Ultra-large number of transmission channels in space division multiplexing using few-mode multi-core fiber with optimized air-hole-assisted double-cladding structure Tatsuhiko Watanabe∗ and Yasuo Kokubun Graduate School of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama, 240-8501, Japan ∗ [email protected]
Abstract: The ultimate number of transmission channels in a fiber for the space division multiplexing (SDM) is shown by designing an air-hole-assisted double-cladding few-mode multi-core fiber. The propagation characteristics such as the dispersion and the mode field diameter are almost equalized for all cores owing to the double cladding structure, and the crosstalk between adjacent cores is extremely suppressed by the heterogeneous arrangement of cores and the air holes surrounding the cores. Optimizing the structure of the air-hole-assisted double-cladding, ultra dense core arrangements, e.g. 129 cores in a core accommodated area with 200 µ m diameter, can be realized with low crosstalk of less than -34.3 dB at 100km transmission. In this design, each core supports 3 modes i.e. LP01 , LP11a , and LP11b as the transmission channels, so that the number of transmission channels can be 3-hold greater than the number of cores. Therefore, 387 transmission channels can be realized. © 2014 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2280) Fiber design and fabrication; (060.4230) Multiplexing.
References and links 1. T. Morioka, “New generation optical infrastructure technologies: ‘EXAT initiative’ towards 2020 and beyond,” The 14th OptoElectronics and Communications Conference (OECC2009), FT4(2009). 2. D. J. Richardson, J. M. Fini and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon. 7, 354–362 (2013). 3. J. Sakaguchi, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi and M. Watanabe, “109-Tb/s (7 97 172-Gb/s SDM/WDM/PDM) QPSK transmission through 16.8-km homogeneous multi-core fiber,” Conference on Optical Fiber Communication 2011 collocated National Fiber Optic Engineers Conference (OFC/NFOEC2011), PDPB6, March (2011). 4. R. Ryf, S. Randel, A.H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy and R. Lingle, “Mode-division multiplexing over 96 km of fewmode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Technol. 30(4), 521–531 (2012). 5. J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanashi, K. Imamura, H. Inaba, K. Musaka, R. Sugizaki, T. Kobayashi and M. Watanabe, “19-core transmission of 19x100x172-Gb/s SDM-WDMPDM-QPSK signals at 305Tb/s,” Conference on Optical Fiber Communication 2012 collocated National Fiber Optic Engineers Conference (OFC/NFOEC2012), Los Angeles, PDP5C.1, March (2012).
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Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8309
6. H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sakaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba and T. Morioka, “1.01-Pb/s (12SDM/222 WDM/456Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregated spectral efficiency,” The 38th European Conference and Exhibition on Optical Communication (ECOC2012), Amsterdam, Th.3.C.1, (2012). 7. D. Qian, E. Ip, M. F. Huang, M. Li, A. Dogariu, S. Zhang, Y. Shao, Y. K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto and T. Wang, “1.05Pb/s transmission with 109b/s/Hz spectral efficiency using hybrid single- and few-mode cores,” Frontier in Optics 2012 (FiO2012), FW6C (2012). 8. M. Koshiba, K. Saitoh and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98-103 (2009). 9. Y. Kokubun and T. Watanabe, “Dense heterogeneous uncoupled multi core fiber using 9 types of cores with double cladding structure,” The 17th MicroOptics Conference 2011 (MOC2011), Sendai, K-5 (2011). 10. T.Watanabe and Y. Kokubun, “High density and low cross talk design of heterogeneous multi-core fiber with air hole assisted double cladding,” The 18th OptoElectronics and Communications Conference/Photonics in Switching (OECC/PS2013), Kyoto, MS1-4 (2013). 11. C. Xia, R. A. Correa, N. Bai, E. A. Lopez, D. M. Arriojo, A. Schulzgen, M. Richardson, J. Linares, C. Montero, E. Mateo, X. Zhou and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photon. Technol. Lett. 24(21), 1914-,1917 (2012). 12. T. Sakamoto, K. Saitoh, N. Hanzawa, K. Tsujikawa, L. Ma, M. Koshiba and F. Yamamoto, “Crosstalk suppressed hole-assisted 6-core fiber with cladding diameter of 125 µ m,” The 38th European Conference and Exhibition on Optical Communication (ECOC2013), Mo.3.A.3 (2013). 13. M. Koshiba, K. Saitoh, K. Takenaga and S. Matsuo, “Multi-core fiber design and analysis: Coupled-mode theory and coupled-power theory,” Opt. Express 19(26), B102-B111 (2011). 14. M. Koshiba, K. Saitoh, K. Takenaga and S. Matsuo, “Analytical expression of average power-coupling coefficient for estimating intercore cross talk in multicore fiber,” IEEE Photon. J. 4(5), 1987-1995 (2012). 15. K. Tomozawa and Y. Kokubun,“Maximum core capacity of heterogeneous uncoupled multi-core fibers,” The 16th OptoElectronics and Communications Conference (OECC2011), 7C2-4 (2011). 16. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki and E. Sasaoka “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express 19(17), 16576-16592 (2011). 17. K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh and Masanori Koshiba, “A large effective area multi-core fiber with an optimized cladding thickness,” Opt. Express 19(26), B543-B550, (2011).
1.
Introduction
To break through the capacity crunch of the optical fiber network, space division multiplexing(SDM) has been proposed [1, 2]. Multi-core fibers (MCFs) [3] and few-mode fibers (FMFs) [4] are the prominent candidates for the ultra-high capacity SDM transmission. Recently, ultra high bit rate transmission experiments using MCFs have been demonstrated such as 305Tb/s transmission using a 19-core fiber [5], 1.01Pb/s transmission using a 12-core fiber [6], and 1.05Pb/s transmission using a 14-core fiber [7]. However, further increase of the number of cores is difficult due to the thick diameter of core with a trench structure and the combination of homogenous cores. Generally, the minimum core spacing between identical cores to achieve low crosstalk, e.g. -30dB at 100km transmission, is much greater than that between non-identical cores, which is the primary factor limiting the core packing density. Thus, the incorporation of non-identical cores have been suggested as a method to increase the packing density [8]. However, when employing many types of non-identical cores, the difference of V parameter among non-identical cores will be large, resulting in significant differences in the propagation characteristics among the cores. To overcome this problem, a double cladding structure which create differences in the equivalent index among several types of cores while maintaining nearly identical propagation characteristics was proposed [9]. Subsequently, we proposed a novel heterogeneous MCF with air hole assisted double cladding structure, which can drastically suppress the crosstalk between adjacent cores and can achieve extremely high density of cores [10]. However, since the adjacent cores almost contact with each other owing to the extremely low crosstalk, further increase of the packing density of cores is almost impossible. Although some MCFs with hole assisted structure have been demon#205215 - $15.00 USD (C) 2014 OSA
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8310
strated [11, 12], identical cores were used and so the core density have not reached its limit. Therefore in this paper, to increase the number of transmission channels in the MCF, we propose a FM heterogeneous MCF with air hole assisted double cladding structure. Firstly we show the design principle of air-hole-assisted double-cladding structure and the design example of dense heterogeneous MCF. Next, the optimization of FM air-hole-assisted double-cladding structure and the ultimate number of transmission channels in a MCF are shown. 2.
