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State-of-the-art multicore fiber amplifiers for space division multiplexing
Optical Fiber Technology xxx (2016) xxx–xxx
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Invited Papers
State-of-the-art multicore fiber amplifiers for space division multiplexing Kazi S. Abedin ⇑, Man F. Yan, Thierry F. Taunay, Benyuan Zhu, Eric M. Monberg, David J. DiGiovanni OFS Laboratories, 19 Schoolhouse Road, Somerset, NJ 08873, United States
a r t i c l e
i n f o
Article history: Received 9 May 2016 Revised 19 September 2016 Accepted 25 September 2016 Available online xxxx Keywords: Optical fiber Multicore Erbium-doped fiber amplifiers Space division multiplexing
a b s t r a c t Space division multiplexing (SDM) has generated much interest lately as a potential means for enhancing the capacity of optical transmission systems. During the past several years, we have observed tremendous research efforts in the development of SDM amplifiers with an aim to increase core and mode counts and to improve amplification properties and pump conversion efficiencies. We report on the recent development of multicore fiber amplifiers suitable for amplifying space division multiplexed signals. Multicore fiber amplifiers with different number of cores, and pumping schemes have been developed to pump the cores individually or through a common cladding. We will report on the structures of SDM amplifiers, their optical properties, and discuss prospects for further development. Ó 2016 Published by Elsevier Inc.
1. Introduction It has been realized lately that various technologies developed for enhancing the transmission capacity in conventional single mode fibers are not adequate to deal with the ever-increasing need for bandwidth [1,2]. Instead of deploying additional single mode fiber to provide more bandwidth, which may seem to be a straight forward solution, other more ingenious schemes have been pursued around the globe to solve this problem. One approach which has drawn widespread interests is space division multiplexing (SDM). It relies on sending data through multiple cores embedded into a single strand of fiber or using multiple transverse modes supported by a core [3,4]. The stimulus behind pursuing SDM involves reducing size through integration, reducing power consumption, and minimizing the cost of deployment and operation. Different forms of high-performance multicore fibers, few-mode fibers, as well as their combination (few-mode/multicore) fibers have been proposed and fabricated, and have been proved to be useful for enhancing the transmission capacity by over an order of magnitude [5–9]. As in conventional transmission systems, optical amplifiers that can compensate for attenuation of signals in the SDM transmission links will be of paramount importance [10–14]. Stimulated by the first demonstration of a 7-core, erbium-doped, fiber amplifier [10] and a multimode amplifier designed for SDM application [11,12] in 2011, much efforts has been put forth in amplifier development ⇑ Corresponding author. E-mail address: [email protected] (K.S. Abedin).
aiming to provide low-cost, energy efficient, and integrated solutions [15–28]. Multicore, few-mode amplifiers with different core and mode counts combined with numerous approaches for efficient coupling signal and combining pump have demonstrated great potential in the areas of SDM. In this paper, we report on the recent advancement made in the development of multicore erbium-doped fiber amplifier’s (MCEDFA). We will describe the different gain fibers and other key components developed for coupling signal and pump light under varying pumping architectures. We will present the amplification and noise properties of various core- and cladding-pumped MCEDFAs and also discuss prospects for multicore fiber amplifiers. 2. Multicore rare-earth doped fiber Multicore fiber amplifiers for SDM employs gain fiber with multiple cores, each doped with erbium ions in order to provide gain to signal around 1.55 lm. These cores are typically arranged in a periodic hexagonal pattern and surrounded by a glass cladding. These cores are separated sufficiently so that electric field of signal within one core interferes minimally with the field of the neighboring core. Such uncoupled cores can be treated as separate entities. In order to establish population inversion and thus gain, the cores are pumped at suitable wavelengths, typically at 980 nm or 1480 nm. Multicore amplifiers can be pumped mainly in two ways; one is ‘‘core pumping”, where the cores are pumped separately by launching single mode pump radiation in either the forward, backward or both directions. The second approach is called ‘‘cladding pumping”; where all cores are being pumped simultaneously using
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multimode pump light launched through cladding. The cores are often co-doped with ytterbium in order to increases pump absorption, which is often desirable for efficient utilization of pump in a relatively short length of fiber and is particularly suited for cladding pumped amplifier. In conventional core-pumped, erbium doped, fiber amplifiers, the core diameter and the numerical aperture are chosen so that single mode propagation is ensured for both pump and signal wavelengths. For example, the commercially available OFS-EDF MP980 has a core diameter of 3.2 lm and a NA of 0.23, which gives V-number of 1.49 and 2.359, for 1550-nm-signal and 980-nm pump, respectively. In a cladding pump amplifier the pump is multimoded; therefore the core diameter can be enlarged further to support the fundamental signal mode. For example, core diameter can be increased to 5.2 lm for the same NA while still ensuring single mode operation at 1550 nm. Such enlargement of the core size can help increase multimode pump absorption (proportional to the ratio of cross-sectional areas of core to cladding) and enhance amplifier saturation power. Moreover, by increasing the core-size further to support a few higher order modes, we can amplify multiple modes simultaneously using the same pump source, which is potentially useful for enhancing transmission capacity. When a multimode pump is launched into a fiber with cylindrical surface, it excites certain modes that propagate like helical rays which have no overlap with a core that is located at the center. Those modes remain unabsorbed, which results in unequal, pump distribution. Such modes with poor overlap are avoided by breaking the structural symmetry, such as by choosing off-centered core or by choosing non-cylindrical cladding surface like D-shape or star shape. However, in a multicore fiber amplifier, even when the cladding is cylindrical, pump distribution is found to be uniform across the cladding. The off-centered cores close to the cladding surface are expected to play a role in preventing the formation of such modes and promote better mixing of modes resulting in uniform pump distribution. Recently, evolution of distribution of multimode pump in multicore double clad fiber has been studied using beam propagation method (BPM), which showed that the injected pump power gets rapidly distributed across the cladding after a propagation length as short as 3 cm [27]. In order to achieve high gain and low noise figure, it is desirable to minimize the cladding size, and to choose a close-packed lattice for the cores. Ultra-low-crosstalk 7-core fiber with core-to-core pitch of 45 lm and cladding diameter of 150 lm for long-haul transmission has been realized, in which the mean crosstalk between neighboring cores were measured to be less than 77.6 dB for k = 1550 nm in a 17.6-km-long fiber [29]. Since, the length of gain fiber used in amplifier is less than a hundred meters, there is scope for further reduction in core-to-core without introducing significant amount of crosstalk between the cores. Recently, a multicore fiber with annular cladding has been proposed to increase the pump intensity [27,28]. In this structure the cores are located within the annular region. The inner circular region is either hollow or comprised of glass with lower refractive index, which causes pump light to be confined in the annular region. This ensures higher pump intensity, though at the expense of a reduction in core count proportional to the area of the lowindex circular region. Fig. 1(a) and (b) show the cross-sections of a 7-core EDF we made for core-pumped and cladding-pumped amplifiers, where the cores are arranged in a hexagonal array with a 41 lm pitch [10]. The core diameter and numerical aperture were equal to 3.2 lm and 0.23, respectively. The mode field diameter (MFD) at 1550 nm was about 6 lm. The erbium-doped core has an absorption coefficient of 2.3 dB/m at 1550 nm. The multicore fiber for core pumping had a cladding diameter of 148 lm, and for cladding
