We propose and numerically investigate annular-cladding erbium doped multicore fibers (AC-EDMCF) with either solid or air hole inner cladding to enhance the pump power efficiency in optical amplifiers for spatial division multiplexing (SDM) transmission links. We first propose an all-glass fiber in which a central inner cladding region with a depressed refractive index is introduced to confine the pump inside a ring-shaped region overlapping the multiple signal cores. Through numerical simulations, we determine signal core and annular pump cladding parameters respecting fabrication constraints. We also propose and examine a multi-spot injection scheme for launching the pump in the annular cladding. With this all-glass fiber with annular cladding, our results predict 10 dB increase in gain and 21% pump power savings compared to the standard double cladding design. We also investigate a fiber with an air hole inner cladding to further enhance the pump power confinement and minimize power leaking into the inner cladding. The results are compared to the all-glass AC-EDMCF.
© 2015 Optical Society of America
The recent exponential growth of data traffic, fueled by applications such as cloud computing and mobile streaming, has by now practically exhausted all known means (e.g. wavelength, polarization and time division multiplexing, and higher-order modulation formats) of increasing the capacity of single-mode fibers (SMFs) [1,2]. Beyond those techniques, space division multiplexing (SDM) is a promising approach to overcome the anticipated capacity crunch [3,4] while minimizing the energy per bit [5,6]. This is realized by exploiting a new degree of freedom, the space, through which one can multiplex a number of data channels within a single fiber strand, i.e. sharing the same cladding. There exists two main SDM schemes, firstly using multimode fibers that can be either graded index  or step index , in which each orthogonal mode corresponds to an independent channel, or secondly using multicore fibers , in which each core corresponds to a different link. Hybrid implementations of these SDM techniques have been performed for increased capacity [10,11] and switching between different SDM schemes along a transmission link has been demonstrated to illustrate their compatibility . This paper is focused on optical amplifier design for the multicore fiber embodiment.
At the heart of any practical implementation of SDM schemes for long-haul transmission links is the development of high-performance and cost-effective inline optical amplifier-s [13,14]. Both erbium doped multicore fiber amplifiers (EDMCFAs)  and multicore Raman amplifiers  have been studied recently. For EDMCFA, the pumping configuration is an important issue. In-core pumping of an EDMCFA avoids the drawback of using multiple parallel erbium doped fiber amplifiers (EDFAs), one for each core of the multicore transmission fiber, but it requires several single-mode pump lasers, WDM couplers, and more importantly spatial channel demultiplexers/multiplexers at the amplifier input (or output for a counter-propagating pumping configuration) that can degrade noise figure (NF) and introduce cross-talk . In order to reduce pumping complexity and related costs, cladding pumping is also actively studied towards efficient multicore SDM amplification . Cladding pumping allows the use of low-cost and high-power multimode diode lasers that pump all erbium doped cores simultaneously. However, an important limitation to the efficiency of this method is the low pump field overlap with the doped cores. This naturally originates from the small aggregate core area compared to pump cladding area (assuming a uniformly distributed pump power). In this regard, the improvement of the signal and pump overlap should ideally be performed by shrinking the cladding rather than enlarging the signal cores that must maintain the single mode propagation condition.
In this paper, we propose and study a double-cladding erbium doped six-core fiber with an annular cladding (AC-EDMCF) to guide the multimode pump field. The paper is organized as follows. In Section 2, we delineate the operating principle of the AC-EDMCF by outlining the combination of core and cladding designs, and we identify the design constraints related to fiber fabrication with modified chemical vapor deposition (MCVD) process. Subsequently, in Section 3, using the determined parameters, we investigate the performance of the novel AC-EDMCF through numerical simulations, calculating signal gain and NF. In Section 4, we discuss three configurations to launch the pump in the annular cladding, enlightening possible solutions to be tested in future experiments. Finally, our conclusion discusses the design of annular cladding for multicore amplifiers in view of the simulation results, as well as future work.
2. Fiber structure and design
2.1 Fiber structure description
The proposed design of an AC-EDMCF is shown in Fig. 1. It consists of a double cladding structure that contains six doped cores for signal amplification. However, in contrast to most previous studies proposing seven core fibers, the center core, which is more susceptible to cross-talk, is absent . This multicore fiber design, placing cores along a ring, has been demonstrated with up to 12 cores . The inner cladding further presents a depressed refractive index value so that the pump is actually guided by an annular (or ring) cladding index profile.
