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Design of low crosstalk and bend insensitive optical interconnect using rectangular array multicore fiber
Optics Communications 331 (2014) 272–277
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Design of low crosstalk and bend insensitive optical interconnect using rectangular array multicore fiber Jitendra Kumar Mishra n, Vishnu Priye Department of Electronics Engineering, Indian School of Mines, Dhanbad 826004, India
art ic l e i nf o
a b s t r a c t
Article history: Received 25 March 2014 Received in revised form 13 June 2014 Accepted 14 June 2014 Available online 25 June 2014
A design strategy for achieving minimum crosstalk in a space division multiplexed 2 4 multicore fiber (MCF) for application in next generation exa-bandwidth optical interconnects is proposed. To evaluate crosstalk in adjacent cores of MCF, a semi-analytical approach based on finite element method and coupled power theory is applied. The dependence of crosstalk on various MCF parameters – such as index profile parameter, core to core pitch and bending radius – is investigated. It is shown that optical interconnects based on heterogeneous core MCF with triangular index profile and optimum core to core pitch, can be configured to have minimum crosstalk per unit length. Moreover, such interconnects show high degree of bend tolerance for both small and large bending radii. & 2014 Elsevier B.V. All rights reserved.
Keywords: Optical interconnects Multicore fibers Space division multiplexing Crosstalk
1. Introduction Due to steadily increasing data rate requirements and to overcome bandwidth density drives, optical interconnect (OI) has become a key technology to realize signal transmission in boxto-box, rack-to-rack, board-to-board, and chip-to-chip interconnect applications [1]. It has triggered research interest as a promising network choice to achieve future exaflop (1018) high performance computing systems [2]. For next generation supercomputing as well as data centers, key issue for design of OI is to increase the channel density with minimum escalation in link cost and power budget [3]. OI configuration based on multicore fiber (MCF) shows promise to cope with ever increasing demands on bandwidth within data centers, terabit switches, core routers, digital cross connect systems and high performance computers [4,5]. MCF supports multichannel transmission compatible with 2D arrays of vertical cavity surface emitting laser (VCSEL) transmitter [6]. Although, fiber ribbons or individual fibers increase the fiber density [7], they are costly, bulky, consume more power and do not meet the very high density requirement of end to end optical interconnects for data transmission. Hence they cannot be an alternative to MCF with space division multiplexing capacity to overcome the exponentially growing demand in data traffic of current optical communication system [8]. MCF which was proposed couple of decades ago [9], due to its space division multiplexing capability has become a strong candidate to configure novel OI [10] which can exploit huge optoelectronic
n
Corresponding author. E-mail address: [email protected] (J.K. Mishra).
http://dx.doi.org/10.1016/j.optcom.2014.06.026 0030-4018/& 2014 Elsevier B.V. All rights reserved.
bandwidth disparity between requirement and availability. For efficient usage of MCF as OI, one of the major issues that has to be addressed is crosstalk between cores which depends on refractive index profile of individual cores and distance between neighboring cores. Moreover as bends are inevitable for interconnects, bend induced index perturbations and core density strongly affects the crosstalk characteristics in MCF [11,12]. To estimate crosstalk between adjacent cores in a MCF, coupled mode theory [13,14] and coupled power theory [14] are applied. Furthermore, to reduce the crosstalk in a MCF, research work on homogeneous MCFs [15], heterogeneous MCFs [16], trench assisted MCFs [17] as well as hole assisted MCFs [18] has been recently published. These novel MCFs maximize channel density and reduce crosstalk but their use as an optical interconnect is relatively less investigated. Recently, α index profile hexagonal seven core single mode MCF has been reported to reduce intercore crosstalk [19]. In order to realize low crosstalk and high core density, a holey microstructured MCF based optical interconnect is also reported recently [20]. The hexagonal arrangement of cores in MCF discussed in Refs. [19,20] is more closely packed but not compatible with edge coupling requirement of silicon photonic transceiver. More compatible is rectangular arrangements of four and eight core fiber proposed for optical interconnects in which crosstalk is calculated by the coupled mode theory followed by experimental results [21,22]. In this paper, quantitative and qualitative design parameters of an optical interconnect are being reported. The optical interconnect consists of 2 4 rectangular arrayed heterogeneous MCF. Individual cores have α index profile that can be made compatible with edge coupling to silicon photonic transceiver chips. The optimal design is based on minimizing crosstalk obtained by coupled power theory [23,24] for index parameter α, intercore distance Λ, and bending radius. The results are compared with
J.K. Mishra, V. Priye / Optics Communications 331 (2014) 272–277
273
In order to analyze intercore crosstalk in MCFs, coupled power theory [23,24] is employed. First, mode coupling coefficient κ and power coupling coefficient h between two neighboring cores of MCFs with α index profile is investigated. The expression of κ between two cores is given as [26] R R ωε þ 1 þ 1 ðN 2 Nn ÞEnm :En dxdy κ mn ¼ R þ 1 R0 þ 11 1 ð2Þ n n 1 1 uz :ðE m H m þ E m H m Þdxdy
Fig. 1. Schematic of 2 4 rectangular array heterogeneous MCF.
that of linear 1 4 core geometry of MCF and hexagonal seven core MCF [25]. The paper is organized as follows: in Section 2, the geometry and design of heterogeneous 2 4 MCF with α index profile is discussed. For sake of continuity, mathematical approach based on coupled power theory [25] to obtain crosstalk in MCF is briefly discussed. The fiber propagation parameters required to implement coupled power theory are obtained through commercial software FemSIM. In Section 3, simulation results and design approach of a bend-insensitive heterogeneous MCF for optical interconnect applications are elucidated. Finally, Section 4 concludes the paper.
