2-LP mode few-mode fiber amplifier employing ring-core erbium-doped fiber

A fiber amplifier supporting 2 LP modes that employs a ringcore erbium-doped fiber (RC-EDF) is investigated to reduce differential modal gain (DMG). The inner and outer radii of the ring-core of the RCEDF are clarified for 2-LP mode operation of the amplifier, and are optimized to reduce the DMG. It is shown that using the overlap integral between the erbium-doped core area and the signal power mode distribution is a good way to optimize the inner and outer radii of the ring-core of the RC-EDF and thus minimize the DMG. A fabricated RC-EDF and a constructed 2-LP mode EDFA are described and a small DMG of around 1 dB is realized for LP01, LP11 and LP21 pumping. ©2015 Optical Society of America OCIS codes: (060.2320) Fiber optics amplifiers and oscillators; (060.2330) Fiber optics communications; (060.2410) Fibers, erbium. References and links 1. T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. 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J. 52(7), 1161–1168 (1973). #245374 Received 6 Jul 2015; revised 28 Sep 2015; accepted 7 Oct 2015; published 9 Oct 2015 © 2015 OSA 19 Oct 2015 | Vol. 23, No. 21 | DOI:10.1364/OE.23.027405 | OPTICS EXPRESS 27405 11. C. Brunet, B. Ung, P.-A. Belanger, Y. Messaddeq, S. LaRochelle, and L. A. Rusch, “Vector mode analysis of ring-core fibers: design tools for spatial division multiplexing,” J. Lightwave Technol. 32(23), 4046–4057 (2014). 12. 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(19), 20835–20843 (2012). 13. Q. Kang, E. Lim, Y. Jun, X. Jin, F. P. Payne, S. Alam, and D. J. Richardson, “Gain equalization of a six-modegroup ring core multimode EDFA,” in The 40th European Conference and Exhibition on Optical Communication (ECOC, 2014), paper P.1.14. 14. H. Ono, T. Hosokawa, K. Ichii, S. Matsuo, and M. Yamada, “Improvement of differential modal gain in fewmode fibre amplifier by employing ring-core erbium-doped fibre,” Electron. Lett. 51(2), 172–173 (2015). 15. Y. Sasaki, Y. Amma, K. Takenaga, S. Matsuo, K. Saitoh, and M. Koshiba, “Trench-assisted low-crosstalk fewmode multicore fiber,” in The 39th European Conference and Exhibition on Optical Communication (ECOC, 2013), paper Mo.3.A.5. 16. K. Shibahara, T. Mizuno, H. Takara, A. Sano, H. Kawakami, D. Lee, Y. Miyamoto, H. Ono, M. Oguma, Y. Abe, T. Kobayashi, T. Matsui, R. Fukumoto, Y. Amma, T. Hosokawa, S. Matsuo, K. Saito, H. Nasu, and T. Morioka, “Dense SDM (12-core × 3-mode) transmission over 527 km with 33.2-ns mode-dispersion employing lowcomplexity parallel MIMO frequency-domain equalization,” in Optical Fiber Communication Conference, OSA Technical Digest Series (OSA, 2015), paper PD.Th5C.3.


Introduction
Space-division-multiplexing (SDM) technologies employing multi-core fiber (MCF) and/or few-mode fiber (FMF) as a transmission line have been investigated in recent years to overcome the capacity crunch faced by optical fiber transmission systems using single-core and single-mode fiber (SMF), which has emerged because of the rapid growth in internet traffic [1,2]. A long-haul transmission system using an MCF and/or FMF requires optical amplifiers in the same way as the current single-core and SMF systems to keep the optical signal power level high. Several long-haul FMF transmission experiments using modedivision-multiplexing (MDM) and employing a few-mode erbium-doped fiber amplifier (FM-EDFA) have been reported [3][4][5]. One issue with FM-EDFAs is the differential modal gain (DMG) needed to minimize the differences between the signal to noise ratios (SNRs) of all the transmitted signals and thus maintain signal quality. To reduce the DMG in FM-EDFAs, it is important to reduce the difference between two overlap integrals, namely that for the excited erbium ion area and the intensity profile of the fundamental mode signal and that for the excited erbium ion area and the intensity profile of higher order signals. For this purpose, the doping of erbium ions with a ring profile and the use of a reconfigurable pump mode have been reported [6][7][8][9]. Another approach, which employs a ring-core erbium-doped fiber (RC-EDF) with a ring-shaped index profile [10,11], has been investigated theoretically [12,13], and RC-EDF has been proven to reduce the DMG experimentally [14].