pumping the fiber clad diameter was reduced to 100 lm in order to increase the intensity of pump and was coated with low-index polymer coating (NA: 0.45) for guiding multi-mode pump light. In the double clad 7-core EDF, the thickness of the cladding region beyond the outer cores was 15 lm, and for a coil diameter of 20 cm, the bending loss in 50-m-long gain fiber were found to be negligible. Fig. 1(c) shows cross section of Er/Yb co-doped 12-core fiber, as reported in Ref. [26], where cores are arranged in the form of a hexagon with an average pitch of 36.6 lm [26]. Core count has been increased further by incorporating additional layer/ring of cores. Reference 19 reports on a multicore core-pumped EDFA that has 19 cores (MFD: 6.6 lm) arranged in three layers within a cladding size of 220-lm. Cross section of a 19-core EDF is shown in Fig. 1(d). Multicore erbium doped fiber with larger core-size supporting few-modes has also been reported recently. Fig. 1(e) shows schematic of an Er doped fiber with 6-cores, each supporting 3 modes (LP01, LP11a and LP11b) [28]. The cores are embedded within an annular cladding region and the distance between two neighboring core was 62 lm. The outer and inner diameters of the annular cladding are 170 lm and 85 lm, respectively. The NA between the core and annular cladding is 0.104, and the NA between the annular cladding and inner circular cladding is 0.11. The inner circular region has lower index than cladding, causing the multimode pump radiation to be confined within the annular region.
3. Signal/Pump coupler for MCFA It is desirable that spatially multiplexed signal from passive multicore transmission fibers be directly launched into the multicore gain fiber without de-multiplexing into separate channels. Currently, however, in the absence of suitable optical components (e.g., WDM, isolator, gain flattening filter, tap-coupler) with proper multicore fiber pigtails required for building fully integrated SDM system, fan-in and fan-out devices are being used for getting access into individual cores. Various fan-in, fan-out devices have been proposed, which includes all-fiber based tapered fiber bundled (TFB) coupler [10,20], bulk-optics couplers [30], reduced-cladding bundled coupler [18], as well as 3-D waveguide based coupler. For amplifying applications, single mode pump radiation can also be added to the signal simply by using commercial fiberoptic wavelength division multiplexers (WDM), before launching into the coupler.
3.1. Couplers for core pumping Tapered fiber bundle (TFB) coupler-based, fan-in/-out devices for core pumping are created by tapering adiabatically a bundle of specially designed single mode fibers by a predetermined ratio so that the core-to-core pitch at the tapered end matches with that of the MC-EDF. Each strands of the fiber bundle could be spliced to separate SMF fibers with low loss. Moreover, at the tapered end, the MFD matches well with that of the MC-EDF. Fig. 2(a) and (b) show schematic and a photograph of the TFB coupler. Bulk-optics based couplers consist mainly of multiple number of bulk-optic lenses that collimates signal from individual single mode fiber and a focusing lens that couples each of these collimated beams into respective cores of the multicore fiber [30]. A schematic is shown in Fig. 2(c). All the lenses and fiber endfacets are provided with broadband, anti-reflection (AR) coating in order to minimize feedback from glass-air interfaces. Coupling to as many as 19 cores in MCF has been already demonstrated using this approach [31]. One advantage of bulk-optic coupling approach is that it can provide room for incorporating other
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Fig. 1. Cross section of different MC-EDF used in constructing SDM amplifiers. (a) 7-core EDF for core pumping [10], (b) 7-core EDF for cladding pumping [20], (c) 12-core EYDF for cladding pumping [26], (d) 19-core EDF for core pumping [19], (e) 6-core EDF with annular cladding for cladding-pumping [28].
Fig. 2. Fan-in/fan-out combiners developed for core pumped MC-EDFA. (a) All-fiber based TFB combiner [10], (b) Photograph of a compact TFB combiner, (c) Bulk-optics based fan-in/fan-out [30], (d) Schematic of fan-in/fan-out based on reduced cladding fibers.
bulk-optic elements, such as a dichroic filter, isolator chip in the intermediate free-space region [19]. A reduced-cladding bundled coupler, shown in Fig 2(d), is fabricated by stacking 7 small-diameter fibers into a glass capillary, where the diameter of small-diameter fiber was equal to the core-to-core pitch of 7-core MC-EDF [18]. Since these thin fibers have the same arrangements as the cores in the MC-EDF and the pitches the same as the gain fiber, the bundle of fibers could be directly connected to the gain fiber by using refractive index matching adhesive. The interface between the fiber-bundle and MC-EDF could also be angled-polish to further suppress the Fresnel reflection at the boundary. 3.2. Couplers for cladding pumping In cladding pump multicore amplifiers, in addition to launching SDM signals to multiple cores, multimode pump radiation needs to be propagated through the cladding. A number of schemes, such as
modified TFB pump-signal combiner [20] bulk-optic coupler [26], and also side-coupled pump coupler [23] have been proposed for doing this. Fig 3(a) shows a schematic of a modified TFB pumpsignal combiner, which is similar to the TFB coupler made for core-pumping, the only difference is that the central fiber is replaced by a multimode fiber with appropriate numerical aperture (NA) and core size. It is ensured that following the tapering of the bundle, the NA of the pump light, which has been increased by a factor dictated by the taper ratio, is still lower than the NA of the double clad multicore fiber. Bulk-optics based couplers have also been developed for cladding pumping [26]. As shown in Fig. 3(b) the coupler consists of lenses and dichroic mirror, and is capable of coupling signal from multicore passive fiber to multicore gain fiber, and simultaneously launching multimode pump radiation through the end-face of the gain fiber. One problem associated with using fan-in and fan-out devices at the amplifier ends is that the throughput loss results in attenuation of the signal. Such device also prevents direct coupling of
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Fig. 3. Fan-in/fan-out combiners developed for cladding-pumped MC-EDFA [20] (a) Modified TFB pump-signal combiner, (b) bulk-optic coupler [26], (c) also side-coupled pump coupler [23].
