emtosecond pump pulses are strongly attenuated in lithium niobate owing to two-photon absorption; the relevant nonlinear coefficient beta_p ranges from ~3.5 cm/GW for lambda_p = 388 nm to ~0.1 cm/GW for 514 nm. In collinear pump-probe experiments the probe transmission at the double pump wavelength 2lambda_p=776 nm is controlled by two different processes: A direct absorption process involving pump and probe photons (beta_r ~ or = 0.9 cm/GW) leads to a pronounced short-duration transmission dip, whereas the probe absorption by pump-excited charge carriers results in a long-duration plateau. Coherent pump-probe interactions are of no importance. Hot-carrier relaxation occurs on the time scale of < or ~0.1 ps

Beyer, O.

Buse, K.

Hsieh, H. T.

Maxein, D.

Psaltis, D.

Sturman, B.

English

Caltech Authors - Main

1366 OPTICS LETTERS / Vol. 30, No. 11 / June 1, 2005Femtosecond time-resolved absorption processes
in lithium niobate crystals
O. Beyer, D. Maxein, and K. Buse
Physikalisches Institut, University of Bonn, Wegelerstraße 8, D-53115 Bonn, Germany
B. Sturman
Institute of Automation and Electrometry, 630090 Novosibirsk, Russia
H. T. Hsieh and D. Psaltis
Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91125
Received November 10, 2004
Femtosecond pump pulses are strongly attenuated in lithium niobate owing to two-photon absorption; the
relevant nonlinear coefficient bp ranges from ,3.5 cm/GW for lp=388 nm to ,0.1 cm/GW for 514 nm. In
collinear pump–probe experiments the probe transmission at the double pump wavelength 2lp=776 nm is
controlled by two different processes: A direct absorption process involving pump and probe photons sbr
.0.9 cm/GWd leads to a pronounced short-duration transmission dip, whereas the probe absorption by
pump-excited charge carriers results in a long-duration plateau. Coherent pump–probe interactions are of
no importance. Hot-carrier relaxation occurs on the time scale of &0.1 ps. © 2005 Optical Society of America
OCIS codes: 160.3730, 320.7110, 190.4180.Lithium niobate sLiNbO3d is a wide-gap s,4 eVd
ferroelectric optical material that is of prime impor-
tance for nonlinear optical and holographic applica-
tions such as frequency conversion, optical filtering
and switching, and data storage.1–3 Large x2 coeffi-
cients, outstanding photorefractive properties, ro-
bustness, and availability make the material promis-
ing for realization of devices.
High intensities and correspondingly short pulses
are required for efficient nonlinear optical processes
and ultrafast holography. However, although LiNbO3
is well investigated in the continuous and
microsecond–nanosecond ranges,4–7 almost nothing
is known about its nonlinear response in the femto-
second range. It is unknown, in particular, which ef-
fects will govern the nonlinear propagation of femto-
second pulses. Free-carrier nonlinearity and
absorption, Kerr nonlinearity, two-photon absorption
(TPA), and photorefractive nonlinearity can compete
in this range.
A crucial advantage of using femtosecond pulses as
compared with picosecond and longer pulses is that
the complicated processes, caused by repopulation
and reexcitation of energy levels, can be separated
from the direct electron excitation processes.8,9 The
reported results on the TPA coefficient of LiNbO3, ob-
tained with nanosecond and subnanosecond pulses,
are highly controversial10; they have a range of more
than 1 order of magnitude at ,530 nm. Thus for
practical purposes and also for physics it is highly
important to explore femtosecond time-resolved ab-
sorption processes in LiNbO3, which is the topic of
this work.
The conditions of our collinear pump–probe experi-
ments are as follows: A single axially symmetric
pump pulse of wavelength lp=388–776 nm,
extracted from a Ti:sapphire femtosecond laser (CPA-
0146-9592/05/111366-3/$15.00 ©2010, Clark-MXR plus an optical parametric ampli-
fier system), is incident normally onto the YZ face of
a LiNbO3 sample; the polar c axis is parallel to the Z
axis. The pulse width and beam diameter (at the
half-intensity) are ,0.24 ps and ,0.6 mm, respec-
tively, for 388 nm. Peak intensity Ip
0 ranges from
,1 to ,276 GW/cm2. The maximum pump fluence
is approximately 59 mJ/cm2. The input polarization
vector of the pump pulse is either parallel or perpen-
dicular to the c axis. Thickness d for three investi-
gated (undoped and congruently melting) samples is
1, 0.5, and 0.07 mm. In the wavelength range used,
the linear absorption is negligibly small. In addition
