Technological University Dublin Technological University Dublin
ARROW@TU Dublin ARROW@TU Dublin
Articles School of Electrical and Electronic Engineering
2008-01-01
Investigation on Singlemode-multimode-singlemode Fiber Investigation on Singlemode-multimode-singlemode Fiber
Structure Structure
Qian Wang
Gerald Farrell
Technological University Dublin
, gerald.farrell@tudublin.ie
W. Yan
Follow this and additional works at: https://arrow.tudublin.ie/engscheceart
Part of the Electrical and Computer Engineering Commons
Recommended Citation Recommended Citation
Wang, Q., Farrell, G., Yan, W.: Investigation on singlemode-multimode-singlemode <ber structure.
IEEE
Journal of Lightwave Technology
, 2008, Vol.26, no. 5, pp.512-519. doi:10.1109/JLT.2007.915205
This Article is brought to you for free and open access by
the School of Electrical and Electronic Engineering at
ARROW@TU Dublin. It has been accepted for inclusion in
Articles by an authorized administrator of ARROW@TU
Dublin. For more information, please contact
arrow.admin@tudublin.ie, aisling.coyne@tudublin.ie.
This work is licensed under a Creative Commons
Attribution-Noncommercial-Share Alike 4.0 License
512 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 5, MARCH 1, 2008
Investigation on Single-Mode–Multimode–
Single-Mode Fiber Structure
Qian Wang, Gerald Farrell, and Wei Yan
Abstract—This paper presents an investigation on a single-
mode–multimode–single-mode fiber structure. A one-way
guided-mode propagation analysis for the circular symmetry
waveguide is employed to model the light propagation and the
approximated formulations are derived and evaluated concerning
the accuracy. Phase conjunction of the multimode interference
within the fiber structure is revealed. A simple way to predict and
analyze the spectral response of the structure is presented through
the space to wavelength mapping with the derived approximated
formulations. The prediction of spectral response is verified
numerically and experimentally.
Index Terms—Fiber optics, multimode interference.
I. INTRODUCTION
T
HE multimode interference (MMI) in a planar waveguide
has been intensively investigated and the self-imaging of
the input light field is well known and widely employed in de-
veloping beam splitters, combiners and multiplexers for optical
communications [1]–[3]. Recently, the multimode interference
occurring in a single-mode–multimode–single-mode (SMS)
fiber structure (or single-mode–multimode fiber structure) has
also been studied and developed to act as novel optical devices,
e.g., a displacement sensor, a fiber lens, a refractometer sensor,
an edge filter for wavelength measurements, and a bandpass
filter [4]–[8]. These optical devices based on an SMS fiber
structure offer all-fiber solutions for optical communications
and optical sensing with the advantages of ease of packaging
and connection to optical fiber system.
[4] and [5] investigated the single-mode–multimode fiber
structure with an emphasis on the light propagation perfor-
mance in the free-space after it comes out of the multimode
fiber end. In [5], the guided-mode propagation analysis is used
and an analytic expression of re-imaging distance was derived.
[6] and [7] employed a numerical beam propagation method
and through scanning the length of the multimode fiber section
found a suitable value for desired applications. [8] demon-
strated experimentally a bandpass filter based on the SMS
Manuscript received May 30, 2007; revised September 24, 2007. This work
was supported by the Irish Research Council for Science, Engineering and Tech-
nology (IRCSET).
Q. Wang was with the Applied Optoelectronics Centre, School of Electronics
and Communications Engineering, Dublin Institute of Technology, Dublin 8,
Ireland. He is now with the Data Storage Institute, Singapore 117608, Singapore
(e-mail: qian.wang@osa.org).
G. Farrell and W. Yan are with the Applied Optoelectronics Centre, School of
Electronics and Communications Engineering, Dublin Institute of Technology,
Dublin 8, Ireland (e-mail: Gerald.farrell@dit.ie).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2007.915205
fiber structure. In this paper, we present an investigation on the
modeling of light propagation within the SMS fiber structure
and an analysis of the multimode interference and the spectral
response of the structure, which have not been addressed in
the literature. There is another type of SMS fiber structure,
of which the multimode fiber has a gradient index profile and
no multimode interference occurs while the light propagates
along the fiber structure [9]. In the present paper, the SMS fiber
structure with a step-index multimode fiber is considered and
the related multimode interference is investigated.
Section II investigates the modeling of light propagation
within the SMS fiber structure. Based on the numerical calcu-
lation and experimental measurement, the reflection occurring
at the interface between the single-mode fiber and multimode
fiber (MMF) due to the mismatch of refractive index is found
to be very small and can be neglected in practice. Therefore, a
one-way guided-mode propagation analysis for the calculation
of light propagation within the multimode fiber section and
the calculation of coupling loss of the SMS fiber structure are
presented. With an approximation to the eigenmode propa-
gation constants of the MMF, the approximated guided-wave
propagation analysis is derived and evaluated concerning the
accuracy issue.
