1214 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 25, NO. 13, JULY 1, 2013
A Novel Mode Multiplexer/Demultiplexer for
Multi-Core Fibers
Junhe Zhou and Philippe Gallion, Senior Member, IEEE
Abstract—In this letter, a mode multiplexer/demultiplexer
(MUX/DEMUX) for multi-core fibers (MCFs) based on multi-
mode interference (MMI) effect is proposed. Due to the coin-
cidence of the rows of the transfer matrix of an MMI coupler
and the modal profile of the MCFs with linearly aligned cores,
an MMI coupler with the aid of a phase shifter array is able
to distinguish different super-modes of the MCFs. The output
port number indicates the number of the super-modes inside the
MCFs. Detailed theoretical derivations and numerical simulations
are provided to demonstrate the multiplexing/demultiplexing
capability of the device. The proposed mode MUX/DEMUX can
be fiber based or waveguide based and is easy to be integrated
with the fiber system.
Index Terms—Multimode waveguides, mode division
multiplexing.
I. INTRODUCTION
M
ODE division multiple access (MDMA) has recently
attracted significant attention due to its higher trans-
mission capacity [1]–[3]. Theoretically speaking, the capacity
of the multimode transmission system is multiplied by the
number of the transmission modes as compared to its single
mode counterpart. One of the approaches to realize the multi-
mode transmission system is to use the MCFs [3]–[6], which
possess multiple cores for signal propagation.
Key devices to implement MCFs include the mode
MUXs/DEMUXs for MCFs. Free space optics can be used to
distinguish different modes [3]. However, it is of significant
complexity and expense, especially while detecting the higher
order modes. Another way to realize mode demultiplexing
is to use the phase matching concept [5]. Although it is
efficient and fiber based, the device is not straightforward to
design for MCFs with a large number of cores. One more
general method for MCF mode MUX/DEMUX design is to
use arrayed waveguide gratings (AWGs) [6]. The order of
the super-modes inside the MCF corresponds to the number
of the output port of the AWG. The pioneering proposal is
ground breaking, but it requires planar lightwave circuit (PLC)
technology to fabricate the AWG, which might not be easy
Manuscript received February 10, 2013; revised April 2, 2013; accepted
May 13, 2013. Date of publication May 16, 2013; date of current version
June 13, 2013. This work was supported in part by the National Science
Foundation of China under Grant 61201068 and in part by the Fundamental
Research Funds for the Central Universities of China.
J. Zhou is with the Department of Electronics Science and Engineering,
Tongji University, Shanghai 200092, China (e-mail: jhzhou@tongji.edu.cn).
P. Gallion is with TELECOM ParisTech, Ecole Nationale Supérieure
des Télécommunications, Paris 75013, France (e-mail: philippe.gallion@
telecom-paristech.fr).
Color versions of one or more of the figures in this letter are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LPT.2013.2263376
to be integrated with the fiber system [5]. Furthermore, the
interference of the field inside the AWG requires the wave
amplitudes at the input ports to be equal; however, the field
distribution of the super-modes inside the MCF fulfills the
sinusoidal function [7]. Therefore, the modal extinction ratio
for the AWG based MUXs/DEMUXs will be degraded if the
number of the cores is large.
An alternative way to achieve mode manipulation is to
use the MMI effect [8]–[13], which has been proposed to
generate [12] and convert [13] the modes in the multimode
waveguides. In this letter, we propose to realize the mode
MUXs/DEMUXs for MCFs using MMI couplers which are
made of fibers with rectangle cores or multimode waveguides
based on the PLC technology. It can be briefly described as
follows: the super-modes of the MCF are passed on to a MMI
coupler. The amplitudes of the waves in the cores of the MCF
fulfill sinusoidal function and their phases are changed by
a phase shifter array. The transfer matrix of the multimode
waveguide [9] is modified by those phase shifters and its
rows coincide with the amplitudes vectors of the super-modes
of the MCF. When a certain super-mode arrives, it is phase
shifted and passed on to the multimode waveguide, and the
corresponding output port of the transformer will output the
optical wave while other ports have no output at all. In this
way, the MUX/DEMUX is realized.
It is worth noting that this method can multiplex/de-
multiplex modes with different amplitude/phase distribution,
while polarization induced mode diversity is not considered
here. However, TM and TE modes MUX/DEMUX are already
discussed in the published literatures [14].
II. M
ATHEMATICAL DESCRIPTION
A. Super-Modes Inside the MCF
In this letter, it is assumed that the identical cores of the
MCF are linearly aligned and equally spaced [5], [6]. If a
single core is mono-mode, N − 1 coupled cores will have
N − 1 super-modes, whose amplitudes on each core fulfill [7]
sin
npπ
N
(1)
where n is the number of the super-mode, p the number of
the cores, and they are integers between 1 and N − 1. The
core diameter is assumed to be a, and the distance between
the core centers is assumed to be D.
B. MCF Mode MUX-DEMUX Based on MMI Couplers
Assuming that the cores of the MCF are connected with a
fiber with a rectangle core or a rectangle multimode waveguide
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