signals from SDM transmission fiber into the amplifier through splicing, posing a bottle neck for the realization of a simple and compact amplifiers. This problem has been eliminated by coupling multimode pump radiation from the sides of the MC-EDF, leaving the ends accessible for splicing to passive MCF. Fig. 3(c) shows a schematic of tapered fiber based, side-coupling method, originally developed as an efficient means of pumping high power lasers and amplifiers [32,33] where a short section of the gain fiber near the input end is stripped of its low-index coating, and the exposed section is brought into optical-contact with a tapered multimode pump fiber. 4. Multicore Erbium-doped fiber amplifier There have been many reports on the demonstration of multicore erbium doped fiber amplifiers utilizing core or cladding pumping. Pumping each core of a multicore amplifier separately using single mode pumps, while involving higher cost, has the advantage of allowing independent control of gain in each core by adjustment of pump power. Cladding pumping, on the other hand, requires fewer optical components, and has the potential to use low-cost, energy efficient multimode diodes. The electrical to optical power conversion efficiency of a multimode pump laser can be as high as 46%, which is more than twice the efficiency of single-mode pump laser diodes (20%) [25]. This indicates that in multimode pumps, a smaller fraction of electrical power is wasted away as heat.
using WDM couplers, and then launched into MC-EDF using another TFB coupler. The length of the MC-EDFA was 15 m. Fig. 5 shows net gain and internal NF measured in the C-band for the seven cores. For an input signal power of 15 dBm and a pump power of 146 mW (980 nm), an average net gain of 25 dB was obtained from the amplifier. From the passive losses (maximum of 5 dB) in the TFBs and splices, the internal gain was estimated to be 30 dB and the internal NF over the whole C-band was found to be 4 dB. Assuming a passive loss of 2.5 dB for the coupler at the input side, the external NF thus can be higher by 2.5 dB than the internal NF values shown in Fig. 5. In a core pumped amplifier, due to the short length (15 m) and high NA (0.23), the cross-talk between the cores introduced in the fiber is negligible. Cross-talk originates primarily from the fan-in and fan-out devices used at the input and output, because of the mismatch in mode-field size and core-to-core pitch between the TFB and the MCF. Fig. 6 shows the loss and cross-talk properties in the TFB-MCEDF-TFB module measured at 1310 nm. The numbers in the horizontal axis represents the core in which light was launched, and the vertical axis shows the attenuation in the signal, measured at seven outputs of the second TFB. Thus attenuation between the corresponding cores represents the insertion loss. The difference (in dB) in attenuations between corresponding and different cores can be considered as a measure of cross-talk. The cross-talk averaged over six cores for TFB-MCEDF-TFB module
4.1. Core-pumped 7-core EDFA The schematic of a core-pumped, multicore fiber amplifier using TFB couplers as fan-in and fan-out devices [10] is shown in Fig. 4. Here SDM signals from a passive MCF is split into individual channels using a TFB coupler, and combined with pump radiation
Fig. 4. Schematic of a core-pumped 7-core EDFA.
Fig. 5. Net gain and internal NF measured for the 7 different cores of the MC-EDFA. Solid line represents average [10].
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Fig. 6. Loss between the various cores at the input and output of the TFB-MCEDFTFB module. #0: Central core, #1 – #6: outer corresponding cores.
was found to vary between 30.2–36.6 dB for the seven channels. The loss between an input and corresponding output core of the gain assembly remained within 2.5–4.9 dB. 4.2. Cladding pumped multicore fiber amplifier A cladding pump multicore amplifier consists of a length of Er-(or Er/Yb-) doped multicore double clad fiber, a pump/signal combiner, and a pump dump. Depending on whether the input signals come from multicore fiber or from multiple SMFs, different forms of signal and pump combiners (similar to those shown in Fig. 3) can be used. Fig. 7(a) and (b) show two different variations of cladding-pump amplifiers for end- [20] and side-coupled pumping [23], respectively. The TFB couplers for end-pumping amplifier as described in Ref. [20] has a central multimode fiber (NA of 0.22, and core/cladding diameter of 105/125 lm) surrounded by six single mode fibers. The central multimode fiber at the input of the TFB coupler was spliced to the multimode fiber pigtail (NA: 0.22, 105/125 lm) of a 980 nm multimode pump laser diode. The signal was launched through the outer six fibers of the TFB coupler. Thus, six outer cores
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of the MC-EDF were used for amplifying signals. The inner cladding had a numerical aperture of 0.45 and was surrounded by a low index polymer coating of 220 lm diameter. The length of the MC-EDF was 50 m. The amplified output signals were extracted by using a second TFB coupler connected to the output end of the doped fiber. In a cladding pumped amplifier designed for broadband amplification, the unabsorbed fraction of the pump needs to be removed from the gain fiber to prevent it from entering the signal path. This is achieved by incorporating at the output end of the MC-EDF a ‘‘pump dump”, where short segment (4 cm) was stripped of its low-index coating, and covered with thermally conductive paste to remove the residual pump [23]. MC-EDFA with side-coupled multimode pumping was realized by using a tapered, multimode fiber [23]. A short section of the gain fiber (8 cm long) near the input end was stripped of its low-index coating, and the exposed section was brought into optical-contact with a tapered multimode pump fiber. The tapered fiber was fabricated by a process involving slowly reducing the diameter of the multimode pump fiber (105/125, NA = 0.15) from 125 to 15 lm over 25 mm, and maintaining a uniform diameter section of length 20 mm followed by an up-tapered section. The down-tapered and uniform diameter sections were wound around the gain fiber to ensure efficient tacking. The pump coupling efficiency was 67%. It has been observed that in a cladding pumped amplifier, as the signal gets amplified along the gain fiber, the intensity can become large compared with the pump. This can deplete the upper state population, which makes it harder to achieve gain in the C-band with low noise figure (especially below 1560 nm) [20]. To extend the gain spectrum to C-band, a shorter length, 34 m, of erbiumdoped fiber was used in the amplifier in the case of side-coupled MC-EDFA. Fig. 8(a) shows the net (external) gain versus wavelength plotted for the six cores, when the pump power was 7.6 W and input signal power levels of 20 dBm, and 0 dBm [20]. For small signals ( 20 dBm), a maximum gain of 32 dB could be obtained from the amplifier. Some variations in the gain in different cores were observed, which were due to differences in the passive losses. Small-signal gain larger than 20 dB is available for signal amplification over a wavelength range of 32 nm. The internal NF for
Fig. 7. Schematic diagram of a cladding pump multicore fiber amplifier. (a) End-pumping. The length of MC-EDFA was 50 m. (b) side-coupled cladding pumping. The length of MC-EDFA was 34 m.