Dense heterogeneous air-hole-assisted double-cladding single mode MCF
2.1. Principle of double-cladding structure Let us consider a core surrounded by a double-cladding structure as shown in Fig. 1. The double cladding structure can be utilized for heterogeneous arrangement of several types of cores. The field profile of the LP01 mode is mostly confined in the core and the first cladding region owing to the refractive index contrast between the core and the first cladding, ∆. If the index contrast ∆ is fixed the same value for all cores, the propagation characteristics such as the dispersion and the mode field diameter (MFD) can be kept identical even for different types of cores. On the other hand, the equivalent index neq can be made different by varying the index difference between the first cladding and the second cladding, ∆nc (= n2 − n3 ). Using this double-cladding structure with low index contrast (∆=0.375%), we assumed multiple cores with different propagation constants while maintaining the same index contrast, ∆. The refractive index of the second cladding, n3 , was assumed to be 1.44402 (pure SiO2 at λ =1550nm). To n (r)
n D
n
D n
n n
F ie ld p r o file 1
E q u iv a le n t in d e x (L P 01) E q u iv a le n t in d e x (L P 11)
e q
2
C
C o r e
3
0
a
1 st c la d d in g
2 n d c la d d in g
a
r 1
Fig. 1. Index and field profile of double-cladding structure.
maximize the core packing density, the radius of the first cladding a1 must be minimized, while keeping the effect of the second cladding on the equivalent index negligibly small. To clarify the radius of the first cladding a1 which required to minimize the effect of second cladding, the relationship between the equivalent index n′eq and the radius of the first cladding a1 was calculated using the perturbation theory and the equation, q neq = n′eq 2 − I (1) where neq is the changed equivalent index due to the existence of the second cladding and n′eq is the equivalent index determined by the normal step-index profile consisting of the core and the cladding. I is the perturbation term given by
I=
Z ∞ a1
(n22 − n23) · E(r)2 · r · dr Z ∞ 0
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(2)
E(r)2 · r · dr
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8311
where, E(r) represents the unperturbed field profile for the case that the refractive index of the second cladding is equal to that of the first cladding, i.e. n2 = n3 . The calculated result is shown in Fig. 2. It can be seen that a1 = 8µ m is sufficient to minimize the effect of the first cladding, because the change in the perturbed equivalent index is less than 2% of the equivalent index determined by ∆, even for the case of sufficiently large value of ∆nc = 0.003 which is the cutoff value of LP11 mode given in the next section. n 8
'
e q
'e q
-n -n
e q 2
< 1 %
< 2 %
< 3 %
F irs t c la d d in g ra d iu s a
1
[m m ]
n
7
D n 6
n
n
e q
c
n 1
D
n
D a
a 3
n 'eq 2
a 1
a = 4 .5 [ m m ] D = 0 .3 7 5 % 5
0
0 .0 0 1
0 .0 0 2
0 .0 0 3
In d e x d iffe re n c e D n
0 .0 0 4 c
Fig. 2. Radius of first cladding required to reduce the effect of second cladding for given ∆nc .
2.2. Principle of hole assisted double-cladding structure In the double cladding structure, the core region is mainly utilized to guide the light and the fundamental mode (LP01 mode) is supported by the index difference between the core and the first cladding. However, since there is also the index difference between the first cladding and the second cladding, the first cladding mode, which is the LP11 mode in the whole structure, is supported and may result in the crosstalk for the fundamental mode guided in the core region. To suppress the excitation of the LP11 mode, air-holes are added to the double-cladding structure. The relation between the equivalent index neq of each mode and the refractive index difference ∆nc between the first cladding and the second cladding was numerically calculated using a mode solver (FemSIM by Rsoft). The calculated results are shown in Fig. 3. It can be seen from this figure that the cutoff ∆nc of LP11 mode of the double cladding structure without air holes is as small as 3 × 10−4 . On the other hand, the cutoff ∆nc of air-hole-assisted doublecladding structure is extended to 3 × 10−3 when the diameter of air-hole is 5µ m and the center of the air-holes are located on the outer circumference of the first cladding. When the equivalent index is less than 1.44402 (refractive index of SiO2 ), it was confirmed that the field spreads out into the whole area and is no longer confined in the core region. Therefore, this corresponds to the cutoff of LP11 . Thus, the index difference ∆nc of non-identical cores can be determined so that the value of ∆nc for different cores are distributed within the range of the single-mode condition. Since the cutoff ∆nc is 0.003, we assumed the value of ∆nc of three types of nonidentical cores to be 0.001, 0.002 and 0.003, for the heterogeneous uncoupled triangle arranged multi-core fiber. Now, the increment of ∆nc between adjacent cores is defined by δ nc in the following sections (see Fig. 5(b)), and in this case δ nc = 0.001.
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Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8312
E q u iv a le n t in d e x n
e q
1 .4 5 4
n 3= n 2= n 1= D =
1 .4 5 2
1 .4 4 n 3+ D n 2/(1 0 .3 7
4 0 2 n C -2 D ) 5 %
L P
1 /2
0 1
n
1 .4 5 0
9 m m 1 6 m m
L P
A ir
= 1 .0
5 m m
1 1
1 .4 4 8 1 .4 4 6 1 .4 4 4 0
5 4
3 2
1
6
In d e x d iffe re n c e D n
[ c
7
1 0 -3 ]
Fig. 3. Equivalent index vs index difference ∆nc defined by the difference (n2 − n3 ).
2.3. Evaluation of crosstalk using coupled power theory The crosstalk (XT) between adjacent cores was evaluated using the coupled power theory (CPT) [13]. In this work, the bending radius R was assumed to be sufficient larger than the critical bending radius i.e. non-phase matching region, and the exponential autocorrelation function for the statistical characteristics of the power coupling coefficients (PCCs) was adopted. Thus, the average PCC [14] between the mth - and nth -core is given by, hmn =
2 d 2Kmn c 1 + (∆βmndc )2
(3)
where Kmn is the coupling coefficient calculated by the coupled mode theory (see Eq. (10) in Ref. [13]), βmn is the propagation-constant difference and dc is the correlation length. The correlation length is defined for the coupling between the fundamental modes of two adjacent cores. These definitions are the same as that in Ref. [14]. The correlation length of 0.05m was hypothetically adopted in this work which was obtained experimentally in Ref. [13]. The calculated results of crosstalk are shown in Fig. 4. In this calculation, we assumed that 0
w /o a ir h o le s
X T @ 1 0 0 k m
[d B ]
2 1 m m
-2 0
n
D = 0 .3 7 5 %
n
2 1
1 1
D
D
D n
n
2 1
n
2 2
n C
3
5 m m
-4 0 2 1 m m
s in g le m o d e
-6 0 0
1
2
3
In d e x d iffe re n c e D n
4 C
5
[ 1 0 -3 ]
Fig. 4. Crosstalk at 100km transmission vs index difference ∆nc .
