Few mode Er3+-doped fiber with micro-structured core for mode division multiplexing in the C-band Guillaume Le Cocq∗ , Yves Quiquempois, Antoine Le Rouge, G´eraud Bouwmans, Hicham El Hamzaoui, Karen Delplace, Mohamed Bouazaoui, and Laurent Bigot PhLAM/IRCICA, Universit´e Lille 1, CNRS UMR8523/USR3380, 59658 Villeneuve d’Ascq, France ∗ [email protected]
Abstract: Design and experimental characterization of Er3+ -doped fiber amplifiers supporting 6 spatial modes in wavelength division multiplexing regime are reported. The study is first focused on Er3+ -doped circular ring-structured profiles accessible with conventional fiber manufacturing techniques. However, these fiber designs, optimized for gain equalization, prove to be difficult to obtain experimentally. So as to go beyond these limits, an alternative approach based on a “pixelated” Er3+ -doped core is proposed. Several possible designs are theoretically investigated and a first fabrication of micro-structured fiber is presented. © 2013 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2320) Fiber optics amplifiers and oscillators.
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#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31646
10. E. Ip, M-J. Li, K. Bennett, Y-K. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λ x6x19-Gbaud Wavelength- and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few- Mode Fiber with a Gain-Equalized Few-Mode EDFA,” OFC 2013, Post-Deadline paper, PDP5A.2 (2013). 11. R. Ryf, R-J. Essiambre, A.H. Gnauck, S. Randel, M.A. Mestre, C. Schmidt, P.J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “Space-Division Multiplexed Transmission over 4200-km 3-Core Microstructured Fiber,” OFC 2012, Post-Deadline paper, PDP5C.2 (2012). 12. N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” Opt. Express 19, 16601–16611 (2011). 13. G. Le Cocq, L. Bigot, A. Le Rouge, M. Bigot-Astruc, P. Sillard, C. Koebele, M. Salsi, and Y. Quiquempois, “Modeling and Characterization of a Few Mode EDFA Supporting Four Mode Groups for Mode Division Multiplexing,” Opt. Express 20, 27051–27061 (2012). 14. Q. Kang, E.L. Lim, Y. Jung, J.K. Sahu, F. Poletti, C. Baskiotis, S.U Alam, and D.J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP01 pump configuration,” Opt. Express 20, 20835–20843 (2012). 15. M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N.K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” ECOC 2012, Post-Deadline paper, Th.3.A.6 (2012). 16. Q. Kang, E. L. Lim, Y. Jung, F. Poletti, S. Alam, and D.J. Richardson, “Design of Four-Mode Erbium Doped Fiber Amplifier with Low Differential Modal Gain for Modal Division Multiplexed Transmissions,” OFC 2013, paper OTu3G.3. (2013). 17. P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” ECOC 2011, paper Tu.5.LeCervin.7 (2011). 18. C.R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991). 19. Z. Jiang and J.R. Marciante, “Impact of transverse spatial-hole burning on beam quality in large-mode-area Ybdoped fibers,” J. Opt. Soc. Am. B 25, 247–254 (2008). 20. Y. Lu, B. Julsgaard, M. Christian Petersen, R.V. Skougaard Jensen,T. Garm Pedersen, K. Pedersen, and A. Nylandsted Larsen, “Erbium diffusion in silicon dioxide,” Appl. Phys. Lett. 97, 141903–141903 (2010). 21. H. El Hamzaoui, L. Bigot, G. Bouwmans, I. Razdobreev, M. Bouazaoui, and B. Capoen, “From molecular precursors in solution to microstructured optical fiber: a Sol-gel polymeric route,” Opt. Mat. Express 1, 234–242 (2011). 22. M. Leich, F. Just, A. Langner, M. Such, G. Schotz, T. Eschrich, and S. Grimm, “Highly efficient Yb-doped silica fibers prepared by powder sinter technology,” Opt. Lett. 36, 1557–1559 (2011). 23. A. Baz, H. El Hamzaoui, I. Fsaifes, G. Bouwmans, M. Bouazaoui, and L. Bigot, “A pure silica ytterbium-doped sol-gel-based fiber laser,” Laser Phys. Lett. 10, 055106 (2013).
1.
Introduction
Recently, there has been renewed interest in Spatial Division Multiplexing (SDM), a technology first proposed in the early 80’s [1], because it represents a possible technological breakthrough that could permit to meet the increasing demand for high bit rates [2]. Among SDM technologies, Few-Mode Fibers (FMF) - used for Mode Division Multiplexing (MDM) - and Multi-Core Fibers (MCF) approaches are both actively studied using either weakly [3–8] or strongly [9–11] coupled channels. Each possesses its own technical advantages and drawbacks and it is presently difficult to predict if one of these technologies - or a combination of the two - will emerge. Whatever, in both cases, not only the transmission fiber has to be re-visited but also the different passive and active optical components that constitute a long-haul transmission, namely multiplexers/demultiplexers, reconfigurable optical add-drop multiplexers and optical amplifiers. In the case of MDM, the architecture of optical amplifiers - the so called Er3+ -Doped Fiber Amplifiers (EDFA) - has to be adapted to the efficient guiding and equalized amplification of the different modes. To reach this second target, several strategies can be combined or used independently: i) tailoring the transverse intensity pattern of the pump [12], ii) tailoring the Er3+ distribution in the core [13,14] or iii) concatenating different kind of fibers [15]. In all cases, the different signals carried by the different modes and the different wavelengths (for Wavelength Division Multiplexing, WDM) have to present high gain and small gain excursion (ΔG) value if one pretends to maintain reasonable equality between all the channels in multi-span transmissions. So that not only Differential Modal Gain (DMG) should be reduced at a particular #192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31647
wavelength, but a compromise must be found between gain equalization for all the modes and for all the wavelengths of the frequency comb. In a previous work, equalized amplification of four modes (namely LP11a&b and LP21a&b modes) was demonstrated by using a ring-doping for Er3+ [13]. A gain of 21 dB and DMG below 0.4 dB around 1550 nm was demonstrated using an Erbium Doped Fiber (EDF) made by Modified Chemical Vapor Deposition (MCVD) process. In this paper, theoretical and experimental investigation of the possibility to equally amplify 6 modes in a MCVD-based fiber are reported, both considering ideal and realistic Erbium Doping Profile (EDP). Special attention has been paid to gain equalization for all the modes but also for all the wavelength channels distributed over the C-band. Designs that minimize gain excursion are investigated without considering the use of spectral filter. It is shown that complex EDP can hardly be achieved by MCVD combined to solution doping. Hence, in the second part of the paper, theoretical approach on micro-structuring the fiber core is investigated as an alternative to conventional MCVD-based fibers. It is shown that “pixelated” distribution of the Er3+ -doping permits to accurately separate regions with and without doping and also enables non-circular EDP. Gain equalization with an accuracy of 3.2 dB for 6 modes over the C-band can theoretically be obtained in this kind of structure, with 21 dB average gain and DMG values down to 0.6 dB over 6 modes at 1540 nm. 2.