In this paper, we describe in detail the design of the RC-EDF and the amplification characteristics of an FM-EDFA that employs the RC-EDF. In section 2, we describe an RC-EDF designed to reduce the DMG. In section 3, we describe the fabricated RC-EDF and report measured amplification characteristics including the DMG of a 2-LP mode fiber amplifier that employs the RC-EDF. Our main conclusions are summarized in Section 4.

Design of ring-core erbium-doped fiber for 2-LP mode amplification
First, we analyze the guided mode of an RC-EDF to determine the inner and outer radii of the ring-core so that only LP01 and LP 11 mode lights propagate at the signal wavelength. Figure 1 shows schematics of the cross-section and the refractive index profile of the RC-EDF that we analyze. Here, R i and R o are the inner and outer radii, respectively, and n core and n clad are the refractive index of the core and cladding, respectively. The inner core and the cladding had the same refractive index and the relative refractive index difference is 1.0%. For the analysis, we calculate the cutoffs using vector mode analysis results [11] to realize a correlation between the allowable modes and the R i and R o combinations. In the analysis the signal wavelength is 1550 nm.  Figure 2 shows a map of the allowable modes for R i and R o combinations for a 1550 nm signal. The physically impossible area is an area where R i ≥ R o . The area shown in yellow allows the LP 01 and LP 11 modes for the signal wavelength, and a 2-LP mode EDFA is achievable with an R i and R o combination in the yellow area. The blue and red lines are LP 21 and LP 11 cutoffs, respecrively. For combinations of R i and R o in the yellow area, we calculate the signal gain in order to optimize the R i and R o values and thus obtain a small DMG with a high pump efficiency. We select three series of R i and R o combinations. In series I and III, the R o values are set at LP 21 cutoff minus 0.2 μm and LP 11 cutoff plus 0.2 μm, respectively. In series II, the R o values are set at an intermediate value between the two cutoffs. Since the R o values of series I and III become closer to that of series II as the R i value increases, we set the maximum R i value in series I and III at 7.0 μm whereas that in series II is 8.5 μm. The gain calculation uses the following simultaneous differential equation for pump, signal and amplified spontaneous emission (ASE) with the dependence of the fiber propagation direction, z, the radius and the azimuth angle of the fiber cross-section, for various modes [12]: where P p,m and P s,m are the pump and signal powers of mode m, respectively, and , k m P ± is the m mode ASE power of the kth frequency slot at ν k with a Δν κ bandwidth for the entire erbium ion emission band. σ e and σ e are the stimulated emission and absorption cross-section of an erbium ion, respectively. The subscripts p, s, k denote those for the pump, signal and ASE, respectively. α p,m , α s,m and α k,m are the m mode background loss coefficients at the pump, signal and ASE wavelengths, respectively. p ψ , s ψ and k ψ are the normalized power distributions of the pump, signal and ASE, respectively. h is the Planck constant. The power couplings between different modes are neglected in this formula in the same way as [12] which includes a calculation of EDF with a ring-core. N 1 and N 2 are the erbium ion densities of the lower and upper levels, and are described as follows: where ρ(r,θ) is the erbium ion density of the erbium-doped fiber, and τ is the spontaneous emission lifetime of an erbium ion. The input signal is a 40-channel wavelength-divisionmultiplexing (WDM) signal whose channel allocation is a 100 GHz spacing in the 1530.3 to 1561.4 nm wavelength range for both the LP 01 and LP 11 modes. We use the stimulated emission and absorption cross-sections of erbium ions at the signal wavelengths shown in Fig.  3, which are