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Selective mode excitation by nonaxial evanescent coupling for Selective mode excitation by nonaxial evanescent coupling for
bandwidth enhancement of multimode 7ber links bandwidth enhancement of multimode 7ber links
Laurent Vaissié
Eric G. Johnson
University of Central Florida
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Recommended Citation Recommended Citation
Vaissié, Laurent and Johnson, Eric G., "Selective mode excitation by nonaxial evanescent coupling for
bandwidth enhancement of multimode 7ber links" (2002).
Faculty Bibliography 2000s
. 3516.
https://stars.library.ucf.edu/facultybib2000/3516
Selective mode excitation by nonaxial
evanescent coupling for bandwidth
enhancement of multimode fiber links
Laurent Vaissie
´
Eric G. Johnson
University of Central Florida
CREOL/School of Optics
4000 Central Florida Boulevard
Orlando, Florida 32816-2700
E-mail: lvaissie@mail.ucf.edu
Abstract. We present an analysis of conditioned launch in a gradient-
index multimode fiber (MMF). Selective mode excitation is obtained by
nonaxial evanescent coupling between two highly asymmetric side-
polished fibers: a single-mode fiber and an MMF with an exposed core.
An index-matching slab improves the coupling efficiency and selectivity.
The simulation shows that about 40% of modes, only high-order modes,
are excited in the MMF. When compared to an overfilled launch, the
bandwidth of a perturbed index fiber is enhanced more than twofold for
large parameter variations.
©
2002 Society of Photo-Optical Instrumentation Engi-
neers.
[DOI: 10.1117/1.1488607]
Subject terms: local area networks; optical fibers; evanescent coupling; gradient
index.
Paper 010289 received Aug. 15, 2001; revised manuscript received Feb. 11,
2002; accepted for publication Feb. 13, 2002.
1 Introduction
The computer interconnects in local area networks 共LANs兲
are today required to transmit data at very high rates to
satisfy the increasing bandwidth demand. The IEEE 802.3
committee underwent a great effort in the past few years to
achieve and standardize a rate of gigabit per second data
transmission for these local networks.
1
The standardization
approved by the committee includes data transmission by
the already installed gradient-index multimode fibers
共MMFs兲 that constitute the dominant backbone of these
networks. These MMFs are operated at 850 or at 1300 nm
and the minimum bandwidth requirement for a long-
wavelength 1300-nm link 共LX兲 was fixed to be 500 MHz
km for a 62.5-
m core fiber.
1
The first technique used to launch light and excite a
maximum number of modes in the MMF consists of radi-
ally overfilling the MMF with a light-emitting diode on-
axis. Because the source is spatially incoherent, almost all
the modes in the MMF are excited with the same amplitude
factor. This technique is called overfilled launch 共OFL兲.
This launching method would be optimal if the actual fiber
index of refraction matched the theoretical dispersion-free
profile that is close to parabolic.
However, defects in the gradient-index profile of in-
stalled gradient index fibers due to the modified chemical
vapor deposition 共MCVD兲 fabrication process limit the
maximum bandwidth achievable by the OFL method, as
first pointed out by Checcacci et al.
2
and investigated nu-
merically by Marcuse.
3
Index variations such as central de-
pression and core-cladding interface dip cause the group
velocity to vary from one mode to another. Consequently
each mode will propagate in the fiber at a slightly different
velocity with respect to each other, causing the pulse to
stretch as it travels from transmitter to receiver. The im-
pulse response of the fiber is therefore stretched and the
corresponding bandwidth, defined as the Fourier transform
of the impulse response, is limited. The resulting dispersion
of index profile defect is referred to as differential mode
delay 共DMD兲 and is generally worse if all the modes are
excited. The dispersion is more important for trajectories
where the index differs significantly from the perfect para-
bolic case, in such locations as the axis or the core-cladding
interface.
The measured bandwidth of such fibers was found to be
far below the 500 MHz km requirement of the IEEE stan-
dard for a 62.5-
m core fiber at 1300 nm. The general
solution to the DMD problem is therefore to excite only a
few modes in the MMF. The idea is to limit the intermodal
dispersion and therefore restore available bandwidth by ex-
citing only modes propagating along trajectories where the
refraction index matches the dispersion-free profile.