Design of the MCVD-based fiber
Starting from the fiber design reported in our previous work [13], our goal was to demonstrate an EDF that equally amplifies 6 modes. As LP11 and LP21 modes were already equally amplified but LP01 and LP02 had lower gains, the amplifier design has been improved in order to equally amplify all the different guided modes. LP11 and LP21 modes are off-centered in the fiber core and can be amplified by a ring EDP. LP01 and LP02 mode are centered in the core, so, in addition to the ring-shape EDP, it is naturally interesting to add some Er3+ in the center of the core in order to amplify the centered modes without major impact on the gain equalization for off-centered modes (LP11 and LP21 ). This approach has recently been theoretically proposed to realize a FM-EDF adapted to the amplification of 6 modes with small DMG [16]. We decided not to change the ring geometry in order to maintain a continuity with our previous work and because this geometry allows gain equalization between LP11 and LP21 modes [13]. So, the ring dimensions are delimited by two radii (internal and external one, namely Rdi and Rde ), that are set at 3.5 μ m and 7.5 μ m. The centered doped region is delimited by a third radius, Rdc , (Fig. 1(a)) that is considered as a variable. Er3+ concentration is assumed to be flat and to be the same in each doped region. In order to ensure mode matching between active and passive fibers, the Refractive Index Profile (RIP) of the EDF is assumed to be the same as the RIP of the passive Few-Mode Fiber (FMF) used in our experimental set-up [17]. So, the RIP is a perfect step index, with a refractive index difference between core and cladding that is set at 9.7 × 10−3 and the core radius (Rcore ) is chosen equal to 7.5 μ m. Optimization of the design follows the description hereafter. It uses an home-made code used to obtain the modal gain in FM-EDFA, based on a modified version of the model proposed by Giles and Desurvire [18] generalized to FMF, as in references [13, 14]. The value of Rdc has been changed from 0 to 3.5 μ m (extreme values that are possible) and the gain of 24 signals (6 modes × 4 wavelengths) simultaneously amplified has been calculated for each EDP, so as to find the EDP that gives the lowest ΔG value between these 24 signals, meaning that a good compromise between modes and spectrum equalization will be found. The signals were distributed over the C-band spectrum (at 1530, 1540, 1550 and 1560 nm) and over the 6 guided modes (namely LP01 , LP11a , LP11b , LP21a , LP21b and LP02 ). Each signal mode has an input power of -17 dBm. Pump beam is considered to be injected at the center of the fiber core,
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31648
Fig. 1. (a) Theoretical Er3+ doped fiber design. Internal and external radii of ring doped region are set at 3.5 and 7.5 μ m respectively, while the radius of central doped region (Rdc ) can vary from 0 to 3.5 μ m. (b) ΔG value between 24 signals distributed over modes and spectrum, calculated as a function of Rdc . Fiber length is 35 m long, optimal length for conserving LP11 and LP21 gain equalization. Pump power is 200 mW at 980 nm and equally distributed on LP01 , LP02 and LP03 modes. Each signal has an input power of 17 dBm. (c) Gain values of the 24 signals (for the different modes and wavelengths) if Rdc is set at 1.75 μ m
so that only LP01 , LP02 and LP03 pump modes are excited at 980 nm. Pump power has been set at 200 mW and is supposed to be equally distributed between these three pump modes. It is worth pointing out that centered injection condition is the easiest way to pump the amplifier, because it only excites LP0m modes. These pump modes don’t create transverse azimuthal dependence of Er3+ population inversion, since their intensity profiles have no azimuthal dependence, and can be efficiently coupled in the fiber (more than 90%). Transverse azimuthal dependence of pump modes can generate high DMG values between spatially degenerated signal modes. Off-centered injection condition will excite other high order modes (HOM), which creates azimuthal dependence for modal gain [12, 19] or induces high coupling losses. Fiber length was considered to be 35 m, because it allows flat gain over spectrum for off-centered modes, with the Er3+ concentration that was set at 1.42 × 1024 ions.m−3 . In the following, the gain excursion, ΔG, is defined as the difference between the highest and the lowest gain values obtained for the 24 signals that are simultaneously amplified in the fiber. DMG corresponds to the difference of gain between the different modes at a given wavelength and Differential Spectral Gain (DSG) is the difference of gain over the C-band, for a given mode. Considering ΔG as a function of Rdc , and with the simple EDP presented in Fig. 1(a), the lowest value for ΔG is equal to 4.1 dB and is obtained for Rdc = 1.75 μ m (Fig. 1(b)). This ΔG value is mainly attributed to the non-flatness of the gain over the spectrum. Indeed, for each wavelength, DMG is between 0.9 and 2.5 dB for all the modes, while gain can change up to 3.6 dB over the spectrum (DSG), for one of the modes (Fig. 1(c)). Gain equalization for off-centered modes has been preserved, as expected: differential gain between LP11 and LP21 modes is between 0.2 and 0.6 dB, while DSG value for these two modes is between 2.0 and 2.1 dB. DSG values for centered modes are relatively larger than for off-centered modes. This phenomenon can be explained by the fact that: • pump intensity is higher at the center of the core (LP0m pump modes are used) implying different optimum lengths between centered and off-centered signal modes (respectively 35 and 41 m). • flat gain over spectrum for a given mode can be achieved by choosing the optimum length of the amplifier (so that signal at 1530 nm is slightly reabsorbed at the end of the fiber, #192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31649
and its gain slightly decreases, becoming equal to the gain at longer wavelengths). If attention is focused on ΔG value rather than on gain equalization for off-centered modes, performances of this amplifier can be improved by slightly changing the fiber length. Further calculations indicate that ΔG value can decrease down to 3.1 dB for an average gain (Gave ) of 20.9 dB, if fiber length is set at 39 m, while maintaining Rdc equal to 1.75 μ m. Results are reported on Fig. 2 and Table 1. In order to study the distribution of the gain values around the average value, the standard deviation of the 24 gain values (σG ) has also been calculated and is equal to 1.2 dB. Very low DMG values over the 6 modes are achievable at a particular wavelength (0.9 dB at 1540 nm, as reported on Table 1). However, even if this value is very low, it can be seen that DMG values can increase up to 2.5 dB for other wavelengths. These results prove that the fiber design must be developed considering the different modes but also the different wavelengths in order to minimize ΔG value instead of just minimizing DMG value at a particular wavelength. Note that, to obtain this low ΔG value, the thickness of the doping depletion has to be very small (1.75 μ m, as can be seen in Fig. 1(b)). Such a small thickness is however not trivial to made while it is a sensitive parameter: slight changes in its dimensions quickly induce a penalty of several decibels on ΔG values (Fig. 1(b)).
Fig. 2. Gain values of the 24 signals (for the different modes and wavelengths) when fiber length is set at 39 m, the length that minimizes gain excursion. Pump power is 200 mW equally distributed on LP01 , LP02 and LP03 modes. Each signal has an input power of -17 dBm. Rdc is set at 1.75 μ m
Table 1. Gain values for the 24 signals that are simultaneously amplified (6 modes × 4 wavelengths) if Rdc is set at 1.75 μ m, and fiber length is set at 39 m. DMG and DSG values are also reported. Average gain is 21 dB.
Gain (dB) 1530 nm 1540 nm 1550 nm 1560 nm DSG (dB)
LP01 22.3 20.1 21.9 21.2 ↓ 2.2
LP02 21.9 19.2 20.5 19.7 ↓ 2.7
LP11a 20.3 19.7 22.3 22.2 ↓ 2.6
Gave 20.9 dB
LP11b 20.3 19.7 22.3 22.2 ↓ 2.6 ΔG 3.1 dB
LP21a 19.5 19.2 22.0 22.0 ↓ 2.8
LP21b 19.5 19.2 22.0 22.0 ↓ 2.8
DMG (dB) → 2.8 → 0.9 → 1.7 → 2.5
σG 1.2 dB
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31650
The validity of these results has been tested for other pump and signal power levels. As can be seen on Fig. 3(a) and Fig. 3(b), it appears that, if fiber length is adjusted so as to optimize the performances of the amplifier (especially the ΔG value), similar performances - here, similar relative gain excursion defined as ΔG/Gave - can be reached for pump power between 200 and 350 mW and signal power between -30 dBm to -10 dBm. This shows that the design proposed can be used for a large range of power configurations.
Fig. 3. Evolution of average gain (Gave ) and gain excursion (ΔG) as a function of pump power for signal power set at -17 dBm per channel (left) or as a function of signal power for pump power set at 200 mW (right). These simulations are performed for the optimized MCVD design presented on Fig. 4(a). In both cases, fiber length is adjusted for each pump or signal power so as to minimize gain excursion.
3.
MCVD fiber fabrication and characterization
Fig. 4. (a) Refractive index profile and EDP that was targeted. (b) Refractive index profile and Er3+ profile that has been obtained by MCVD process.