obtained for aluminum-codoped erbium-doped fiber, and an absorption crosssection of 1.73 × 10 −25 m 2 at the pump wavelength of 980 nm. The erbium ions are assumed to be doped uniformly in the ring-core and its density is 2.0 × 10 25 m −3 . The spontaneous emission lifetime is 10.5 ms. The background losses of the signal and pump are 0.02 and 0.1 dB/m for all the modes, respectively. The normalized scalar power distributions are obtained by using a commercially available mode solver that employs the imaginary-distance beam propagation method with a discretized size of 0.1 μm which is sufficiently small to allow us to calculate and compare the gains of different mode signals. Since higher order modes than LP 11 are allowable in the yellow area in Fig. 2 for a pumping wavelength of 980 nm, we chose the LP 01 , LP 11 and LP 21 pumping modes. We set the EDF length so that the minimum gain among all the signal channels of both the LP 01 and LP 11 modes for the pumping modes of LP 01 , LP 11 and LP 21 is larger than the value determined in a flat gain operation, which is similar to designing an EDFA for a transmission system. We set the minimum gain at 17 dB. The EDF length for each R i and R o combination is plotted in Fig. 4. The difference between the EDF lengths for different R i and R o combinations arises from the difference between the overlap integrals of the erbium-doped core area and the signal power mode distribution. The input signal power is −20 dBm/ch/mode (−4 dBm/mode), and the pump powers are set so that the differential channel gain (DCG) of the LP 01 mode signal, which is the difference between the maximum and minimum channel gain, is minimized at less than 3 dB for all the calculations. In this pumping condition, although the EDFA operates in a flat gain condition for an LP 01 mode signal, the amplifier does not necessarily operate in a flat gain condition for an LP 11 mode signal and sometimes has a slight gain tilt. For pumping with higher order modes, we assume the same pump power in the odd (LP 11o or LP 21o ) and even (LP 11e or LP 21e ) modes to take account of the averaging effect because of the rotation during pump light propagation.  Figures 5(a) and 5(b), respectively, show the DMG and the pump power for each R i and R o combination of the three series. The DMG is defined here as the channel gain of LP 01 mode minus the channel gain of LP 11 mode when the absolute value of the channel gain difference between the LP 01 and LP 11 modes is maximized: where G 01 (λ) and G 11 (λ) are the gain of LP 01 and LP 11 modes at the channel wavelength λ, respectively. The DMG becomes zero when R i is about 2.5-4.5 μm and R o is near the LP 21 cutoff, series I. The pump power is minimized when R i is about 2.0-2.5 μm and R o is near the LP 21 cutoff, series I. The pump power increases when the DMG is large because the gain of one of the signal modes greatly exceeds 17 dB. The pump power also increases for R i < 6 μm because of the small confinement of the signal and pump modes in the ring-core. These results suggest that the DMG and pump efficiency can be optimized by choosing an R i of around 2.5 μm and an R o value near the LP 21 cutoff.  Figure 6 shows the relationship between the overlap integral of the signal power distribution and the erbium ion doped area and the absolute value of the DMG. Here, the overlap integral of the signal power distribution of the LP 01 mode and the erbium ion doped area is Γ 01 and that of the LP 11 mode is Γ 11 . The DMG has a strong correlation with both Γ 01 − Γ 11 and Γ 11 /Γ 01 , and increases as Γ 01 − Γ 11 increases and Γ 11 /Γ 01 decreases. Therefore, both Γ 01 − Γ 11 and Γ 11 /Γ 01 are good parameters for designing a few-mode RC-EDF to reduce the DMG. Fig. 6. Relation between the overlap integral of the signal power distribution and the erbium ion doped area and the absolute value of the differential modal gain.