∆nc of one of the two adjacent cores is zero, i.e. n2 = n3 , because the coupling in this case is
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Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8313
stronger than the case of ∆nc ≥ 0. The crosstalk of the double-cladding structure without airholes is about 0dB in the case of 100km transmission when the core pitch is 21µ m. When the air-holes are located on the outer circumference of the first cladding, the crosstalk for 100km transmission is as low as -40dB or less in the range of 0.0005 < ∆nc < 0.003. Here, the core spacing can be greatly reduced to 21 µ m, and so the adjacent core regions consisting of the core and the first cladding are in contact with each other. These data show that the crosstalk between adjacent cores can be extremely suppressed by the air holes. In addition to the crosstalk, another important parameter is the critical bending radius, because the crosstalk increases when the bending radius approaches the critical bending radius. Therefore, the critical bending radius should be as small as possible. The critical bending radius Rc is given by Λ · n3 (4) Rc = δ neq where Λ is the adjacent core spacing and δ neq is the difference of the equivalent index between adjacent cores. In this case, since Λ can be greatly reduced to 21 µ m and δ neq nearly corresponds to δ nc of 0.001, the critical bending radius can be reduced to 30 mm. 3.
Optimization of few mode air hole assisted double cladding structure
g
a 1
d
h o le
d n g
a
h
a
h o le
a = 4 .5 m m a 1= 8 .0 m m a h o le = a 1 + g / 2
h o le
L = 2 a 1+ g
L
D n C
# i
C
D
D n C
# i+ 1
n 1
D
n n
a a 1
c o re ty p e : # i
c o re ty p e : # i+ 1 (b) index profile
(a) core structure
Fig. 5. Definition of structural and optical parameters of cores.
Figure 5(a) shows the schematic view and the definition of structural parameters of air hole assisted double cladding structure. a and a1 are the core and first cladding radii, respectively, and h is the diameter of the air hole. In this work, a and a1 were assumed to be 4.5µ m and 8µ m, respectively, the same as the case of single mode design. The core pitch is Λ and the gap between circumferences of adjacent first cladding is g. Then, ahole , the distance between the center of the core and the center of the hole, is half of Λ, which means holes are located at the midpoint between adjacent cores. Here, ∆ is the refractive index contrast between the core and the first cladding which is kept identical for all cores. To increase the number of modes without deteriorating the core density, ∆ was increased. In this design, the index contrast ∆ of 0.7% was adopted so that 3 modes, i.e. LP01 , LP11a and LP11b modes can be supported. Then, in this paper, since the triangle arrangement of non-identical three types of cores was adopted and numbered as #1, #2, and #3, three different values of ∆nc were determined to be ∆nc = 0.001 for core #1, 0.002 for core #2 and 0.003 for core #3. Here, δ nc represents the index difference of first cladding between the core #i and the core #i + 1 as shown in Fig. 5(b). First, the theoretical cutoff wavelength of the LP21 for this structure was calculated. Fig. 6 shows the relationship between g and the theoretical cutoff wavelength of LP21 mode against the hole diameter h. Here, the theoretical cutoff wavelength λc was calculated for the core #3, #205215 - $15.00 USD (C) 2014 OSA
2
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8314
3
g h
h = h = h = h = h =
a 1= 8 m m
1 5 5 0
c
[n m ]
1 6 0 0
C u to ff w a v e le n g th o f L P
2 1
l
a
1 5 3 0 1 5 0 0 a
h o le
5 m 6 m 7 m 8 m 9 m
m m m m m
h o le
= g /2 + 8 m m
1 4 5 0 C o re # 3
1 4 0 0
D = 0 .7 % D n c = 0 .0 0 3
1 3 5 0 0
2
4
6
8
1 0
G a p b e tw e e n firs t c la d d in g s g [m m ] Fig. 6. Cutoff wavelength of LP02 of core #3.
because that of core #3 should be longest among the three types of cores due to the large ∆nc . It can be seen that the theoretical cutoff wavelength can be shorter as the overlap area of the air hole to the first cladding become larger. The design condition for the cutoff wavelength λc was assumed to be 1530nm in consideration for the use of C- and L-band. Next, the crosstalk of LP11 modes between adjacent cores at the 100km transmission was
C ro s s ta lk o f L P
1 1
m o d e s @ 1 0 0 k m
[d B ]
C o re p itc h L [m m ] 0
1 6
2 0
1 8
2 2
2 4
h = 7 m m h = 7 .5 m m h = 8 m m
-2 0 -3 0
h = 9 m m
-4 0
-6 0
C o m b in a tio n o f c o re # 1 a n d # 2 h
g
-8 0
L -1 0 0
D = 0 .7 %
D = 0 .7 %
0
1
2
D n c= 0 .0 0 1
3
4
5
6
7
D n c= 0 .0 0 2
8 9
G a p b e tw e e n firs t c la d d in g s g [m m ]
Fig. 7. Worst crosstalk of LP11 between core #1 and core #2.
calculated using the PCC given by Eq. (3). Although the correlation length was defined for the calculation of the crosstalk between the fundamental modes in Ref. [13], the correlation length dc was assumed to be 0.05m [13]. In this work, since the difference between the equivalent index of LP11 mode and the refractive index of the first cladding n2 is almost equal to that in the single mode case, we assumed this value. Fig. 7 shows the calculated results. It is seen that the crosstalk is extremely suppressed as the core pitch is reduced, when the hole diameter is
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Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8315
constant. Usually, the crosstalk becomes large as the core pitch is reduced. However, in this case, the field is more effectively shielded by the holes as the hole approaches the core with the decrease of core pitch according to the relation ghole = (Λ − 2a1 − h)/2. Therefore, the crosstalk is suppressed with the decrease of the core pitch. In the case of hole diameter of 9µ m, the crosstalk is less than -30dB for any core pitch as shown in Fig. 7. Lastly, the optimum design condition was obtained using the calculated results of the theoretical cutoff wavelength of LP21 and the crosstalk of LP11 modes between adjacent cores as shown in Fig. 8. Here, ghole indicates the gap between the circumference of the hole and the core, and dhole indicates the gap between the circumferences of the adjacent holes as shown Fig. 5. In the sky blue region which is surrounded by the lines of ghole =0 and dhole =0, and the curves of XT=-30dB and λth =1530nm, the air hole assisted double cladding structure can be designed. However, it is not practical that the holes contact each other, i.e. dhole =0 µ m, and the holes and the core contact with each other. Therefore, the deep blue region which is surrounded by the lines of ghole = 2µ m and dhole =2 µ m and the curves of XT=-30dB and λth =1530nm represents the more practical design region. g
1 3
O p tic a l re s tric tio n c u to ff w a v e le n g th o f L P c ro s s ta lk S tru c tu a l lim it g h o le d h o le
1 2 1 1
g
= 0 m m
h o le
= 2 m m
2 1
d
e h o l
1 0
m m = 0
d
e h o l
m m = 2
C 9
B
0 d B X T = -3
= 1 53 0n m
8
A 7
21
H o le d ia m e te r h [m m ]
h o le
5
l 0
2
4
6
th
of L P
6
8
1 0
G a p b e tw e e n firs t c la d d in g s g [m m ] Fig. 8. Design restriction on air hole diameter and gap between first cladding.
