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OPTO−ELECTRONICS REVIEW 22(3), 166–170
DOI: 10.2478/s11772−014−0193−z
Ultra-wide bandwidth wavelength selective couplers based on the all solid
multi-core Ge-doped fibre
X. Li, B. Sun*, and Y. Yu
College of Automation, Harbin Engineering University, Harbin, 150001, China
A novel wavelength selective coupler based on the all solid nine−core Ge−doped fibre has been proposed. The wavelength se−
lective coupler is based on the phenomenon of a multi−core coupling. All the cores are made of Ge−doped silica and the index
of central core is larger than the outer core. At the fixed fibre length, the different wavelength can be selected. The perfor−
mances of coupling and propagation characteristics have been numerically investigated by using a full beam propagation
method (BPM). Simulation results show that the all solid nine−core Ge−doped fibre can achieve simultaneous shorter coupler
length and wideband filtering characteristics. The 0.763 mm and 0.745 mm wavelength selective coupler are proposed to
achieve different wavelength division and the bandwidth is up to the 400 nm, and 300 nm, respectively.
Keywords: multi−core fibre, wavelength selective coupler, Ge−doped fibre.
1. Introduction
Multi−core fibres are well known to possess remarkable fea−
tures compared to the traditional single−core fibre. Multi−
−core fibres have two or more single mode or multimode or
simultaneously both kinds of cores distributed in the clad−
ding. The multi−core fibres, because of their unique struc−
ture, possess distinct characteristics and open new possibili−
ties beyond traditional fibre [1,2]. It offers new opportuni−
ties for versatile operation and control of guided light. They
have been widely applied to the sensing elements, spatial
division multiplexing [3], microwave photonics [4], fibre
lasers [5], amplifiers [6] and passive optical network [7],
etc.. With the development of multi−core fibres, the cou−
pled−power theory and the coupled−mode theory have been
widely studied [8]. It can be also used to apply in couplers’
manufacturing [9].
Wavelength−selective couplers are important compo−
nents for wavelength−division demultiplexing (WDD) of
optical fibre measurements and optical fibre communica−
tions [10]. On the network, WDD provides a flexible, con−
venient method for selecting different groups of subscribers.
The practical execution of WDD systems needs an efficient
method for extracting light of one wavelength from light
containing a number of other different discrete wavelengths
that are assumed to be already propagating in a fibre. The
operation of fibre filters typically involves energy transfer
over a coupling length between two distinct fibre cores cou−
pled by proximity interaction [11]. To this day, many types
of wavelength−selective couplers have been proposed.
These include photonic crystal fibre coupler [12,13], con−
*e−mail:
166
[email protected]
catenated fused−taper coupler [14], polished dissimilar fibre
coupler [15] and dissimilar fibre Mach−Zehnder interferom−
eters [16]. They have shown many advantages, but they also
have some different drawbacks, for example, which exhibit
narrowband filtering characteristics, a long coupler length is
required or the manufacture of highly complex structures.
In this paper, a novel wavelength selective coupler based
on the all solid nine−core Ge−doped fibre has been proposed.
Based on the phenomenon of multi−core coupling, we chan−
ge the index of central core different from the outer core and
realize the wavelength division. In comparison to a conven−
tional wavelength selective coupler, the all solid nine−core
Ge−doped fibre can achieve a simultaneous shorter coupler
length, wideband filtering characteristics, and easy fabri−
cation.
2. Fibre structure design and theoretical
analysis
We consider all solid multi−core Ge−doped fibre structures
as shown in Fig. 1, where d1 is the hole diameter, and d2 is
the hole pitch. The optical fibre includes a central core
(namely, core 1) of germanium−doped silica whose refrac−
tive index is n 1 surrounded by eight outer cores (namely,
core 2, 3,…, 9) of germanium−doped silica whose refractive
index is n 2 , and a layer of cladding material that surrounds
these cores. The cladding comprises approximately pure sil−
ica, whose refractive index is n 3 . We assume that d1 = 7mm,
d2 = 10mm, n 1 = 1.4574, n 2 = 1.456 and n 3 = 1.45.