Ring-core erbium-doped fiber
When fabricating RC-EDF, we chose the R i and R o combination that minimized the DMG and maximized the pump efficiency. Figures 7(a) and 7(b), respectively, show the core crosssection image and the relative refractive index difference (Δ) profile of the RC-EDF we fabricated, along with the calculated intensity profiles of LP 01 and LP 11 mode signals in the 1.55 μm band. Since the Δ profile was not rectangular as a result of the use of a modified chemical vapor deposition (MCVD) fabrication process, R i and R o were defined here as the radii at half maximum and were 2.1 and 4.4 μm, respectively. The inner core radius was slightly different from the optimal value due to a fabrication error. The high-refractive index area was constructed by doping aluminum ions as shown Fig. 8 which shows the radial distributions of the doped aluminum and erbium ions in the RC-EDF measured with an electron probe microanalyzer (EPMA). Although the measured erbium distribution was rather noisy because of the low detection sensitivity, the erbium ion distribution coincided well with that of the aluminum ions, which suggested that erbium ions were doped uniformly in the area of the fiber with a high refractive index. Table 1 summarizes the parameters of the RC-EDF. As shown in Fig. 6(b), both the LP 01 and LP 11 mode signals overlapped well with the erbiumdoped core and the overlap integrals were 0.69 and 0.66, respectively, indicating that the RC-EDF can be expected to exhibit similar gain values. The RC-EDF also exhibited a high erbium absorption of 22.7 dB at 1.53 μm as shown in Fig. 9, and a low background loss of 0.018 dB/m at 1.18 μm, which allowed the use of a short length of fiber for amplification. This RC-EDF has been proven to have a smaller DMG than circle-core EDF (CC-EDF) supporting 2 LP modes in the signal band [14]. In addition to the small DMG, an RC-EDF has the potential to be spliced to an FMF with a small loss although the refractive index profile of the core is different from that of an FMF. For example, we estimate the connection loss between RC-EDF or CC-EDF whose core radius and step-like refractive index difference were 4.0 μm and 1.4%, respectively, and the transmission FMF with a trench-assisted core described in [15] whose core radius and refractive index difference are 6.4 μm and 0.42%, respectively. The connection losses between the RC-EDF and the transmission FMF for 1.55 μm LP01 and LP 11 lights, which are estimated from the coupling efficiencies of the two fibers, are 0.38 and 0.91 dB, respectively, while those between the CC-EDF and the transmission FMF are 1.60 and 1.99 dB, respectively. In this connection loss estimation, the radii of both the EDFs were much smaller than that of the FMF and the outer radius of core of the RC-EDF was larger than the core radius of the CC-EDF. In this case, the large amplitude portion of the LP 01 mode of the RC-EDF overlaps better with the large amplitude portion of the LP 01 mode of the FMF than that of the CC-EDF, which results in a smaller field mismatch in the RC-EDF than in the CC-EDF. This result suggests that the RC-EDF has the potential to be spliced to an FMF with a small splice loss despite the refractive index profile of the core being different from that of an FMF.   We measured the differential transmission power spectrum of the RC-EDF wound with different bending diameters to estimate the cut-off wavelength as shown in Fig. 10. P 0 and P 1 were the transmitted powers through a 2-m long RC-EDF wound with 1 turn with diameters of 100 and 60 mm, respectively, when the same power was launched into the RC-EDF. The cut-off wavelength was estimated from the wavelength dependence of P 0 − P 1 . Since P 0 and P 1 were not measured accurately at around 980 and 1530 nm because of the large absorption of the erbium ions and P 0 − P 1 yielded noise peaks, we eliminated the noise peaks in Fig. 10. The dashed lines show the theoretically calculated cut-off wavelength estimated by taking the refractive index profile of the RC-EDF into account, which coincided well with the peaks of the differential power spectrum. The cut-off wavelength of the LP 21 mode was 1435 nm for the 2-m long RC-EDF wound with 1 turn with a diameter of 100 mm, which indicates that only LP 01 and LP 11 mode signals propagated in the C-band. There was no excess loss increase at wavelengths longer than the C-band, suggesting that there was no bending loss for the LP 11 signal even when the RC-EDFA was wound with a diameter of 60 mm.