2. Theory The schematic cross section of proposed optical interconnect with rectangular arrayed MCF is shown Fig. 1. It is designed such that MCF with rectangular array of eight cores [5] is well matched to the computer compatible parallel communication links. The cores can have α index profile tailored and can have same or different core diameters. The refractive index profile of the core is expressed as nðrÞ ¼ nc
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f1 2Δðr=aÞα g
aZr Z0
ð1Þ
here, nðrÞ is refractive index at a radial distance r from fiber axis, a is the core radius, nc is the refractive index of the core at r ¼ 0, ncl is homogeneous ðnðrÞ ¼ ncl for r Z a) refractive index of the cladding, Δ represents relative refractive index difference between core and cladding and α defines the shape of the profile. To reduce crosstalk, there should be a large phase difference between modes of the adjacent cores and moreover power in the core should be tightly confined to reduce effect of perturbations. One way to increase the difference in propagation constant and power confinement is to increase the relative index difference. However, to maintain the single mode propagation, core diameter is proportionately reduced. For homogenous MCF, individual cores are of diameter d1 ¼ 5 μm with relative refractive index difference Δ ¼ 0:8% and cladding refractive index 1.45. Inhomogeneous MCF is designed with adjacent cores of different diameter and Δ. Relative refractive index differences considered are Δ1 ¼ 0:8% and Δ2 ¼ 0:6% with core diameters d1 ¼ 5 μm and d2 ¼ 4.8 μm for bigger and smaller cores respectively. With the above parameters, in FemSIM, all cores in rectangular array are arranged with pitch and separation between the linear arrays of two rows is 2Λ. The operating wavelength is assumed to be 1.55 μm. The cladding diameter depends on number of cores and core to core pitch. When spacing between cores is large, the flexibility of fiber reduces having a serious impact on mechanical reliability due to large cladding diameter. For present analysis, the cladding diameter is assumed to be 200 μm [20].
where, ω is angular frequency of sinusoidally varying electromagnetic field, ε0 is permittivity of the medium, and uz represents outwardly directed unit vector. The pair m and n is either (1, 2) or (2, 1). E and H represent the electric and magnetic fields respectively. The refractive-index distribution in the entire coupled region is expressed as [17]. N2 ¼ N21 þ N 22 n2
ð3Þ
where N1 and N2 represent the refractive index distribution of each core with α index profile, and n represents the refractive index distribution outside the cores. N2 N 22 is zero except inside the core 1, while N 2 N 21 is zero everywhere except inside core 2. To calculate coupling coefficient κ full vector finite element method have been proposed [27]. In this paper finite element method based commercial mode solver FemSIM is used to evaluate effective index and electric field distribution of both MCF models. The data thus obtained is numerically integrated in MATLAB to calculate κ between adjacent cores. Analytical approaches based on exponential, Gaussian, and triangular autocorrelation functions were proposed to evaluate the power coupling coefficient h for bend fibers [14]. However, for bending radius larger than a threshold value Rth the crosstalk behaviors are not well simulated with Gaussian autocorrelation function in phase mismatched region [11,12,14]. Moreover, value of h predicted by triangular autocorrelation function is not accurate [14]. The reason for discrepancy of the two autocorrelation functions is that they work satisfactorily when crosstalk is independent of segment length [14]. It is true for homogenous core straight MCF when modes are phase matched. The two correlation functions do not give appropriate results in case of index mismatch for small bending radius when crosstalk is strongly dependent on the segment length [14]. Therefore, to realize accurate estimation of intercore crosstalk for phase mismatch configurations in MCF exponential autocorrelation is more efficient [25]. The power coupling coefficient for exponential autocorrelation is expressed as [25] hmn ¼
2K 2mn dc
1 þ ðΔβmn dc Þ2
ð4Þ
where m, n represent the core m and n, K mn is the average value of κ mn and κ nm and satisfies the law of power conservation [14], Δβmn is the difference of equivalent propagation constant between cores m and n, and dc is the correlation length. The simulation results with dc ¼ 0.05 m agree well with the measurement data [28], and it is the preferred value for the estimation of crosstalk in this paper. The crosstalk between two α index profile cores of MCF over a length L and average power coupling coefficient h mn is estimated by coupled power theory as [25] X T ¼ tanhðhmn LÞ
ð5Þ
The above expression is independent of the twist rate of the fiber which has to be considered otherwise [11,14,28]. 3. Results and discussion For calculation, core to core pitch Λ and spacing 2Λ between two linear arrays of core as shown in Fig. 1, is assumed to be 30 μm
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Fig. 2. Variation of effective index with bending radius for homogeneous 2 4 MCF with pitch Λ ¼ 30 μm.
Fig. 4. Crosstalk variation with bending radius for homogeneous 2 4 MCF for different α.
Fig. 3. Variation of effective index with bending radius for heterogeneous 2 4 MCF with pitch Λ ¼ 30 μm.
Fig. 5. Crosstalk variation with bending radius for heterogeneous 2 4 MCF for different α with Λ ¼ 30 μm.
