Numerical simulation of the energy distribution
characteristics in the far-field of the single-mode
annular core optical fibers
Xiangyun Hui, Kailiang Duan
*
State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of
Sciences, Xi'an 710119, China
Abstract— the far-field intensity distribution characteristics of
fundamental mode of the annular core optical fibers (ACF) are
calculated theoretically based on the weak waveguide
approximation in this paper. The simulation results demonstrate
that provided the parameters of the ACF are designed properly,
the ACF can realize single-mode operation. Besides, the beam
will concentrate to the principal maximum position to form a
central bright spot indicating great enhancement for the energy
focusability of beam, which is valuable for the energy-demand
applications in the far-field. These theoretical results possess
great significance in designing and manufacturing ACF.
Key words: annular core optical fibers, far-field, energy
distribution
I. Introduction
Fiber lasers have attracted a great deal of attentions owing
to their merit of compact configuration, high efficiency, good
heat dispersion, and high beam quality [1]. High power fiber
lasers have already been widely used in the fields of military,
industry, iatrology, and so on [2]. An indicator, namely energy
focusability, is usually employed to characterize the far-field
beam quality quantitatively [3-4]. In order to increase the
energy focusablity, fibers with various new forms of
geometrical cross-sections have been designed in the past
decades, such as elliptical, rectangular, triangular, parabolic
cylindrical, polygonal [5], among which the annular core
optical fiber (ACF) is of increasing interest recently. As shown
in Fig. 1, the ACF is composed of a guiding section (fiber core)
with a high-refractive index and two non-guiding sections
(inner cladding and outer cladding) with a low-refractive index.
This special configuration endues ACF with practical
advantages over conventional double cladding fiber, such as
greater energy, larger mode area and more controllable
parameters. In addition, the non-linear effects of ACF can be
suppressed effectively bearing great advantages in single mode
operation in low dispersion. Choudhury et al. analyzed the
relative power distributions in the different sections of a step-
index plastic clad annular core optical fiber [6]. Lessard et al.
theoretically analyzed the power transmission characteristics of
lower and higher modes in ACF [7]. Sarkar et al. studied the
relationships of the cut-off condition to the radius and
refractive index difference of the ACF [8].
However, all the investigations mentioned above focused
on the characteristics of light wave inside the ACF and the
potentials applications in optical sensing and communications,
and to our best knowledge, there is no paper about the
requirements of the ACF to realize single-mode operation, and
the diffractive feature of light wave emitted from ACF up to
now.
In this paper, we have demonstrated the parameters design
of ACF, including the refractive index difference and fiber
geometrical sizes, to realize single-mode operation.
Furthermore, we have also given the energy distribution
characteristics of light wave emitted from ACF, and discussed
the beam quality in the far-field. And by our design parameters,
the energy could be centralized at a bright spot which greatly
improves the beam quality. These results can provide a
theoretical guidance for the design and manufacture of ACF on
the communication and energy demanding applications.
II. THEORETICAL MODEL
The configuration of the ACF is schematically shown in
Figure. 1, where r
1
and r
2
are the radii of the inner cladding and
fiber core, respectively. The refractive indices of the inner and
outer cladding are in the same value of n
1
and n
2
for the fiber
core satisfying n
1
<n
2
and the weak guidance approximation
(n
2
-n
1
)/n
2
<<n
2
. We neglect the fiber loss due to the isotropy of
the ACF and employ the cylindrical coordinate system(r,
M
, z)
in calculation for convenience.
Figure 1. Cross-section view of an annular core optical fiber
In the cylindrical coordinate system, the scalar fields in
the three sections of the ACF can be described by the linear
combination of Bessel and modified Bessel functions as [5]
Supported by the National Natural Science Foundation of China
(No.61138007))
1932
978-1-4577-1415-3/12/$26.00 ©2012 IEEE