Starting from the above-discussed simple theoretical profile (Fig. 4(a)), a first test of feasibility has been made by conventional MCVD combined with solution doping technique (characteristics reported in Fig. 4(b)). A RIP close to the target (passive FMF) has been obtained, which is important to reduce crosstalk between the two fibers when they are spliced or connected together. However, even if a structure made of a ring and an additional centered doped region can be observed, EDP is quite far from what was expected. This is attributed to the difficulty to manage solution doping (Er3+ -doped region) and vapor deposition (undoped region) in the different core regions to obtain the suited EDP and RIP. Moreover, Er3+ diffusion all-along
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31651
the fabrication process has also to be anticipated so as to accurately control both thickness and concentration level in each doped region [20]. Nevertheless, modal gain obtained with this fiber has been measured. We used the same experimental set-up as in reference [13] to measure LP01 , LP11 and LP21 modal gains, individually amplified, no phase mask being available to test LP02 mode. Pump (974 nm laser diode) and signal beams are multiplexed in free space and injected into a piece of passive FMF spliced to the EDF under test. Phase plates are used to shape the desired signal field profile at the input and no demultiplexing set-up is used to separate modes at the output. Fiber length was set at 2 m. This short experimental fiber length (compare to simulation fiber lengths) is mainly due to the fact that erbium concentration in the fabricated fiber is about 20 times than the one used in the simulation (Fig. 4). The modal gain has been measured as a function of pump power. The FM-EDF was centered spliced to the passive FMF. Mode matching between the two fibers is ensured by the good fit of their RIP.
Fig. 5. Experimental results of gain as a function of pump power coupled in the FM-EDF with opto-geometrical characteristics reported in Fig. 4(b).
LP01 gets a higher gain compared to LP11 and LP21 modes (Fig. 5). Gain values of 21.9, 14.1 and 12.3 dB are respectively measured at 1550 nm if pump power is 150 mW. This is due to the fact that Er3+ concentration in centered region is twice larger than in the ring (Fig. 4(b)), which favors the gain of centered modes. The large DMG observed makes this fiber unusable for MDM transmissions with all the modes. 4.
Towards more realistic designs
As it can be seen on Fig. 4(b), EDP is far from being made of perfect steps. Since there is some Er3+ diffusion during fabrication process, the spatial distribution of the Er3+ is close from Gaussian. So, some other simulations were performed with a more realistic EDP, considering that each doped zone is Gaussian-like shaped. In order to be closer to what can be expected, the EDP has been considered to be the experimental ring shaped Er3+ distribution reported in our previous work [13]. Some Er3+ at the center of the fiber has been added, following a Gaussian distribution delimited by a waist ωdc (half width at 1/e2 ) in order to find which Gaussian dimension will lead to the smallest value for ΔG (Fig. 6(a)). Then, for each EDP (meaning each value of ωdc ), the gain of 24 signals simultaneously amplified has been calculated in this fiber. By considering ΔG as a function of ωdc , it has been possible to find the Gaussian distribution that allows the lowest difference of gain over the modes and over the spectrum. This optimal Gaussian distribution is defined by
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31652
Fig. 6. (a) Er3+ doped fiber design that considers a more realistic profile. Ring EDP is taken from our previous fabrication. Centered doping region is calculated following a Gaussian distribution. (b) Δ G value between 24 signals distributed over modes and spectrum, calculated as a function of ωdc . Pump power is 200 mW equally distributed on LP01 , LP02 and LP03 modes. Each signal has an input power of -17 dBm. c) Gain values of the 24 signals (for the different modes and wavelengths) if ωdc is equal to 1.4 μ m
ωdc = 1.4 μ m (Fig. 6(b)). This particular dimension is quite close to the one found previously for centered doped size (Rdc = 1.75 μ m, Fig. 1(a)), meaning that the dimensions of EDP don’t change whereas its shape does. This kind of realistic EDP can only ensure ΔG value of 6.2 dB (Fig. 6(b) and Fig. 6(c))), which is a considerable degradation of gain equalization compared to the previous theoretical profile (Fig. 1(c)). So, even if one succeeds in making such an EDP with ωdc = 1.4 μ m (which is a difficult value to achieve since it depends on the thickness of the doped layer that will be deposited and the temperature that rules the doping diffusion), the performance of this amplifier will be humdrum because gain equalization will be poor. Even if improved designs can be imagined, these results suggest that MCVD combined to solution doping is probably not a process perfectly adapted to make the EDP required for MDM transmissions. 5.
Micro-structuring the fiber core
Based on the previous conclusions, a technique inspired from the stack-and-draw process is then proposed as an easiest alternative to tailor the EDP in the fiber core (Fig. 7). As a proof of concept, micro-structuring the core of an air/silica Photonic Crystal Fiber (PCF) is demonstrated to be an interesting way to make Few-Mode EDFA (FM-EDFA). This concept can, of course, be extended to an all-solid fiber, with a cladding made of an homogeneous material, more suited for Telecom application. The study is focused on developing a design of microstructured EDP in a core that supports 6 spatial modes and allows low ΔG value. The core has been chosen to be a 19-cell defect because this number of rods offers several degrees of freedom to accurately “pixelate” the core with a reasonable fabrication complexity. The optogeometrical parameters of this 19-cell defect PCF have been chosen so that its dimensions and the waist of the fundamental mode at 1550 nm are close to the one of the passive FMF, hence and cladding parameters are: Λ = 3.3 μ m and d/Λ = 0.3 (Fig. 7). Micro-structuring the core ensures preserving targeted Er3+ profile and allows more flexibility, because Er3+ transverse distribution can be “pixelated” and because cylindrical symmetry can be broken. Several EDPs are possible, just by doping with the same concentration (or not doping at all) each one of the 19 elements that compose the core. Some of these microstructured EDP have been investigated in order to find some profiles that allow low DMG and flat gain over the C-band. With this relatively simple fiber geometry, fabrication process should be easy to achieve and compared to MCVD process, the resulting fiber should have a better
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31653
Fig. 7. Schematic illustration of the concept proposed in this paper: silica capillary, pure sol-gel silica glass and sol-gel Er3+ doped rods are stacked together to obtain a PCF with micro-structured core and air/silica cladding.
Fig. 8. Intensity profiles of the guided modes in the PCF, Λ = 3.3 μ m and d/Λ = 0.3, at: a) 1550 nm b) 980 nm.
assurance to be close to the targeted profile. Micro-structuring the fibre core also opens several possibilities by slightly changing the Er3+ concentration for each rod, or by using thinner Er3+ doped rod, jacketed into a silica capillary (overcladding the Er3+ doped rods). As a first trial, the following simulations are based on the hypothesis that i) all the core rods are entirely doped or undoped, ii) all the core rods have the same refractive index as pure silica, iii) Er3+ doped rods have a flat doping profile and iv) Er3+ spectroscopic properties are those of aluminosilicate glasses. Technically, such core rods could be obtained by the Sol-Gel technique [21], powder approach [22] and maybe by MCVD or OVD. Simulations were performed considering the calculated mode profiles of the PCF (using a finite element method), both at signal and pump wavelengths (Fig. 8). As the core of the structure is no more cylindrical, there is a lift of azimuthal degeneracy between LPlma and LPlmb modes, and their intensity profiles are no more symmetrical via a rotation of π /2l. The gain of 24 signals has been computed over modes and wavelengths, as in the previous sections. Pump power has been set at 200 mW and has been equally distributed between LP01 and LP02 pump modes (centered injection conditions). Compared to the MCVD-based design reported in the previous parts, LP03 mode exhibits high confinement losses in this PCF geometry at 980 nm, so it can’t be used to pump the amplifier. Each doped region is considered to have an Er3+ concentration of 8×1024 ions/m3 . Fiber length is chosen so as to minimize ΔG value.
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31654
Fig. 9. (a) Design of the micro-structured -ring shaped EDP in the PCF with additional Er3+ doping at the center of the core. Fiber length is 7.5 m (length that minimizes gain excursion) (b) Gain values of the 24 signals (for the different modes and wavelengths) achievable with this design.
Fig. 10. (a) Micro-structured EDP in the PCF, with two additional doped cells in the second rod rings region of the core. Fiber length is 7 m (length that minimizes gain excursion). (b) Gain values of the 24 signals (for the different modes and wavelengths) achievable with this design.