[25] and 60 μm [21]. As discussed in previous section, to obtain crosstalk in adjacent cores due to bending, effective index has to be obtained for all bending radii. Figs. 2 and 3 show the effective index neff of respective homogeneous and heterogeneous 2 4 MCF for different index profiles α at various bending radius calculated by Rsoft FemSIM. The results illustrate that effective index neff decreases with increasing bending radius in both the cases. The neff of homogeneous 2 4 MCF is greater than that of heterogeneous 2 4 MCF of corresponding α value, reason being lower refractive index ðΔ2 ¼ 0:6%Þ of smaller core (diameter 4.8 μm) dictates the value of effective index. Fig. 4 shows variation of crosstalk calculated from Eq. (5), between two adjacent cores in a row with bending radius for rectangular array 2 4 MCF for different α. The crosstalk depends on the direction of bend with respect to core geometry and the angle of the line segment connecting core and the center from the radial direction of bending [12,25]. In this simulation, the fiber length L is 100 m, and other parameters are same as that in Fig. 2. The plot shows that for given α index, crosstalk increases with bending radius. This anomalous behavior can be explained by considering that small bending radius modifies the refractive index [12] substantially. For large bending radius which implies straight fiber there is strong phase matching (Δβ 0) between
modes of adjacent homogenous cores resulting in larger crosstalk. However, for smaller bending radii, the refractive index of adjacent cores are modified differently according to their position from the core resulting in phase mismatch ðΔβ a 0Þ, thus less coupling of power in adjacent cores and ultimately low crosstalk. For a given bending radius, crosstalk decreases for low α value because mismatch in refractive index of adjacent cores due to bend is more pronounced for triangular refractive index ðα ¼ 1Þ than that of step index ðα ¼ 1Þ profile. From the simulated results it is observed that, the crosstalk per 100 m propagation of 2 4 MCF is less than 40 dB at Λ ¼ 30 μm if bending radius is 150 mm and index profile parameter α ¼ 1. The crosstalk reduces by more than 18 dB if profile parameter unity rather than infinity is selected. Next, the dependence of crosstalk on bending radius is calculated for heterogeneous 2 4 MCF for different α. Fig. 5 shows the crosstalk versus bending radius for heterogeneous 2 4 MCF for different index profile parameter for same parameters discussed above. By making the adjacent cores dissimilar in both dimension and refractive index, crosstalk reduces drastically as compared with MCF having similar core diameter and refractive indices (see Fig. 4). Moreover, it can be observed from Fig. 5 that for every α value, a threshold bending radius exists for which crosstalk is maximum. A worthwhile explanation of the observed behavior is
J.K. Mishra, V. Priye / Optics Communications 331 (2014) 272–277
that firstly for heterogeneous cores there is phase mismatch even for straight fibers resulting in less crosstalk. Secondly, for smaller bending radius there is a threshold value for which adjacent dissimilar cores have their refractive indices modified due to bending and satisfy phase matching condition resulting in enhanced crosstalk. For each index profile, there is an optimum value of bending radius beyond which crosstalk variation is minimal. Moreover, for same bending radius 150 mm and index profile, crosstalk in heterogeneous MCF is less than 100 dB as compared to homogenous counterpart. Moreover, the threshold value of low bend radius where crosstalk is maximum shifts below 50 mm. However, if the bending radius is 150 mm the crosstalk of more 14 dB can be reduced by changing the profile parameter from infinity to 1. We can see that the crosstalk is less than 152 dB after the 100 m propagation at index profile parameter α ¼ 1. Simulation results show that unity profile parameter gives rise to better performance. For α o1, crosstalk will increase again as the profile is no longer linear and moreover such profiles are not in literature to best of our knowledge. From the results depicted in Figs. 4 and 5, it can be inferred that heterogeneous rectangular array MCF with index profile α ¼ 1 is most tolerant to crosstalk and can be treated as bend insensitive for bend radius more than an optimum value. Another important parameter that will decide crosstalk performance of MCF based OI is the core to core pitch Λ (see Fig. 1). The results in Fig. 6 show that peak crosstalk shifts towards lower bending radius if core to core separation is reduced to Λ ¼ 30 μm or less. The crosstalk of 2 4 MCF for triangular index profile is estimated to be less than 185 dB at Λ ¼ 50 μm if bending radius is 200 mm. On the other hand, maximum crosstalk decreases when core to core pitch increases and the peak also shifts resulting in low crosstalk for tight bend (low bending radius). It can be inferred that MCF based OI can be designed which requires different bending tolerance for long and short distance applications. For longer length interconnects larger core to core separation should be preferred where as for lengths requiring tighter bends smaller Λ will be beneficial. The possible values of Λ is selected such that they can be easily fabricated within the cladding diameter of 200 μm. To investigate the effect of two rows on crosstalk performance, a comparison is made between heterogeneous 2 4 and 1 4 MCFs and is depicted in Fig. 7. For an optimum value of bending radius the crosstalk values for both 2 4 and 1 4 MCFs are enhanced as phase matching condition is satisfied. Below and above the optimum value of bending radius, crosstalk decreases due to phase detuning at different bending radii. It can be
Fig. 6. Crosstalk variation with bending radius for heterogeneous 2 4 MCF for different core to core pitch with α ¼ 1.
275
Fig. 7. Crosstalk variation with bending radius for heterogeneous 1 4 and 2 4 MCF for triangular index profile with Λ ¼ 30 μm.
Table 1 Threshold bending Rth radius for the heterogeneous MCFs with core to core pitch Λ ¼ 30 μm. Types of MCF
1 4 MCF 2 4 MCF
Threshold bending radius Rth (in mm) α¼1
α¼2
α¼3
α¼1
46.31 47.40
52.57 54.26
60.32 63.70
72.83 76.53
observed that there is minimal coupling of power between the linear arrays of two rows, which is a trade off for optimized 2 4 MCF for optical interconnect application. Above results also show that to realize high bend tolerance, threshold bending radius Rth corresponding to maximum crosstalk for heterogeneous MCF has to be evaluated. The results are summarized in Tables 1 and 2. Table 1 shows that Rth decreases by changing the profile parameter from infinity to 1 for both the MCFs and it is longer for 2 4 MCF than 1 4 MCF. However, the differences between Rth is minimum for α ¼ 1. Table 2 illustrates that for α ¼ 1 MCF, Rth can be made larger by increasing the separation between adjacent cores. These results show that index profile and pitch of the core can be suitably selected to meet the optical interconnect usage for long distance (loose bends) or small distances (tight bends). To validate our approach, we have calculated crosstalk for homogeneous 2 4 MCF and compared with the experimental value reported in Ref. [22]. In 2 4 homogeneous MCF having parameters 50 μm core to core pitch, 100 m length of MCF and 250 mm bending radius, the present approach gives 48 dB crosstalk between adjacent cores, which is within the range from 45 dB to 54 dB as measured by authors of Ref. [22]. Trench assisted MCF can also be used for low crosstalk bend insensitive optical interconnect applications. The crosstalk estimated in hexagonal seven core homogeneous trench assisted MCF reported in Ref. [17] is more than 4 dB as compared to 2 4 homogeneous MCF considered in the present paper. Crosstalk between two adjacent cores of MCF may be affected by temperature variations as refractive index of a fiber changes with temperature [29]. Crosstalk may increase if phase matching conditions are satisfied at certain temperature for a given bending radius. However, in the present case temperature effects are ignored to avoid complexity and will be a topic of further investigation. Lastly, crosstalk obtained in proposed heterogeneous 2 4 MCF shown in Fig. 1 with triangular index profile ðα ¼ 1Þ is compared
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Table 2 Threshold bending radius Rth for the heterogeneous MCFs with index profile parameter α ¼ 1. Types of MCF
1 4 MCF 2 4 MCF
Threshold bending radius Rth (in mm) Λ ¼ 30 μm
Λ ¼ 35 μm
Λ ¼ 40 μm
Λ ¼ 45 μm
Λ ¼ 50 μm
46.31 47.40
54.56 56.14
63.63 64.25
79.10 80.48
85.01 87.56
fibers [33]. Similarly, once applications of triangular index profile MCF are well established as ultrafast optical components, interest in application of similar fabrication techniques for MCFs will become realistic.