4.
Number of transmission channels
Using the optimum design parameters obtained above, ultra-high density multi-core fiber can be designed. In this study, the triangle arrangement using three types of non-identical cores was adopted since it can realize the highest core density. Once the core pitch, the core arrangement, the number of non-identical core types and the diameter of core accommodation area are given, the number of cores can be calculated using the lattice algorithm [15]. The algorithm to calculate the maximum core capacity in the triangle lattice arrangement can be briefly summarized as follows. Let us consider a case #1 that core center is located at the vertex of the triangular lattice as shown in Fig. 9. The distance between the center of fiber and the lattice point Rik is given
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Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8316
Fig. 9. Lattice point in a triangle arrangement and definition of label i and k.
by Eq. (5). The number of cores existing in the circle with radius R is determined by counting the lattice points satisfying Rik < R. This counting procedure is equivalent to the sum of the unit step function U(R − Rik ) with respect to i and k. Thus the summation of the lattice points in the normalized circle R/D is given by Eq. (6), where µ and ν are the maximum ranges of summation √ with respect to i and k and D is the core spacing between identical cores which is equal to 3Λ. q 1 (5) Rik = Λ (2i + k)2 + 3k2 2 µ
N#1 =
ν
∑ ∑
i=− µ k=−ν
U (R − Rik )
(6)
The maximum core capacity for cases #2 and #3 where the center of fiber is located at the middle point between adjacent lattice points and the center of triangle, respectively as shown in Fig. 9, can be calculated in the same manner. The maximum core capacity for a given R/D is determined by comparing these numbers using Eq. (7). Ncore = max(N#1 , N#2 , N#3 )
(7)
Using the lattice algorithm, the maximum core capacities for triangle lattice were calculated for three cases where the diameter of effective fiber area 2R were assumed to be 100µ m, 150µ m and 200µ m, as shown in Fig. 10. Here, we sampled three designed parameters from Fig. 8 Table 1. Design examples of ultra-large number of channels.
Case SM A B C
Hole Dia. Core pitch Worst XT Number of cores hhole Λ @100km 2R=100µ m 2R=150µ m 2R=200µ m 5µ m 21µ m -37.0dB 21 48 85 7µ m 17µ m -34.3dB 31 73 129 8µ m 20µ m -39.0dB 22 55 91 9µ m 23µ m -46.6dB 19 42 70 Note) CaseA, B, and C correspond to the points A, B, and C in Fig.8.
and the case of single mode MCF as described in Sec. 2. The maximum number of cores was evaluated using Fig. 10 and is summarized in Table 1. Cases A, B, and C correspond
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Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8317
G a p b e tw e e n 1 s t c la d d in g s g [m m ] 0
2
4
6
8
1 0
1 2
1 4
T ria n g le a rra n g e m e n t o f th re e ty p e s o f c o re s
1 2 0
g
N u m b e r o f c o re N
c o re
1 0 0 L
A
8 0
B C
2 R = 2 0 0 m m 2 R = 1 5 0 m m 2 R = 1 0 0 m m
6 0 4 0 2 0
1 6
2 0
1 8
2 2
2 4
2 6
2 8
3 0
C o re p itc h L [m m ] Fig. 10. Maximum number of cores vs core pitch against diameter of effective fiber area.
to the points A, B, and C in Fig. 8, respectively. In the design of few mode transmission, three channels, i.e. LP01 , LP11a and LP11b modes, are supported per core. Thus, the number of transmission channels in a fiber will be 3 times the number of the cores. In the case of these three sampled structures, the number of transmission channels ranges from 129 to 387 when the effective fiber area diameter 2R is assumed to be 200µ m. Even in the case of 2R=100µ m which is almost equivalent to the conventional single mode fiber, the number of transmission channels can be increased to 57-93. Fig. 11 shows the example of case C for 2R = 200µ m, which corresponds to the number of transmission channels of 210. In addition, the critical bending radius for the cases A, B, and C were calculated to be 24mm, 29mm, and 33mm, respectively, using Eq. (4). 2 3 m m 3 3 2 3
2
2
1
1
3
2 3
3
1
1 2 3 2
1 2
3
X T < - 4 6 .4 d B 1
1 2
2 3 1
3
3 1
1 2
1 2
2
2
2 3
3 2
3
1
1 2
1
N o f c o re s : 7 0 3
1 3
3
3
3
1 2
2
2
2
2
1
1
3 1
3
3
3
2 1
1 2
1
1
3
2 0 0 m m
Fig. 11. Design example of 70 core few-mode multi-core fiber.
5.
Conclusion
The air hole assisted double cladding few-mode multi-core fiber has been proposed to achieve the ultra number of transmission channels in a fiber. Optimizing the air hole assisted double cladding structure from the view point of crosstalk suppression and cutoff wavelength, we have #205215 - $15.00 USD (C) 2014 OSA
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8318
shown that several hundreds of transmission channels can be accommodated in a fiber. We represented the tremendous potential of the air hole assisted structure by optimizing the core structure. In the view point of fabrication, two fabrication methods, i.e. rod-in-tube method [16] and stack and draw method [11, 17], can be used to realize the proposed hole-assisted double cladding structure. In the case of rod-in-tube method, the air-holes are formed by drilling in the preform rod which has double-cladding structure. In the case of stack and draw method, the preform rod is prepared by stacking rods which have several types of index and diameter and thin capillary tubes in a silica tube. Acknowledgment This work was supported by the National Institute of Information and Communications Technology (NICT), Japan, under “RD of Innovative Optical Fiber and Communication Technology.”