Amplifier configuration
Figures 11(a) and 11(b), respectively, show the configuration of an FM-EDFA that employed the RC-EDF, and the WDM couplers used in the FM-EDFA. The amplifier configuration was similar to that in a previous report [14], and a polarization-multiplexed pump light was used in this measurement to increase the available pump power. A difference from the WDM coupler is that it was also used a phase plate to convert an LP 01 mode pump light to an LP 21 mode light. Thus, the pumping modes were LP 01 , LP 11 or LP 21 . The RC-EDF was 3 m long and fusion-spliced to the WDM couplers. Figure 11(a) also shows the beam profiles at the input, RC-EDF and output of the RC-EDF. The LP 11 mode signal was observed as a mode group when the same signal powers for the two orthogonal modes (LP 11o and LP 11e modes) were input into the amplifier. It should be noted that since the beam profiles of the amplified signal in the RC-EDF were difficult to measure because of the relatively high pump intensity, we observed them by using a very short unpumped RC-EDF with a length of about 5 cm. The radial distributions of each beam are shown in Fig. 12. Although some imbalances were observed in the beam profiles of the RC-EDF, it was confirmed that the beam profiles of the LP 01 and LP 11 modes in the RC-EDF were converted to a ring-shaped profile, simply by splicing the RC-EDF to the step-index FMF. The beam profiles of both the LP 01 and LP 11 modes in the RC-EDF coincided well with the calculated profiles; the intensity near the center of the fiber for the LP 01 signal was not zero while that for the LP 11 mode signal was almost zero. The beam profiles at the amplifier output were converted again to a step-index-like FMF profile. Fig. 11. Configuration of (a) few-mode fiber amplifier employing the ring-core erbium-doped fiber, (b) wavelength-division-multiplexing module.  Figure 13 shows the experimental setup for measuring the gain and the noise figure (NF) of the FM-EDFA that employed the ring-core EDF described in 3.1. An eight-channel WDM signal located from 1531.1 to 1561.4 nm was used as the input signal. The WDM signal was modulated with 10-Gb/s non-return to zero differential phase-shift keying (NRZ-DPSK) and then divided into two lights by using a 3-dB coupler. The two lights were polarizationmultiplexed with a polarization beam combiner (PBC) employing a delay between the two polarized signals. The polarization-multiplexed signal was divided into three lights and multiplexed LP 01 , LP 11 odd and even (LP 11o and LP 11e ) signals with a mode multiplexer (Mode Mux), and the polarization-and mode-multiplexed signal was input into the FM-EDFA. Using a modulated signal as the input signal made it possible to measure the gain and NF regardless of mode coupling between the LP 11o and LP 11e signals along the fiber [8]. The mode-multiplexed output signals of the FM-EDFA were fed into a mode demultiplexer (Mode Demux), and measured with an optical spectrum analyzer (OSA). The gains and the NFs of the LP 01 mode and LP 11 mode group signals were measured in the experiment.  (c) show the gains and NFs of an LP 01 mode signal with various input signal powers for the LP 01 , LP 11 and LP 21 mode pumping, respectively, and (d), (e) and (f) show those of the LP 11 mode signals. The pump power was adjusted so that the DCG of the LP 01 mode was less than 3 dB for each input signal power. In the higher order mode pumping, the gains and NFs were measured after optimizing the rotational angle of the phase plates to maximize the gain. The gain changes of the LP 11 mode signal along with the input signal power change were slightly larger than those of the LP 01 mode signals because the pump powers were adjusted based on the LP 01 signal gain. These gain changes of the LP 11 mode signal were larger with LP 11 mode pumping than with LP 01 and LP 21 pumping. This gain change difference was possibly caused by the azimuthal non-uniformity in the ring-core of the RC-EDF, and it was more noticeable with LP 11 mode than LP 01 and LP 21 mode pumping because the intensity of the LP 11 mode had a larger azimuthal dependence than those of the LP 01 and LP 21 modes. Figure 15 plots the dependence of the DMG on the input signal power for the three pumping modes. The DMGs were almost independent of the input signal power and small DMGs of 1.0, 0.8 and 1.1 dB, respectively, were achieved for LP 01 , LP 11 and LP 21 pumping modes. The NFs of the amplifier were less than 5.2 dB and less than 5.8 dB for the LP 01 and LP 11 mode signals for all the pumping modes.   