The first micro-structured EDP that has been investigated is an equivalent of the MCVD-one reported on Fig. 1(a)), with Er3+ -ring doping and additional doping at the center of the core. This “pixelated” EDP is reported on Fig. 9(a) and the gain of 24 signals has been calculated (Fig. 9(b)). ΔG value is 10.0 dB for an average gain of 20.3 dB, obtained with a 7.5 m -long fiber. This high ΔG value is due to the fact that it is not possible to freely adjust the thickness of the doped regions so as to reach gain equalization, if homogeneous rods are used. Another phenomenon that can be observed is that LP11a&b or LP21a&b have no longer the same gains, which is due to the lack of cylindrical symmetry of the fiber core. LP02 is the most amplified mode because Er3+ profile fits well its intensity profile. DSG values are between 1.9 and 3.3 dB. In order to ensure more gain to LP01 and LP11 modes, an improved design could consist in adding Er3+ doping in the core regions where the other modes (namely LP02 and LP21 modes) have low intensity. On Fig. 10(a), two Er3+ rods have been added in the second ring of the micro-structured core in order to obtain a lower ΔG value. Such a flexibility on the EDP is possible only with “pixelated” EDP. ΔG value decreases to 8.2 dB and average gain increases up to 20.8 dB (Fig. 10(b)). Fiber length has to be adjusted to 7 m. Even if the performances of this design are still poor, the results illustrate how much cylindrical symmetry can be broken,
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31655
Fig. 11. (a) Micro-structured EDP in the PCF, with three doped cells in the second ring of the core region, and centered doped cell. Fiber length is 6.5 m (length that minimizes gain excursion). (b) Gain values of the 24 signals (for the different modes and wavelengths) achievable with this design. (c) Design of the PCF with three additional doped cells in the second ring of the core region and undoped centered cell. Fiber length is 7 m (length that minimizes gain excursion). (d) Gain values of the 24 signals (for the different modes and wavelengths) achievable with this design.
because DMG up to 3.3 dB can be observed between LP11a&b . This proves that all the modes have to be considered separately in this kind of fiber geometry. If a third cell is added in the second ring of the core, two cases can be compared namely doped or undoped centered cell (Fig. 11(a) and Fig. 11(c)). Indeed, order is reversed between the two cases and centered and off-centered modes swap their roles (Fig. 11(b) and Fig. 11(d)). In both cases, average gain is about 20.5 dB and ΔG value is about 7 dB. Finally, in order to find a trade-off between these two last EDP and to further investigate this concept, the EDP has been adjusted so that the centered rod is now doped with half the concentration of the other doped cells (meaning a concentration of 4×1024 ions/m3 ). This new EDP is reported on Fig. 12(a). With such a design, very low DMG values (between 0.6 and 2.1 dB) can be obtained all over the C-band, if fiber length is set at 6.5 m. DSG values are between 2.1 and 2.8 dB, so that DSG is higher than DMG. The average gain for the 24 signals is 21 dB with ΔG = 3.2 dB and the distribution of gain values can be described by σG , which is equal to 0.9 dB, proving that the 24 gain values are quite centered around the average gain (Fig. 12(b) and Table 2). ΔG value is 0.1 dB larger than the results reported on Table 1, however, this slight degradation of gain equalization is counterbalanced by a higher average gain and a smaller standard deviation. The validity of these results has been tested for other pump and signal power levels. As can be seen on Fig. 13(a) and Fig. 13(b), it appears that, if fiber length is adjusted so as to optimize the performances of the amplifier (especially the ΔG value), similar performances - here, similar
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31656
Fig. 12. (a) Micro-structured EDP in the PCF, with three doped cells in the second ring region of the core, and centered doped cell doped with half the concentration compared to the others. Fiber length is 6.5 m (length that minimizes gain excursion). (b) Gain values of the 24 signals (for the different modes and wavelengths) achievable with this design. Table 2. Gain values for the 24 signals that are simultaneously amplified (6 modes × 4 wavelengths) in the micro-structured EDP reported in Fig. 12. DMG and DSG values are also reported. Average gain is 21 dB.
Gain (dB) 1530 nm 1540 nm 1550 nm 1560 nm DSG (dB)
LP01 22.6 20.0 21.5 20.8 ↓ 2.6
LP02 22.4 19.7 21.2 20.4 ↓ 2.7
LP11a 21.3 19.8 21.9 21.6 ↓ 2.2
Gave 21.0 dB
LP11b 21.2 19.7 21.8 21.5 ↓ 2.1 ΔG 3.2 dB
LP21a 20.5 19.4 21.7 21.5 ↓ 2.3
LP21b 20.8 19.7 22.1 21.9 ↓ 2.4
DMG (dB) → 2.1 → 0.6 → 0.9 → 1.4
σG 0.9 dB
Fig. 13. Evolution of average gain (Gave ) and gain excursion (ΔG) as a function of pump power for signal power set at -17 dBm per channel (left) or as a function of signal power for pump power set at 200 mW (right). These simulations are performed for the optimized micro-structured core design presented on Fig. 12(a). In both cases, fiber length is adjusted for each pump or signal power so as to minimize gain excursion.
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31657
relative gain excursion defined as ΔG/Gave - can be reached for pump power between 200 and 350 mW and signal power between -30 dBm to -10 dBm. As was the case for the MCVD design previously investigated, this shows that the micro-structured core design proposed here can be used for a large range of power configurations. 6.
Fiber realization
Fig. 14. Pictures of the micro-structured cane of the PCF. Back-Scattered Electron (BSE) image of the cane (in the center of the picture) and classical Scanning Electron Microscopy (SEM) of the fiber have been superimposed to demonstrate the feasibility of the concept proposed in this work. The erbium profile, obtained by EPMA, along the green dotted axis is presented in inset.
As a proof of concept, the design proposed on Fig. 11 has been made. To this end, 15 millimeter-sized Er3+ -doped rods drawn from a Sol-Gel -made rod have been combined with 4 pure silica Sol-Gel -made rods (also drawn from a centimeter-sized ”mother” rod) so as to constitute the fiber core. These 19 elements have been assembled with pure silica capillaries (Heraeus) and the whole stack has been jacketed into a tube. The resulting preform has been drawn into cane and then into fiber. A piece of cane has been analyzed by Electron Probe MicroAnalysis (EPMA) and the results are presented on Fig. 14 superimposed on a SEM image of the fiber. When Fig. 14 is compared to Fig. 11, it is clearly seen that the obtained geometry is identical to the targeted one. The EPMA profile clearly shows the absence of erbium diffusion in the undoped regions with sharp transition between erbium-doped and pure silica regions. Er3+ concentration in the three doped regions is not as flat as suited, which can be improved as has been shown recently [23]. This demonstrates the technical feasibility of the approach proposed in the second part of this paper. #192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31658
7.
Conclusion
In this paper, simulations and experimental characterization of 6 modes EDFA have been reported. Differential gain over modes and spectrum as small as 3.1 dB could be theoretically achieved in MCVD -based fibers. However, it has been shown that such an EDP seems hard to obtain by MCVD, partly because of Er3+ diffusion that leads to a deterioration of gain equalization over modes and spectrum. An alternative has been proposed, based on micro-structuring the 19-cell core of an air/silica PCF. Such a fiber design has been investigated and differential gain over spectrum and modes down to 3.2 dB for 21 dB average gain has been predicted. DMG values are lower than DSG values, making this fiber close to a usable one. Acknowledgment This work has been supported by the French government, in the frame of STRADE research project (ANR-09-VERS-010). We also acknowledge financial support from the Ministry of Higher Education and Research, the Nord-Pas de Calais Regional Council and the FEDER through the “Contrat de Projets Etat Region (CPER) 2007-2013”.