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Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8319
Abstract: The ultimate number of transmission channels in a fiber for the space division multiplexing (SDM) is shown by designing an air-hole-assisted double-cladding few-mode multi-core fiber. The propagation characteristics such as the dispersion and the mode field diameter are almost equalized for all cores owing to the double cladding structure, and the crosstalk between adjacent cores is extremely suppressed by the heterogeneous arrangement of cores and the air holes surrounding the cores. Optimizing the structure of the air-hole-assisted double-cladding, ultra dense core arrangements, e.g. 129 cores in a core accommodated area with 200 µ m diameter, can be realized with low crosstalk of less than -34.3 dB at 100km transmission. In this design, each core supports 3 modes i.e. LP01 , LP11a , and LP11b as the transmission channels, so that the number of transmission channels can be 3-hold greater than the number of cores. Therefore, 387 transmission channels can be realized. © 2014 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2280) Fiber design and fabrication; (060.4230) Multiplexing.
References and links 1. T. Morioka, “New generation optical infrastructure technologies: ‘EXAT initiative’ towards 2020 and beyond,” The 14th OptoElectronics and Communications Conference (OECC2009), FT4(2009). 2. D. J. Richardson, J. M. Fini and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nature Photon. 7, 354–362 (2013). 3. J. Sakaguchi, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi and M. Watanabe, “109-Tb/s (7 97 172-Gb/s SDM/WDM/PDM) QPSK transmission through 16.8-km homogeneous multi-core fiber,” Conference on Optical Fiber Communication 2011 collocated National Fiber Optic Engineers Conference (OFC/NFOEC2011), PDPB6, March (2011). 4. R. Ryf, S. Randel, A.H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy and R. Lingle, “Mode-division multiplexing over 96 km of fewmode fiber using coherent 6 × 6 MIMO processing,” J. Lightw. Technol. 30(4), 521–531 (2012). 5. J. Sakaguchi, B. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanashi, K. Imamura, H. Inaba, K. Musaka, R. Sugizaki, T. Kobayashi and M. Watanabe, “19-core transmission of 19x100x172-Gb/s SDM-WDMPDM-QPSK signals at 305Tb/s,” Conference on Optical Fiber Communication 2012 collocated National Fiber Optic Engineers Conference (OFC/NFOEC2012), Los Angeles, PDP5C.1, March (2012).
#205215 - $15.00 USD (C) 2014 OSA
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8309
6. H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sakaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba and T. Morioka, “1.01-Pb/s (12SDM/222 WDM/456Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregated spectral efficiency,” The 38th European Conference and Exhibition on Optical Communication (ECOC2012), Amsterdam, Th.3.C.1, (2012). 7. D. Qian, E. Ip, M. F. Huang, M. Li, A. Dogariu, S. Zhang, Y. Shao, Y. K. Huang, Y. Zhang, X. Cheng, Y. Tian, P. Ji, A. Collier, Y. Geng, J. Linares, C. Montero, V. Moreno, X. Prieto and T. Wang, “1.05Pb/s transmission with 109b/s/Hz spectral efficiency using hybrid single- and few-mode cores,” Frontier in Optics 2012 (FiO2012), FW6C (2012). 8. M. Koshiba, K. Saitoh and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98-103 (2009). 9. Y. Kokubun and T. Watanabe, “Dense heterogeneous uncoupled multi core fiber using 9 types of cores with double cladding structure,” The 17th MicroOptics Conference 2011 (MOC2011), Sendai, K-5 (2011). 10. T.Watanabe and Y. Kokubun, “High density and low cross talk design of heterogeneous multi-core fiber with air hole assisted double cladding,” The 18th OptoElectronics and Communications Conference/Photonics in Switching (OECC/PS2013), Kyoto, MS1-4 (2013). 11. C. Xia, R. A. Correa, N. Bai, E. A. Lopez, D. M. Arriojo, A. Schulzgen, M. Richardson, J. Linares, C. Montero, E. Mateo, X. Zhou and G. Li, “Hole-assisted few-mode multicore fiber for high-density space-division multiplexing,” IEEE Photon. Technol. Lett. 24(21), 1914-,1917 (2012). 12. T. Sakamoto, K. Saitoh, N. Hanzawa, K. Tsujikawa, L. Ma, M. Koshiba and F. Yamamoto, “Crosstalk suppressed hole-assisted 6-core fiber with cladding diameter of 125 µ m,” The 38th European Conference and Exhibition on Optical Communication (ECOC2013), Mo.3.A.3 (2013). 13. M. Koshiba, K. Saitoh, K. Takenaga and S. Matsuo, “Multi-core fiber design and analysis: Coupled-mode theory and coupled-power theory,” Opt. Express 19(26), B102-B111 (2011). 14. M. Koshiba, K. Saitoh, K. Takenaga and S. Matsuo, “Analytical expression of average power-coupling coefficient for estimating intercore cross talk in multicore fiber,” IEEE Photon. J. 4(5), 1987-1995 (2012). 15. K. Tomozawa and Y. Kokubun,“Maximum core capacity of heterogeneous uncoupled multi-core fibers,” The 16th OptoElectronics and Communications Conference (OECC2011), 7C2-4 (2011). 16. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki and E. Sasaoka “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express 19(17), 16576-16592 (2011). 17. K. Takenaga, Y. Arakawa, Y. Sasaki, S. Tanigawa, S. Matsuo, K. Saitoh and Masanori Koshiba, “A large effective area multi-core fiber with an optimized cladding thickness,” Opt. Express 19(26), B543-B550, (2011).
1.
Introduction
To break through the capacity crunch of the optical fiber network, space division multiplexing(SDM) has been proposed [1, 2]. Multi-core fibers (MCFs) [3] and few-mode fibers (FMFs) [4] are the prominent candidates for the ultra-high capacity SDM transmission. Recently, ultra high bit rate transmission experiments using MCFs have been demonstrated such as 305Tb/s transmission using a 19-core fiber [5], 1.01Pb/s transmission using a 12-core fiber [6], and 1.05Pb/s transmission using a 14-core fiber [7]. However, further increase of the number of cores is difficult due to the thick diameter of core with a trench structure and the combination of homogenous cores. Generally, the minimum core spacing between identical cores to achieve low crosstalk, e.g. -30dB at 100km transmission, is much greater than that between non-identical cores, which is the primary factor limiting the core packing density. Thus, the incorporation of non-identical cores have been suggested as a method to increase the packing density [8]. However, when employing many types of non-identical cores, the difference of V parameter among non-identical cores will be large, resulting in significant differences in the propagation characteristics among the cores. To overcome this problem, a double cladding structure which create differences in the equivalent index among several types of cores while maintaining nearly identical propagation characteristics was proposed [9]. Subsequently, we proposed a novel heterogeneous MCF with air hole assisted double cladding structure, which can drastically suppress the crosstalk between adjacent cores and can achieve extremely high density of cores [10]. However, since the adjacent cores almost contact with each other owing to the extremely low crosstalk, further increase of the packing density of cores is almost impossible. Although some MCFs with hole assisted structure have been demon#205215 - $15.00 USD (C) 2014 OSA
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8310
strated [11, 12], identical cores were used and so the core density have not reached its limit. Therefore in this paper, to increase the number of transmission channels in the MCF, we propose a FM heterogeneous MCF with air hole assisted double cladding structure. Firstly we show the design principle of air-hole-assisted double-cladding structure and the design example of dense heterogeneous MCF. Next, the optimization of FM air-hole-assisted double-cladding structure and the ultimate number of transmission channels in a MCF are shown. 2.