Figure 2 shows the refractive index profiles of several types of EDMCFs, namely the annular cladding design with depressed-index inner silica cladding [ACS-EDMCF, Fig. 2(a)], depressed-index inner cladding made by an air hole [ACA-EDMCF, Fig. 2(b)], the standard double cladding fiber (DC-EDMCF) that will be used for comparison [Fig. 2(c)], and the conventional single cladding fiber which will be used to determine the minimum annular cladding thickness [Fig. 2(d)]. In all cases, the fiber cladding is populated by six cores, as shown in Fig. 1. The cores are arranged in a ring with a core-to-core pitch (and core-to-center distance), Λ. Based on previous studies of multicore transmission fibers , acceptable cross-talk level is achieved with Λ = 40 μm and a similar value was chosen here. This six-core geometry was recently demonstrated with a standard double cladding EDMCF [12,20]. The pump annular cladding is assumed to be pure silica, with refractive index nclad,p, and the outer cladding is a low-refractive index polymer, with refractive index nclad,out. The inner cladding could be formed by two means: a solid all-glass inner cladding or an air hole inner cladding. In Fig. 2(a), the depressed-index inner cladding is made with fluorine-doped silica, with refractive index nclad,in. We consider that a maximum refractive index step nclad,p−nclad,in = 5.9 × 10−3 is achievable with fluorine-doped silica. Certainly, the use of an air hole as inner cladding [Fig. 2(b)] provides a much larger index step. Table 1 shows the definition of the respective refractive indices and the main geometrical parameters of all designs where several values are left to be specified. In sub-sections 2.3 and 2.4 below, we will determine the signal core parameters and design the pump ring accordingly.
The benefits brought about by such cladding geometry are motivated by the reduced power consumption and lower achievable NFs due to the larger pump-signal field overlap. In general the required pump power, Pd, for a given inversion ratio η, is related to the power density, Sp, through ,
2.2 Amplifier modeling
Some fiber parameters, such as (rcore) and numerical aperture (NA) can be optimized through numerical calculations, using standard coupled rate equations , to evaluate the expected small signal gain (G) and NF with given amplifier operation scenarios. Here, we note that there is no conceptual difference between a solid and an air hole inner cladding design under a uniform pump power distribution assumption as they both achieve similar overlap factors of the pump with the cores. Consequently, in the following model, we only consider the solid inner cladding case. For simplicity, particularly for the signal core optimization in Section 2.3, signal power amplification is simulated in only one core but the pump absorption takes into account the presence of all cores. The equations describing power evolution along the fiber are thus given by ,
2.3 Signal core design
Prior to designing the pump ring, the signal core parameters of the AC-EDMCF, i.e. core radius and numerical aperture, must be selected so as to achieve decent signal gain (> 20 dB) with the typical parameters shown in Table 2. Simulations for optimizing the core parameters consider a single core (Ncore = 1) since all six cores are theoretically identical. In this initial step, we consider a conventional double cladding design [Fig. 2(c)]. We assume that erbium ions are uniformly distributed across the core, with a 2.62 × 1025 m−3 concentration, while background propagation loss and ion-ion interactions are neglected. We further assume that the pump is uniformly distributed inside the pump cladding that has a 110 μm diameter and 0.46 numerical aperture (fused silica surrounded by low index polymer) as is generally the case in cladding pumping operation. A pump source at 980 nm is injected in a co-propagating configuration with respect to the signal. The pump absorption cross-section was taken to be 2.18 × 10−25 m2. To examine small signal gain, we performed the simulations with −30 dBm input signal at 1550 nm in a 5 m long DC-EDMCF.