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Fig. 8. The gain (a) and NF (b) plotted as a function of wavelength for outer 6-cores of the multicore EDF amplifier, cladding pumped through the end. The input pump and coupled pump power were 10.6 and 7.6 W, respectively.
Fig. 9. Gain (a) and NF (b) measured for the 7 different cores of the MC-EDFA, with side-coupled cladding pumping. The input pump and coupled pump power were 7.6 and 4.7 W, respectively. The central core is represented by core 0.
different cores, as a function of wavelength, is shown in Fig. 8(b). Average NF was about 6 dB for wavelength longer than 1560 nm. Fig. 9(a) shows the gross gain versus wavelength measured in the seven cores for input signal powers of 20 and 0 dBm, when the pump power (coupled) was 4.7 W [23]. The gross gain is the gain that signals from a multicore transmission fiber will experience when spliced directly to the multicore gain fiber. The maximum gross gain was about 36 dB near 1560 nm, and gain over 25 dB was obtained over a bandwidth of 40 nm. Shortening the length of the gain fiber thus resulted in a significant expansion of the bandwidth into the C-band. At 1530 nm, the small-signal gain was about 20 dB. Note that due to the absence of TFB couplers, we were able to obtain higher external gain in comparison to the endpumped amplifier, even at a lower pump power. The internal NF for different cores as a function of wavelength is shown in Fig. 9 (b) for input signal power of 0 dBm. As shown in the figure, the NF becomes high for wavelength shorter than 1540 nm, while it tends to decrease for longer wavelengths. The NF was 5 dB for the signal wavelength of 1560 nm and it increased to about 8 dB at 1530 nm.
5. Discussion In making a cladding pump, erbium doped, multicore, fiber amplifier, it is critical to optimize the length of the gain fiber by taking into consideration the input signal and pump power, required gain, acceptable noise figure, output saturation power as
well as cross-talk. The amplification and noise performance can be simulated fairly accurately by numerical methods under the assumption of uniform pump distribution [20,25,34]. It has been observed that output power of the amplifier can be enhanced significantly by enlarging the core size to an extent permissible by the V-number specified. For a typical NA of 0.23 for erbium-doped silica single mode operation at 1550 nm is allowed for a core diameter up to 5.2 lm. Considering a 7-core fiber and a cladding diameter of 100 lm, and a multimode pump at 980 nm, it was found from numerical simulation that a small signal gain over 30 dB can be obtained throughout the C-band using 20 m of fiber, and for a 0 dBm signal input a saturated output power over 20dBm from each cores can be obtained, clearly showing the potential advantages of increasing the core size in enhancing the amplifier saturation power. A further increase in gain should be possible by further increasing the core size and proportionately reducing the core NA. It is to be noted however that, while larger core size could yield higher gain, at the same time it could cause an increase in NF. We therefore, need to carefully choose the fiber parameters so that NA remains within the acceptable limit over the wavelength range of interest. In the last few years, several research groups have reported on improving the performance of multicore fiber amplifiers (See Table 1). A multicore core-pumped amplifier with as many as 19 cores with bulk-optics based WDM and isolator have been reported in Ref. [19]. Also a 7-core, cladding pumped, fiber amplifier for L-band operation, with saturation power as much as 20.6 dBm per core has been demonstrated [18]. A MCF amplifier has
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K.S. Abedin et al. / Optical Fiber Technology xxx (2016) xxx–xxx Table 1 Optical performance of different multicore fiber amplifiers. Type of Amplifier
Core number
Mode number
Pump power
Peak gain
Bandwidth
Psat/core
NF
Length
Ref
Core-pumped Core-pumped Core-pumped Cladding pumped Cladding pumped Cladding pumped Cladding pumped Cladding pumped
7 7 19 6 7 7 12 6
1 1 1 1 1 1 1 3
146 mW/core 40 mW/core 400 mW/core 10.6 W 7.6 W 17 W 1.9 W (launched) 25 W
23–27 dB 20 dB 23 dB 32 dB 25 dB 20 dB 18.3 dB 20 dB
1530–1565 nm 1530–1565 nm 1520–1560 nm (@20 dB) 1542–1576 nm (@20 dB) 1532–1582 nm @20 dB 1578.4–1608.1 nm 1534–1561.4 nm @11 dB 1530–1560 nm
10dBm 12–17 dBm 15 dBm 15 dBm 20.6 dBm
4 dB <7 dB 6–7 dB 6 dB 5–7 dB 10–5 dB
15 dBm /mode /core
6–9 dB
14 m 16 m – 50 m 34 m 107 m 5 m (Er/Yb) 2.1 m
10 18 19 20 23 24 26 28
also been developed using Er/Yb codoped, 12 core fiber, which allowed reducing the length to 5 m [26]. Very recently, cladding pumped, multicore, multimode amplifiers with 6 core and 3 modes have been reported [28]. Six, few-moded cores, 16–17 lm in diameter, relatively heavily-doped (Er concentration: 2.8 1025 ions/ m3) were arranged in an annular cladding region, occupying about 8% of cladding area, reportedly offering 15 dBm output per mode. Due to the use of confined cores uniformly doped with erbium, there remains the problem of differential modal gain, which could be eliminated by using ring doping [16] or extended rare-earth doped cores [34]. Such approaches may result in the realization of multicore amplifiers with higher core, mode counts and pump to signal conversion efficiencies as well as with improved amplification and noise properties that would be more suitable for deployment in practical SDM systems.