In a nine−core fibre, neighbouring cores must be suffi−
ciently close to allow evanescent wave coupling between
fundamental optical modes associated with each core. It can
lead to the transfer of power from one core to another [17].
Opto−Electron. Rev., 22, no. 3, 2014
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3. Simulation results
Fig. 1. Cross section of the nine−core fibre structure.
The coupled−mode equation (CME) is considered as one of
the most effective method to analyze the coupling propaga−
tion of the light wave in optical waveguides. The coupled
mode equations are given by [18,19]
dA( z)
= -CA( Z ),
dz
(1)
where A( Z ) = [ A1 ( Z ) A2 ( Z )... A9 ( Z )] T denotes the mode am−
plitude, z denotes the propagation direction, C denotes
a matrix with elements c mn defined by
ì jC exp[ j( b m - b n ) z ] m ¹ n
,
(2)
c mn = í mn
jM m
m =n
î
where b m n denotes the propagation constant of core m and
n. denotes the mode−coupling coefficient from core m to
core n. M m denotes the self−coupling coefficient of core m.
The normalized C mn and M m can be written as
C mn =
Mm =
we 0
4
òò (n co - n cl ) Fm Fn dW,
(3)
we 0
4
òò (n co - n cl ) Fm Fn dW,
(4)
2
2
*
¥
2
2
*
¥
where Fm n denotes the normalized electric field distribution
of core m and n. n co and n cl denote the refractive index of
the core and the cladding, respectively.
The power conversion efficiency based on the coupled−
−mode theory is dependent on the mode−coupling coeffi−
cient and the difference in propagation constants of each
waveguide. The power conversion efficiency can be written
as [20]
é æ b - b n öù
(5)
F = ê 1+ ç m
÷ ú .
êë è 2C mn ø úû
The propagation constant can be controlled by changing the
refractive index of the core or the wavelength. In this paper,
we realize the 100% power transmittance from the central
core to the eight outer cores by changing the refractive index
of the central core. When Gaussian beam at wavelength
l = 1550 nm is launched into central core and propagation
distance z = 0.763 mm, the transmittance of central core and
outer core as a function of refractive index of central core is
shown in Fig. 2. From the figure, we can find that the trans−
mittance of central core first decreases and then increases
with the increase of refractive index of central core, the
transmittance of outer core first increases and then decre−
ases with the increase of refractive index of central core.
When the index of central core n 1 = 1.4573, the transmit−
tance of central core is up to 413
. ´ 10 -4 , the major optical
power is coupled into the outer core, and the optical power
of the central core approaches to zero.
In the meantime the wavelength has a significant effect
on the propagation constant. The power conversion effi−
ciency F decreases when the propagation constants are dif−
ferent. When Gaussian beam is launched into central core
and propagation distance z = 0.763 mm, the transmittance of
central core and outer core as a function of wavelength is
shown in Fig. 3. In Fig. 3, we can clearly see that the major
optical power transmits in the central core at the short−wave−
length, however, the major optical power is coupled into the
outer core at the long−wavelength. When the wavelength is
shorter than 900 mm, the optical power of central core
decreases, since the Gaussian beam fluctuates significantly
in the shorter wavelength. Furthermore, from the curve of
the optical power of outer core, we can find that the optical
power of the outer core approaches to zero and it does not
increase the coupling capability. Therefore, the nine−core
fibre can be used as wavelength selective coupler.
To further numerically analyse the working performance
of the proposed wavelength selective coupling, we define
The propagation constant b m n of any mode of fibre
is limited within the interval n cl k £ b m n £ n cok, where
k = 2p l is the wave number in free space. l is the free
space wavelength. When the propagation constants of the
core m and n are equal, 100% power coupling occurs at the
length of [21,22]
Lc =
p
.
2C mn
Opto−Electron. Rev., 22, no. 3, 2014
(6)
Fig. 2. Transmittance of central core and outer core as a function of
refractive index of central core.
167
X. Li
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Ultra−wide bandwidth wavelength selective couplers based on the all solid multi−core Ge−doped fibre
Fig. 3. Transmittance of central core and outer core as a function of
wavelength.