to the pump transmission, the transmission coeffi-
cient for a weak probe pulse slr=2lp=776 nmd is
measured as a function of its time delay Dt. The
probe pulse width and diameter are not essentially
different from those of the pump.
Before presenting our experimental data, we con-
sider the pump transmission coefficient in the pres-
ence of TPA. Pump intensity Ip obeys the nonlinear
wave equation
S ]
]x
+
1
vp
]
]t
DIp = − bpIp2, s1d
where x is the propagation coordinate, bp is the TPA
coefficient for the pump pulse, and vp=c /np is the
pulse velocity with np being the relevant refractive
index. Equation (1) follows from Maxwell’s equations
under the assumption of negligible diffraction broad-
ening and frequency dispersion, which is well justi-
fied for the experimental conditions. Equation (1) has
to be solved with a boundary condition at the input
x=0; here we use a Gaussian profile Ipsx=0d
0 2 2 0=Ip expf−st / tpd − sr /rpd g, where Ip is the input peak
2005 Optical Society of America
June 1, 2005 / Vol. 30, No. 11 / OPTICS LETTERS 1367intensity; r is the radial coordinate; and rp and tp
characterize the pump beam radius and the pulse
half-width, respectively. The solution of Eq. (1) meet-
ing this boundary condition is given by
Ip
0
Ip
= bpIp
0x + expFst − xvp−1d2
tp
2 +
r2
rp
2G . s2d
It describes the propagation of the pump pulse with
velocity vp, the decrease in the peak intensity, and
flattening of the top of the pulse (in the transverse di-
rections and in time) owing to the preferential ab-
sorption at the beam center.
To find the normalized transmission coefficient for
the pump, Tp, we integrate output intensity Ipsd ,r , td
over time and the transverse coordinates and divide
the quantity obtained by its value at d=0. The final
result is
Tp =
2
qp˛p
E
0
‘
lnf1 + qp exps− j2dgdj, s3d
with qp=bpIp
0d (see also Ref. 9). The transmission
thus depends only on the product bpIp
0d. The solid
curve in Fig. 1 shows calculated dependence Tpsqpd.
This dependence is rather specific. After a rapid ini-
tial fall, the further decrease of Tp occurs slowly; this
is indeed due to the relatively weak energy absorp-
tion on the pulse wings.
The squares, triangles, and crosses in Fig. 1 repre-
sent experimental data for the samples with d=1,
0.5, and 0.07 mm, respectively. The only variable pa-
rameter to fit the theoretical curve, Eq. (3), to all the
experimental data is the TPA coefficient bp. Excellent
agreement between theory and experiment within
the large intensity range is evident. This proves un-
ambiguously that TPA is the reason for the pump at-
tenuation. The estimated value of the TPA coefficient
at 388 nm is bp,3.5 cm/GW. The maximum value of
the product bpIp
0d is approximately 96, 48, and 7 for
the samples with d=1, 0.5, and 0.07 mm, respec-
tively; the pump pulse is subjected to a strong non-
linear absorption even in relatively thin samples.
In a similar manner, the values of bp have been de-
Fig. 1. Dependence of normalized transmission coefficient
Tp on the product bpIp
0d. The squares, triangles, and
crosses correspond to the data obtained for d=1, 0.5, and
0.07 mm.duced for different pump wavelengths. The corre-sponding data are presented by circles in Fig. 2. One
sees from Fig. 2 that the TPA coefficient decreases
strongly as the wavelength increases. For lp
*600 nm the energy of two photons is insufficient for
band–band transitions and bp approaches zero.
Note that the previous TPA measurements for
LiNbO3 crystals were performed with nanosecond
and subnanosecond pulses. The corresponding data
for bp are highly controversial,
10 probably because of
a strong influence of secondary excitation processes
typical for this material.5,6 The energy of our femto-
second pulses is insufficient for such processes.
Now we turn to our experimental data on the probe
transmission. Figure 3 shows the dependence of
probe transmission coefficient Tr on time delay Dt be-
tween the pump pulse and the probe pulse for Ip
0
,107 GW/cm2, d=0.07 mm, and four different com-
binations of beam polarizations. It includes a great
deal of information about the light–matter interac-
tions. Dependence TrsDtd is characterized by a nar-
row dip (its width is comparable with the pulse
width) followed by a quasi-permanent section (pla-
teau). The plateau value of Tr remains unchanged at
least on the scale of 10−11 s. The dip amplitude is
largest in the cases of parallel polarization of the
pump and probe (ZZ and YY); the influence of the ori-