4. Conclusion
Fig. 8. Crosstalk variation with bending radius for heterogeneous 2 4 MCF for triangular index profile and seven-core MCF [25].
with hexagonal seven core MCF reported in Ref. [25]. The seven core MCF has diameters 8.1 μm and 9.4 μm of center core and outer core respectively. The relative refractive index difference for the two cores are fixed at Δ ¼ 0:38%. Fig. 8 highlights that for identical pitch Λ, large reduction in crosstalk can be achieved using proposed heterogeneous MCF as compared with hexagonal seven core MCF. It can be noted here that hexagonal seven core MCF has larger core size and low Δ resulting in mode confinement almost equivalent to 2 4 MCF having smaller core and high Δ. To apply the proposed MCF based OI in optical communication system, it will be required to connect it to a single mode fiber. Seven core hexagonal MCF can be connected to single mode fiber by fusion splicing to tapered multicore coupler [30], lens optics [31] and using fan-in fan-out devices [31]. A precise ferrule floating mechanism with a split sleeve can be used with careful calibration alignment for optimizing the rectangular array MCF fan-in and fan-out device of the desired core size. Fiber bundle type fan-out device is reported to realize full-face connection between MCF to independent single core fibers [32]. Similar techniques can be modified to connect proposed 2 4 MCF to single mode fiber as well and is a separate topic of research. Bit error rates can be lower than the forward error correction threshold by using MCF and fan-in/fan-out device. The crosstalk requirement to achieve the bit rate of 10 Gbps is within 50 dB to 60 dB at operating wavelength of 1550 nm [5]. For application in next generation exa-bandwidth optical interconnects operating at very high bit rates (100 Tera to Exa bps) minimum crosstalk tolerance required can be expected to be less than 100 dB. In the proposed MCF, crosstalk obtained is less than 140 dB (see Fig. 7) making it suitable for ultrahigh bit rates. The heterogeneous MCF can be manufactured using MCVD process [33] and stack and draw method [20] with silicate or doped glass. Interest in fabrication of low loss triangular index profile ðα ¼ 1Þ single mode fiber was initiated when it was established that such fibers can be used as dispersion shifted fibers. MCVD method was used to fabricate such
A novel optical interconnect configuration based on heterogeneous 2 4 core MCF is proposed for application in silicon photonic transceiver chip. The major issue of crosstalk in the proposed MCF is quantified using semi-analytical method based on FemSIM and coupled power theory. Crosstalk dependence on various MCF parameters such as core to core pitch distances, index profile and effect of bend has been addressed. The results are compared with 1 4 core MCF to ascertain the trade off incurred by adding a new row of cores to suit future optical interconnect specifications. Comparison is also made with already reported 7 core hexagonal MCF with same pitch. It is confirmed that lower crosstalk can be achieved for a MCF with index profile α ¼ 1 for a given bending radius. It is further proposed that keeping the overall clad diameter constant, core to core separation can be tailored according to desired optical interconnect application requiring bend insensitivity for either large bending radius or tight bends. These results offer a framework that enables further exploration of design of MCF for practical optical interconnects. References [1] M.A. Taubenblatt, J. Lightwave Technol. 30 (2012) 448. [2] J.A. Kash, A. Benner, F.E. Doany, D. Kuchta, B.G. Lee, P. Pepeljugoski, L. Schares, C. Schow, M. Taubenblatt, Optical interconnects in future servers, in: Proceedings of the Optical Fiber Communication Conference and Exposition (OFC/ NFOEC), and the National Fiber Optic Engineers Conference, 2011, pp. 1–3. [3] C. Kachris, K. Kanonakis, I. Tomkos, IEEE Commun. Mag. 51 (2013) 39. [4] D.M. Taylor, C.R. Bennett, T.J. Shepherd, L.F. Michaille, M.D. Nielsen, H. R. Simonsen, Electron. Lett. 42 (2006) 331. [5] D.L. Butler, M.J. Li, S. Li, K.I. Matthews, V.N. Nazarov, A. Koklyushkin, R.L. McCollum, Y. Geng, J.P. Luther, Proceedings of the IEEE Optical Interconnects Conference, 2013, pp. 9. [6] B. Rosinski, J.D. Chi, P. Grosso, J.L. Bihan, J. Lightwave Technol. 17 (1999) 807. [7] S. Abrate, R. Gaudino, C. Zerna, B. Offenbeck, J. VinogradovJ. Lambkin, A. Nocivelli, , 10 Gbps POF ribbon transmission for optical interconnects, in: Proceeding of the IEEE Photonics Conference, 2011, pp. 230–231. [8] T. Morioka, New generation optical infrastructure technologies: EXAT initiative towards 2020 and beyond, in: Proceedings of the 14th OptoElectronics and Communications Conference, 2009, pp. 1–2. [9] S. Inao, T. Sato, S. Sentsui, T. Kuroha, Y. Nishimura, Multicore optical fiber, in: Proceedings of the Optical Fiber Communications Conference, 1979, pp. 46–48. [10] B.G. Lee, D.M. Kuchta, F.E. Doany, C.L. Schow, P. Pepeljugoski, C. Baks, T. F. Taunay, B. Zhu, M.F. Yan, G.E. Oulundsen, D.S. Vaidya, W. Luo, N. Li, J. Lightwave Technol. 