Fig. 4. Power difference of central core and outer core as a function
of b−wavelength.
the power difference (PD) of a−wavelength and b−wave−
length, PDC and PDO, respectively, as
splitting capability gradually increases with the decrease of
wavelength. The bandwidth is up to the 400 nm.
In the nine−core fibre, d2 is the crucial parameter and it
affects the coupling characteristics. Next, we analyse the
effect of the d2 on the properties of the wavelength selective
couplers. When a Gaussian beam is launched into the cen−
tral core and propagation distance z = 0.763 mm, the output
optical power variation of the central core and out core as
a function of d2 is shown in Fig. 6. In Fig. 6 we can find that
the coupling capability decreases with the increase of d2 .
When l = 1550 nm, the transmittance of the central core
first decreases and then increases with the increase of d2 ,
since when the d2 is shorter than 8000 nm, the coupling
capability increases and the coupling lengths become shor−
ter with the decrease of the d2 at the fixed length. Therefore,
the shorter wavelength can be separated from different lon−
ger wavelength by changing the d2 . When d2 = 9.45, the
shorter wavelength and wavelength l = 1480 nm can be
preferably separated. The transmittance of l = 1480 nm,
980 nm and 850 nm as a function of distance are shown in
Fig. 7. We can find that the wavelength l = 850 nm and 980
nm can be preferably separated from the wavelength l =
1480 nm. The optical power at l = 850 nm, and 980 nm are
limited well in the central core, while major optical power at
l = 1480 nm is coupled into the outer core, and the optical
power in the central core approaches zero. In the meantime,
it also has wide bandwidth. When a−wavelength l = 1480
nm, and z = 0.745 mm, Figure 8 shows the power difference
as a function of b−wavelength varying from 700 nm to 1700
nm. In Fig. 8 we can clearly see that when the short wave−
length varies from 700 nm to 1000 nm, the short wavelength
and wavelength l = 1480 nm can be preferably separated at
z = 0.745 mm. The bandwidth is up to the 300 nm.
Compared with the other established technologies, the
novel wavelength selective coupler can achieve different
wavelength division and has the ultra−wide bandwidth. It can
be widely applied in various fields such as optical fibre com−
munications, optical switch or optical filter etc. In the practi−
PDC = 10 log 10
PDO(n) = 10 log 10
a
Pout
, central
b
Pout
, central
b
Pout
, outer
a
Pout
, outer
,
(7)
n = 2, 3 , ... 9,
(8)
a
b
where Pout
, central and Pout , central are the output power of the
a
b
central core for a− and b−wavelength. Pout
, outer and Pout , outer
are the output power of the outer core for a− and b−wave−
length.
When a−wavelength l = 1550 nm, Figure 4 shows the
power difference as a function of b−wavelength varying
from 700 nm to 1700 nm. The bandwidth of this kind wave−
length selective coupler is defined as the wavelength range
within which PDC or PDO is better than –20dB. From the
figure, we can clearly see that the bandwidth of –20 dB PDC
is almost 763 nm from 700 nm to 1463 nm and the band−
width of –20 dB PDO is almost 250 nm from 700 nm to
950 nm. That is because the power conversion efficiency
becomes weaker in a short−wavelength. In most wavelength
ranges, the bandwidth of PDO is greater than PDC, since the
coupling energy of outer core is divided into eight parts. To
achieve preferably splitting capability, we take into account
the PDC and PDO, simultaneously. We can see that
the b−wavelength varying from 700 nm to 1100 nm and
a−wavelength l = 1550 nm can be preferably separated at
z = 0.763 mm. The calculated mode field distributions of the
nine−core fibre at the propagation length of z = 0.763 mm,
the wavelength l = 850 nm, 980 nm, 1100 nm and 1550 nm
are shown in Fig. 5. In Fig. 5 we can find that the wave−
length l = 850 nm, 980 nm and 1100 nm can be preferably
separated from the wavelength l = 1550 nm. The major
optical power transmits in the central core at wavelength l =
850 nm, 980 nm and 1100 nm, however, the major optical
power is coupled into the outer core at l = 1550 nm. The
168
Opto−Electron. Rev., 22, no. 3, 2014
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Fig. 5. Mode field distributions of the nine−core fibre at the propagation length z = 0.763 mm, the wavelength l = (a) 850 nm, (b) 980 nm,
(c) 1100 nm, and (d) 1550 nm.