Several methods have been investigated for selective
mode excitation in a gradient-index fiber. One method con-
sists of exciting high-order modes of the MMF through
butt-coupling with a single-mode fiber 共SMF兲 off axis. This
method was first presented by Jeunhomme and Pocholle
4
for index profile measurement and applied to bandwidth
enhancement by Webster et al.,
5
Raddatz et al.,
6,7
and
Johnson and Stack.
8
It was shown that this method enables
us to achieve a bandwidth comparable to the OFL.
Another method investigated uses a vortex lens to phase
match the launched field to a couple of modes by trans-
forming a plane wave to a donut-shaped energy distribution
with a spiral phase to couple light to a very restricted num-
ber of modes.
8
However, it requires a diffractive element to
transform the launched field into a donut shape.
Webster et al. pointed out that launching light at an
angle greater or equal to 6 deg could prevent bandwidth
collapse in MMF links.
5
Following this analysis, the
method presented here employs tilted evanescent coupling
from a side-polished single-mode 共SPSM兲 to a side-
1821Opt. Eng. 41(8) 1821–1828 (August 2002) 0091-3286/2002/$15.00 © 2002 Society of Photo-Optical Instrumentation Engineers
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polished gradient-index fiber 共SPMM兲 to launch skew rays
and excite higher order modes. Bandwidth enhancement
ratios at least similar to the offset launch technique are
expected using this technique.
First, we will describe the numerical framework of this
paper. We consider an index profile close to parabolic case
but perturbed by a central depression and a core-cladding
negative distortion. Rigorous ray tracing in the gradient-
index fiber is calculated and compared to energy trajecto-
ries of excited modes simulated by the beam-propagation
method. The ray simulation is used to confirm that the cou-
pling technique excites modes propagating along defect-
free paths of the index profile.
From the perturbed profile we derive the DMD that is
scaled to the 2 ns/km limit set by the gigabit Ethernet com-
mittee. The bandwidth is then computed consistently with
the procedure described by Marcuse and used previously in
the literature.
7
In the second part of the paper, we present the results of
bandwidth enhancement over the OFL bandwidth for the
new method based on evanescent coupling. The effective
number of excited modes is also presented. We then discuss
the results to determine which method should be used in
LANs.
2 Nonaxial Evanescent Coupling
of Side-Polished Fibers
The key to achieve bandwidth enhancement of perturbed-
index profile MMFs is to excite a limited number of modes
that will propagate along trajectories where the index does
not present large deviation. To do so, we propose to use the
technique of evanescent coupling between an SPSM and an
SPMM. The mechanical polishing technique is well known
now and fabrication of such elements is described in nu-
merous papers.
9
The control of polishing depth may be con-
trolled to within an accuracy
10
of ⫾0.25
m.
Coupling between asymmetric fibers has been investi-
gated for more than a decade, including adiabatic and side-
polished couplers.
11
They have been proven useful as a
flexible alternative to a 3-dB coupler in a linear data bus
12
or a nonreciprocal directional coupler.
13
Valentin and Igor
also investigated oblique coupling between two dissimilar
fibers through fused tapered fibers. Their concept was re-
cently applied to pumping of multimode fibers.
14
In this paper, we propose to investigate a nonaxial eva-
nescent coupling scheme between highly asymmetric fibers
and its application to bandwidth enhancement of nonperfect
MMFs in LANs. We also investigate the role of an inter-
mediate index-matching slab between the fibers for im-
proved coupling efficiency and selectivity.
Figure 1 represents the coupling scheme proposed for
evanescent coupling. An SMF is polished down to within 2
m close to the core. This fiber is used to launch light in a
gradient index fiber that was polished until the core was
exposed. The distance between the axis of the MMF and
the cladding plane is the polishing depth. The MMF pre-
sents an exposed core for two reasons. First, the coupling
will have a better bandwidth enhancement ratio if the light
is not launched at the core-cladding discontinuity. Second,
the coupling will be more efficient if the index of refraction
in the core of the SMF and at the cladding plane of the
MMF are similar. A 3-
m-thick layer of index matching
fluid (n⫽ 1.457) is used to enhance the coupling efficiency,
which could also be achieved by depositing an oxide film
on the SPMM. Its important role for coupling efficiency is
demonstrated in Sec. 4.3.