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Contents lists available at ScienceDirect
Optical Fiber Technology www.elsevier.com/locate/yofte
Invited Papers
State-of-the-art multicore fiber amplifiers for space division multiplexing Kazi S. Abedin ⇑, Man F. Yan, Thierry F. Taunay, Benyuan Zhu, Eric M. Monberg, David J. DiGiovanni OFS Laboratories, 19 Schoolhouse Road, Somerset, NJ 08873, United States
a r t i c l e
i n f o
Article history: Received 9 May 2016 Revised 19 September 2016 Accepted 25 September 2016 Available online xxxx Keywords: Optical fiber Multicore Erbium-doped fiber amplifiers Space division multiplexing
a b s t r a c t Space division multiplexing (SDM) has generated much interest lately as a potential means for enhancing the capacity of optical transmission systems. During the past several years, we have observed tremendous research efforts in the development of SDM amplifiers with an aim to increase core and mode counts and to improve amplification properties and pump conversion efficiencies. We report on the recent development of multicore fiber amplifiers suitable for amplifying space division multiplexed signals. Multicore fiber amplifiers with different number of cores, and pumping schemes have been developed to pump the cores individually or through a common cladding. We will report on the structures of SDM amplifiers, their optical properties, and discuss prospects for further development. Ó 2016 Published by Elsevier Inc.
1. Introduction It has been realized lately that various technologies developed for enhancing the transmission capacity in conventional single mode fibers are not adequate to deal with the ever-increasing need for bandwidth [1,2]. Instead of deploying additional single mode fiber to provide more bandwidth, which may seem to be a straight forward solution, other more ingenious schemes have been pursued around the globe to solve this problem. One approach which has drawn widespread interests is space division multiplexing (SDM). It relies on sending data through multiple cores embedded into a single strand of fiber or using multiple transverse modes supported by a core [3,4]. The stimulus behind pursuing SDM involves reducing size through integration, reducing power consumption, and minimizing the cost of deployment and operation. Different forms of high-performance multicore fibers, few-mode fibers, as well as their combination (few-mode/multicore) fibers have been proposed and fabricated, and have been proved to be useful for enhancing the transmission capacity by over an order of magnitude [5–9]. As in conventional transmission systems, optical amplifiers that can compensate for attenuation of signals in the SDM transmission links will be of paramount importance [10–14]. Stimulated by the first demonstration of a 7-core, erbium-doped, fiber amplifier [10] and a multimode amplifier designed for SDM application [11,12] in 2011, much efforts has been put forth in amplifier development ⇑ Corresponding author. E-mail address: [email protected] (K.S. Abedin).
aiming to provide low-cost, energy efficient, and integrated solutions [15–28]. Multicore, few-mode amplifiers with different core and mode counts combined with numerous approaches for efficient coupling signal and combining pump have demonstrated great potential in the areas of SDM. In this paper, we report on the recent advancement made in the development of multicore erbium-doped fiber amplifier’s (MCEDFA). We will describe the different gain fibers and other key components developed for coupling signal and pump light under varying pumping architectures. We will present the amplification and noise properties of various core- and cladding-pumped MCEDFAs and also discuss prospects for multicore fiber amplifiers. 2. Multicore rare-earth doped fiber Multicore fiber amplifiers for SDM employs gain fiber with multiple cores, each doped with erbium ions in order to provide gain to signal around 1.55 lm. These cores are typically arranged in a periodic hexagonal pattern and surrounded by a glass cladding. These cores are separated sufficiently so that electric field of signal within one core interferes minimally with the field of the neighboring core. Such uncoupled cores can be treated as separate entities. In order to establish population inversion and thus gain, the cores are pumped at suitable wavelengths, typically at 980 nm or 1480 nm. Multicore amplifiers can be pumped mainly in two ways; one is ‘‘core pumping”, where the cores are pumped separately by launching single mode pump radiation in either the forward, backward or both directions. The second approach is called ‘‘cladding pumping”; where all cores are being pumped simultaneously using
http://dx.doi.org/10.1016/j.yofte.2016.09.010 1068-5200/Ó 2016 Published by Elsevier Inc.
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multimode pump light launched through cladding. The cores are often co-doped with ytterbium in order to increases pump absorption, which is often desirable for efficient utilization of pump in a relatively short length of fiber and is particularly suited for cladding pumped amplifier. In conventional core-pumped, erbium doped, fiber amplifiers, the core diameter and the numerical aperture are chosen so that single mode propagation is ensured for both pump and signal wavelengths. For example, the commercially available OFS-EDF MP980 has a core diameter of 3.2 lm and a NA of 0.23, which gives V-number of 1.49 and 2.359, for 1550-nm-signal and 980-nm pump, respectively. In a cladding pump amplifier the pump is multimoded; therefore the core diameter can be enlarged further to support the fundamental signal mode. For example, core diameter can be increased to 5.2 lm for the same NA while still ensuring single mode operation at 1550 nm. Such enlargement of the core size can help increase multimode pump absorption (proportional to the ratio of cross-sectional areas of core to cladding) and enhance amplifier saturation power. Moreover, by increasing the core-size further to support a few higher order modes, we can amplify multiple modes simultaneously using the same pump source, which is potentially useful for enhancing transmission capacity. When a multimode pump is launched into a fiber with cylindrical surface, it excites certain modes that propagate like helical rays which have no overlap with a core that is located at the center. Those modes remain unabsorbed, which results in unequal, pump distribution. Such modes with poor overlap are avoided by breaking the structural symmetry, such as by choosing off-centered core or by choosing non-cylindrical cladding surface like D-shape or star shape. However, in a multicore fiber amplifier, even when the cladding is cylindrical, pump distribution is found to be uniform across the cladding. The off-centered cores close to the cladding surface are expected to play a role in preventing the formation of such modes and promote better mixing of modes resulting in uniform pump distribution. Recently, evolution of distribution of multimode pump in multicore double clad fiber has been studied using beam propagation method (BPM), which showed that the injected pump power gets rapidly distributed across the cladding after a propagation length as short as 3 cm [27]. In order to achieve high gain and low noise figure, it is desirable to minimize the cladding size, and to choose a close-packed lattice for the cores. Ultra-low-crosstalk 7-core fiber with core-to-core pitch of 45 lm and cladding diameter of 150 lm for long-haul transmission has been realized, in which the mean crosstalk between neighboring cores were measured to be less than 77.6 dB for k = 1550 nm in a 17.6-km-long fiber [29]. Since, the length of gain fiber used in amplifier is less than a hundred meters, there is scope for further reduction in core-to-core without introducing significant amount of crosstalk between the cores. Recently, a multicore fiber with annular cladding has been proposed to increase the pump intensity [27,28]. In this structure the cores are located within the annular region. The inner circular region is either hollow or comprised of glass with lower refractive index, which causes pump light to be confined in the annular region. This ensures higher pump intensity, though at the expense of a reduction in core count proportional to the area of the lowindex circular region. Fig. 1(a) and (b) show the cross-sections of a 7-core EDF we made for core-pumped and cladding-pumped amplifiers, where the cores are arranged in a hexagonal array with a 41 lm pitch [10]. The core diameter and numerical aperture were equal to 3.2 lm and 0.23, respectively. The mode field diameter (MFD) at 1550 nm was about 6 lm. The erbium-doped core has an absorption coefficient of 2.3 dB/m at 1550 nm. The multicore fiber for core pumping had a cladding diameter of 148 lm, and for cladding
