January 10, 2010 / Vol. 8, No. 1 / CHINESE OPTICS LETTERS 93
Quantitative deviation of the two-photon absorption
coefficient based on three laser pulse models
Peide Zhao (ëëë)
∗
, Yong Zhang (ÜÜÜ ]]]), Wenxia Bao (©©©___), Zhongya Zhang (ÜÜܧ§§æææ),
Dayun Wang (), Ming Liu (444 µµµ), and Zhidong Zhang (ÜÜÜÀÀÀ)
Scho ol of Science, Hebei University of Technology, Tianjin 300130, China
∗
E-mail: pdzhao@eyou.com
Received February 23, 2009
The pulse profile influence of excitation light on the two-photon absorption coefficient β is theoretically
and numerically studied. Based on Gaussian spatial and temporal laser, we obtain an expansion formula
of energy transmission. As compared with a plain beam and a pulse beam that is rectangular in time but
Gaussian in space, the relative deviations of β turn out to be about 214% and 47%, respectively. These
differences indicate that a smaller β may be obtained than the real one in usual nonlinear transmission.
Our result suggests that by taking real pulse profile into account, a more exact β can be derived in energy
transmission measurement.
OCIS co des: 190.4710, 020.4180, 140.3538, 160.4330.
doi: 10.3788/COL20100801.0093.
The two-photon-induced behavior of organic materials
has received increasing attention in recent years due
to its applications in two-photon fluorescent microscopy
and imaging
[1−3]
, optical limiting of two-photon absorp-
tion (TPA)
[4−9]
, three-dimensional (3D) optical data
storage
[10−12]
, fabrication of photonic crystal
[13]
, and
two-photon photodynamic therapy
[14,15]
. The wave-
length used for two-photon excitation is roughly twice
that for one-photon excitation, so the influences of scat-
tering on the beam intensity (1/λ
4
) and photodamage
to a healthy tissue can be greatly reduced. In the usual
TPA process, ultra-short pulse lasers are often used as the
two-photon excitation source because of their high peak
power, which gives rise to the high transition probability
of TPA with a comparatively small average power
[1,16]
.
The material properties of TPA can be described partly
but very importantly by the TPA cross-section of a
molecule (σ
2
). Therefore, a lot of efforts
[17−37]
have been
exerted to examine it experimentally and theoretically.
There are many methods, such as nonlinear transmission,
Z-scan, and two-photon-induced fluorescent comparison,
to obtain molecular absorption cross-section experimen-
tally. In these measurements, nonlinear energy transmis-
sion is often performed mainly for its easier setup.
Boggess et al.
[4,38]
presented the experimental princi-
ple of nonlinear transmission. According to the principle
of the TPA process, the beam intensity change along the
propagation direction (z axis) can be described as
dI/d z + αI + βI
2
= 0, (1)
where α is the attenuation coefficient due to linear ab-
sorption and scattering, and β is the nonlinear absorp-
tion coefficient due to TPA. The excitation irradiance I
= I(r, z, t) is a function of time t and the transverse
position r as well as z.
Assume that there is a uniform transverse intensity dis-
tribution in the beam section, one of which is a plain
beam; for example, in the case of αz ¿ 1, the transmis-
sion solution of Eq. (1) is
[39]
T (z) = I(z)/I(0) =
e
−αz
1 + βzI
0
=
T
lin
1 + βzI
0
= T
lin
· T
p
nonlin
, (2)
where
T
p
nonlin
=
1
1 + βzI
0
, (3)
I
0
= I(0) is the initial intensity, T
lin
is the linear trans-
mittivity independent of I
0
, and T
p
nonlin
is the nonlinear
transmission dependent on I
0
.
A focused pulse laser is more frequently used to reach
a high-intensity level for nonlinear absorption measure-
ments. In this case, a Gaussian transverse distribution
in the nonlinear medium can b e assumed, and Eq. (3)
should be modified. For a pulse laser that is rectangular
in time but Gaussian in space, Eq. (3) can be rewritten
as
[4]
T
G
nonlin
=
ln(1 + βzI
0
)
βzI
0
. (4)
Based on Eq. (4), the frequency-dependent TPA
coefficient β (in units of cm/GW) of the sample can
be determined by measuring the nonlinear transmissivity
T
G
nonlin
for a given input intensity I
0
and a given sample
thickness z = L.
Equation (4) is often used as the basic formula to ob-
tain the TPA coefficient of some materials in nonlinear
transmission measurements. However, to enhance non-
linear absorption, ultra-short pulse lasers are often used
nowadays as the excitation sources. In this situation, the
temporal profile of a real laser pulse is usually not rect-
angular. On the other hand, Oulianov et al.
[40]
indicate
that under certain conditions, the nonlinear transmission
method, without consideration of other nonlinear effects,
results in erroneous values for the TPA cross-sections.
1671-7694/2010/010093-06
c
° 2010 Chinese Optics Letters
资源评论
weixin_38558186
- 粉丝: 4
- 资源: 878
最新资源
- 基于RedisSpider分布式爬虫实现高分项目+详细文档+全部资料.zip
- 基于scrapy的大规模定向爬虫高分项目+详细文档+全部资料.zip
- 基于scrapy的爬虫，抓取新华财经文章存入ES做为语料高分项目+详细文档+全部资料.zip
- 基于scrapy框架的爬虫，用以爬取中药材和中西成药的信息高分项目+详细文档+全部资料.zip
- 基于SSM+maven+httpClient+jsoup实现的java爬虫项目，一个完整的小说网站高分项目+详细文档+全部资料.zip
- 基于Scrapy爬虫获取相关旅游信息，并将数据可视化此项目为出游选择目的地提供解决方案高分项目+详细文档+全部资料.zip
- 基于WebMagic的b站视频爬虫高分项目+详细文档+全部资料.zip
- Lecture 9-August 30 (Tutorial).pptx
- 焊接相关国内外标准汇编.pdf
- Lecture 10-August 31.pptx
- Web网页设计期末大作业（完美大作业）.zip
- 基于WebMagic封装的垂直爬虫高分项目+详细文档+全部资料.zip
- 基于Winform的一套商家管理工具，用来练习界面布局，自动更新，事件，异步，多线程，网络请求，缓存使用，任务存储，设计模式，爬虫流程，反爬虫机制等高分项目+详细文档+全部资料.zip
- 基于爬虫和文本挖掘技术对知乎上的主题进行分析高分项目+详细文档+全部资料.zip
- 基于豆瓣电影的爬虫实例高分项目+详细文档+全部资料.zip
- 基于若依的爬虫百度云爬虫高分项目+详细文档+全部资料.zip
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