The characteristics of the multimode interference and the
spectral response of the SMS structure are investigated in
Section III. First, the phase conjugate characteristic of the light
field about the half imaging distance
is revealed. Second,
a simple method is presented to predict the spectral response of
the fiber structure without scanning the wavelength. With this
simple method, it can be easily seen this SMS fiber structure
can act as an edge filter at
and or a bandpass filter
at
according to the relationship between the length of MMF
and transmission. All these analysis and predictions are verified
numerically and experimentally.
Conclusions are presented in Section IV.
II.
MODELING OF LIGHT
PROPAGATION IN
THE SMS STRUCTURE
A. modeling With the Guided-Mode Propagation Analysis
The single-mode–multimode–single-mode fiber structure is
presented schematically in Fig. 1. The multimode fiber section
has a step-index profile. The single-mode and multimode fibers
are assumed to be aligned along the same axis, i.e., there is no
offset between the single-mode and multimode fibers at the two
interfaces.
There is usually a mismatch of the refractive index between
the single-mode and multimode fibers, which can cause a re-
flection at the interface as shown in Fig. 1. To find out the re-
0733-8724/$25.00 © 2008 IEEE
Authorized licensed use limited to: DUBLIN INSTITUTE OF TECHNOLOGY. Downloaded on March 19, 2009 at 07:47 from IEEE Xplore. Restrictions apply.
WANG et al.: INVESTIGATION ON SINGLE-MODE–MULTIMODE–SINGLE-MODE FIBER STRUCTURE 513
Fig. 1. Schematic configuration of the single-mode–multimode–single-mode
fiber structure.
Fig. 2. Light propagation within the multimode fiber calculated by (3).
flectance at the interface, a beam propagation method in the
time-domain for the circular symmetry waveguide developed in
[10] or a simple Fresnel calculation can be employed and these
two method lead to very close simulation results. As a numerical
example, an SMF28 is chosen as the single-mode fiber section,
of which the parameters are: the refractive index for the core
and cladding is 1.4504 and 1.4447, respectively, at wavelength
1550 nm and the radius of core is 4.15
[11]. For practical re-
fractive index of the multimode fiber core, which is around 1.5,
the calculated reflectance with the above methods is very small
.
For the experimental verification, the multimode fiber
AFS105/125Y is chosen, of which the parameters are: refrac-
tive index for the core and cladding is 1.4446 and 1.4271,
respectively. The core radius is 52.5
. The SMF28 is
spliced with the MMF and the measured reflectance is around
50 dB through measuring the return loss of the structure.
Therefore, the reflection occurring at the interface between the
single-mode and multimode fibers is neglectable in practice and
in the following modeling a one-way guided-mode propagation
analysis is used to predict the light propagation within the fiber
structure.
Due to the circular symmetric characteristic of fundamental
mode of the single-mode fiber, the input light is assumed to
have a field distribution of
. When the light launches
the multimode fiber, the input field can be decomposed by
the eigenmodes
of the multimode fiber. Due to the
circular symmetric of input field and an ideal alignment as-
sumed above, only the
modes can be excited, which has
been also addressed in [5]. Denote the field profile of
as
, (the eigenmodes of the multimode fiber are normalized
as
, ) and
Fig. 3. Calculated coupling loss to output single-mode fiber for different MMF
length.
Fig. 4. Errors of approximated propagation constants.
neglect the small amount of radiation from the multimode fiber,
we have
(1)
where
is the excitation coefficient of each mode and it can be
calculated by the overlap integral between
and
(2)
The excited mode number of the
multimode fiber
( , where is the radius of the
multimode fiber core,
and is refractive index for the core
and cladding of the multimode fiber, respectively and
is the
wavelength in the free-space).
Authorized licensed use limited to: DUBLIN INSTITUTE OF TECHNOLOGY. Downloaded on March 19, 2009 at 07:47 from IEEE Xplore. Restrictions apply.
514 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 5, MARCH 1, 2008
Fig. 5. Calculated lateral field profile with (3) and (6) at (a)
z
=
Lz=
4
and
L
=
4
, (b)
z
=
Lz=
2
and
L
=
2
, (c)
z
=3
Lz=
4
and
3
L
=
4
, (d)
z
=
Lz
and
L
. Red
curves are based on (6) and blue curves are based on (3).
As the light propagates in the multimode fiber section, the
field at the propagation distance
can be calculated by [1], [5],
[8]
(3)
where
is the propagation constant of each eigenmode of the
multimode fiber.
