Optik
157
(2018)
675–683
Contents lists available at ScienceDirect
Optik
journal homepage:
www.elsevier.de/ijleo
Original
research
article
Focal
shift
of
radial
varying
polarized
Bessel-Gauss
beam
with
radial
phase
modulation
Bei
Wu
a
,
Xiangyu
Zeng
a
,
Yu
Miao
a
,
Yongtao
Fan
b
,
Xiumin
Gao
a,∗
,
Songlin
Zhuang
a
a
University
of
shanghai
for
Science
and
Technology,
Shanghai
200093,
China
b
Shanghai
Institute
of
Optics
and
Fine
Mechanics,
Shanghai
201800,
China
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
30
August
2017
Accepted
1
November
2017
Keywords:
Focusing
shift
Bessel-Gauss
beam
Vector
diffraction
theory
a
b
s
t
r
a
c
t
Focusing
shift
of
Bessel-Gauss
(BG)
beam
with
radial
varying
polarization
is
investigated
by
vector
diffraction
theory
in
this
article.
The
radial
phase
modulation
is
given
by
a
function
of
radial
direction
angle
and
m.
It
was
found
that
the
focal
shift
only
can
be
altered
considerably
by
the
phase
modulation
parameter
m,
and
the
focus
region
intensity
shape
is
variable
with
the
change
of
the
others
parameters
except
m,
turning
into
different
shapes
such
as
multiple
intensity
rings,
dark
hollow
focus
without
the
focus
shift.
There
is
an
interesting
phenomenon
that
the
focus
shifts
along
with
the
horizontal
axis
when
the
phase
modulation
parameter
m
is
changing,
and
the
shifts
distance
is
linearity
to
the
variation
of
the
phase
modulation
parameter
m.
©
2017
Elsevier
GmbH.
All
rights
reserved.
1.
Introduction
It
is
known
that
Bessel-Gauss
(BG)
beams
provide
valid
solutions
to
Helmholtz
equation,
having
attracted
many
researchers
to
study
it’s
properties
[1–7]
for
their
non-diffracting
characteritics,
and
BG
beams
represent
a
class
of
solu-
tions
to
the
Helmholtz
equationhave
been
researched
extensively,
especially
which
had
been
modulated
by
some
kinds
of
polarization
parameters
or
beam
parameters
[8].
The
distribution
in
focal
region
plays
a
crucial
role
in
many
optical
systems
[9–14].
Such
as,
in
optical
trapping
system,
the
particle
would
be
forced
by
two
kinds
of
forces,
one
is
the
optical
gradient
force,
the
other
kind
of
force
is
scattering
force.Two
kinds
of
forces
both
have
complex
forms,
because
the
two
forces
are
not
only
related
to
the
optical
intensity,
but
also
the
properties
of
the
trapped
particles
[15].
According
to
this
phenomenon,
a
particle
may
be
transported
from
one
poit
to
another
point
by
controlling
the
optical
intensity
distribution
in
focal
region,
which
had
been
known
as
optical
trap
[8].
In
addition
to
this,
the
focusing
properties
of
BG
beams
had
been
widely
investigated,especially
the
focusing
shift
of
various
laser
beams
have
been
an
interesting
and
practical
topic,
and
many
researchers
had
been
tracing
the
movement
of
the
point
of
absolute
maximum
intensity
along
optical
axis
for
several
decades
[16–20].
Gao,
Li,
Dong
et.
al
[21–28]
have
done
so
much
going
and
painstaking
studying
on
the
focus
shifts
properties,
such
as
the
focal
shift
of
radially
polarized
Bessel-
modulated
Gaussian
beam
by
phase
shifting.
Li.etal
have
studied
the
focal
shift
by
radial
cosine
phase
masks.Further
more,
the
focal
shift
with
rotational
tunable
phase
also
be
researched.
In
addition
to
theses,
the
focus
shifting
with
three-portion
concentric
piecewise
cylindrical
vector
beam,
and
with
apodized
truncated
hyperbolic-cosine-Gaussian
beam
figured
out
∗
Corresponding
author.
E-mail
address:
gxm@usst.edu.cn
(X.
Gao).
https://doi.org/10.1016/j.ijleo.2017.11.005
0030-4026/©
2017
Elsevier
GmbH.
All
rights
reserved.