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31659
Abstract: Design and experimental characterization of Er3+ -doped fiber amplifiers supporting 6 spatial modes in wavelength division multiplexing regime are reported. The study is first focused on Er3+ -doped circular ring-structured profiles accessible with conventional fiber manufacturing techniques. However, these fiber designs, optimized for gain equalization, prove to be difficult to obtain experimentally. So as to go beyond these limits, an alternative approach based on a “pixelated” Er3+ -doped core is proposed. Several possible designs are theoretically investigated and a first fabrication of micro-structured fiber is presented. © 2013 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2320) Fiber optics amplifiers and oscillators.
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#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31646
10. E. Ip, M-J. Li, K. Bennett, Y-K. Huang, A. Tanaka, A. Korolev, K. Koreshkov, W. Wood, E. Mateo, J. Hu, and Y. Yano, “146λ x6x19-Gbaud Wavelength- and Mode-Division Multiplexed Transmission over 10x50-km Spans of Few- Mode Fiber with a Gain-Equalized Few-Mode EDFA,” OFC 2013, Post-Deadline paper, PDP5A.2 (2013). 11. R. Ryf, R-J. Essiambre, A.H. Gnauck, S. Randel, M.A. Mestre, C. Schmidt, P.J. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “Space-Division Multiplexed Transmission over 4200-km 3-Core Microstructured Fiber,” OFC 2012, Post-Deadline paper, PDP5C.2 (2012). 12. N. Bai, E. Ip, T. Wang, and G. Li, “Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump,” Opt. Express 19, 16601–16611 (2011). 13. G. Le Cocq, L. Bigot, A. Le Rouge, M. Bigot-Astruc, P. Sillard, C. Koebele, M. Salsi, and Y. Quiquempois, “Modeling and Characterization of a Few Mode EDFA Supporting Four Mode Groups for Mode Division Multiplexing,” Opt. Express 20, 27051–27061 (2012). 14. Q. Kang, E.L. Lim, Y. Jung, J.K. Sahu, F. Poletti, C. Baskiotis, S.U Alam, and D.J. Richardson, “Accurate modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping and a simple LP01 pump configuration,” Opt. Express 20, 20835–20843 (2012). 15. M. Salsi, R. Ryf, G. Le Cocq, L. Bigot, D. Peyrot, G. Charlet, S. Bigo, N.K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” ECOC 2012, Post-Deadline paper, Th.3.A.6 (2012). 16. Q. Kang, E. L. Lim, Y. Jung, F. Poletti, S. Alam, and D.J. Richardson, “Design of Four-Mode Erbium Doped Fiber Amplifier with Low Differential Modal Gain for Modal Division Multiplexed Transmissions,” OFC 2013, paper OTu3G.3. (2013). 17. P. Sillard, M. Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-mode fiber for uncoupled mode-division multiplexing transmissions,” ECOC 2011, paper Tu.5.LeCervin.7 (2011). 18. C.R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271–283 (1991). 19. Z. Jiang and J.R. Marciante, “Impact of transverse spatial-hole burning on beam quality in large-mode-area Ybdoped fibers,” J. Opt. Soc. Am. B 25, 247–254 (2008). 20. Y. Lu, B. Julsgaard, M. Christian Petersen, R.V. Skougaard Jensen,T. Garm Pedersen, K. Pedersen, and A. Nylandsted Larsen, “Erbium diffusion in silicon dioxide,” Appl. Phys. Lett. 97, 141903–141903 (2010). 21. H. El Hamzaoui, L. Bigot, G. Bouwmans, I. Razdobreev, M. Bouazaoui, and B. Capoen, “From molecular precursors in solution to microstructured optical fiber: a Sol-gel polymeric route,” Opt. Mat. Express 1, 234–242 (2011). 22. M. Leich, F. Just, A. Langner, M. Such, G. Schotz, T. Eschrich, and S. Grimm, “Highly efficient Yb-doped silica fibers prepared by powder sinter technology,” Opt. Lett. 36, 1557–1559 (2011). 23. A. Baz, H. El Hamzaoui, I. Fsaifes, G. Bouwmans, M. Bouazaoui, and L. Bigot, “A pure silica ytterbium-doped sol-gel-based fiber laser,” Laser Phys. Lett. 10, 055106 (2013).
1.
Introduction
Recently, there has been renewed interest in Spatial Division Multiplexing (SDM), a technology first proposed in the early 80’s [1], because it represents a possible technological breakthrough that could permit to meet the increasing demand for high bit rates [2]. Among SDM technologies, Few-Mode Fibers (FMF) - used for Mode Division Multiplexing (MDM) - and Multi-Core Fibers (MCF) approaches are both actively studied using either weakly [3–8] or strongly [9–11] coupled channels. Each possesses its own technical advantages and drawbacks and it is presently difficult to predict if one of these technologies - or a combination of the two - will emerge. Whatever, in both cases, not only the transmission fiber has to be re-visited but also the different passive and active optical components that constitute a long-haul transmission, namely multiplexers/demultiplexers, reconfigurable optical add-drop multiplexers and optical amplifiers. In the case of MDM, the architecture of optical amplifiers - the so called Er3+ -Doped Fiber Amplifiers (EDFA) - has to be adapted to the efficient guiding and equalized amplification of the different modes. To reach this second target, several strategies can be combined or used independently: i) tailoring the transverse intensity pattern of the pump [12], ii) tailoring the Er3+ distribution in the core [13,14] or iii) concatenating different kind of fibers [15]. In all cases, the different signals carried by the different modes and the different wavelengths (for Wavelength Division Multiplexing, WDM) have to present high gain and small gain excursion (ΔG) value if one pretends to maintain reasonable equality between all the channels in multi-span transmissions. So that not only Differential Modal Gain (DMG) should be reduced at a particular #192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31647
wavelength, but a compromise must be found between gain equalization for all the modes and for all the wavelengths of the frequency comb. In a previous work, equalized amplification of four modes (namely LP11a&b and LP21a&b modes) was demonstrated by using a ring-doping for Er3+ [13]. A gain of 21 dB and DMG below 0.4 dB around 1550 nm was demonstrated using an Erbium Doped Fiber (EDF) made by Modified Chemical Vapor Deposition (MCVD) process. In this paper, theoretical and experimental investigation of the possibility to equally amplify 6 modes in a MCVD-based fiber are reported, both considering ideal and realistic Erbium Doping Profile (EDP). Special attention has been paid to gain equalization for all the modes but also for all the wavelength channels distributed over the C-band. Designs that minimize gain excursion are investigated without considering the use of spectral filter. It is shown that complex EDP can hardly be achieved by MCVD combined to solution doping. Hence, in the second part of the paper, theoretical approach on micro-structuring the fiber core is investigated as an alternative to conventional MCVD-based fibers. It is shown that “pixelated” distribution of the Er3+ -doping permits to accurately separate regions with and without doping and also enables non-circular EDP. Gain equalization with an accuracy of 3.2 dB for 6 modes over the C-band can theoretically be obtained in this kind of structure, with 21 dB average gain and DMG values down to 0.6 dB over 6 modes at 1540 nm. 2.