15. Dependence of the differential modal gain on the input signal power for LP 01 , LP 11 and LP 21 mode pumping. Figure 16 shows the input signal power dependence of the pump power used to obtain a flat gain condition. The pump powers for LP 01 and LP 11 pumping were almost the same, and the pump power for LP 21 pumping was about 20-30% larger than those for LP 01 and LP 11 pumping. The reason for this could be the difference in the propagation and bending losses for different modes. We also measured the modal crosstalk between different signal modes. Figure 17(a) and (b), respectively, show examples of the output spectra of the LP 01 and LP 11 mode signals along with the crosstalk spectra of the different mode signals. The spectra in Fig. 17(a) are the output of the LP 01 port of the mode demultiplexer in the measurement setup described in Fig.  13. The spectra colored in red and blue are the LP 01 mode signal output measured by inputting only the LP 01 mode signal into the FM-EDFA and the crosstalk power measured by inputting only the LP 11 mode signal, respectively. The spectra in Fig. 17(b) are the total output of the LP 11o and LP 11e ports of the mode demultiplexer. The spectra colored in red and blue are the LP 11 mode signal output measured by inputting only the LP 11o and LP 11e mode signals into the FM-EDFA and the crosstalk power measured by inputting only the LP 01 mode signal, respectively. In every case, the pump power was adjusted so that a flat gain was obtained. All the spectra were compensated for the insertion loss of the mode demultiplexer and the optical switch. The wavelength resolution of the optical spectrum analyzer was 0.2 nm. The input signal powers were −5 dBm/mode (−14 dBm/ch/mode × 8 ch) in both cases. The nominal maximum crosstalk from the LP 11 mode to the LP 01 mode was −5.6 dB and that from the LP 01 mode to the LP 11 mode was −5.7 dB, which become a crosstalk of -6.1 dB for both, taking account of the mode demultiplexer crosstalks of −15.4 and −13.6 dB for LP 11 → LP 01 and LP 01 → LP 11 , respectively.  Figure 18 shows the input signal power dependence of the modal crosstalk for LP 01 , LP 11 and LP 21 mode pumping. The modal crosstalk was measured in the same way as in Fig. 17(a) and (b) for all the input signal powers and pumping modes. The plotted crosstalk is the maximum for each input signal power and pumping mode. There was no apparent dependence of the modal crosstalk on the input signal power. The observed modal crosstalk was in the −6.7 to −5.0 dB range, which was relatively large because of the large coupling between different signal modes.

Conclusion
We described in detail the design of an RC-EDF for reducing the DMG of a 2-LP mode EDFA. First, we clarified the R i and R o combination area of the RC-EDF that allows the propagation only of the LP 01 and LP 11 mode signals and optimized the R i and R o combination to reduce the DMG with a maximized pump efficiency. When designing the RC-EDF, we showed that the DMG is decreased by minimizing Γ 01 − Γ 11 and maximizing Γ 11 /Γ 01 . We successfully fabricated an RC-EDF and constructed a 2-LP mode EDFA with a small DMG of around 1 dB for LP 01 , LP 11 and LP 21 mode pumping. The RC-EDFA has been employed in a long-haul multi-core and few-mode transmission experiment [16], and could be a useful amplifier for constructing an SDM transmission system/network in the future.