Optik
155
(2018)
97–104
Contents lists available at
ScienceDirect
Optik
journal homepage: www.elsevier.de/ijleo
Full
length
article
Study
on
spatiotemporal
evolution
of
chirped
femtosecond
laser
pulses
at
specific
spatial
position
during
small-scale
self-focusing
Yangbao
Deng
a,∗
,
Shuguang
Deng
a,∗
,
Chao
Tan
b
,
Cuixiu
Xiong
a
,
Guangfu
Zhang
a
,
Ye
Tian
a
a
College
of
information
and
Electronic
Engineering,
Hunan
City
University,
Yiyang
413002,
People’s
Republic
of
China
b
School
of
Information
and
Electrical
Engineering,
Hunan
University
of
Science
and
Technology,
Xiangtan
411201,
People’s
Republic
of
China
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
17
October
2017
Accepted
23
October
2017
Keywords:
Spatiotemporal
evolution
Chirped
femtosecond
laser
pulses
Small-scale
self-focusing
Spatiotemporal
coupling
effect
a
b
s
t
r
a
c
t
We
experimentally
study
the
spatiotemporal
evolution
of
chirped
femtosecond
laser
pulses
at
a
specific
spatial
position,
such
as
the
modulation
peak
position
(MPP),
during
small-
scale
self-focusing
(SSSF).
It
is
found
that
the
spatial
peak
intensity
at
the
MPP
increases
rapidly
initially
with
increment
of
input
power
due
to
the
effect
of
SSSF,
however
it
becomes
saturated
at
the
higher
power
because
the
finite
energy
of
the
beam
restraints
increasing
of
the
peak
intensity
at
the
MPP.
The
pulse
width
at
the
MPP
is
compressed
gradually
with
rising
power
owing
to
the
spatiotemporal
coupling
effect,
which
will
reach
the
narrowest
when
the
spatial
peak
intensity
at
the
MPP
reaches
the
maximum.
Further,
the
influence
of
chirp
on
the
pulse
width
evolution
at
the
MPP
is
discussed
theoretically.
We
find
that
the
negative
chirp
accelerates
the
pulse
width
compression
because
the
negative
chirp
enhances
the
process
of
SSSF,
but
the
positive
chirp
is
counterproductive.
Our
results
may
provide
some
helps
for
propagation
and
amplification
of
broadband
laser
pulses.
©
2017
Elsevier
GmbH.
All
rights
reserved.
1.
Introduction
Nowadays,
Ultrashort-Pulse
Laser
is
used
by
the
mode-lock
technology,
while
amplification
of
ultrashort
laser
pulses
is
usually
based
on
the
chirped
pulse
amplification
technology
[1],
thus
propagation
of
laser
pulses
is
related
to
chirp
in
these
technologies.
In
fact,
the
ultrashort
laser
pulses
output
from
the
solid
state
laser
system
are
often
chirped
pulses,
which
have
an
extensive
application
in
many
fields,
such
as
population
inversion,
pump-probe
spectroscopy,
Raman
spectroscopy
and
high-order
harmonic
generation
[2–6].
Chirp
as
an
important
parameter
can
be
used
to
manipulate
laser
pulses
[7–16],
therefore
many
researchers
have
focused
on
the
influence
of
chirp
on
the
propagation
characteristics
of
laser
pulses.
For
example,
the
initial
chirp
has
an
effect
on
the
formation
of
soliton
during
nonlinear
propagation
[10].
When
the
chirp
is
relatively
large,
the
effect
of
second-order
polarization
mode
dispersion
depended
on
chirp
will
affect
the
propagation
characteristics
of
laser
pulses
and
degrade
the
system
performance
[11].
When
the
chirped
pulses
propagate
in
an
optical
fiber,
the
initial
chirp
not
only
adjusts
and
controls
the
magnitude
of
pulse
broadening,
but
also
affects
the
shape
of
broadened
∗
Corresponding
authors.
E-mail
addresses:
dyb5202008@aliyun.com
(Y.
Deng),
shuguangdeng@163.com
(S.
Deng).
https://doi.org/10.1016/j.ijleo.2017.10.112
0030-4026/©
2017
Elsevier
GmbH.
All
rights
reserved.