Figure 3(a) shows the small signal gain over a region delimited by the single-mode cut-off V = 2.405 (top right), and insufficient gain condition, i.e. G < 20 dB (bottom left). As expected, the signal gain increases with core radius since the overlap factor of the pump with the doped core can be estimated by the geometric ratio Γp = Acore/Aclad. However, it should be noted that the NF [Fig. 3(b)], simultaneously increases. Keeping within acceptable gain and NF values, while enforcing the single mode regime, we choose rcore = 4.5 μm and NA = 0.11 (marked with a cross in Fig. 3) as the core parameters. The set of parameters rcore = 2.5 μm and NA = 0.15 (solid square in Fig. 3), is used here for comparison purposes. This latter set of parameters, from a previous work [22,23], would be more representative of a core pumped EDF. Both sets yield signal gain over 20 dB at 1550 nm, the former achieves 29.07 dB small signal gain (NF = 7.45), while the latter provides 24.35 dB small signal gain (NF = 6.90) using a 1 W pump.
2.4 Pump ring design
In order to increase the overlap between erbium ions and the pump, the thickness of the pump ring should be minimized while keeping the core diameter (dcore) fixed. The total thickness of the pump ring (tring) can be divided into three parts,Fig. 2). The two distances (dring,in and dring,out) have a practical limit in that their narrowing should not distort too much the signal mode field guided in the core. This impact can be estimated by calculating the relative effective index difference (Feff) of the signal mode guided by the core with and without the presence of the pump ring,Fig. 2(d)].
Again, we examine the properties of a single core in a pump ring cladding having a solid inner cladding [Fig. 2(a)] or an air hole inner cladding [Fig. 2(b)]. The results are compared to an infinite cladding [Fig. 2(d)] in order to assess the influence on the signal mode introduced by the pump ring thickness variations. As the pump ring becomes increasingly thin, the evanescent part of the signal mode field will start to overlap with the ring cladding boundaries which can increase scattering losses of the signal due to surface roughness at these interfaces. Simultaneously, the overlap of the signal mode field with the outer and inner cladding will impact the modal effective index and we therefore use the calculated Feff as a metric to verify that the signal mode is not perturbed by the presence of the ring.
First, we examined the depressed inner cladding case with fluorine-doped silica [Fig. 2(a)] and signal core parameters set rcore = 4.5 μm and NA = 0.11. Figure 4(a) plots Feff as a function of dring,in and dring,out that are concurrently varied from 1 μm to 11 μm. Also shown in Fig. 4(a) is the boundary (solid white line) for which Feff < 1% (top right part of the graph). These results thus indicate that if dring,in and dring,out are properly chosen within the Feff < 1% region, the effect on the signal mode field caused by the finite pump ring thickness can be ignored. For instance, the modal field corresponding to the dot marker in Fig. 4(a) (dring,in = dring,out = 1.5 μm) turns out to be elliptical, which means that it is strongly distorted, while the star (dring,in = dring,out = 10.5 μm) shows a perfectly symmetric modal field with signal confinement of 0.74 in the core. The different values for the minimum dring,in and dring,out [dring,in = 4.88 μm and dring,out = 5.5 μm, solid red triangle in Fig. 4(a)] come from the different index contrast at the inner and outer cladding boundaries. Figure 4(b) shows similar calculations performed for the case of an air hole inner cladding, while keeping remaining parameters the same. In this case, the minimum dring,in and dring,out values are identical since the index contrast is almost the same at both boundaries. The minimum value of ring thickness, tring = 20.86 μm, indicated by the open red triangle in Fig. 4(b), corresponds to dring,in = 5.86 μm and dring,out = 6.0 μm.
In most cases of cladding pumping, assuming that all the pump power is confined in the cladding ring and furthermore considering its largely multimoded, an indicator of the pump power savings, Pe, enabled by the ring design can be estimated by,Fig. 1). We find that Pe = 0.21 (i.e. saving 21% power) can be achieved through annular pump cladding with dring,in = dring,out = 10.5 μm (solid and open star in Fig. 4). Alternatively, a factor Pe = 0.32 can be achieved for dring,in = dring,out = 6.5 μm (solid and open diamond in Fig. 4). With the minimum ring thickness, the annular cladding design could reduce the required pump power by up to 38% [red triangle in Fig. 4(a)] compared to a conventional geometry without annular cladding.
