate 
.step. For positive hysteresis, the width of 
the hysteresis loop increases with an in- 
(crease in the modulation frequency, and 
'we find a scaling exponent that is differ- 
lent from those reported in the literature.' 
'The negative hysteresis is a new dynam- 
iical phenomena, and theoretical work is 
currently underway to analyze the ex- 
perimental observations. 
'I. A. Hohl et al., Phys. Rev. Lett. 74, 
2220 (1995); P. Jung et al., ibid. 65, 
1873 (1990). 
QWE6 
lrransition to an oscillator for double phase- 
conjugate mirror 
13. Engin, M. C. Cross,, A. Yariv, 
Id. Segev," AV. Phys. Dept., 
California Znstitute of Technology, 128-95, 
Pasadena, California 91125 
Double phase conjugate mirror (DPCM) 
is a unique device in which two mutually 
incoherent pump beams are phase con- 
j.ugated' simultaneously, (Fig. 1, inset). 
Currently there is a disagreement in the 
field about the nature of the linear insta- 
bility (oscillator or amplifier"). The con- 
troversy originates from the wide gap in 
complexity between the analytical prob- 
lcems considered and the usual experi- 
mental conditions. The more realistic, nu- 
merical studies' and experiments exhibit 
QWE6 Fig. 1 The profile of the 
nonlinear front solution for E e 
Inset: DPCM configuration. 
E > G. 
a rich spatial behavior for the DPCM. The 
nature of the linear instability is essential 
for understanding the behavior of DPCM 
in different regimes and hence for im- 
proving the device performance. 
The problem is approached as one of 
pattem formation outside of equilibrium' 
and an "amplitude equation" is derived. 
This equation is an established, unified 
approach to systems that exhibit critical 
transitions. It has been successful in 
quantifying many of the experimental 
observations in these systems. Here, 
some of the novel quantified character- 
istics for DPCM are the effects of the non- 
linearity on the critical dynamics (ap- 
proach to saturation) and on the spatial 
distribution of the grating (large scales 
distortion of the beams and conjugation 
fidelity) and sensitivity to noise (seed- 
ing). The approach also clarifies the ques- 
tion of linear instability and predicts a 
new transition to an oscillatory regime. 
A slow modulation C of the phase- 
matched, shared grating (with grating 
wave number k8), as C exp(i&x) is con- 
sidered. The "amplitude equation" gov- 
ems the spatial and temporal evolution 
of C in the weakly nonlinear regime: 
Toa,c + .rosoa.c = EC 
Equation (1) is derived from the Helm- 
holtz and Kukhtarevs equations for pho- 
torefractive effect using a perturbative 
approach, "multi-scaling analysis,"' with 
the smallness parameter, E = ((TL), - 
TL)/(r'L)c, (TL, gain-length product, (W, 
= -2 for degenerate pump beams). The 
coefficients of Eq. (1) are calculated for 
different system parameters: a, the full 
angle between the two pump beams, 
pump intensity ratios and frequency dif- 
ference; Debye length, etc. 
The behavior of the convective system 
above the threshold is readily predicted 
from Eq. (1). For small E there is expo- 
nential growth of C in the + x  direction 
away from the lower boundary (Fig. 1) as 
the noise is amplified while the group 
velocity, so, carries the disturbance up- 
ward, until the nonlinear term in Eq. (1) 
saturates the growth. The length over 
WEDNESDAY AFTERNOON QELS’96 1 11 9 
0 . 0 5  I 
0.01 / 
“Elec. Eng. Dept., Princeton University, 
Princeton, New Iersey 08544 
1. S. Weiss et al., Opt. Lett. 12, 114 
(1987). 
2. A. A. Zozulya, Opt. Lett. 16, 545 
3. A. A. Zazulya et al., J. Opt. Soc. Am 
B 12, 255 (1994); D. Engin et al., 
Phys. Rev. Lett. 74, 1743 (1995). 
4. M. C. Cross et al., Rev. Mod. Phys. 
65, 851 (1993). 
5. M. C. Cross, Phys. Rev. Lett. 57, 
2935 (1986). 
(1991). 
a (de& 
QWEC Fig. 2 K;’ as a function of a. 
Inset: E. as a function of a (for 
degenerate pump beams); thick solid 
lines, analytical solution; diamonds, 
numerical solutions. 
which the solution grows to saturation 
~ ~ ( S - ~ ) E - ~ S ~ T ~  (with s the seed at the lower 
boundary) can be quite large near thresh- 
old and for small noise, leading to large 
scale distortions in the grating amplitude 
and hence the beams. As rL is increased 
further the system exhibits a transition to 
oscillator. Above this transition the front 
shown in Fig. 1 has propagated back- 
ward, since now the growth dominates 
the advection, to fill the region with the 
saturated nonlinear solution except for a 
”healing” length near the lower bound- 
ary, which is now independent of the 
noise level and only depends on the par- 
ameters of the amplitude equation (the 
characteristic length -50 and E. - 0.3). 
The developed grating is not sensitive to 
fluctuations in the seed level and is self- 
sustaining even in the absence of noise (a 
characteristic behavior of self-oscillation). 
The transition to this state is precisely de- 
termined by the zero propagation veloc- 
ity of the front solution connecting the 
nonlinear state to the zero amplitude 
state? 
The propagation velocity of the front 
in Eq. 1 is given by a stationary phase 
analysis. The analysis yields the follow- 
ing transition parameters: 
where the tail of the stationary front is 
of the form exp(-j(qL - ~ K ~ ) x  + (a, + 
ja,)t]]. Equation (2) identifies the transi- 
tion rL value to be about -2, - 2% - 
-2.6. Figure 2 shows E. and K;’ as func- 
tions of a for degenerate pump beams. 
The disagreement between the two sets 
(numerical, analytical) at small U origi- 
nates from the growing importance of the 
grating wave number dependence of TL 
relative to the phase matching. 
We expect careful experiments will re- 
veal that double phase conjugation trans- 