pumping the fiber clad diameter was reduced to 100 lm in order to increase the intensity of pump and was coated with low-index polymer coating (NA: 0.45) for guiding multi-mode pump light. In the double clad 7-core EDF, the thickness of the cladding region beyond the outer cores was 15 lm, and for a coil diameter of 20 cm, the bending loss in 50-m-long gain fiber were found to be negligible. Fig. 1(c) shows cross section of Er/Yb co-doped 12-core fiber, as reported in Ref. [26], where cores are arranged in the form of a hexagon with an average pitch of 36.6 lm [26]. Core count has been increased further by incorporating additional layer/ring of cores. Reference 19 reports on a multicore core-pumped EDFA that has 19 cores (MFD: 6.6 lm) arranged in three layers within a cladding size of 220-lm. Cross section of a 19-core EDF is shown in Fig. 1(d). Multicore erbium doped fiber with larger core-size supporting few-modes has also been reported recently. Fig. 1(e) shows schematic of an Er doped fiber with 6-cores, each supporting 3 modes (LP01, LP11a and LP11b) [28]. The cores are embedded within an annular cladding region and the distance between two neighboring core was 62 lm. The outer and inner diameters of the annular cladding are 170 lm and 85 lm, respectively. The NA between the core and annular cladding is 0.104, and the NA between the annular cladding and inner circular cladding is 0.11. The inner circular region has lower index than cladding, causing the multimode pump radiation to be confined within the annular region.
3. Signal/Pump coupler for MCFA It is desirable that spatially multiplexed signal from passive multicore transmission fibers be directly launched into the multicore gain fiber without de-multiplexing into separate channels. Currently, however, in the absence of suitable optical components (e.g., WDM, isolator, gain flattening filter, tap-coupler) with proper multicore fiber pigtails required for building fully integrated SDM system, fan-in and fan-out devices are being used for getting access into individual cores. Various fan-in, fan-out devices have been proposed, which includes all-fiber based tapered fiber bundled (TFB) coupler [10,20], bulk-optics couplers [30], reduced-cladding bundled coupler [18], as well as 3-D waveguide based coupler. For amplifying applications, single mode pump radiation can also be added to the signal simply by using commercial fiberoptic wavelength division multiplexers (WDM), before launching into the coupler.
3.1. Couplers for core pumping Tapered fiber bundle (TFB) coupler-based, fan-in/-out devices for core pumping are created by tapering adiabatically a bundle of specially designed single mode fibers by a predetermined ratio so that the core-to-core pitch at the tapered end matches with that of the MC-EDF. Each strands of the fiber bundle could be spliced to separate SMF fibers with low loss. Moreover, at the tapered end, the MFD matches well with that of the MC-EDF. Fig. 2(a) and (b) show schematic and a photograph of the TFB coupler. Bulk-optics based couplers consist mainly of multiple number of bulk-optic lenses that collimates signal from individual single mode fiber and a focusing lens that couples each of these collimated beams into respective cores of the multicore fiber [30]. A schematic is shown in Fig. 2(c). All the lenses and fiber endfacets are provided with broadband, anti-reflection (AR) coating in order to minimize feedback from glass-air interfaces. Coupling to as many as 19 cores in MCF has been already demonstrated using this approach [31]. One advantage of bulk-optic coupling approach is that it can provide room for incorporating other
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Fig. 1. Cross section of different MC-EDF used in constructing SDM amplifiers. (a) 7-core EDF for core pumping [10], (b) 7-core EDF for cladding pumping [20], (c) 12-core EYDF for cladding pumping [26], (d) 19-core EDF for core pumping [19], (e) 6-core EDF with annular cladding for cladding-pumping [28].
Fig. 2. Fan-in/fan-out combiners developed for core pumped MC-EDFA. (a) All-fiber based TFB combiner [10], (b) Photograph of a compact TFB combiner, (c) Bulk-optics based fan-in/fan-out [30], (d) Schematic of fan-in/fan-out based on reduced cladding fibers.
bulk-optic elements, such as a dichroic filter, isolator chip in the intermediate free-space region [19]. A reduced-cladding bundled coupler, shown in Fig 2(d), is fabricated by stacking 7 small-diameter fibers into a glass capillary, where the diameter of small-diameter fiber was equal to the core-to-core pitch of 7-core MC-EDF [18]. Since these thin fibers have the same arrangements as the cores in the MC-EDF and the pitches the same as the gain fiber, the bundle of fibers could be directly connected to the gain fiber by using refractive index matching adhesive. The interface between the fiber-bundle and MC-EDF could also be angled-polish to further suppress the Fresnel reflection at the boundary. 3.2. Couplers for cladding pumping In cladding pump multicore amplifiers, in addition to launching SDM signals to multiple cores, multimode pump radiation needs to be propagated through the cladding. A number of schemes, such as
modified TFB pump-signal combiner [20] bulk-optic coupler [26], and also side-coupled pump coupler [23] have been proposed for doing this. Fig 3(a) shows a schematic of a modified TFB pumpsignal combiner, which is similar to the TFB coupler made for core-pumping, the only difference is that the central fiber is replaced by a multimode fiber with appropriate numerical aperture (NA) and core size. It is ensured that following the tapering of the bundle, the NA of the pump light, which has been increased by a factor dictated by the taper ratio, is still lower than the NA of the double clad multicore fiber. Bulk-optics based couplers have also been developed for cladding pumping [26]. As shown in Fig. 3(b) the coupler consists of lenses and dichroic mirror, and is capable of coupling signal from multicore passive fiber to multicore gain fiber, and simultaneously launching multimode pump radiation through the end-face of the gain fiber. One problem associated with using fan-in and fan-out devices at the amplifier ends is that the throughput loss results in attenuation of the signal. Such device also prevents direct coupling of
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Fig. 3. Fan-in/fan-out combiners developed for cladding-pumped MC-EDFA [20] (a) Modified TFB pump-signal combiner, (b) bulk-optic coupler [26], (c) also side-coupled pump coupler [23].