The index profile of the MMF presents an important
central depression on axis, where DMD was shown to in-
crease dramatically.
2,7
Thus we propose to launch light into
skew rays of the SPMM by coupling at an angle between
the two side-polished fibers. For the simulations the angle
varies from 2 to 10 deg.
3 Framework of Investigation
3.1
Perturbed Index Profile
The MCVD fabrication process mainly yields defects at
two distinct locations in a gradient-index MMF, on axis and
at the core cladding interface.
4
These perturbed profiles
have been investigated in different DMD surveys and a
statistical investigation of a profile variation based on these
perturbations helped to provide some insight into the pos-
sible bandwidth enhancement obtained with an offset
launch technique. Based on these studies, we consider in
this paper a case combining a central depression and dis-
continuity of refractive index distribution at the core-
cladding interface. The index of refraction in the core falls
abruptly to equal the cladding index at a radius of 28
m,
considering a 62.5-
m core fiber. The central depression is
modeled by a 5-
m-radius central dip such that ⌬n
⫽n(5)⫺n(0)⫽0.0044. The cladding index is 1.457.
The departure of the index profile with respect to the
perfect parabolic profile n⫽1.477
关
1⫺2⫻0.0135
⫻(r/31)
2
兴
1/2
is shown in Fig. 2.
The next section describes the derivation of ray equa-
tions for a parabolic index profile MMF. These equations
are used in comparison with the beam propagation results
to confirm that light is launched along helical paths.
Fig. 1 Proposed evanescent coupling scheme between SPSM and
SPMM. The MMF presents a perturbed parabolic profile and is pol-
ished to a distance
d
from the axis. The SMF cladding plane is at 2
m above the core. The bandwidth enhancement is investigated
with respect to the coupling angle
0
and the polishing depth
d
of
the MMF.
Vaissie
´
and Johnson: Selective mode excitation...
1822 Optical Engineering, Vol. 41 No. 8, August 2002
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3.2
Ray Equations in Parabolic Index Multimode
Fiber
Following the framework of Cozannet et al.,
15
we derive
the equations describing the propagation of rays in optical
fibers with parabolic gradient-index without approxima-
tions. The ray parameters are defined in Fig. 3. In cylindri-
cal coordinates the vector OM can be expressed as
OM⫽r⫽
u
r
⫹zk. 共1兲
And the tangent vector T is defined by
T⫽
dr
ds
⫽
d
ds
u
r
⫹
du
r
ds
⫹
dz
ds
k
⫽sin
共
兲
cos
共
兲
u
r
⫹sin
共
兲
sin
共
兲
u
⫹cos
共
兲
k. 共2兲
We assume the index is dependent only on
as we inves-
tigate gradient-index fibers.
The ray equation can be written as
n
dr
ds
⫽grad
共
S
兲
, 共3兲
Fig. 2 Perturbed index profile of the MMF and perfect parabolic profile (dashed line). The perturbed
index presents a 5-
m wide central depression and a core-cladding discontinuity located 3
m before
the cladding.
Fig. 3 Ray parameters. The
z
axis defines the axis of the multimode fiber.
Vaissie
´
and Johnson: Selective mode excitation...
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where S is a surface of constant phase. Taking the deriva-
tive with respect to s leads to
1
d
ds
冉
n
dr
ds
冊
⫽grad
共
n
兲
. 共4兲
By projection on (u
r
,u
,k) and using
du
r
ds
⫽
d
ds
u
,
du
ds
⫽⫺
d
ds
u
r
,
Eq. 共4兲 becomes the system
15
n
冉
d
ds
冊
2
冉
⬙
⫺2
⬘
2
⫺
冊
⫽
dn
d
, 共5兲
n
冉
d
ds
冊
2
⫽
␣
⫽n
共
0
兲
0
sin
共
0
兲
sin
共
0
兲
, 共6兲
n
冉
d
ds
冊
z
⬘
⫽n
共
0
兲
cos
共
0
兲
, 共7兲
where the derivative with respect to
is designed by a
prime.