30 (2012) 886. [11] T. Hayashi, T. Nagashima, O. Shimakawa, T. Sasaki, E. Sasaoka, Crosstalk variation of multi-core fibre due to fibre bend, in: Proceedings of the 36th European Conference and Exhibition on Optical Communication, 2010, pp. 1–3. [12] J.M. Fini, B. Zhu, T.F. Taunay, M.F. Yan, Opt. Express 18 (2010) 15122. [13] T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, E. Sasaoka, Opt. Express 19 (2011) 16576. [14] M. Koshiba, K. Saitoh, K. Takenaga, S. Matsuo, Opt. Express 19 (2011) B102. [15] K. Takenaga, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, M. Koshiba, Reduction of crosstalk by quasi-homogeneous solid multi-core fiber, in: Proceedings of the Optical Fiber Communication Conference (OFC/NFOEC), and the National Fiber Optic Engineers Conference, 2010, pp. 1–3. [16] M. Koshiba, K. Saitoh, Y. Kokubun, IEICE Electron. Express 6 (2009) 98. [17] J. Tu, K. Saitoh, M. Koshiba, K. Takenaga, S. Matsuo, Opt. Express 20 (2012) 15157. [18] K. Saitoh, T. Matsui, T. Sakamoto, M. Koshiba, S. Tomita, Multi-core holeassisted fibers for high core density space division multiplexing, in: Proceeding of the 15th OptoElectronics and Communications Conference, 2010, pp. 164–165. [19] S. Yamamoto, M. Ohashi, Y. Miyoshi, Crosstalk in multi-core fibers with αindex single-mode cores, in: Proceeding of the 17th OptoElectronics and Communications Conference, 2012, pp. 355–356. [20] V. Francois, F. Laramee, J. Lightwave Technol. 31 (2013) 4022. [21] M.J. Li, B. Hoover, V.N. Nazarov, D.L. Butler, Multicore fiber for optical interconnect applications, in: Proceedings of the 17th OptoElectronics and Communications Conference, 2012, pp. 564–565.
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Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Design of low crosstalk and bend insensitive optical interconnect using rectangular array multicore fiber Jitendra Kumar Mishra n, Vishnu Priye Department of Electronics Engineering, Indian School of Mines, Dhanbad 826004, India
art ic l e i nf o
a b s t r a c t
Article history: Received 25 March 2014 Received in revised form 13 June 2014 Accepted 14 June 2014 Available online 25 June 2014
A design strategy for achieving minimum crosstalk in a space division multiplexed 2 4 multicore fiber (MCF) for application in next generation exa-bandwidth optical interconnects is proposed. To evaluate crosstalk in adjacent cores of MCF, a semi-analytical approach based on finite element method and coupled power theory is applied. The dependence of crosstalk on various MCF parameters – such as index profile parameter, core to core pitch and bending radius – is investigated. It is shown that optical interconnects based on heterogeneous core MCF with triangular index profile and optimum core to core pitch, can be configured to have minimum crosstalk per unit length. Moreover, such interconnects show high degree of bend tolerance for both small and large bending radii. & 2014 Elsevier B.V. All rights reserved.
Keywords: Optical interconnects Multicore fibers Space division multiplexing Crosstalk
1. Introduction Due to steadily increasing data rate requirements and to overcome bandwidth density drives, optical interconnect (OI) has become a key technology to realize signal transmission in boxto-box, rack-to-rack, board-to-board, and chip-to-chip interconnect applications [1]. It has triggered research interest as a promising network choice to achieve future exaflop (1018) high performance computing systems [2]. For next generation supercomputing as well as data centers, key issue for design of OI is to increase the channel density with minimum escalation in link cost and power budget [3]. OI configuration based on multicore fiber (MCF) shows promise to cope with ever increasing demands on bandwidth within data centers, terabit switches, core routers, digital cross connect systems and high performance computers [4,5]. MCF supports multichannel transmission compatible with 2D arrays of vertical cavity surface emitting laser (VCSEL) transmitter [6]. Although, fiber ribbons or individual fibers increase the fiber density [7], they are costly, bulky, consume more power and do not meet the very high density requirement of end to end optical interconnects for data transmission. Hence they cannot be an alternative to MCF with space division multiplexing capacity to overcome the exponentially growing demand in data traffic of current optical communication system [8]. MCF which was proposed couple of decades ago [9], due to its space division multiplexing capability has become a strong candidate to configure novel OI [10] which can exploit huge optoelectronic
n
Corresponding author. E-mail address: [email protected] (J.K. Mishra).
http://dx.doi.org/10.1016/j.optcom.2014.06.026 0030-4018/& 2014 Elsevier B.V. All rights reserved.