cal application, the fabrication of the all solid nine−core Ge−
−doped fibre is not difficult by using the current multi−core fi−
bre fabrication techniques available. In the meantime the low
loss optical connection module for a multi−core fibre and sin−
gle−mode fibres has been demonstrated recently [23,24]. The−
refore, we can utilize this optical connection module to real−
ize effective separation of eight outer cores and a central core,
and then use the wavelength division multiplexing to multi−
plex eight outer cores optical carrier signals onto a single
optical fibre and obtain the wavelength selective.
Fig. 6. Output optical power variation of the central core and out
core as a function of d2.
Fig. 7. Transmittance of wavelength l = 1480 nm, 980 nm, and
850 nm as a function of distance.
Opto−Electron. Rev., 22, no. 3, 2014
169
X. Li
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Ultra−wide bandwidth wavelength selective couplers based on the all solid multi−core Ge−doped fibre
Fig. 8. Power difference of the central core and outer core as a func−
tion of b−wavelength.
4. Conclusions
In summary, a novel wavelength selective coupler based on
the all solid nine−core Ge−doped fibre has been proposed. In
comparison to a conventional wavelength selective coupler,
the all solid nine−core Ge−doped fibre can achieve simulta−
neous shorter coupler length, wideband filtering characteris−
tics, and easy fabrication. At the fixed fibre length, the differ−
ent wavelength can be selected. The 0.763 mm wavelength se−
lective coupler is proposed to achieve the wavelength division
of short−wavelength varying from 700 nm to 1100 nm and the
wavelength l = 1550 nm. The bandwidth is up to 400 nm. In the
meantime by changing the hole pitch, the 0.745 mm the wave−
length selective coupler is proposed to achieve the wavelength
division of short−wavelength varying from 700 nm to 1000 nm
and the wavelength l = 1480 nm. The bandwidth is up to 300
nm. The simulation results show that it can be preferably sepa−
rated. The novel wavelength selective coupler implements the
wide−bandwidth wavelength division at the shorter length.
References
1. Y. Yan, J. Toulouse, I. Velchev, and V.R. Slava, “Decoup−
ling and asymmetric coupling in triple−core photonic crystal
fibres”, J. Opt. Soc. Am. B25, 1488–1495 (2008).
2. D. Dorosz, and M. Kochanowicz, “Model analysis of super−
mode generation in active 5−core optical fibre”, Opto−Elec−
tron. Rev. 19, 40–45 (2011).
3. X. Liu, S. Chandrasekhar, X. Chen, P.J. Winzer, Y. Pan, T.F.
Taunay, B. Zhu, M. Fishteyn, M.F. Yan, J.M. Fini, E.M.
Monberg, and F.V. Dimarcello, “1.12−Tb/s 32−QAM−OFDM
superchannel with 8.6–b/s/Hz intrachannel spectral efficien−
cy and space−division multiplexed transmission with
60−b/s/Hz aggregate spectral efficiency”, Opt. Express 19,
B958–B964 (2011).
4. I. Gasulla and J. Capmany, “Microwave Photonics Applica−
tions of Multicore Fibres”, IEEE Photonics J. 4, 877–888 (2012).
5. B.M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges−Ber−
thelemot, and A. Barthélémy, “Phase−locked supermode
emissions from a dual multicore fibre laser” , Appl. Phys.
B105, 213–217 (2011).
170
6. Y. Huo, P. Cheo, and G. King, “Fundamental mode opera−
tion of a 19−core phase−locked Yb−doped fibre ampli−
fier”, Opt. Express 12, 6230–6239 (2004).
