Optically trapping Rayleigh particles by using
focused partially coherent multi-rotating
elliptical Gaussian beams
Xi Peng (彭 喜)
1,2
, Chidao Chen (陈迟到)
1,2
, Bo Chen (陈 波)
1,2
, Yulian Peng (彭玉莲)
1,2
,
Meiling Zhou (周美玲)
1,2
, Xiangbo Yang (杨湘波)
1
, and Dongmei Deng (邓冬梅)
1,2,
*
1
Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices,
South China Normal University, Guangzhou 510631, China
2
CAS Key Laboratory of Geospace Environment, University of Science & Technology of China,
Chinese Academy of Sciences, Hefei 230026, China
*Corresponding author: dmdeng@263.net
Received June 23, 2015; accepted November 6, 2015; posted online December 18, 2015
By investigating the cross-spectral density of partially coherent multi-rotating elliptical Gaussian beams
(REGBs) that propagate through a focusing optical system, we obtain the radiation force on a Rayleigh particle.
The radiation force distribution is studied under different beam indexes, coherence widths, and elliptical ratios of
the partially coherent multi REGBs. The transverse and the longitudinal trapping ranges can increase at the
focal plane by increasing the beam index or decreasing the coherence width. The range of the trapped particle
radii increases as the elliptical ratio increases. Furthermore, we analyze the trapping stability.
OCIS codes: 140.3295, 140.7010, 350.5500.
doi: 10.3788/COL201614.011405.
In recent years, light beams with rotating characteristics
have attracted quite a lot of interest due to their peculiar
properties, which present opportunities for research in the
fields of science and technology
[1–5]
. For example, the abil-
ity of rotating beams to rotate particles provides a new
degree of control for micrometer-sized particles, and has
important applications in optical manipulating and bio-
logical specimens rotating. In optics, a more general form
of rotating elliptical Gaussian beams (REGBs) are thor-
oughly studied
[1,5–9]
. REGBs, which have an elliptical light
spot and whose phase front rotates along the propagating
axis of the beam, are obtained from an ordinary Gaussian
beam
[7]
.
Ashkin and colleagues demonstrated radiation pressure-
trapping particles
[10–12]
in a series of pioneering Letters,
through which the “optical trap” came to be known.
The optical force has traditionally been decomposed into
two components: one is the scattering force, which is in
the direction of the light propagation, and the other is
the gradient force, which is in the direction of the spatial
light gradient
[13]
. Optical trapping and manipulation of
micrometer-sized particles produced by piconewton-level
forces while simultaneously measuring displacement with
nanometer-level precision have attracted a very wide range
of attention
[14–18]
. Since their invention, optical trapping
techniques continue to improve and become better
established, and have emerged as a powerful tool with
broad-reaching applications in physics and life sciences re-
search
[19,20]
. Today, many researchers report optical trap-
ping produced by beams such as Gaussian Schell model
beams
[21]
, Laguerre–Gaussian beams
[22]
, highly focused
Lorentz–Gaussian beams
[23]
, and highly focused, elegant
Hermite-cosine-Gaussian beams
[24]
. In most studies, the in-
cident light beams for optical traps are assumed to be fully
coherent
[21–24]
. As we know, any laser field is always partially
coherent in practice
[25–28]
. In this Letter, the cross-spectral
density (CSD) of partially coherent multi-REGBs propa-
gating through a focusing optical syste m is derived and
used to investigate the radiation forces on a Rayleigh par-
ticle. Compared to the work in Ref. [
16], the radiation force
of the partially coherent multi-REGBs can rotate. To trap
oval particles, we can adjust the sizes of the forces in some
directions by changing the elliptical ratio of the elliptical
beams, which ordinary Gaussian beams cannot do. Fur-
thermore, the trapping stability conditions are analyzed.
Under the free-space rectangular coordinates system,
the electric field of the REGB in the z ¼ 0 plane can be
expressed as
[1,5]
E
0
ðx
0
; y
0
Þ¼A
0
exp
−
x
02
w
2
x
þ
y
02
w
2
y
þ
ix
0
y
0
R
0
; (1)
where A
0
is the constant complex amplitude of E
0
, w
x
and
w
y
are the initial beam widths on the x- and y-axes, respec-
tively, and R
0
specifies the beam rotation. Without loss of
generality, the spectral degree of coherence is given by
[29]
gðr
0
1
− r
0
2
Þ¼exp
−
ðr
0
1
− r
0
2
Þ
2
δ
2
; (2)
where r
0
1
ðx
0
1
; y
0
1
Þ and r
0
2
ðx
0
2
; y
0
2
Þ are the original position
vectors, and δ is the coherence length. By taking all of
the above assumptions into consideration, the CSD of the
partially coherent multi-REGBs of the source plane can be
written in the Cartesian coordinates as
[25]
COL 14(1), 011405(2016) CHINESE OPTICS LETTERS January 10, 2016
1671-7694/2016/011405(5) 011405-1 © 2016 Chinese Optics Letters