bandwidth disparity between requirement and availability. For efficient usage of MCF as OI, one of the major issues that has to be addressed is crosstalk between cores which depends on refractive index profile of individual cores and distance between neighboring cores. Moreover as bends are inevitable for interconnects, bend induced index perturbations and core density strongly affects the crosstalk characteristics in MCF [11,12]. To estimate crosstalk between adjacent cores in a MCF, coupled mode theory [13,14] and coupled power theory [14] are applied. Furthermore, to reduce the crosstalk in a MCF, research work on homogeneous MCFs [15], heterogeneous MCFs [16], trench assisted MCFs [17] as well as hole assisted MCFs [18] has been recently published. These novel MCFs maximize channel density and reduce crosstalk but their use as an optical interconnect is relatively less investigated. Recently, α index profile hexagonal seven core single mode MCF has been reported to reduce intercore crosstalk [19]. In order to realize low crosstalk and high core density, a holey microstructured MCF based optical interconnect is also reported recently [20]. The hexagonal arrangement of cores in MCF discussed in Refs. [19,20] is more closely packed but not compatible with edge coupling requirement of silicon photonic transceiver. More compatible is rectangular arrangements of four and eight core fiber proposed for optical interconnects in which crosstalk is calculated by the coupled mode theory followed by experimental results [21,22]. In this paper, quantitative and qualitative design parameters of an optical interconnect are being reported. The optical interconnect consists of 2 4 rectangular arrayed heterogeneous MCF. Individual cores have α index profile that can be made compatible with edge coupling to silicon photonic transceiver chips. The optimal design is based on minimizing crosstalk obtained by coupled power theory [23,24] for index parameter α, intercore distance Λ, and bending radius. The results are compared with
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In order to analyze intercore crosstalk in MCFs, coupled power theory [23,24] is employed. First, mode coupling coefficient κ and power coupling coefficient h between two neighboring cores of MCFs with α index profile is investigated. The expression of κ between two cores is given as [26] R R ωε þ 1 þ 1 ðN 2 Nn ÞEnm :En dxdy κ mn ¼ R þ 1 R0 þ 11 1 ð2Þ n n 1 1 uz :ðE m H m þ E m H m Þdxdy
Fig. 1. Schematic of 2 4 rectangular array heterogeneous MCF.
that of linear 1 4 core geometry of MCF and hexagonal seven core MCF [25]. The paper is organized as follows: in Section 2, the geometry and design of heterogeneous 2 4 MCF with α index profile is discussed. For sake of continuity, mathematical approach based on coupled power theory [25] to obtain crosstalk in MCF is briefly discussed. The fiber propagation parameters required to implement coupled power theory are obtained through commercial software FemSIM. In Section 3, simulation results and design approach of a bend-insensitive heterogeneous MCF for optical interconnect applications are elucidated. Finally, Section 4 concludes the paper.
2. Theory The schematic cross section of proposed optical interconnect with rectangular arrayed MCF is shown Fig. 1. It is designed such that MCF with rectangular array of eight cores [5] is well matched to the computer compatible parallel communication links. The cores can have α index profile tailored and can have same or different core diameters. The refractive index profile of the core is expressed as nðrÞ ¼ nc
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f1 2Δðr=aÞα g
aZr Z0
ð1Þ
here, nðrÞ is refractive index at a radial distance r from fiber axis, a is the core radius, nc is the refractive index of the core at r ¼ 0, ncl is homogeneous ðnðrÞ ¼ ncl for r Z a) refractive index of the cladding, Δ represents relative refractive index difference between core and cladding and α defines the shape of the profile. To reduce crosstalk, there should be a large phase difference between modes of the adjacent cores and moreover power in the core should be tightly confined to reduce effect of perturbations. One way to increase the difference in propagation constant and power confinement is to increase the relative index difference. However, to maintain the single mode propagation, core diameter is proportionately reduced. For homogenous MCF, individual cores are of diameter d1 ¼ 5 μm with relative refractive index difference Δ ¼ 0:8% and cladding refractive index 1.45. Inhomogeneous MCF is designed with adjacent cores of different diameter and Δ. Relative refractive index differences considered are Δ1 ¼ 0:8% and Δ2 ¼ 0:6% with core diameters d1 ¼ 5 μm and d2 ¼ 4.8 μm for bigger and smaller cores respectively. With the above parameters, in FemSIM, all cores in rectangular array are arranged with pitch and separation between the linear arrays of two rows is 2Λ. The operating wavelength is assumed to be 1.55 μm. The cladding diameter depends on number of cores and core to core pitch. When spacing between cores is large, the flexibility of fiber reduces having a serious impact on mechanical reliability due to large cladding diameter. For present analysis, the cladding diameter is assumed to be 200 μm [20].
where, ω is angular frequency of sinusoidally varying electromagnetic field, ε0 is permittivity of the medium, and uz represents outwardly directed unit vector. The pair m and n is either (1, 2) or (2, 1). E and H represent the electric and magnetic fields respectively. The refractive-index distribution in the entire coupled region is expressed as [17]. N2 ¼ N21 þ N 22 n2
ð3Þ
where N1 and N2 represent the refractive index distribution of each core with α index profile, and n represents the refractive index distribution outside the cores. N2 N 22 is zero except inside the core 1, while N 2 N 21 is zero everywhere except inside core 2. To calculate coupling coefficient κ full vector finite element method have been proposed [27]. In this paper finite element method based commercial mode solver FemSIM is used to evaluate effective index and electric field distribution of both MCF models. The data thus obtained is numerically integrated in MATLAB to calculate κ between adjacent cores. Analytical approaches based on exponential, Gaussian, and triangular autocorrelation functions were proposed to evaluate the power coupling coefficient h for bend fibers [14]. However, for bending radius larger than a threshold value Rth the crosstalk behaviors are not well simulated with Gaussian autocorrelation function in phase mismatched region [11,12,14]. Moreover, value of h predicted by triangular autocorrelation function is not accurate [14]. The reason for discrepancy of the two autocorrelation functions is that they work satisfactorily when crosstalk is independent of segment length [14]. It is true for homogenous core straight MCF when modes are phase matched. The two correlation functions do not give appropriate results in case of index mismatch for small bending radius when crosstalk is strongly dependent on the segment length [14]. Therefore, to realize accurate estimation of intercore crosstalk for phase mismatch configurations in MCF exponential autocorrelation is more efficient [25]. The power coupling coefficient for exponential autocorrelation is expressed as [25] hmn ¼
2K 2mn dc
1 þ ðΔβmn dc Þ2
ð4Þ
where m, n represent the core m and n, K mn is the average value of κ mn and κ nm and satisfies the law of power conservation [14], Δβmn is the difference of equivalent propagation constant between cores m and n, and dc is the correlation length. The simulation results with dc ¼ 0.05 m agree well with the measurement data [28], and it is the preferred value for the estimation of crosstalk in this paper. The crosstalk between two α index profile cores of MCF over a length L and average power coupling coefficient h mn is estimated by coupled power theory as [25] X T ¼ tanhðhmn LÞ
ð5Þ
The above expression is independent of the twist rate of the fiber which has to be considered otherwise [11,14,28]. 3. Results and discussion For calculation, core to core pitch Λ and spacing 2Λ between two linear arrays of core as shown in Fig. 1, is assumed to be 30 μm
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Fig. 2. Variation of effective index with bending radius for homogeneous 2 4 MCF with pitch Λ ¼ 30 μm.