Dense heterogeneous air-hole-assisted double-cladding single mode MCF
2.1. Principle of double-cladding structure Let us consider a core surrounded by a double-cladding structure as shown in Fig. 1. The double cladding structure can be utilized for heterogeneous arrangement of several types of cores. The field profile of the LP01 mode is mostly confined in the core and the first cladding region owing to the refractive index contrast between the core and the first cladding, ∆. If the index contrast ∆ is fixed the same value for all cores, the propagation characteristics such as the dispersion and the mode field diameter (MFD) can be kept identical even for different types of cores. On the other hand, the equivalent index neq can be made different by varying the index difference between the first cladding and the second cladding, ∆nc (= n2 − n3 ). Using this double-cladding structure with low index contrast (∆=0.375%), we assumed multiple cores with different propagation constants while maintaining the same index contrast, ∆. The refractive index of the second cladding, n3 , was assumed to be 1.44402 (pure SiO2 at λ =1550nm). To n (r)
n D
n
D n
n n
F ie ld p r o file 1
E q u iv a le n t in d e x (L P 01) E q u iv a le n t in d e x (L P 11)
e q
2
C
C o r e
3
0
a
1 st c la d d in g
2 n d c la d d in g
a
r 1
Fig. 1. Index and field profile of double-cladding structure.
maximize the core packing density, the radius of the first cladding a1 must be minimized, while keeping the effect of the second cladding on the equivalent index negligibly small. To clarify the radius of the first cladding a1 which required to minimize the effect of second cladding, the relationship between the equivalent index n′eq and the radius of the first cladding a1 was calculated using the perturbation theory and the equation, q neq = n′eq 2 − I (1) where neq is the changed equivalent index due to the existence of the second cladding and n′eq is the equivalent index determined by the normal step-index profile consisting of the core and the cladding. I is the perturbation term given by
I=
Z ∞ a1
(n22 − n23) · E(r)2 · r · dr Z ∞ 0
#205215 - $15.00 USD (C) 2014 OSA
(2)
E(r)2 · r · dr
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8311
where, E(r) represents the unperturbed field profile for the case that the refractive index of the second cladding is equal to that of the first cladding, i.e. n2 = n3 . The calculated result is shown in Fig. 2. It can be seen that a1 = 8µ m is sufficient to minimize the effect of the first cladding, because the change in the perturbed equivalent index is less than 2% of the equivalent index determined by ∆, even for the case of sufficiently large value of ∆nc = 0.003 which is the cutoff value of LP11 mode given in the next section. n 8
'
e q
'e q
-n -n
e q 2
< 1 %
< 2 %
< 3 %
F irs t c la d d in g ra d iu s a
1
[m m ]
n
7
D n 6
n
n
e q
c
n 1
D
n
D a
a 3
n 'eq 2
a 1
a = 4 .5 [ m m ] D = 0 .3 7 5 % 5
0
0 .0 0 1
0 .0 0 2
0 .0 0 3
In d e x d iffe re n c e D n
0 .0 0 4 c
Fig. 2. Radius of first cladding required to reduce the effect of second cladding for given ∆nc .
2.2. Principle of hole assisted double-cladding structure In the double cladding structure, the core region is mainly utilized to guide the light and the fundamental mode (LP01 mode) is supported by the index difference between the core and the first cladding. However, since there is also the index difference between the first cladding and the second cladding, the first cladding mode, which is the LP11 mode in the whole structure, is supported and may result in the crosstalk for the fundamental mode guided in the core region. To suppress the excitation of the LP11 mode, air-holes are added to the double-cladding structure. The relation between the equivalent index neq of each mode and the refractive index difference ∆nc between the first cladding and the second cladding was numerically calculated using a mode solver (FemSIM by Rsoft). The calculated results are shown in Fig. 3. It can be seen from this figure that the cutoff ∆nc of LP11 mode of the double cladding structure without air holes is as small as 3 × 10−4 . On the other hand, the cutoff ∆nc of air-hole-assisted doublecladding structure is extended to 3 × 10−3 when the diameter of air-hole is 5µ m and the center of the air-holes are located on the outer circumference of the first cladding. When the equivalent index is less than 1.44402 (refractive index of SiO2 ), it was confirmed that the field spreads out into the whole area and is no longer confined in the core region. Therefore, this corresponds to the cutoff of LP11 . Thus, the index difference ∆nc of non-identical cores can be determined so that the value of ∆nc for different cores are distributed within the range of the single-mode condition. Since the cutoff ∆nc is 0.003, we assumed the value of ∆nc of three types of nonidentical cores to be 0.001, 0.002 and 0.003, for the heterogeneous uncoupled triangle arranged multi-core fiber. Now, the increment of ∆nc between adjacent cores is defined by δ nc in the following sections (see Fig. 5(b)), and in this case δ nc = 0.001.
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Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8312
E q u iv a le n t in d e x n
e q
1 .4 5 4
n 3= n 2= n 1= D =
1 .4 5 2
1 .4 4 n 3+ D n 2/(1 0 .3 7
4 0 2 n C -2 D ) 5 %
L P
1 /2
0 1
n
1 .4 5 0
9 m m 1 6 m m
L P
A ir
= 1 .0
5 m m
1 1
1 .4 4 8 1 .4 4 6 1 .4 4 4 0
5 4
3 2
1
6
In d e x d iffe re n c e D n
[ c
7
1 0 -3 ]
Fig. 3. Equivalent index vs index difference ∆nc defined by the difference (n2 − n3 ).
2.3. Evaluation of crosstalk using coupled power theory The crosstalk (XT) between adjacent cores was evaluated using the coupled power theory (CPT) [13]. In this work, the bending radius R was assumed to be sufficient larger than the critical bending radius i.e. non-phase matching region, and the exponential autocorrelation function for the statistical characteristics of the power coupling coefficients (PCCs) was adopted. Thus, the average PCC [14] between the mth - and nth -core is given by, hmn =
2 d 2Kmn c 1 + (∆βmndc )2
(3)
where Kmn is the coupling coefficient calculated by the coupled mode theory (see Eq. (10) in Ref. [13]), βmn is the propagation-constant difference and dc is the correlation length. The correlation length is defined for the coupling between the fundamental modes of two adjacent cores. These definitions are the same as that in Ref. [14]. The correlation length of 0.05m was hypothetically adopted in this work which was obtained experimentally in Ref. [13]. The calculated results of crosstalk are shown in Fig. 4. In this calculation, we assumed that 0
w /o a ir h o le s
X T @ 1 0 0 k m
[d B ]
2 1 m m
-2 0
n
D = 0 .3 7 5 %
n
2 1
1 1
D
D
D n
n
2 1
n
2 2
n C
3
5 m m
-4 0 2 1 m m
s in g le m o d e
-6 0 0
1
2
3
In d e x d iffe re n c e D n
4 C
5
[ 1 0 -3 ]
Fig. 4. Crosstalk at 100km transmission vs index difference ∆nc .