forms from convective amplifier into an 
oscillator at closely spaced gain thresh- 
olds. 
‘Physics Dept., California Institute of 
Technology, 11436, Pasadena, Califbrnia 
91125 
QWE7 
light structures created in one spatial 
dimension 
E Mitschke, G. Steinmeyer, A. Schwache, 
U. Morgner, lnstitut fur Angewandte Physik, 
Universitdt Milnster, Cwrensstr. 2/4, 
0-48149 Milnster, Germany 
A fiber ring resonator constitutes a model 
system of a nonlinear feedback system in 
which the combination of self-phase 
modulation, group velocity dispersion, 
and interference can create amazingly 
complex phenomena. We consider such a 
resonator, driven by a sequence of pico- 
second pulses from a modelocked laser. 
We report on experiments and corre- 
sponding numerical simulations that re- 
veal a wide variety of possibilities, de- 
pending on the choice of parameters. 
In the simplest case, one can have a 
sequence of pulses with stationary shape 
resembling the input pulse shape but 
with pulse powers varying from shot to 
shot in a periodic or even nonperiodic 
way; these are referred to as sequences 
that are subharmonic to the repetition 
rate, or chaotic. More intriguingly, the 
pulse shapes can be modified substan- 
tially with respect to the smooth input 
pulse shapes; rich substructures can 
evolve. There are sequences of pulses in 
which no pulse shape is ever repeated. 
Among the cases of nonrepetitive 
pulse shape, one has to distinguish be- 
tween conditions of normal or anoma- 
lous group velocity dispersion. For nor- 
mal dispersion we obtain what we call 
optical turbulence: a spatiotemporal in- 
stability that can be described in terms 
borrowed from fluid dynamics (“spatial” 
here refers to the light propagation direc- 
tion and encompasses just a single spatial 
dimension). For anomalous group veloc- 
ity dispersion there is formation of sub- 
pulses that have properties of solitons, 
are localized at (effectively) rihdom po- 
sitions within the width of the input 
pulses, and move around. This case we 
call a (one-dimensional) soliton gas. 
It goes without saying that nonlinear 
resonators are ubiquitous in all kinds of 
optical systems, including lasers. We will 
discuss relations to instabilities recently 
reported from some other systems in the 
light of the findings from our passive 
fiber ring resonator, which is simple 
enough to allow some detailed under- 
standing, yet complex enough to create 
an amazing richness of types of behavior. 
QWE8 
Role of self-focusing and phase modulation 
in the large spectral bandwidth stimulated 
Rayleigh scattering 
D. Wang, R. Barille, X. Nguyen Phu, 
G. Rivoire, Laboratory of Optical Properties of 
Materials and Applications, 4, Ed Lavoisier, 
BI? 2018,49016 Angers Cedex, France 
The study of Rayleigh light scattering is 
interesting not only for its applications 
such as phase conjugation but also as a 
way to explore the interactions between 
matter and light. Recently a large spectral 
bandwidth stimulated scattering from 
CS, has been investigated in bulk:-3 liq- 
uid hollow-core fibers,?” and micro- 
 drop^.'^ However, despite all the results 
and explanations, one question remains: 
the origin of such a large spectral broad- 
ening mostly because several physical 
processes are involved simultaneously in 
the scattering. We discuss the role of self- 
focusing and phase modulation on the 
large spectral bandwidth stimulated Ray- 
leigh-wing scattering (SRWS). 
In the experiment a Nd:YAG laser is 
used to provide pump pulses of 25 ps at 
A = 532 nm. The laser beam is usually 
focused by a 1-m focus lens into a l-cm- 
long cell containing Cq. The scattered 
light generated in both forward and 
backward directions is sent to a spectro- 
graph and CCD image systems for spec- 
tral and spatial analyses. A microscope 
associated with the spectrograph is also 
employed to study local behaviors of the 
phenomenon. 
The forward and backward large 
band SRWS at high excitation levels have 
been well described in Ref. 1. In com- 
pleting that work, we now pay more at- 
tention to the start of the SRWS and its 
developments. At an excitation near 
threshold of SRWS, we can see clearly the 
presence of Kerr effects such as self-fo- 
cusing and phase modulation. We have 
found also that these effects play a dra- 
matic role in the generation of the large 
band SRWS. 
The role of self-focusing is, in short, to 
induce and to localize the source of 
SRWS. That is strongly supported by the 
following results: (i) the self-focusing 
process starts before the generation of 
SRWS, and the focused beam has a di- 
ameter on the order of 6 p~ at the end 
of the cell; (ii) forward and backward 
scatterings are produced in the self-fo- 
cusing zone; (iii) the ratio of the thresh- 
olds of SRWS linear polarization state 
over circular polarization state is mea- 
sured at 2.6. However the calculation 
gives two values of 0.6 and 3.6, respec- 
tively, for the cases of a threshold result- 
ing from pure scattering effects and to 
pure self-focusing effects; and (iv) the cal- 
culated threshold value of SRWS in ow’ 
exatation condition is at least 10 GW/ 
cm2, whereas we obtain SRWS at an in- 
cident intensity of 0.8 GW/anz. There- 
fore, self-focusing increases local inten- 
sity allow SRWS to reach its threshold. 
The role of phase modulation is 
shown by the spectral observation near 
the threshold excitation. It can be sum- 


Transition to an oscillator for double phase-conjugate mirror

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Transition to an oscillator for double phase-conjugate mirror

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