As the numerical example, the multimode fiber AFS105/
125Y is chosen and SMF28 is chosen as the input single-mode
fiber. The considered light wavelength is 1550 nm in free-space.
The multimode fiber has a step-index profile and so propagation
constants can be calculated numerically with the well-known
characteristic equation using the bisection method, which is
easy for programming and has a good accuracy. Fig. 2 presents
the amplitude of the calculated field along the multimode fiber.
From Fig. 2 one can see the light spreads and converges while
propagating along the multimode fiber, and it is re-imaged
within the range
(cm) of the propagation distance.
As presented in Fig. 2, different propagation distances cor-
respond to different field profiles at the cross-section. There-
fore, coupling efficiency to the output single-mode fiber (i.e.,
the transmission of the SMS fiber structure) depends on the
length of MMF. To calculate the transmission of the fiber struc-
ture, a conventional method is to employ the overlap integral be-
tween the light field
and eigenmode of the output single-
mode fiber as shown in [5], In practice, the output single-mode
fiber usually has the same fiber parameters with the input fiber,
. For this case, with the orthogonal relations be-
tween the eigenmodes of the MMF, the coupling loss can be
calculated with the following [8]:
(4)
For the above numerical example, the coupling loss is pre-
sented in Fig. 3. The exact re-imaging distance can be defined
as the propagation distance with a maximal coupling efficiency.
According to this definition, the re-imaging distance for this nu-
merical example is
with a coupling loss of
.
B. Approximated Guided-Mode Propagation
Analysis-Formulation and Evaluation
The above equations provide a convenient modeling tool to
predict the light propagation in the fiber structure and the trans-
mission of the SMS fiber structure. However, in their current
format they cannot offer a physical insight of the multimode in-
terference occurring inside the multimode fiber section. To de-
termine the light propagation characteristics in the multimode
fiber section, an approximation to the propagation constants of
the multimode fiber is taken.
For a step-index multimode fiber, it is known that the propa-
gation constant of the
th mode can be approximated by
(5)
Authorized licensed use limited to: DUBLIN INSTITUTE OF TECHNOLOGY. Downloaded on March 19, 2009 at 07:47 from IEEE Xplore. Restrictions apply.
WANG et al.: INVESTIGATION ON SINGLE-MODE–MULTIMODE–SINGLE-MODE FIBER STRUCTURE 515
Fig. 6. Real part of calculated field for the: (a) first location range and (b) second location range. (c) Imaginary part of the calculated field for the first range.
(d) Minus value of the imaginary part of the calculated field for the second range.
where . Substituting this approximated propagation
constant in (3) and it results in the following:
(6)
where
. In practical applications the common
phase factor
can be dropped. Correspondingly, with
the approximation of propagation constants, the transmission of
SMS fiber structure can be calculated by
(7)
With (6) and (7), one can see when the propagation distance
, the corresponding phase item
. Therefore,
and . This means that the light at
has the same lateral profile as the input, i.e., it is re-imaged at
propagation distance
. It is identical to the re-
sult presented in [5], but the derivation procedure in the present
paper is much simpler and intuitive as compared to that in [5],
which involves the analysis of phase difference between excited
eigenmode with the maximal excitation coefficient and other
modes. The beat length between the first two eigenmodes is
according to the approximated expression
(5) of propagation constants. Thus, one can see the re-imaged
distance
.
For the above numerical example, the approximated propaga-
tion constants
are calculated with (5) and the errors as com-
pared to the real values
are shown in Fig. 4, from which it can
be seen that the error increases for the high order eigenmodes
and these errors cause the divergence between the approximated
re-imaging distance and real value calculated with the formula-
tion in Section II-A. With the approximations of the propagation
constants, the re-imaging distance is
. As com-
pared to the re-imaging distance of
obtained
in Section II-B, the relative error is
. For the propagation
distance
, the actual coupling loss is .
Therefore, in practical design of SMS fiber structure, the exact
guided-mode propagation method should be used as the accu-
racy is concerned.
Our investigation indicates the above approximation only
shortens the self-image distance of multimode interference
from
to but the simulations based on these two ap-
proaches have a similar multimode interference pattern. For the
above numerical example, the lateral field profile calculated
with (3) at a propagation distance of
, , , and
is plotted in Fig. 5(a)–(d) with a blue curve, respectively.
For comparison, the lateral field profile calculated with (6)
at a propagation distance of
, , , and is
plotted in Fig. 5(a)–(d) with a red dashed curve, respectively.
Obviously, the two calculation results are substantially similar.
Authorized licensed use limited to: DUBLIN INSTITUTE OF TECHNOLOGY. Downloaded on March 19, 2009 at 07:47 from IEEE Xplore. Restrictions apply.
