Scintillations of optical vortex in randomly
inhomogeneous medium
Valerii P. Aksenov* and Valeriy V. Kolosov
V. E. Zuev Institute of Atmospheric Optics, Russian Academy of Sciences,
Siberian Branch 1 Academician Zuev Square, Tomsk 634021, Russia
*Corresponding author: avp@iao.ru
Received October 8, 2014; revised January 13, 2015; accepted January 28, 2015;
posted January 28, 2015 (Doc. ID 224153); published March 17, 2015
The comparative numerical and analytical analysis of scintillation indices of the vortex Laguerre–Gaussian beam
and the nonvortex doughnut hole and Gaussian beams propagating in the randomly inhomogeneous atmosphere
has been performed. It has been found that the dependence of the scintillation index at the axis of the optical vortex
on the turbulence intensity at the path has the form of a unit step. It has been shown that the behavior of scin-
tillations in the cross sections of vortex and nonvortex beams differs widely. Despite the scintillation index of
vortex beams has been calculated only for the simplest LG
1
0
mode, the obtained results are quite general, because
they demonstrate the main properties inherent in scintillations of vortex beams of any type. © 2015 Chinese
Laser Press
OCIS codes: (010.1300) Atmospheric propagation; (010.1330) Atmospheric turbulence; (030.1640)
Coherence; (050.4865) Optical vortices; (260.6042) Singular optics; (030.6140) Speckle.
http://dx.doi.org/10.1364/PRJ.3.000044
Laser beams having the orbital angular momentum (OAM)
[
1–3] attract recently great attention owing to their particular
properties, which have found numerous applications [
4–6].
Due to the presence of the transverse circulation component
of the Pointing vector [
1], such beams are referred to as
optical vortices. In particular, the possibility of using optical
vortices for information coding and transmission is studied
intensely [
7,8]. For optical communication systems, it is
necessary to study the influence of a medium on the optical
vortex propagation. It is known that the medium through
which the beam propagates distorts the beam. Beam wander-
ing and fluctuations of the beam intensity are the main factors
restricting the data throughput of optical systems for data
transmission along horizontal and slant paths; in particular,
Earth–space paths. Intensity fluctuations of Gaussian laser
beams in the turbulent atmosphere are studied quite thor-
oughly now.
To describe fluctuation characteristics of these beams,
numerical and analytical methods have been developed [
9].
A common feature of an optical vortex in the free space is that
the beam structure includes the helical phase distribution and
zero intensity at the beam axis [
10]. For an analytical descrip-
tion of the propagation of laser beams under conditions of
weak atmospheric turbulence, the Rytov method is used most
often [
9]. It was shown in [11,12] that the direct application of
the Rytov method for description of vortex beams gives rise to
serious problems, because the intensity at the axis of the beam
propagating in the undisturbed medium becomes zero. The
numerical simulation of laser beam propagation is usually
based on the Monte Carlo technique with the use of phase
screens [
13]. However, the numerically calculated values of
intensity fluctuations of vortex beams do not allow us to judge
unambiguously the influence of the energy circulation in the
beam on the intensity fluctuations in the beam cross section.
Thus, it follows from the results of [
14] that intensity fluc-
tuations in the Laguerre–Gaussian beam differ only slightly
from intensity fluctuations in the Gaussian beam. The similar
conclusion, except for some details, can also be drawn from
[
15]. From [16,17], it follows that under conditions of weak
turbulence the intensity fluctuations of laser beam close to
the Laguerre–Gaussian one appear to be much stronger than
those of the Gaussian beam. In [
18], the intensity fluctuations
of the vortex Bessel beam behave qualitatively in the same
manner as the fluctuations of the Bessel beam having no vor-
tex properties, but their scintillation index appears to be
higher. The results [
14–18] were obtained with computational
grids having different dimensions and at the different number
of realizations used for the calculation of the scintillation
index. To draw an unambiguous conclusion about the depend-
ence of the scintillation level on the beam type, we perform
the numerical simulation of the propagation of different types
of beams: Gaussian beam, Laguerre–Gaussian beam LG
1
0
, and
doughnut hole (DH) beam in the turbulent atmosphere [
19].
Then the numerical results are compared with the asymptotic
estimation of scintillation at the beam axis.
We use the following representation of the complex ampli-
tude of the field in the initial plane (z 0)
ur; φ; 0
4
a
Φ
c
r
2
p
r
a
p
exp
−
r
2
a
2
expfilϕg; (1)
where fr; φ;zg are cylindrical coordinates, Φ is the total
energy flux, a is the initial radius of the Gaussian source,
and c is the speed of light. If we take p 1 and l 1, then
Eq. (
1) describes the circular mode of the Laguerre–Gaussian
beam LG
1
0
.Ifp 1 and l 0, then Eq. (1) corresponds to the
44 Photon. Res. / Vol. 3, No. 2 / April 2015 V. P. Aksenov and V. V. Kolosov
2327-9125/15/020044-04 © 2015 Chinese Laser Press