signals from SDM transmission fiber into the amplifier through splicing, posing a bottle neck for the realization of a simple and compact amplifiers. This problem has been eliminated by coupling multimode pump radiation from the sides of the MC-EDF, leaving the ends accessible for splicing to passive MCF. Fig. 3(c) shows a schematic of tapered fiber based, side-coupling method, originally developed as an efficient means of pumping high power lasers and amplifiers [32,33] where a short section of the gain fiber near the input end is stripped of its low-index coating, and the exposed section is brought into optical-contact with a tapered multimode pump fiber. 4. Multicore Erbium-doped fiber amplifier There have been many reports on the demonstration of multicore erbium doped fiber amplifiers utilizing core or cladding pumping. Pumping each core of a multicore amplifier separately using single mode pumps, while involving higher cost, has the advantage of allowing independent control of gain in each core by adjustment of pump power. Cladding pumping, on the other hand, requires fewer optical components, and has the potential to use low-cost, energy efficient multimode diodes. The electrical to optical power conversion efficiency of a multimode pump laser can be as high as 46%, which is more than twice the efficiency of single-mode pump laser diodes (20%) [25]. This indicates that in multimode pumps, a smaller fraction of electrical power is wasted away as heat.
using WDM couplers, and then launched into MC-EDF using another TFB coupler. The length of the MC-EDFA was 15 m. Fig. 5 shows net gain and internal NF measured in the C-band for the seven cores. For an input signal power of 15 dBm and a pump power of 146 mW (980 nm), an average net gain of 25 dB was obtained from the amplifier. From the passive losses (maximum of 5 dB) in the TFBs and splices, the internal gain was estimated to be 30 dB and the internal NF over the whole C-band was found to be 4 dB. Assuming a passive loss of 2.5 dB for the coupler at the input side, the external NF thus can be higher by 2.5 dB than the internal NF values shown in Fig. 5. In a core pumped amplifier, due to the short length (15 m) and high NA (0.23), the cross-talk between the cores introduced in the fiber is negligible. Cross-talk originates primarily from the fan-in and fan-out devices used at the input and output, because of the mismatch in mode-field size and core-to-core pitch between the TFB and the MCF. Fig. 6 shows the loss and cross-talk properties in the TFB-MCEDF-TFB module measured at 1310 nm. The numbers in the horizontal axis represents the core in which light was launched, and the vertical axis shows the attenuation in the signal, measured at seven outputs of the second TFB. Thus attenuation between the corresponding cores represents the insertion loss. The difference (in dB) in attenuations between corresponding and different cores can be considered as a measure of cross-talk. The cross-talk averaged over six cores for TFB-MCEDF-TFB module
4.1. Core-pumped 7-core EDFA The schematic of a core-pumped, multicore fiber amplifier using TFB couplers as fan-in and fan-out devices [10] is shown in Fig. 4. Here SDM signals from a passive MCF is split into individual channels using a TFB coupler, and combined with pump radiation
Fig. 4. Schematic of a core-pumped 7-core EDFA.
Fig. 5. Net gain and internal NF measured for the 7 different cores of the MC-EDFA. Solid line represents average [10].
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Fig. 6. Loss between the various cores at the input and output of the TFB-MCEDFTFB module. #0: Central core, #1 – #6: outer corresponding cores.
was found to vary between 30.2–36.6 dB for the seven channels. The loss between an input and corresponding output core of the gain assembly remained within 2.5–4.9 dB. 4.2. Cladding pumped multicore fiber amplifier A cladding pump multicore amplifier consists of a length of Er-(or Er/Yb-) doped multicore double clad fiber, a pump/signal combiner, and a pump dump. Depending on whether the input signals come from multicore fiber or from multiple SMFs, different forms of signal and pump combiners (similar to those shown in Fig. 3) can be used. Fig. 7(a) and (b) show two different variations of cladding-pump amplifiers for end- [20] and side-coupled pumping [23], respectively. The TFB couplers for end-pumping amplifier as described in Ref. [20] has a central multimode fiber (NA of 0.22, and core/cladding diameter of 105/125 lm) surrounded by six single mode fibers. The central multimode fiber at the input of the TFB coupler was spliced to the multimode fiber pigtail (NA: 0.22, 105/125 lm) of a 980 nm multimode pump laser diode. The signal was launched through the outer six fibers of the TFB coupler. Thus, six outer cores
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of the MC-EDF were used for amplifying signals. The inner cladding had a numerical aperture of 0.45 and was surrounded by a low index polymer coating of 220 lm diameter. The length of the MC-EDF was 50 m. The amplified output signals were extracted by using a second TFB coupler connected to the output end of the doped fiber. In a cladding pumped amplifier designed for broadband amplification, the unabsorbed fraction of the pump needs to be removed from the gain fiber to prevent it from entering the signal path. This is achieved by incorporating at the output end of the MC-EDF a ‘‘pump dump”, where short segment (4 cm) was stripped of its low-index coating, and covered with thermally conductive paste to remove the residual pump [23]. MC-EDFA with side-coupled multimode pumping was realized by using a tapered, multimode fiber [23]. A short section of the gain fiber (8 cm long) near the input end was stripped of its low-index coating, and the exposed section was brought into optical-contact with a tapered multimode pump fiber. The tapered fiber was fabricated by a process involving slowly reducing the diameter of the multimode pump fiber (105/125, NA = 0.15) from 125 to 15 lm over 25 mm, and maintaining a uniform diameter section of length 20 mm followed by an up-tapered section. The down-tapered and uniform diameter sections were wound around the gain fiber to ensure efficient tacking. The pump coupling efficiency was 67%. It has been observed that in a cladding pumped amplifier, as the signal gets amplified along the gain fiber, the intensity can become large compared with the pump. This can deplete the upper state population, which makes it harder to achieve gain in the C-band with low noise figure (especially below 1560 nm) [20]. To extend the gain spectrum to C-band, a shorter length, 34 m, of erbiumdoped fiber was used in the amplifier in the case of side-coupled MC-EDFA. Fig. 8(a) shows the net (external) gain versus wavelength plotted for the six cores, when the pump power was 7.6 W and input signal power levels of 20 dBm, and 0 dBm [20]. For small signals ( 20 dBm), a maximum gain of 32 dB could be obtained from the amplifier. Some variations in the gain in different cores were observed, which were due to differences in the passive losses. Small-signal gain larger than 20 dB is available for signal amplification over a wavelength range of 32 nm. The internal NF for
Fig. 7. Schematic diagram of a cladding pump multicore fiber amplifier. (a) End-pumping. The length of MC-EDFA was 50 m. (b) side-coupled cladding pumping. The length of MC-EDFA was 34 m.