As indicated in Fig. 4, although the minimum ring thickness of the air hole scheme is thicker than the solid inner cladding one, it is expected that the former will enable stronger pump power confinement within the pump ring than the latter that is likely to show pump power leakage into the inner cladding. To verify this assumption, we calculated the first 500 pump modes of the ring cladding without signal cores and with dring,in = dring,out = 10.5 μm using COMSOL® for both solid [Fig. 2(a)] and air hole [Fig. 2(b)] inner cladding. The normalized intensity of each mode along an axis cutting through the center of the fiber (in this case the x-axis along line A in Fig. 1) are plotted in Fig. 5 where shaded gray area represents the inner cladding region. Modes are normalized to carry unit power. The calculations confirm that no guided mode exist in the inner cladding in case of air hole [Fig. 5(b)] contrary to a solid inner cladding [Fig. 5(a)]. Assuming all the 500 modes are equally excited, there would be 8% (average) of total power contained in solid inner cladding, the power fraction of solid inner cladding for some high order modes can reach 95%. In section 4, we will re-examine this issue via simulations using the beam propagation method (BPM).
Practical limitations of our current in-house fiber fabrication methods (preform produced by MCVD and stack-and-draw) require that tring 30 μm. In this particular instance, diamond markers in Fig. 4 identify manufacturing compliant parameters. As previously discussed, nclad,in is also limited by the maximum amount of fluorine that can be incorporated into the silica glass giving nclad,in = 1.43812 at λ = 1550 nm. The final parameters of the proposed AC-EDMCF design are listed in Table 3.
3. Amplification performance simulation
Using the model described in Section 2.2, we now examine the gain and NF of the proposed MCF designs with cladding pumping. We inject pump powers from 0.5 W to 1.5 W in the annular cladding, while the signal (1550 nm) input power is set at −30 dBm. For each pump power value, we find the optimum fiber length and calculate gain and NF. We assume six identical cores (Ncore = 6). Results are shown in Fig. 6 for the proposed AC-EDMCF design with the parameter sets identical to the ones identified by the same solid markers (diamond and star) in Fig. 4(a), while the open markers correspond to a standard double cladding (DC-) EDMCF [i.e. nclad,in = nclad,p, Fig. 2(c)] but with otherwise the same parameters. For the AC-EDMCF, the model assumes that all the pump power is uniformly distributed in the annular cladding and there is therefore no distinction between the air hole and depressed-index silica inner claddings. Figure 6(a) indicates that for a given gain level, for example 30 dB, the AC-EDMCF requires 1.1 W of pump power, which is 300 mW less than the DC-EDMCF. For the same pump power, considering pump power levels producing > 20 dB gain, the AC-EDMCF achieves between 4 to 10 dB higher gain than the DC-EDMCF, as well as a lower NF at all pump levels (especially for Pp < 1.1 W). Note that NF calculations are performed for conditions leading to G > 10 dB. Furthermore, the thinner pump ring scheme (diamond in Fig. 4), i.e. dring,in = dring,out = 6.5 μm, achieves up to 8 dB better gain than a thicker one (star in Fig. 4).
The saturated output power is calculated for 1 W pump and optimized fiber length (calculated for a −30 dBm input signal power). We varied the input signal power from −50 dBm to 10 dBm, at 1550 nm with results shown in Fig. 7. Again, for each input signal power, the AC-EDMCF achieves better gain, e.g. 12 dB more at −30 dBm, as well as smaller NF. The dynamic range associated with saturated input power (defined for the 3 dB gain compression), for AC-EDMCF is narrower than a DC-EDMCF. Design optimization towards increasing the saturation output power, as can be required for WDM inline amplifiers, will require further investigation.
A usual performance metric for EDFAs with in-core pumping is the power conversion efficiency (PCE) defined as PCE = (Ps,out−Ps,in)/Pp, where Ps,out is the output signal power. In the case of cladding pumping, where the pump power is typically larger than the signal power by three orders of magnitude, we propose the modified PCEclad defined as,
Figure 8 shows the PCEclad against pump power for AC-EDMCF and DC-EDMCF with different cladding parameters. Figure 8 indicates that at high pump power the proposed annular cladding design improves pump power utilization significantly, e.g. about 16 times higher PCEclad than a comparable DC-EDMCF with 1 W of pump power for dring,in = dring,out = 6.5 μm. Compared to thicker pump ring scheme (dring,in = dring,out = 10.5 μm), a thinner ring enables a more efficient usage of pump power, i.e. more net signal gain is obtained per unit pump power (1 mW).