Design of the MCVD-based fiber
Starting from the fiber design reported in our previous work [13], our goal was to demonstrate an EDF that equally amplifies 6 modes. As LP11 and LP21 modes were already equally amplified but LP01 and LP02 had lower gains, the amplifier design has been improved in order to equally amplify all the different guided modes. LP11 and LP21 modes are off-centered in the fiber core and can be amplified by a ring EDP. LP01 and LP02 mode are centered in the core, so, in addition to the ring-shape EDP, it is naturally interesting to add some Er3+ in the center of the core in order to amplify the centered modes without major impact on the gain equalization for off-centered modes (LP11 and LP21 ). This approach has recently been theoretically proposed to realize a FM-EDF adapted to the amplification of 6 modes with small DMG [16]. We decided not to change the ring geometry in order to maintain a continuity with our previous work and because this geometry allows gain equalization between LP11 and LP21 modes [13]. So, the ring dimensions are delimited by two radii (internal and external one, namely Rdi and Rde ), that are set at 3.5 μ m and 7.5 μ m. The centered doped region is delimited by a third radius, Rdc , (Fig. 1(a)) that is considered as a variable. Er3+ concentration is assumed to be flat and to be the same in each doped region. In order to ensure mode matching between active and passive fibers, the Refractive Index Profile (RIP) of the EDF is assumed to be the same as the RIP of the passive Few-Mode Fiber (FMF) used in our experimental set-up [17]. So, the RIP is a perfect step index, with a refractive index difference between core and cladding that is set at 9.7 × 10−3 and the core radius (Rcore ) is chosen equal to 7.5 μ m. Optimization of the design follows the description hereafter. It uses an home-made code used to obtain the modal gain in FM-EDFA, based on a modified version of the model proposed by Giles and Desurvire [18] generalized to FMF, as in references [13, 14]. The value of Rdc has been changed from 0 to 3.5 μ m (extreme values that are possible) and the gain of 24 signals (6 modes × 4 wavelengths) simultaneously amplified has been calculated for each EDP, so as to find the EDP that gives the lowest ΔG value between these 24 signals, meaning that a good compromise between modes and spectrum equalization will be found. The signals were distributed over the C-band spectrum (at 1530, 1540, 1550 and 1560 nm) and over the 6 guided modes (namely LP01 , LP11a , LP11b , LP21a , LP21b and LP02 ). Each signal mode has an input power of -17 dBm. Pump beam is considered to be injected at the center of the fiber core,
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31648
Fig. 1. (a) Theoretical Er3+ doped fiber design. Internal and external radii of ring doped region are set at 3.5 and 7.5 μ m respectively, while the radius of central doped region (Rdc ) can vary from 0 to 3.5 μ m. (b) ΔG value between 24 signals distributed over modes and spectrum, calculated as a function of Rdc . Fiber length is 35 m long, optimal length for conserving LP11 and LP21 gain equalization. Pump power is 200 mW at 980 nm and equally distributed on LP01 , LP02 and LP03 modes. Each signal has an input power of 17 dBm. (c) Gain values of the 24 signals (for the different modes and wavelengths) if Rdc is set at 1.75 μ m
so that only LP01 , LP02 and LP03 pump modes are excited at 980 nm. Pump power has been set at 200 mW and is supposed to be equally distributed between these three pump modes. It is worth pointing out that centered injection condition is the easiest way to pump the amplifier, because it only excites LP0m modes. These pump modes don’t create transverse azimuthal dependence of Er3+ population inversion, since their intensity profiles have no azimuthal dependence, and can be efficiently coupled in the fiber (more than 90%). Transverse azimuthal dependence of pump modes can generate high DMG values between spatially degenerated signal modes. Off-centered injection condition will excite other high order modes (HOM), which creates azimuthal dependence for modal gain [12, 19] or induces high coupling losses. Fiber length was considered to be 35 m, because it allows flat gain over spectrum for off-centered modes, with the Er3+ concentration that was set at 1.42 × 1024 ions.m−3 . In the following, the gain excursion, ΔG, is defined as the difference between the highest and the lowest gain values obtained for the 24 signals that are simultaneously amplified in the fiber. DMG corresponds to the difference of gain between the different modes at a given wavelength and Differential Spectral Gain (DSG) is the difference of gain over the C-band, for a given mode. Considering ΔG as a function of Rdc , and with the simple EDP presented in Fig. 1(a), the lowest value for ΔG is equal to 4.1 dB and is obtained for Rdc = 1.75 μ m (Fig. 1(b)). This ΔG value is mainly attributed to the non-flatness of the gain over the spectrum. Indeed, for each wavelength, DMG is between 0.9 and 2.5 dB for all the modes, while gain can change up to 3.6 dB over the spectrum (DSG), for one of the modes (Fig. 1(c)). Gain equalization for off-centered modes has been preserved, as expected: differential gain between LP11 and LP21 modes is between 0.2 and 0.6 dB, while DSG value for these two modes is between 2.0 and 2.1 dB. DSG values for centered modes are relatively larger than for off-centered modes. This phenomenon can be explained by the fact that: • pump intensity is higher at the center of the core (LP0m pump modes are used) implying different optimum lengths between centered and off-centered signal modes (respectively 35 and 41 m). • flat gain over spectrum for a given mode can be achieved by choosing the optimum length of the amplifier (so that signal at 1530 nm is slightly reabsorbed at the end of the fiber, #192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31649
and its gain slightly decreases, becoming equal to the gain at longer wavelengths). If attention is focused on ΔG value rather than on gain equalization for off-centered modes, performances of this amplifier can be improved by slightly changing the fiber length. Further calculations indicate that ΔG value can decrease down to 3.1 dB for an average gain (Gave ) of 20.9 dB, if fiber length is set at 39 m, while maintaining Rdc equal to 1.75 μ m. Results are reported on Fig. 2 and Table 1. In order to study the distribution of the gain values around the average value, the standard deviation of the 24 gain values (σG ) has also been calculated and is equal to 1.2 dB. Very low DMG values over the 6 modes are achievable at a particular wavelength (0.9 dB at 1540 nm, as reported on Table 1). However, even if this value is very low, it can be seen that DMG values can increase up to 2.5 dB for other wavelengths. These results prove that the fiber design must be developed considering the different modes but also the different wavelengths in order to minimize ΔG value instead of just minimizing DMG value at a particular wavelength. Note that, to obtain this low ΔG value, the thickness of the doping depletion has to be very small (1.75 μ m, as can be seen in Fig. 1(b)). Such a small thickness is however not trivial to made while it is a sensitive parameter: slight changes in its dimensions quickly induce a penalty of several decibels on ΔG values (Fig. 1(b)).
Fig. 2. Gain values of the 24 signals (for the different modes and wavelengths) when fiber length is set at 39 m, the length that minimizes gain excursion. Pump power is 200 mW equally distributed on LP01 , LP02 and LP03 modes. Each signal has an input power of -17 dBm. Rdc is set at 1.75 μ m
Table 1. Gain values for the 24 signals that are simultaneously amplified (6 modes × 4 wavelengths) if Rdc is set at 1.75 μ m, and fiber length is set at 39 m. DMG and DSG values are also reported. Average gain is 21 dB.
Gain (dB) 1530 nm 1540 nm 1550 nm 1560 nm DSG (dB)
LP01 22.3 20.1 21.9 21.2 ↓ 2.2
LP02 21.9 19.2 20.5 19.7 ↓ 2.7
LP11a 20.3 19.7 22.3 22.2 ↓ 2.6
Gave 20.9 dB
LP11b 20.3 19.7 22.3 22.2 ↓ 2.6 ΔG 3.1 dB
LP21a 19.5 19.2 22.0 22.0 ↓ 2.8
LP21b 19.5 19.2 22.0 22.0 ↓ 2.8
DMG (dB) → 2.8 → 0.9 → 1.7 → 2.5
σG 1.2 dB
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31650
The validity of these results has been tested for other pump and signal power levels. As can be seen on Fig. 3(a) and Fig. 3(b), it appears that, if fiber length is adjusted so as to optimize the performances of the amplifier (especially the ΔG value), similar performances - here, similar relative gain excursion defined as ΔG/Gave - can be reached for pump power between 200 and 350 mW and signal power between -30 dBm to -10 dBm. This shows that the design proposed can be used for a large range of power configurations.
Fig. 3. Evolution of average gain (Gave ) and gain excursion (ΔG) as a function of pump power for signal power set at -17 dBm per channel (left) or as a function of signal power for pump power set at 200 mW (right). These simulations are performed for the optimized MCVD design presented on Fig. 4(a). In both cases, fiber length is adjusted for each pump or signal power so as to minimize gain excursion.
3.
MCVD fiber fabrication and characterization
Fig. 4. (a) Refractive index profile and EDP that was targeted. (b) Refractive index profile and Er3+ profile that has been obtained by MCVD process.
