A fiber amplifier supporting 2 LP modes that employs a ring-core erbium-doped fiber (RC-EDF) is investigated to reduce differential modal gain (DMG). The inner and outer radii of the ring-core of the RC-EDF 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
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 mode-division-multiplexing (MDM) and employing a few-mode erbium-doped fiber amplifier (FM-EDFA) have been reported [3–5]. 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 [6–9]. 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 .
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.
2. 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 LP11 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, Ri and Ro are the inner and outer radii, respectively, and ncore and nclad 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  to realize a correlation between the allowable modes and the Ri and Ro combinations. In the analysis the signal wavelength is 1550 nm.
Figure 2 shows a map of the allowable modes for Ri and Ro combinations for a 1550 nm signal. The physically impossible area is an area where Ri ≥ Ro. The area shown in yellow allows the LP01 and LP11 modes for the signal wavelength, and a 2-LP mode EDFA is achievable with an Ri and Ro combination in the yellow area. The blue and red lines are LP21 and LP11 cutoffs, respecrively. For combinations of Ri and Ro in the yellow area, we calculate the signal gain in order to optimize the Ri and Ro values and thus obtain a small DMG with a high pump efficiency.
We select three series of Ri and Ro combinations. In series I and III, the Ro values are set at LP21 cutoff minus 0.2 μm and LP11 cutoff plus 0.2 μm, respectively. In series II, the Ro values are set at an intermediate value between the two cutoffs. Since the Ro values of series I and III become closer to that of series II as the Ri value increases, we set the maximum Ri 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] which includes a calculation of EDF with a ring-core. N1 and N2 are the erbium ion densities of the lower and upper levels, and are described as follows:Fig. 3, which are obtained for aluminum-codoped erbium-doped fiber, and an absorption cross-section of 1.73 × 10−25 m2 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 × 1025 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 LP11 are allowable in the yellow area in Fig. 2 for a pumping wavelength of 980 nm, we chose the LP01, LP11 and LP21 pumping modes. We set the EDF length so that the minimum gain among all the signal channels of both the LP01 and LP11 modes for the pumping modes of LP01, LP11 and LP21 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 Ri and Ro combination is plotted in Fig. 4. The difference between the EDF lengths for different Ri and Ro 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 LP01 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 LP01 mode signal, the amplifier does not necessarily operate in a flat gain condition for an LP11 mode signal and sometimes has a slight gain tilt. For pumping with higher order modes, we assume the same pump power in the odd (LP11o or LP21o) and even (LP11e or LP21e) 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 Ri and Ro combination of the three series. The DMG is defined here as the channel gain of LP01 mode minus the channel gain of LP11 mode when the absolute value of the channel gain difference between the LP01 and LP11 modes is maximized:
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 LP01 mode and the erbium ion doped area is Γ01 and that of the LP11 mode is Γ11. The DMG has a strong correlation with both Γ01 − Γ11 and Γ11/Γ01, and increases as Γ01 − Γ11 increases and Γ11/Γ01 decreases. Therefore, both Γ01 − Γ11 and Γ11/Γ01 are good parameters for designing a few-mode RC-EDF to reduce the DMG.
3. Fabrication of ring-core EDF and characterization of 2-LP mode EDFA
3.1 Ring-core erbium-doped fiber
When fabricating RC-EDF, we chose the Ri and Ro combination that minimized the DMG and maximized the pump efficiency. Figures 7(a) and 7(b), respectively, show the core cross-section image and the relative refractive index difference (Δ) profile of the RC-EDF we fabricated, along with the calculated intensity profiles of LP01 and LP11 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, Ri and Ro 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 LP01 and LP11 mode signals overlapped well with the erbium-doped 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 . 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  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 LP11 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 LP01 mode of the RC-EDF overlaps better with the large amplitude portion of the LP01 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. P0 and P1 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 P0 − P1. Since P0 and P1 were not measured accurately at around 980 and 1530 nm because of the large absorption of the erbium ions and P0 − P1 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 LP21 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 LP01 and LP11 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 LP11 signal even when the RC-EDFA was wound with a diameter of 60 mm.