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Fig. 8. The gain (a) and NF (b) plotted as a function of wavelength for outer 6-cores of the multicore EDF amplifier, cladding pumped through the end. The input pump and coupled pump power were 10.6 and 7.6 W, respectively.
Fig. 9. Gain (a) and NF (b) measured for the 7 different cores of the MC-EDFA, with side-coupled cladding pumping. The input pump and coupled pump power were 7.6 and 4.7 W, respectively. The central core is represented by core 0.
different cores, as a function of wavelength, is shown in Fig. 8(b). Average NF was about 6 dB for wavelength longer than 1560 nm. Fig. 9(a) shows the gross gain versus wavelength measured in the seven cores for input signal powers of 20 and 0 dBm, when the pump power (coupled) was 4.7 W [23]. The gross gain is the gain that signals from a multicore transmission fiber will experience when spliced directly to the multicore gain fiber. The maximum gross gain was about 36 dB near 1560 nm, and gain over 25 dB was obtained over a bandwidth of 40 nm. Shortening the length of the gain fiber thus resulted in a significant expansion of the bandwidth into the C-band. At 1530 nm, the small-signal gain was about 20 dB. Note that due to the absence of TFB couplers, we were able to obtain higher external gain in comparison to the endpumped amplifier, even at a lower pump power. The internal NF for different cores as a function of wavelength is shown in Fig. 9 (b) for input signal power of 0 dBm. As shown in the figure, the NF becomes high for wavelength shorter than 1540 nm, while it tends to decrease for longer wavelengths. The NF was 5 dB for the signal wavelength of 1560 nm and it increased to about 8 dB at 1530 nm.
5. Discussion In making a cladding pump, erbium doped, multicore, fiber amplifier, it is critical to optimize the length of the gain fiber by taking into consideration the input signal and pump power, required gain, acceptable noise figure, output saturation power as
well as cross-talk. The amplification and noise performance can be simulated fairly accurately by numerical methods under the assumption of uniform pump distribution [20,25,34]. It has been observed that output power of the amplifier can be enhanced significantly by enlarging the core size to an extent permissible by the V-number specified. For a typical NA of 0.23 for erbium-doped silica single mode operation at 1550 nm is allowed for a core diameter up to 5.2 lm. Considering a 7-core fiber and a cladding diameter of 100 lm, and a multimode pump at 980 nm, it was found from numerical simulation that a small signal gain over 30 dB can be obtained throughout the C-band using 20 m of fiber, and for a 0 dBm signal input a saturated output power over 20dBm from each cores can be obtained, clearly showing the potential advantages of increasing the core size in enhancing the amplifier saturation power. A further increase in gain should be possible by further increasing the core size and proportionately reducing the core NA. It is to be noted however that, while larger core size could yield higher gain, at the same time it could cause an increase in NF. We therefore, need to carefully choose the fiber parameters so that NA remains within the acceptable limit over the wavelength range of interest. In the last few years, several research groups have reported on improving the performance of multicore fiber amplifiers (See Table 1). A multicore core-pumped amplifier with as many as 19 cores with bulk-optics based WDM and isolator have been reported in Ref. [19]. Also a 7-core, cladding pumped, fiber amplifier for L-band operation, with saturation power as much as 20.6 dBm per core has been demonstrated [18]. A MCF amplifier has
Please cite this article in press as: K.S. Abedin et al., State-of-the-art multicore fiber amplifiers for space division multiplexing, Opt. Fiber Technol. (2016), http://dx.doi.org/10.1016/j.yofte.2016.09.010
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K.S. Abedin et al. / Optical Fiber Technology xxx (2016) xxx–xxx Table 1 Optical performance of different multicore fiber amplifiers. Type of Amplifier
Core number
Mode number
Pump power
Peak gain
Bandwidth
Psat/core
NF
Length
Ref
Core-pumped Core-pumped Core-pumped Cladding pumped Cladding pumped Cladding pumped Cladding pumped Cladding pumped
7 7 19 6 7 7 12 6
1 1 1 1 1 1 1 3
146 mW/core 40 mW/core 400 mW/core 10.6 W 7.6 W 17 W 1.9 W (launched) 25 W
23–27 dB 20 dB 23 dB 32 dB 25 dB 20 dB 18.3 dB 20 dB
1530–1565 nm 1530–1565 nm 1520–1560 nm (@20 dB) 1542–1576 nm (@20 dB) 1532–1582 nm @20 dB 1578.4–1608.1 nm 1534–1561.4 nm @11 dB 1530–1560 nm
10dBm 12–17 dBm 15 dBm 15 dBm 20.6 dBm
4 dB <7 dB 6–7 dB 6 dB 5–7 dB 10–5 dB
15 dBm /mode /core
6–9 dB
14 m 16 m – 50 m 34 m 107 m 5 m (Er/Yb) 2.1 m
10 18 19 20 23 24 26 28
also been developed using Er/Yb codoped, 12 core fiber, which allowed reducing the length to 5 m [26]. Very recently, cladding pumped, multicore, multimode amplifiers with 6 core and 3 modes have been reported [28]. Six, few-moded cores, 16–17 lm in diameter, relatively heavily-doped (Er concentration: 2.8 1025 ions/ m3) were arranged in an annular cladding region, occupying about 8% of cladding area, reportedly offering 15 dBm output per mode. Due to the use of confined cores uniformly doped with erbium, there remains the problem of differential modal gain, which could be eliminated by using ring doping [16] or extended rare-earth doped cores [34]. Such approaches may result in the realization of multicore amplifiers with higher core, mode counts and pump to signal conversion efficiencies as well as with improved amplification and noise properties that would be more suitable for deployment in practical SDM systems.
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