∆nc of one of the two adjacent cores is zero, i.e. n2 = n3 , because the coupling in this case is
#205215 - $15.00 USD (C) 2014 OSA
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8313
stronger than the case of ∆nc ≥ 0. The crosstalk of the double-cladding structure without airholes is about 0dB in the case of 100km transmission when the core pitch is 21µ m. When the air-holes are located on the outer circumference of the first cladding, the crosstalk for 100km transmission is as low as -40dB or less in the range of 0.0005 < ∆nc < 0.003. Here, the core spacing can be greatly reduced to 21 µ m, and so the adjacent core regions consisting of the core and the first cladding are in contact with each other. These data show that the crosstalk between adjacent cores can be extremely suppressed by the air holes. In addition to the crosstalk, another important parameter is the critical bending radius, because the crosstalk increases when the bending radius approaches the critical bending radius. Therefore, the critical bending radius should be as small as possible. The critical bending radius Rc is given by Λ · n3 (4) Rc = δ neq where Λ is the adjacent core spacing and δ neq is the difference of the equivalent index between adjacent cores. In this case, since Λ can be greatly reduced to 21 µ m and δ neq nearly corresponds to δ nc of 0.001, the critical bending radius can be reduced to 30 mm. 3.
Optimization of few mode air hole assisted double cladding structure
g
a 1
d
h o le
d n g
a
h
a
h o le
a = 4 .5 m m a 1= 8 .0 m m a h o le = a 1 + g / 2
h o le
L = 2 a 1+ g
L
D n C
# i
C
D
D n C
# i+ 1
n 1
D
n n
a a 1
c o re ty p e : # i
c o re ty p e : # i+ 1 (b) index profile
(a) core structure
Fig. 5. Definition of structural and optical parameters of cores.
Figure 5(a) shows the schematic view and the definition of structural parameters of air hole assisted double cladding structure. a and a1 are the core and first cladding radii, respectively, and h is the diameter of the air hole. In this work, a and a1 were assumed to be 4.5µ m and 8µ m, respectively, the same as the case of single mode design. The core pitch is Λ and the gap between circumferences of adjacent first cladding is g. Then, ahole , the distance between the center of the core and the center of the hole, is half of Λ, which means holes are located at the midpoint between adjacent cores. Here, ∆ is the refractive index contrast between the core and the first cladding which is kept identical for all cores. To increase the number of modes without deteriorating the core density, ∆ was increased. In this design, the index contrast ∆ of 0.7% was adopted so that 3 modes, i.e. LP01 , LP11a and LP11b modes can be supported. Then, in this paper, since the triangle arrangement of non-identical three types of cores was adopted and numbered as #1, #2, and #3, three different values of ∆nc were determined to be ∆nc = 0.001 for core #1, 0.002 for core #2 and 0.003 for core #3. Here, δ nc represents the index difference of first cladding between the core #i and the core #i + 1 as shown in Fig. 5(b). First, the theoretical cutoff wavelength of the LP21 for this structure was calculated. Fig. 6 shows the relationship between g and the theoretical cutoff wavelength of LP21 mode against the hole diameter h. Here, the theoretical cutoff wavelength λc was calculated for the core #3, #205215 - $15.00 USD (C) 2014 OSA
2
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8314
3
g h
h = h = h = h = h =
a 1= 8 m m
1 5 5 0
c
[n m ]
1 6 0 0
C u to ff w a v e le n g th o f L P
2 1
l
a
1 5 3 0 1 5 0 0 a
h o le
5 m 6 m 7 m 8 m 9 m
m m m m m
h o le
= g /2 + 8 m m
1 4 5 0 C o re # 3
1 4 0 0
D = 0 .7 % D n c = 0 .0 0 3
1 3 5 0 0
2
4
6
8
1 0
G a p b e tw e e n firs t c la d d in g s g [m m ] Fig. 6. Cutoff wavelength of LP02 of core #3.
because that of core #3 should be longest among the three types of cores due to the large ∆nc . It can be seen that the theoretical cutoff wavelength can be shorter as the overlap area of the air hole to the first cladding become larger. The design condition for the cutoff wavelength λc was assumed to be 1530nm in consideration for the use of C- and L-band. Next, the crosstalk of LP11 modes between adjacent cores at the 100km transmission was
C ro s s ta lk o f L P
1 1
m o d e s @ 1 0 0 k m
[d B ]
C o re p itc h L [m m ] 0
1 6
2 0
1 8
2 2
2 4
h = 7 m m h = 7 .5 m m h = 8 m m
-2 0 -3 0
h = 9 m m
-4 0
-6 0
C o m b in a tio n o f c o re # 1 a n d # 2 h
g
-8 0
L -1 0 0
D = 0 .7 %
D = 0 .7 %
0
1
2
D n c= 0 .0 0 1
3
4
5
6
7
D n c= 0 .0 0 2
8 9
G a p b e tw e e n firs t c la d d in g s g [m m ]
Fig. 7. Worst crosstalk of LP11 between core #1 and core #2.
calculated using the PCC given by Eq. (3). Although the correlation length was defined for the calculation of the crosstalk between the fundamental modes in Ref. [13], the correlation length dc was assumed to be 0.05m [13]. In this work, since the difference between the equivalent index of LP11 mode and the refractive index of the first cladding n2 is almost equal to that in the single mode case, we assumed this value. Fig. 7 shows the calculated results. It is seen that the crosstalk is extremely suppressed as the core pitch is reduced, when the hole diameter is
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Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8315
constant. Usually, the crosstalk becomes large as the core pitch is reduced. However, in this case, the field is more effectively shielded by the holes as the hole approaches the core with the decrease of core pitch according to the relation ghole = (Λ − 2a1 − h)/2. Therefore, the crosstalk is suppressed with the decrease of the core pitch. In the case of hole diameter of 9µ m, the crosstalk is less than -30dB for any core pitch as shown in Fig. 7. Lastly, the optimum design condition was obtained using the calculated results of the theoretical cutoff wavelength of LP21 and the crosstalk of LP11 modes between adjacent cores as shown in Fig. 8. Here, ghole indicates the gap between the circumference of the hole and the core, and dhole indicates the gap between the circumferences of the adjacent holes as shown Fig. 5. In the sky blue region which is surrounded by the lines of ghole =0 and dhole =0, and the curves of XT=-30dB and λth =1530nm, the air hole assisted double cladding structure can be designed. However, it is not practical that the holes contact each other, i.e. dhole =0 µ m, and the holes and the core contact with each other. Therefore, the deep blue region which is surrounded by the lines of ghole = 2µ m and dhole =2 µ m and the curves of XT=-30dB and λth =1530nm represents the more practical design region. g
1 3
O p tic a l re s tric tio n c u to ff w a v e le n g th o f L P c ro s s ta lk S tru c tu a l lim it g h o le d h o le
1 2 1 1
g
= 0 m m
h o le
= 2 m m
2 1
d
e h o l
1 0
m m = 0
d
e h o l
m m = 2
C 9
B
0 d B X T = -3
= 1 53 0n m
8
A 7
21
H o le d ia m e te r h [m m ]
h o le
5
l 0
2
4
6
th
of L P
6
8
1 0
G a p b e tw e e n firs t c la d d in g s g [m m ] Fig. 8. Design restriction on air hole diameter and gap between first cladding.
