COL 10(10), 101902(2012) CHINESE OPTICS LETTERS October 10, 2012
Modeling and identification on nonlinear saturable and
reverse-saturable absorptions of gold nanorods using
femtosecond Z-scan technique
Rui Wang (
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1
, Yingshuai Wang (
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1
, Dan’ao Han (
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, Chuantao Zheng (
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1
,
Jiyan Leng (
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2
, and Han Yang (
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)
1∗
1
State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering,
Jilin University, Changchun 130012, China
2
First Hospital of Jilin University, Changchun 130021, China
∗
Corresponding author: Yanghan@jlu.edu.cn
Received March 5, 2012; accepted April 13, 2012; posted online August 3, 2012
An improved Z-scan analysis approach is proposed by establishing and solving the saturable absorption
(SA) and reverse-SA (RSA) models, respectively. Near-infrared femtosecond Z-scans are carried out on
the synthesized gold nanorods (NRs) possessing the average length of 46 nm using a femtosecond laser
operated at the wavelength of 800 nm, which is close to the peak position of longitudinal surface plasmon
resonance (SPR) (710 nm) of gold NRs. At lower input intensity of less than 400 GW/cm
2
, the normalized
transmission exhibits only SA phenomenon; however, when it exceeds 400 GW/cm
2
, both SA and RSA
are observed. By using the presented Z -scan modeling and theory, the three-photon absorption (3PA) is
identified in the material, and the 3PA cross-section is determined to be 1.58×10
−71
cm
6
s
2
.
OCIS codes: 190.0190, 190.4400.
doi: 10.3788/COL201210.101902.
Generally speaking, nonlinear absorption, which includes
saturable absorption (SA), re verse-SA (RSA), multi-
photon absorption (MPA), and free carrier absorption
(FCA), possess e s various applications
[1−3]
. For exam-
ple, SA materials are applied extensively in laser pulse
compression
[4]
, and optical bistability, among others,
whereas RSA, 2PA, and MPA materials are applied in
two-photon fluorescence microscopy and imaging
[5−7]
,
3D optical storage , microfabrication
[8−10]
, up-conversion
lasing
[11−13]
, and optical limiting
[14]
. Therefore, identify-
ing different nonlinear absorptio n process e s is important,
especially for the acquisition of c orresponding nonlinear
absorption parameters, such as the saturable intensity for
saturable absorber, 2PA cross-section for 2PA material,
and MPA coefficient for MPA material.
The Z-scan technique, which was first proposed by
Sheik-Bahae et al.
[15]
, was widely used for characteriz-
ing the optical nonlinearities of a sa mple with simple ap-
paratus, a s well as relatively high sensitivity. In Ref.
[15], 2PA was analyzed as an example, where the nor-
malized energy transmittance was expressed as a sum-
mation of numeric al evaluations, thereby obtaining the
2PA coe fficient . With the re search of diverse ma terials,
other nonlinear and simultaneously appearing absorption
processes have bee n observed from open aperture (OA)
Z-scan traces
[16−19]
. Therefore, distinguishing the non-
linear absorption effects and ac quiring the related non-
linear parameters for the materials possessing more than
one nonlinear absorption effect are important.
Consequently, in this letter, we establish an improved
Z-scan technique model for charactering a nonlinear, op-
tical, and thin absorber with SA, RSA (including 2PA,
3PA, and other MPA), or both processes. We divide
the absorption term into two parts, SA and RSA, and
the solution of each pheno menon is derived individually.
First, for SA, by using the similar main principle Gu
et al.
[20]
, the computational difficulty is reduced by uti-
lizing the improved Adomian operator. The first seven
terms of normalized transmittance polynomial are iden-
tified, which are sufficient for characterizing the com-
plicated nonlinear absorption process. After acquiring
the saturable intensity from the first step, the numerical
expression of RSA cross-section is achieved through the
analytical polynomial expressions of reverse-saturable Z-
scan trace
[21]
. Gold nanorods (NRs)
[22−24]
are utilized as
the sample due to their complicated nonlinear absorption
process. By using the proposed SA and RSA models and
their related solutions, the nonlinear a bsorption parame-
ters are determined by best fitting the theor e tical curve
(represented by nonlinear absorption par ameters) to the
exp erimental data. To the best of our knowledge, we are
the first to present a quantitative analysis of the non-
linear absorption process of gold NRs, although similar
material regarding this phenomenon has been reported
previously
[25]
. The good agreement between the theo-
retical curve and the experimental results verify that our
modeling and solutions can efficiently identify and evalu-
ate both s aturable intensity a nd MPA coefficie nts, which
can also be adapted to the OA Z-scam analysis on other
SA or RSA materials.
Considering the beam propagation in a thin nonlinear
absorber, the optical intensity lo ss is governed by
dI
dz
′
= −α (I) I, (1)
where z
′
and I are the propagation distance and optical
intensity inside the nonlinear sample, respectively, and
α (I) is the abs orption coefficient dependent on the in-
tensity. Supposing that both SA and RSA exist simulta-
1671-7694/2012/101902(5) 101902-1
c
2012 Chinese Optics Letters