7. B. Zhu, T.F. Taunay, M.F. Yan, J.M. Fini, M. Fishteyn, E.M.
Monberg, and F.V. Dimarcello, “Seven−core multicore fibre
transmissions for passive optical network”, Opt. Express 18,
11117–11122 (2012).
8. M. Koshiba, K. Saitoh, K. Takenaga, and S. Matsuo, “cou−
pled−mode theory and coupled−power theory”, Opt. Express
19, B102–B111 (2011).
9. K. Szaniawska, T. Nasilowski, and T.R. Wolinski, “Simpli−
fied coupling power model for fibres fusion”, Opto−Electron.
Rev. 17, 193–199 (2009).
10. V. Grubsky, D.S. Starodubov, and J. Feinberg, “Wavelength−
−selective coupler and add−drop multiplexer using long−pe−
riod fibre gratings”, Opt. Fibre Commun. Conf. 4, 28–30
(2000).
11. D.C. Johnson, K.O. Hill, F. Bilodeau, and S. Faucher, “New
design concept for a narrowband wavelength−selective opti−
cal tap and combiner”, Electron. Lett. 23, 668–669 (1987).
12. X. Sun, “Wavelength−selective coupling of dual−core pho−
tonic crystal fibre with a hybrid light−guiding mechanism”,
Opt. Lett. 32, 2484–2486 (2007).
13. J. Zimmermann, M. Kamp, A.Forchel, and R. Marz, “Photo−
nic crystal waveguide directional couplers as wavelength se−
lective optical filters”, Opt. Commun. 230, 387–392 (2004).
14. M.S. Yataki, D.N. Payne, and M.P. Varnham, “All−fibre
polarising beamsplitter”, Electron. Lett. 21, 249–251 (1985).
15. R. Zengerle and O. Leminger, “Narrow−band wavelength−se−
lective directional couplers made of dissimilar single−mode
fibres”, J. Lightwave Technol. 5, 1196–1198 (1987).
16. B. Malo, F. Bilodeau, K.O. Hill, D.C. Johnson, and J. Albert,
“Unbalanced dissimilar−fibre Mach−Zehnder interferometer:
application as filter”, Electron. Lett. 25, 1416–1417 (1989).
17. Y. Yan and J. Toulouse, “Polarization dependence of the
inter−core coupling in triple−core photonic crystal fibres”, J.
Opt. Soc. Am. B26, 762–767 (2009).
18. S. Zheng, G. Ren, Z. Lin, and S.S. Jian, “Mode−coupling
analysis and trench design for large−mode−area low−cross−
−talk multicore fibre”, Appl. Opt. 52, 4541–4548 (2013).
19. H. Zhou, G. Xia, and Y. Fan “Output characteristics of weak−
−coupling fibre grating external cavity semiconductor laser”,
Opto−Electron. Rev.13, 27–30 (2005)
20. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka,
“Design and fabrication of ultra−low crosstalk and low−loss
multi−core fibre”, Opt. Express 19, 16576–16592 (2011).
21. S. Liu, S.G. Li, G.B. Yin, R.P. Feng, and X.Y. Wang, “A novel
polarization splitter in ZnTe tellurite glass three−core photonic
crystal fibre”, Opt. Commun. 285, 1097–1102 (2012).
22. A. Rizea “Design technique for all−dielectric non−polarizing
beam splitter plate”, Opto−Electron. Rev. 20, 96–99 (2012).
23. Y. Tottori, T. Kobayashi, and M. Watanabe, “Low loss opti−
cal connection module for seven−core multicore fibre and
seven single−mode fibres”, IEEE Photonics Tech. L. 24,
1926–1928 (2012).
24. J. Sakaguchi, W. Klaus, B. J. Puttnam, J. M. D. Mendinueta,
Y. Awaji, N. Wada, Y. Tsuchida, K. Maeda, M. Tadakuma,
K. Imamura, R. Sugizaki, T. Kobayashi, Y. Tottori, M. Wa−
tanabe, and R.V. Jensen, “19−core MCF transmission system
using EDFA with shared core pumping coupled via free−
−space optics”, Opt. Express 22, 90–95 (2014).
Opto−Electron. Rev., 22, no. 3, 2014
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