Fig. 4. Crosstalk variation with bending radius for homogeneous 2 4 MCF for different α.
Fig. 3. Variation of effective index with bending radius for heterogeneous 2 4 MCF with pitch Λ ¼ 30 μm.
Fig. 5. Crosstalk variation with bending radius for heterogeneous 2 4 MCF for different α with Λ ¼ 30 μm.
[25] and 60 μm [21]. As discussed in previous section, to obtain crosstalk in adjacent cores due to bending, effective index has to be obtained for all bending radii. Figs. 2 and 3 show the effective index neff of respective homogeneous and heterogeneous 2 4 MCF for different index profiles α at various bending radius calculated by Rsoft FemSIM. The results illustrate that effective index neff decreases with increasing bending radius in both the cases. The neff of homogeneous 2 4 MCF is greater than that of heterogeneous 2 4 MCF of corresponding α value, reason being lower refractive index ðΔ2 ¼ 0:6%Þ of smaller core (diameter 4.8 μm) dictates the value of effective index. Fig. 4 shows variation of crosstalk calculated from Eq. (5), between two adjacent cores in a row with bending radius for rectangular array 2 4 MCF for different α. The crosstalk depends on the direction of bend with respect to core geometry and the angle of the line segment connecting core and the center from the radial direction of bending [12,25]. In this simulation, the fiber length L is 100 m, and other parameters are same as that in Fig. 2. The plot shows that for given α index, crosstalk increases with bending radius. This anomalous behavior can be explained by considering that small bending radius modifies the refractive index [12] substantially. For large bending radius which implies straight fiber there is strong phase matching (Δβ 0) between
modes of adjacent homogenous cores resulting in larger crosstalk. However, for smaller bending radii, the refractive index of adjacent cores are modified differently according to their position from the core resulting in phase mismatch ðΔβ a 0Þ, thus less coupling of power in adjacent cores and ultimately low crosstalk. For a given bending radius, crosstalk decreases for low α value because mismatch in refractive index of adjacent cores due to bend is more pronounced for triangular refractive index ðα ¼ 1Þ than that of step index ðα ¼ 1Þ profile. From the simulated results it is observed that, the crosstalk per 100 m propagation of 2 4 MCF is less than 40 dB at Λ ¼ 30 μm if bending radius is 150 mm and index profile parameter α ¼ 1. The crosstalk reduces by more than 18 dB if profile parameter unity rather than infinity is selected. Next, the dependence of crosstalk on bending radius is calculated for heterogeneous 2 4 MCF for different α. Fig. 5 shows the crosstalk versus bending radius for heterogeneous 2 4 MCF for different index profile parameter for same parameters discussed above. By making the adjacent cores dissimilar in both dimension and refractive index, crosstalk reduces drastically as compared with MCF having similar core diameter and refractive indices (see Fig. 4). Moreover, it can be observed from Fig. 5 that for every α value, a threshold bending radius exists for which crosstalk is maximum. A worthwhile explanation of the observed behavior is
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that firstly for heterogeneous cores there is phase mismatch even for straight fibers resulting in less crosstalk. Secondly, for smaller bending radius there is a threshold value for which adjacent dissimilar cores have their refractive indices modified due to bending and satisfy phase matching condition resulting in enhanced crosstalk. For each index profile, there is an optimum value of bending radius beyond which crosstalk variation is minimal. Moreover, for same bending radius 150 mm and index profile, crosstalk in heterogeneous MCF is less than 100 dB as compared to homogenous counterpart. Moreover, the threshold value of low bend radius where crosstalk is maximum shifts below 50 mm. However, if the bending radius is 150 mm the crosstalk of more 14 dB can be reduced by changing the profile parameter from infinity to 1. We can see that the crosstalk is less than 152 dB after the 100 m propagation at index profile parameter α ¼ 1. Simulation results show that unity profile parameter gives rise to better performance. For α o1, crosstalk will increase again as the profile is no longer linear and moreover such profiles are not in literature to best of our knowledge. From the results depicted in Figs. 4 and 5, it can be inferred that heterogeneous rectangular array MCF with index profile α ¼ 1 is most tolerant to crosstalk and can be treated as bend insensitive for bend radius more than an optimum value. Another important parameter that will decide crosstalk performance of MCF based OI is the core to core pitch Λ (see Fig. 1). The results in Fig. 6 show that peak crosstalk shifts towards lower bending radius if core to core separation is reduced to Λ ¼ 30 μm or less. The crosstalk of 2 4 MCF for triangular index profile is estimated to be less than 185 dB at Λ ¼ 50 μm if bending radius is 200 mm. On the other hand, maximum crosstalk decreases when core to core pitch increases and the peak also shifts resulting in low crosstalk for tight bend (low bending radius). It can be inferred that MCF based OI can be designed which requires different bending tolerance for long and short distance applications. For longer length interconnects larger core to core separation should be preferred where as for lengths requiring tighter bends smaller Λ will be beneficial. The possible values of Λ is selected such that they can be easily fabricated within the cladding diameter of 200 μm. To investigate the effect of two rows on crosstalk performance, a comparison is made between heterogeneous 2 4 and 1 4 MCFs and is depicted in Fig. 7. For an optimum value of bending radius the crosstalk values for both 2 4 and 1 4 MCFs are enhanced as phase matching condition is satisfied. Below and above the optimum value of bending radius, crosstalk decreases due to phase detuning at different bending radii. It can be
Fig. 6. Crosstalk variation with bending radius for heterogeneous 2 4 MCF for different core to core pitch with α ¼ 1.