Starting from the above-discussed simple theoretical profile (Fig. 4(a)), a first test of feasibility has been made by conventional MCVD combined with solution doping technique (characteristics reported in Fig. 4(b)). A RIP close to the target (passive FMF) has been obtained, which is important to reduce crosstalk between the two fibers when they are spliced or connected together. However, even if a structure made of a ring and an additional centered doped region can be observed, EDP is quite far from what was expected. This is attributed to the difficulty to manage solution doping (Er3+ -doped region) and vapor deposition (undoped region) in the different core regions to obtain the suited EDP and RIP. Moreover, Er3+ diffusion all-along
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31651
the fabrication process has also to be anticipated so as to accurately control both thickness and concentration level in each doped region [20]. Nevertheless, modal gain obtained with this fiber has been measured. We used the same experimental set-up as in reference [13] to measure LP01 , LP11 and LP21 modal gains, individually amplified, no phase mask being available to test LP02 mode. Pump (974 nm laser diode) and signal beams are multiplexed in free space and injected into a piece of passive FMF spliced to the EDF under test. Phase plates are used to shape the desired signal field profile at the input and no demultiplexing set-up is used to separate modes at the output. Fiber length was set at 2 m. This short experimental fiber length (compare to simulation fiber lengths) is mainly due to the fact that erbium concentration in the fabricated fiber is about 20 times than the one used in the simulation (Fig. 4). The modal gain has been measured as a function of pump power. The FM-EDF was centered spliced to the passive FMF. Mode matching between the two fibers is ensured by the good fit of their RIP.
Fig. 5. Experimental results of gain as a function of pump power coupled in the FM-EDF with opto-geometrical characteristics reported in Fig. 4(b).
LP01 gets a higher gain compared to LP11 and LP21 modes (Fig. 5). Gain values of 21.9, 14.1 and 12.3 dB are respectively measured at 1550 nm if pump power is 150 mW. This is due to the fact that Er3+ concentration in centered region is twice larger than in the ring (Fig. 4(b)), which favors the gain of centered modes. The large DMG observed makes this fiber unusable for MDM transmissions with all the modes. 4.
Towards more realistic designs
As it can be seen on Fig. 4(b), EDP is far from being made of perfect steps. Since there is some Er3+ diffusion during fabrication process, the spatial distribution of the Er3+ is close from Gaussian. So, some other simulations were performed with a more realistic EDP, considering that each doped zone is Gaussian-like shaped. In order to be closer to what can be expected, the EDP has been considered to be the experimental ring shaped Er3+ distribution reported in our previous work [13]. Some Er3+ at the center of the fiber has been added, following a Gaussian distribution delimited by a waist ωdc (half width at 1/e2 ) in order to find which Gaussian dimension will lead to the smallest value for ΔG (Fig. 6(a)). Then, for each EDP (meaning each value of ωdc ), the gain of 24 signals simultaneously amplified has been calculated in this fiber. By considering ΔG as a function of ωdc , it has been possible to find the Gaussian distribution that allows the lowest difference of gain over the modes and over the spectrum. This optimal Gaussian distribution is defined by
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31652
Fig. 6. (a) Er3+ doped fiber design that considers a more realistic profile. Ring EDP is taken from our previous fabrication. Centered doping region is calculated following a Gaussian distribution. (b) Δ G value between 24 signals distributed over modes and spectrum, calculated as a function of ωdc . Pump power is 200 mW equally distributed on LP01 , LP02 and LP03 modes. Each signal has an input power of -17 dBm. c) Gain values of the 24 signals (for the different modes and wavelengths) if ωdc is equal to 1.4 μ m
ωdc = 1.4 μ m (Fig. 6(b)). This particular dimension is quite close to the one found previously for centered doped size (Rdc = 1.75 μ m, Fig. 1(a)), meaning that the dimensions of EDP don’t change whereas its shape does. This kind of realistic EDP can only ensure ΔG value of 6.2 dB (Fig. 6(b) and Fig. 6(c))), which is a considerable degradation of gain equalization compared to the previous theoretical profile (Fig. 1(c)). So, even if one succeeds in making such an EDP with ωdc = 1.4 μ m (which is a difficult value to achieve since it depends on the thickness of the doped layer that will be deposited and the temperature that rules the doping diffusion), the performance of this amplifier will be humdrum because gain equalization will be poor. Even if improved designs can be imagined, these results suggest that MCVD combined to solution doping is probably not a process perfectly adapted to make the EDP required for MDM transmissions. 5.
Micro-structuring the fiber core
Based on the previous conclusions, a technique inspired from the stack-and-draw process is then proposed as an easiest alternative to tailor the EDP in the fiber core (Fig. 7). As a proof of concept, micro-structuring the core of an air/silica Photonic Crystal Fiber (PCF) is demonstrated to be an interesting way to make Few-Mode EDFA (FM-EDFA). This concept can, of course, be extended to an all-solid fiber, with a cladding made of an homogeneous material, more suited for Telecom application. The study is focused on developing a design of microstructured EDP in a core that supports 6 spatial modes and allows low ΔG value. The core has been chosen to be a 19-cell defect because this number of rods offers several degrees of freedom to accurately “pixelate” the core with a reasonable fabrication complexity. The optogeometrical parameters of this 19-cell defect PCF have been chosen so that its dimensions and the waist of the fundamental mode at 1550 nm are close to the one of the passive FMF, hence and cladding parameters are: Λ = 3.3 μ m and d/Λ = 0.3 (Fig. 7). Micro-structuring the core ensures preserving targeted Er3+ profile and allows more flexibility, because Er3+ transverse distribution can be “pixelated” and because cylindrical symmetry can be broken. Several EDPs are possible, just by doping with the same concentration (or not doping at all) each one of the 19 elements that compose the core. Some of these microstructured EDP have been investigated in order to find some profiles that allow low DMG and flat gain over the C-band. With this relatively simple fiber geometry, fabrication process should be easy to achieve and compared to MCVD process, the resulting fiber should have a better
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31653
Fig. 7. Schematic illustration of the concept proposed in this paper: silica capillary, pure sol-gel silica glass and sol-gel Er3+ doped rods are stacked together to obtain a PCF with micro-structured core and air/silica cladding.
Fig. 8. Intensity profiles of the guided modes in the PCF, Λ = 3.3 μ m and d/Λ = 0.3, at: a) 1550 nm b) 980 nm.
assurance to be close to the targeted profile. Micro-structuring the fibre core also opens several possibilities by slightly changing the Er3+ concentration for each rod, or by using thinner Er3+ doped rod, jacketed into a silica capillary (overcladding the Er3+ doped rods). As a first trial, the following simulations are based on the hypothesis that i) all the core rods are entirely doped or undoped, ii) all the core rods have the same refractive index as pure silica, iii) Er3+ doped rods have a flat doping profile and iv) Er3+ spectroscopic properties are those of aluminosilicate glasses. Technically, such core rods could be obtained by the Sol-Gel technique [21], powder approach [22] and maybe by MCVD or OVD. Simulations were performed considering the calculated mode profiles of the PCF (using a finite element method), both at signal and pump wavelengths (Fig. 8). As the core of the structure is no more cylindrical, there is a lift of azimuthal degeneracy between LPlma and LPlmb modes, and their intensity profiles are no more symmetrical via a rotation of π /2l. The gain of 24 signals has been computed over modes and wavelengths, as in the previous sections. Pump power has been set at 200 mW and has been equally distributed between LP01 and LP02 pump modes (centered injection conditions). Compared to the MCVD-based design reported in the previous parts, LP03 mode exhibits high confinement losses in this PCF geometry at 980 nm, so it can’t be used to pump the amplifier. Each doped region is considered to have an Er3+ concentration of 8×1024 ions/m3 . Fiber length is chosen so as to minimize ΔG value.
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31654
Fig. 9. (a) Design of the micro-structured -ring shaped EDP in the PCF with additional Er3+ doping at the center of the core. Fiber length is 7.5 m (length that minimizes gain excursion) (b) Gain values of the 24 signals (for the different modes and wavelengths) achievable with this design.
Fig. 10. (a) Micro-structured EDP in the PCF, with two additional doped cells in the second rod rings region of the core. Fiber length is 7 m (length that minimizes gain excursion). (b) Gain values of the 24 signals (for the different modes and wavelengths) achievable with this design.