4. Pump injection scheme
Unlike the conventional DC-EDMCF, in which the center cladding area can be fed by a multimode pump laser , we propose an alternate method to couple the pump in our annular-clad fiber using multiple injection spots. In this scheme one could simultaneously inject the pump and the signals, through modern coupler fabrication techniques such as tapered fiber bundles  or 3D photo-written waveguides , by strategically locating pump injection spots between the cores. Here, we examine three configurations of multi-spots injection of the pump in the cladding. We consider that the spots are mutually incoherent and model the multimode field of each spot as a 20 μm diameter flat-top intensity profile (with uniform phase). Figure 9 shows the injection pattern with one spot [Fig. 9(a)], three spots [Fig. 9(b)] and six spots [Fig. 9(c)]. In all cases, the pump is injected half-way between cores. In the case of three spots and six spots, the phase of each spot is chosen randomly between 0 and 2π before we perform BPM simulations (OptiBPM®) over a maximum propagation length of 40 mm.
We propagated the field along the fiber and calculated the intensity distributions after each 100 μm along the z-axis. We then performed a summation of all intensity distributions over a length of 10 mm and then the summation was normalized. Figure 10 illustrates this length averaged intensity distributions after 10 mm, 20 mm, and 30 mm long pump power propagation. As we can see in Fig. 10, after propagating over a length of 20 mm in the AC-EDMCF, the average intensity in the cladding is already well distributed across the annular cladding (dashed white circle). Because of the uniform phase front assumption of the input pump field, the injection into the multimode annular cladding can lead to a self-imaging phenomenon (Talbot effect) as shown, for example, in the single spot excitation of Fig. 10(a). In a practice, we expect the multimode pump laser input to have a random phase for each mode, which would result in a uniform pump power distribution. This simulation shows that the injected pump power gets rapidly distributed across the cladding.
Using BPM simulations, we examined if the injected pump power leaks into the inner cladding region (six-spot excitation after 40 mm). As predicted in Section 2, we observed a small amount of pump power leaking to the inner solid silica cladding [Fig. 11(a)], while the pump power is well confined within the annular pump cladding when the inner cladding is an air hole [Fig. 11(b)].
Besides the end-facet signal and pump injection, the side-coupling of pump power is another option that has been investigated for double cladding single core fibers. Before applying the technique on multi-core fiber, one needs to be aware that most of these techniques, such as v-groove coupling , require precise mechanical alignment and can suffer from stability issues, with the exception of the side-coupling tapered-fused fiber combiner . Furthermore, owing to the multicore fiber structure, either methods can perturb the signal cores due to their close proximity to the cladding boundary . Such a side-coupling pump injection scheme has recently been used to pump a multicore amplifier with multimode cores demonstrating the potential of this technique for annular cladding fibers .
We proposed a six-core erbium doped fiber with an annular-cladding design to increase the pumping efficiency of cladding pumped multi-core fiber amplifiers. After optimizing the signal core parameters (core size and NA), we investigated and compared several cladding designs that efficiently confine and guide the pump. The dimensions of the annular claddings were chosen so as to reduce the perturbation of the signal core modes. The annular cladding designs include an inner cladding index depression formed by either doping the silica glass with fluorine or by placing an air hole in the central region of the fiber. Both of these designs comply with practical considerations related to preform fabrication with MCVD. The proposed design demonstrates lower pump power requirements compared to standard double cladding design. Simulations also indicate that the annular cladding multi-core fiber design is superior in terms of gain and NF as well as power conversion efficiency, given similar core parameters. As with all multi-core fiber proposals, combination of pump and signals poses important challenges. Cladding pumping enables the use of multimode laser diodes delivering high pumping power that can be shared between cores. An end-facet multi-spot pump injection configurations could be used to deliver one to six pump beams in the cladding. BPM simulations indicate that multi-spots injected pump power will spread rapidly in the annular cladding so as to pump all cores. Other possibilities, such as side-coupling, could also be applied.
This work was supported by the Canada Research Chair in Advanced photonics technologies for communications (APTEC), by the Canada Excellence Research Chair in Enabling Photonic innovations for information and communications (CERCP) and by the Natural sciences and engineering research council of Canada (NSERC). C. Jin acknowledges the support of the China Scholarship Council.
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