3.2 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 , 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 LP01 mode pump light to an LP21 mode light. Thus, the pumping modes were LP01, LP11 or LP21. 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 LP11 mode signal was observed as a mode group when the same signal powers for the two orthogonal modes (LP11o and LP11e 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 LP01 and LP11 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 LP01 and LP11 modes in the RC-EDF coincided well with the calculated profiles; the intensity near the center of the fiber for the LP01 signal was not zero while that for the LP11 mode signal was almost zero. The beam profiles at the amplifier output were converted again to a step-index-like FMF profile.
3.3 Amplifier characterization
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 polarization-multiplexed 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 LP01, LP11 odd and even (LP11o and LP11e) 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 LP11o and LP11e signals along the fiber . 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 LP01 mode and LP11 mode group signals were measured in the experiment.
Figures 14(a), 14(b), and 14(c) show the gains and NFs of an LP01 mode signal with various input signal powers for the LP01, LP11 and LP21 mode pumping, respectively, and (d), (e) and (f) show those of the LP11 mode signals. The pump power was adjusted so that the DCG of the LP01 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 LP11 mode signal along with the input signal power change were slightly larger than those of the LP01 mode signals because the pump powers were adjusted based on the LP01 signal gain. These gain changes of the LP11 mode signal were larger with LP11 mode pumping than with LP01 and LP21 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 LP11 mode than LP01 and LP21 mode pumping because the intensity of the LP11 mode had a larger azimuthal dependence than those of the LP01 and LP21 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 LP01, LP11 and LP21 pumping modes. The NFs of the amplifier were less than 5.2 dB and less than 5.8 dB for the LP01 and LP11 mode signals for all the pumping modes.
Figure 16 shows the input signal power dependence of the pump power used to obtain a flat gain condition. The pump powers for LP01 and LP11 pumping were almost the same, and the pump power for LP21 pumping was about 20–30% larger than those for LP01 and LP11 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 LP01 and LP11 mode signals along with the crosstalk spectra of the different mode signals. The spectra in Fig. 17(a) are the output of the LP01 port of the mode demultiplexer in the measurement setup described in Fig. 13. The spectra colored in red and blue are the LP01 mode signal output measured by inputting only the LP01 mode signal into the FM-EDFA and the crosstalk power measured by inputting only the LP11 mode signal, respectively. The spectra in Fig. 17(b) are the total output of the LP11o and LP11e ports of the mode demultiplexer. The spectra colored in red and blue are the LP11 mode signal output measured by inputting only the LP11o and LP11e mode signals into the FM-EDFA and the crosstalk power measured by inputting only the LP01 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 LP11 mode to the LP01 mode was −5.6 dB and that from the LP01 mode to the LP11 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 LP11 → LP01 and LP01 → LP11, respectively.
Figure 18 shows the input signal power dependence of the modal crosstalk for LP01, LP11 and LP21 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.
We described in detail the design of an RC-EDF for reducing the DMG of a 2-LP mode EDFA. First, we clarified the Ri and Ro combination area of the RC-EDF that allows the propagation only of the LP01 and LP11 mode signals and optimized the Ri and Ro combination to reduce the DMG with a maximized pump efficiency. When designing the RC-EDF, we showed that the DMG is decreased by minimizing Γ01 − Γ11 and maximizing Γ11/Γ01. We successfully fabricated an RC-EDF and constructed a 2-LP mode EDFA with a small DMG of around 1 dB for LP01, LP11 and LP21 mode pumping. The RC-EDFA has been employed in a long-haul multi-core and few-mode transmission experiment , and could be a useful amplifier for constructing an SDM transmission system/network in the future.
Part of this research is supported by the National Institute of Information and Communications Technology (NICT), Japan under “R&D of Innovative Optical Communication Infrastructure”.
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