The first micro-structured EDP that has been investigated is an equivalent of the MCVD-one reported on Fig. 1(a)), with Er3+ -ring doping and additional doping at the center of the core. This “pixelated” EDP is reported on Fig. 9(a) and the gain of 24 signals has been calculated (Fig. 9(b)). ΔG value is 10.0 dB for an average gain of 20.3 dB, obtained with a 7.5 m -long fiber. This high ΔG value is due to the fact that it is not possible to freely adjust the thickness of the doped regions so as to reach gain equalization, if homogeneous rods are used. Another phenomenon that can be observed is that LP11a&b or LP21a&b have no longer the same gains, which is due to the lack of cylindrical symmetry of the fiber core. LP02 is the most amplified mode because Er3+ profile fits well its intensity profile. DSG values are between 1.9 and 3.3 dB. In order to ensure more gain to LP01 and LP11 modes, an improved design could consist in adding Er3+ doping in the core regions where the other modes (namely LP02 and LP21 modes) have low intensity. On Fig. 10(a), two Er3+ rods have been added in the second ring of the micro-structured core in order to obtain a lower ΔG value. Such a flexibility on the EDP is possible only with “pixelated” EDP. ΔG value decreases to 8.2 dB and average gain increases up to 20.8 dB (Fig. 10(b)). Fiber length has to be adjusted to 7 m. Even if the performances of this design are still poor, the results illustrate how much cylindrical symmetry can be broken,
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31655
Fig. 11. (a) Micro-structured EDP in the PCF, with three doped cells in the second ring of the core region, and centered doped cell. Fiber length is 6.5 m (length that minimizes gain excursion). (b) Gain values of the 24 signals (for the different modes and wavelengths) achievable with this design. (c) Design of the PCF with three additional doped cells in the second ring of the core region and undoped centered cell. Fiber length is 7 m (length that minimizes gain excursion). (d) Gain values of the 24 signals (for the different modes and wavelengths) achievable with this design.
because DMG up to 3.3 dB can be observed between LP11a&b . This proves that all the modes have to be considered separately in this kind of fiber geometry. If a third cell is added in the second ring of the core, two cases can be compared namely doped or undoped centered cell (Fig. 11(a) and Fig. 11(c)). Indeed, order is reversed between the two cases and centered and off-centered modes swap their roles (Fig. 11(b) and Fig. 11(d)). In both cases, average gain is about 20.5 dB and ΔG value is about 7 dB. Finally, in order to find a trade-off between these two last EDP and to further investigate this concept, the EDP has been adjusted so that the centered rod is now doped with half the concentration of the other doped cells (meaning a concentration of 4×1024 ions/m3 ). This new EDP is reported on Fig. 12(a). With such a design, very low DMG values (between 0.6 and 2.1 dB) can be obtained all over the C-band, if fiber length is set at 6.5 m. DSG values are between 2.1 and 2.8 dB, so that DSG is higher than DMG. The average gain for the 24 signals is 21 dB with ΔG = 3.2 dB and the distribution of gain values can be described by σG , which is equal to 0.9 dB, proving that the 24 gain values are quite centered around the average gain (Fig. 12(b) and Table 2). ΔG value is 0.1 dB larger than the results reported on Table 1, however, this slight degradation of gain equalization is counterbalanced by a higher average gain and a smaller standard deviation. The validity of these results has been tested for other pump and signal power levels. As can be seen on Fig. 13(a) and Fig. 13(b), it appears that, if fiber length is adjusted so as to optimize the performances of the amplifier (especially the ΔG value), similar performances - here, similar
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31656
Fig. 12. (a) Micro-structured EDP in the PCF, with three doped cells in the second ring region of the core, and centered doped cell doped with half the concentration compared to the others. Fiber length is 6.5 m (length that minimizes gain excursion). (b) Gain values of the 24 signals (for the different modes and wavelengths) achievable with this design. Table 2. Gain values for the 24 signals that are simultaneously amplified (6 modes × 4 wavelengths) in the micro-structured EDP reported in Fig. 12. DMG and DSG values are also reported. Average gain is 21 dB.
Gain (dB) 1530 nm 1540 nm 1550 nm 1560 nm DSG (dB)
LP01 22.6 20.0 21.5 20.8 ↓ 2.6
LP02 22.4 19.7 21.2 20.4 ↓ 2.7
LP11a 21.3 19.8 21.9 21.6 ↓ 2.2
Gave 21.0 dB
LP11b 21.2 19.7 21.8 21.5 ↓ 2.1 ΔG 3.2 dB
LP21a 20.5 19.4 21.7 21.5 ↓ 2.3
LP21b 20.8 19.7 22.1 21.9 ↓ 2.4
DMG (dB) → 2.1 → 0.6 → 0.9 → 1.4
σG 0.9 dB
Fig. 13. Evolution of average gain (Gave ) and gain excursion (ΔG) as a function of pump power for signal power set at -17 dBm per channel (left) or as a function of signal power for pump power set at 200 mW (right). These simulations are performed for the optimized micro-structured core design presented on Fig. 12(a). In both cases, fiber length is adjusted for each pump or signal power so as to minimize gain excursion.
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31657
relative gain excursion defined as ΔG/Gave - can be reached for pump power between 200 and 350 mW and signal power between -30 dBm to -10 dBm. As was the case for the MCVD design previously investigated, this shows that the micro-structured core design proposed here can be used for a large range of power configurations. 6.
Fiber realization
Fig. 14. Pictures of the micro-structured cane of the PCF. Back-Scattered Electron (BSE) image of the cane (in the center of the picture) and classical Scanning Electron Microscopy (SEM) of the fiber have been superimposed to demonstrate the feasibility of the concept proposed in this work. The erbium profile, obtained by EPMA, along the green dotted axis is presented in inset.
As a proof of concept, the design proposed on Fig. 11 has been made. To this end, 15 millimeter-sized Er3+ -doped rods drawn from a Sol-Gel -made rod have been combined with 4 pure silica Sol-Gel -made rods (also drawn from a centimeter-sized ”mother” rod) so as to constitute the fiber core. These 19 elements have been assembled with pure silica capillaries (Heraeus) and the whole stack has been jacketed into a tube. The resulting preform has been drawn into cane and then into fiber. A piece of cane has been analyzed by Electron Probe MicroAnalysis (EPMA) and the results are presented on Fig. 14 superimposed on a SEM image of the fiber. When Fig. 14 is compared to Fig. 11, it is clearly seen that the obtained geometry is identical to the targeted one. The EPMA profile clearly shows the absence of erbium diffusion in the undoped regions with sharp transition between erbium-doped and pure silica regions. Er3+ concentration in the three doped regions is not as flat as suited, which can be improved as has been shown recently [23]. This demonstrates the technical feasibility of the approach proposed in the second part of this paper. #192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31658
7.
Conclusion
In this paper, simulations and experimental characterization of 6 modes EDFA have been reported. Differential gain over modes and spectrum as small as 3.1 dB could be theoretically achieved in MCVD -based fibers. However, it has been shown that such an EDP seems hard to obtain by MCVD, partly because of Er3+ diffusion that leads to a deterioration of gain equalization over modes and spectrum. An alternative has been proposed, based on micro-structuring the 19-cell core of an air/silica PCF. Such a fiber design has been investigated and differential gain over spectrum and modes down to 3.2 dB for 21 dB average gain has been predicted. DMG values are lower than DSG values, making this fiber close to a usable one. Acknowledgment This work has been supported by the French government, in the frame of STRADE research project (ANR-09-VERS-010). We also acknowledge financial support from the Ministry of Higher Education and Research, the Nord-Pas de Calais Regional Council and the FEDER through the “Contrat de Projets Etat Region (CPER) 2007-2013”.
#192329 - $15.00 USD Received 14 Jun 2013; revised 2 Sep 2013; accepted 5 Sep 2013; published 13 Dec 2013 (C) 2013 OSA 16 December 2013 | Vol. 21, No. 25 | DOI:10.1364/OE.21.031646 | OPTICS EXPRESS 31659