275
Fig. 7. Crosstalk variation with bending radius for heterogeneous 1 4 and 2 4 MCF for triangular index profile with Λ ¼ 30 μm.
Table 1 Threshold bending Rth radius for the heterogeneous MCFs with core to core pitch Λ ¼ 30 μm. Types of MCF
1 4 MCF 2 4 MCF
Threshold bending radius Rth (in mm) α¼1
α¼2
α¼3
α¼1
46.31 47.40
52.57 54.26
60.32 63.70
72.83 76.53
observed that there is minimal coupling of power between the linear arrays of two rows, which is a trade off for optimized 2 4 MCF for optical interconnect application. Above results also show that to realize high bend tolerance, threshold bending radius Rth corresponding to maximum crosstalk for heterogeneous MCF has to be evaluated. The results are summarized in Tables 1 and 2. Table 1 shows that Rth decreases by changing the profile parameter from infinity to 1 for both the MCFs and it is longer for 2 4 MCF than 1 4 MCF. However, the differences between Rth is minimum for α ¼ 1. Table 2 illustrates that for α ¼ 1 MCF, Rth can be made larger by increasing the separation between adjacent cores. These results show that index profile and pitch of the core can be suitably selected to meet the optical interconnect usage for long distance (loose bends) or small distances (tight bends). To validate our approach, we have calculated crosstalk for homogeneous 2 4 MCF and compared with the experimental value reported in Ref. [22]. In 2 4 homogeneous MCF having parameters 50 μm core to core pitch, 100 m length of MCF and 250 mm bending radius, the present approach gives 48 dB crosstalk between adjacent cores, which is within the range from 45 dB to 54 dB as measured by authors of Ref. [22]. Trench assisted MCF can also be used for low crosstalk bend insensitive optical interconnect applications. The crosstalk estimated in hexagonal seven core homogeneous trench assisted MCF reported in Ref. [17] is more than 4 dB as compared to 2 4 homogeneous MCF considered in the present paper. Crosstalk between two adjacent cores of MCF may be affected by temperature variations as refractive index of a fiber changes with temperature [29]. Crosstalk may increase if phase matching conditions are satisfied at certain temperature for a given bending radius. However, in the present case temperature effects are ignored to avoid complexity and will be a topic of further investigation. Lastly, crosstalk obtained in proposed heterogeneous 2 4 MCF shown in Fig. 1 with triangular index profile ðα ¼ 1Þ is compared
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Table 2 Threshold bending radius Rth for the heterogeneous MCFs with index profile parameter α ¼ 1. Types of MCF
1 4 MCF 2 4 MCF
Threshold bending radius Rth (in mm) Λ ¼ 30 μm
Λ ¼ 35 μm
Λ ¼ 40 μm
Λ ¼ 45 μm
Λ ¼ 50 μm
46.31 47.40
54.56 56.14
63.63 64.25
79.10 80.48
85.01 87.56
fibers [33]. Similarly, once applications of triangular index profile MCF are well established as ultrafast optical components, interest in application of similar fabrication techniques for MCFs will become realistic.
4. Conclusion
Fig. 8. Crosstalk variation with bending radius for heterogeneous 2 4 MCF for triangular index profile and seven-core MCF [25].
with hexagonal seven core MCF reported in Ref. [25]. The seven core MCF has diameters 8.1 μm and 9.4 μm of center core and outer core respectively. The relative refractive index difference for the two cores are fixed at Δ ¼ 0:38%. Fig. 8 highlights that for identical pitch Λ, large reduction in crosstalk can be achieved using proposed heterogeneous MCF as compared with hexagonal seven core MCF. It can be noted here that hexagonal seven core MCF has larger core size and low Δ resulting in mode confinement almost equivalent to 2 4 MCF having smaller core and high Δ. To apply the proposed MCF based OI in optical communication system, it will be required to connect it to a single mode fiber. Seven core hexagonal MCF can be connected to single mode fiber by fusion splicing to tapered multicore coupler [30], lens optics [31] and using fan-in fan-out devices [31]. A precise ferrule floating mechanism with a split sleeve can be used with careful calibration alignment for optimizing the rectangular array MCF fan-in and fan-out device of the desired core size. Fiber bundle type fan-out device is reported to realize full-face connection between MCF to independent single core fibers [32]. Similar techniques can be modified to connect proposed 2 4 MCF to single mode fiber as well and is a separate topic of research. Bit error rates can be lower than the forward error correction threshold by using MCF and fan-in/fan-out device. The crosstalk requirement to achieve the bit rate of 10 Gbps is within 50 dB to 60 dB at operating wavelength of 1550 nm [5]. For application in next generation exa-bandwidth optical interconnects operating at very high bit rates (100 Tera to Exa bps) minimum crosstalk tolerance required can be expected to be less than 100 dB. In the proposed MCF, crosstalk obtained is less than 140 dB (see Fig. 7) making it suitable for ultrahigh bit rates. The heterogeneous MCF can be manufactured using MCVD process [33] and stack and draw method [20] with silicate or doped glass. Interest in fabrication of low loss triangular index profile ðα ¼ 1Þ single mode fiber was initiated when it was established that such fibers can be used as dispersion shifted fibers. MCVD method was used to fabricate such
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