Using the new variable
v
⫽ 1/
, Eqs. 共5兲 and 共6兲 give
␣
2
共v
⬙
⫹
v
兲
⫽n
冉
dn
d
v
冊
. 共8兲
We consider now the parabolic index profile given by
n⫽n
1
冉
1⫺2⌬
冉
a
冊
2
冊
1/2
if
⭐a
n⫽n
2
if
⬎a,
where ⌬⫽ (n
1
2
⫺n
2
2
)/(2n
1
2
) and a is the core radius of fiber.
Then Eq. 共8兲 becomes
v
2
共vv
⬙
⫹
v
2
兲
⫽
2n
1
2
⌬
␣
2
a
2
⫽
␥
2
, 共9兲
The general solution of Eq. 共9兲 is
v
2
⫽A cos
关
2
共
⫺
i
兲
兴
⫹
共
A
2
⫹
␥
2
兲
1/2
. 共10兲
Equation 共10兲 defines an ellipse where the great axis
M
and small axis
m
are obtained for
⫽
i
and
⫽
i
⫹
/2, respectively.
m
⫽
冋
1
⫺A⫹
共
A
2
⫹
␥
2
兲
1/2
册
1/2
, 共11兲
M
⫽
冋
1
A⫹
共
A
2
⫹
␥
2
兲
1/2
册
1/2
. 共12兲
The initial conditions are defined by OM
0
(
0
,0,z
0
) and T
0
关sin(
0
)cos(
0
), sin(
0
)sin(
0
), cos(
0
)兴. The constants A
and
i
are obtained by rewriting Eq. 共2兲 such that
T⫽
冉
d
ds
冊
d
d
u
r
⫹
d
ds
u
⫹
dz
ds
k
⫽sin
共
兲
cos
共
兲
u
r
⫹sin
共
兲
共
sin
兲
共
兲
u
⫹cos
共
兲
k. 共13兲
From which one can derive
tan
共
兲
⫽
⬘
⫽
1
A
2
sin
关
2
共
⫺
i
兲
兴
. 共14兲
Plugging the result into Eq. 共10兲 yields
A⫽
兵
1⫹
关
2 cos
共
0
兲
兴
/
关
sin
共
0
兲
共
1⫺
0
4
␥
2
兲
兴
其
1/2
共
1⫺
0
4
␥
2
兲
2
0
2
,
共15兲
i
⫽
0
⫹
arctan
兵
2/
关
tan
0
共
1⫺
0
4
␥
2
兲
兴
其
2
. 共16兲
Then one can express
as a function of z by integrating Eq.
共7兲 to eliminate
, which yields
2
⫽
M
2
再
sin
2
冋
2
T
共
z⫺z
i
兲
册
⫹
冉
m
M
冊
2
cos
2
冋
2
T
共
z⫺z
i
兲
册
冎
,
共17兲
where
T⫽
2
n
共
0
兲
cos
0
a
n
1
冑
2⌬
共18兲
z
i
⫽z
0
⫹
T
2
arctan
冋
m
M
tan
共
i
兲
册
. 共19兲
Taking into account the rotation of the axis of the ellipse
with respect to (x,y) set of axis, the ray coordinates are
then defined in Cartesian coordinates by
冉
x
y
冊
⫽
再
m
cos
冋
2
T
共
z⫺z
i
兲
册
*
cos
共
i
兲
⫺
M
sin
冋
2
T
共
z⫺z
i
兲
册
*
sin
共
i
兲
m
cos
冋
2
T
共
z⫺z
i
兲
册
*
sin
共
i
兲
⫹
M
sin
冋
2
T
共
z⫺z
i
兲
册
*
cos
共
i
兲
冎
.
共20兲
3.3
Modal Fields and Propagation Constants
of Perturbed-Index Profile MMF
Given the index profile presented in Fig. 2, we used the
mode solver module of beam propagation method 共BPM兲-
CAD to find its propagating mode fields as well as the
corresponding propagation constants. Given a 2-D permit-
tivity distribution, the algorithm assumes the waveguide is
z-invariant and launches a Gaussian input field off axis for
imaginary propagation. The alternating direction implicit
method, which splits the propagation operator along the x
Vaissie
´
and Johnson: Selective mode excitation...
1824 Optical Engineering, Vol. 41 No. 8, August 2002
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