entation of the polarization plane is fairly weak. In
Fig. 2. Dependence of quadratic absorption coefficient bp
on pump wavelength lp.
Fig. 3. Normalized transmission coefficient Tr for the
probe pulse versus time delay Dt; first and second symbols
in the inset specify the orientation of the polarization vec-
tor of the pump and the probe, respectively.
1368 OPTICS LETTERS / Vol. 30, No. 11 / June 1, 2005the cases of orthogonal polarizations of the pump and
probe (YZ and ZY) the dip is less pronounced. The
plateau value of Tr is determined by the probe polar-
ization; the absorption effect is slightly larger for a
Y-polarized probe beam.
The plateau section in TrsDtd (Fig. 3) is attributed
to the probe absorption by the carriers (electrons
and/or holes) excited through two-photon pump ab-
sorption. It is known from experiments with LiNbO3
crystals and nanosecond pulses that excitation of
charge carriers causes light absorption that persists
for some microseconds.6,11 Some polarization depen-
dence of the plateau value is explained by the crystal
anisotropy.
The dip in TrsDtd contrasts with the effect of de-
creasing probe absorption owing to coherent para-
metric pump–probe interactions that are known for a
number of semiconductors (see Ref. 12 and references
therein). The increase in the probe absorption in the
presence of the pump pulse is of different origin. We
attribute it to two-photon transitions involving both
pump and probe photons; their total energy
s,4.8 eVd exceeds the width of the forbidden gap of
LiNbO3 crystals. Identical polarizations of the pump
and probe facilitate this direct process.
The dependences of the dip amplitude and the pla-
teau absorption 1−T r
plat on the pump intensity are
different. Although the dip amplitude tends to satu-
rate with increasing qp=bpIp
0d the plateau absorption
shows a superlinear behavior in the range qp=1–8.
This is explained by different orders (in Ip
0) of the rel-
evant nonlinear processes. The pump-induced TPA
coefficient for the probe pulse and the absorption
cross section of the pump-excited carriers at lr esti-
mated from our experimental data are br
<0.9 cm/GW and sr<0.8310−17 cm−2, respectively.
These quantities do not show strong polarization sen-
sitivity.
The data on dependence TrsDtd show no indication
of the relaxation of hot charge carriers excited during
the two-photon processes: The dip is almost symmet-
ric and no features with a characteristic time differ-
ent from the pulse duration time are present. The re-
laxation time of nonthermalized carriers in solids is
expected to be in the range 0.1–10 ps.8 Most prob-
ably, the 0.1-ps boundary of this interval is relevant
to LiNbO3 crystals.
With the Kerr coefficients expected for lithium
niobate,13 the light-induced index changes cannot af-
fect the pump–probe transmission. The situation
should be different in the case of nonlinear wave mix-ing and grating recording. Since the TPA coefficients
of LiNbO3 are high, both absorption and index grat-
ings have to be involved in Bragg-diffraction pro-
cesses.
In conclusion, we have shown that TPA processes
strongly affect the propagation of subpicosecond light
pulses in lithium niobate crystals within the blue–
green spectral range. The measured TPA coefficient
is a strongly decreasing function of the wavelength,
and overlap of pump and probe pulses leads to de-
creasing probe transmission owing to combined TPA
transitions. This phenomenon is opposite to the effect
of increasing probe transmission owing to coherent
pump–probe interactions known in semiconductors.
Excitation of free carriers results in long-lasting light
absorption, and hot-carrier relaxation cannot be re-
solved on the scale of 10−13 s. Competition of TPA and
Kerr gratings is expected to be important for femto-
second holography phenomena.
Financial support from the Deutsche Telekom AG,
the Deutsche Forschungsgemeinschaft (award BU
913/13-1), and the National Science Foundation
(award EEC-9402726 and award INT-0233988) is
gratefully acknowledged. O. Beyer’s e-mail address is
beyer@physik.uni-bonn.de.
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Femtosecond time-resolved absorption processes in lithium niobate crystals

Infrared Holography for Optical Communications (SpringerVerlag,

Laser-Induced Dynamic Gratings (Springer-Verlag,

https://authors.library.caltech.edu/4291/1/BEYol05.pdf

Femtosecond time-resolved absorption processes in lithium niobate crystals

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