4.
Number of transmission channels
Using the optimum design parameters obtained above, ultra-high density multi-core fiber can be designed. In this study, the triangle arrangement using three types of non-identical cores was adopted since it can realize the highest core density. Once the core pitch, the core arrangement, the number of non-identical core types and the diameter of core accommodation area are given, the number of cores can be calculated using the lattice algorithm [15]. The algorithm to calculate the maximum core capacity in the triangle lattice arrangement can be briefly summarized as follows. Let us consider a case #1 that core center is located at the vertex of the triangular lattice as shown in Fig. 9. The distance between the center of fiber and the lattice point Rik is given
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Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8316
Fig. 9. Lattice point in a triangle arrangement and definition of label i and k.
by Eq. (5). The number of cores existing in the circle with radius R is determined by counting the lattice points satisfying Rik < R. This counting procedure is equivalent to the sum of the unit step function U(R − Rik ) with respect to i and k. Thus the summation of the lattice points in the normalized circle R/D is given by Eq. (6), where µ and ν are the maximum ranges of summation √ with respect to i and k and D is the core spacing between identical cores which is equal to 3Λ. q 1 (5) Rik = Λ (2i + k)2 + 3k2 2 µ
N#1 =
ν
∑ ∑
i=− µ k=−ν
U (R − Rik )
(6)
The maximum core capacity for cases #2 and #3 where the center of fiber is located at the middle point between adjacent lattice points and the center of triangle, respectively as shown in Fig. 9, can be calculated in the same manner. The maximum core capacity for a given R/D is determined by comparing these numbers using Eq. (7). Ncore = max(N#1 , N#2 , N#3 )
(7)
Using the lattice algorithm, the maximum core capacities for triangle lattice were calculated for three cases where the diameter of effective fiber area 2R were assumed to be 100µ m, 150µ m and 200µ m, as shown in Fig. 10. Here, we sampled three designed parameters from Fig. 8 Table 1. Design examples of ultra-large number of channels.
Case SM A B C
Hole Dia. Core pitch Worst XT Number of cores hhole Λ @100km 2R=100µ m 2R=150µ m 2R=200µ m 5µ m 21µ m -37.0dB 21 48 85 7µ m 17µ m -34.3dB 31 73 129 8µ m 20µ m -39.0dB 22 55 91 9µ m 23µ m -46.6dB 19 42 70 Note) CaseA, B, and C correspond to the points A, B, and C in Fig.8.
and the case of single mode MCF as described in Sec. 2. The maximum number of cores was evaluated using Fig. 10 and is summarized in Table 1. Cases A, B, and C correspond
#205215 - $15.00 USD (C) 2014 OSA
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8317
G a p b e tw e e n 1 s t c la d d in g s g [m m ] 0
2
4
6
8
1 0
1 2
1 4
T ria n g le a rra n g e m e n t o f th re e ty p e s o f c o re s
1 2 0
g
N u m b e r o f c o re N
c o re
1 0 0 L
A
8 0
B C
2 R = 2 0 0 m m 2 R = 1 5 0 m m 2 R = 1 0 0 m m
6 0 4 0 2 0
1 6
2 0
1 8
2 2
2 4
2 6
2 8
3 0
C o re p itc h L [m m ] Fig. 10. Maximum number of cores vs core pitch against diameter of effective fiber area.
to the points A, B, and C in Fig. 8, respectively. In the design of few mode transmission, three channels, i.e. LP01 , LP11a and LP11b modes, are supported per core. Thus, the number of transmission channels in a fiber will be 3 times the number of the cores. In the case of these three sampled structures, the number of transmission channels ranges from 129 to 387 when the effective fiber area diameter 2R is assumed to be 200µ m. Even in the case of 2R=100µ m which is almost equivalent to the conventional single mode fiber, the number of transmission channels can be increased to 57-93. Fig. 11 shows the example of case C for 2R = 200µ m, which corresponds to the number of transmission channels of 210. In addition, the critical bending radius for the cases A, B, and C were calculated to be 24mm, 29mm, and 33mm, respectively, using Eq. (4). 2 3 m m 3 3 2 3
2
2
1
1
3
2 3
3
1
1 2 3 2
1 2
3
X T < - 4 6 .4 d B 1
1 2
2 3 1
3
3 1
1 2
1 2
2
2
2 3
3 2
3
1
1 2
1
N o f c o re s : 7 0 3
1 3
3
3
3
1 2
2
2
2
2
1
1
3 1
3
3
3
2 1
1 2
1
1
3
2 0 0 m m
Fig. 11. Design example of 70 core few-mode multi-core fiber.
5.
Conclusion
The air hole assisted double cladding few-mode multi-core fiber has been proposed to achieve the ultra number of transmission channels in a fiber. Optimizing the air hole assisted double cladding structure from the view point of crosstalk suppression and cutoff wavelength, we have #205215 - $15.00 USD (C) 2014 OSA
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8318
shown that several hundreds of transmission channels can be accommodated in a fiber. We represented the tremendous potential of the air hole assisted structure by optimizing the core structure. In the view point of fabrication, two fabrication methods, i.e. rod-in-tube method [16] and stack and draw method [11, 17], can be used to realize the proposed hole-assisted double cladding structure. In the case of rod-in-tube method, the air-holes are formed by drilling in the preform rod which has double-cladding structure. In the case of stack and draw method, the preform rod is prepared by stacking rods which have several types of index and diameter and thin capillary tubes in a silica tube. Acknowledgment This work was supported by the National Institute of Information and Communications Technology (NICT), Japan, under “RD of Innovative Optical Fiber and Communication Technology.”
#205215 - $15.00 USD (C) 2014 OSA
Received 23 Jan 2014; revised 17 Mar 2014; accepted 18 Mar 2014; published 1 Apr 2014 7 April 2014 | Vol. 22, No. 7 | DOI:10.1364/OE.22.008309 | OPTICS EXPRESS 8319
