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Abstract
Few-mode EDFAs with low channel crosstalk can replace multiple parallel single-mode EDFAs in single-mode fiber trunk lines and networks. Here we proposed a low-crosstalk few-mode EDFA by exploiting the unitary property of the coupling matrix of a symmetric photonic lantern. We experimentally demonstrated a 3-channel few-mode EDFA using retro-reflection of a 3-mode symmetric photonic lantern. The small signal gain for all three channels are measured to be larger than 25 dB over the entire C-band and the crosstalks are below −10 dB.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Space-division multiplexing (SDM) has attracted serious attention in the past decade as a promising scheme to overcome the capacity crunch in single-mode fiber (SMF) communication systems [1,2]. To date, several transmission experiments including using mode-division multiplexing (MDM) in few-mode fibers (FMFs), or core multiplexing in multicore fibers (MCFs) have been reported [3–6]. Erbium-doped fiber amplifiers (EDFAs) for SDM systems are highly desirable since they are essential for long-haul transmissions. Alternatively, one SDM EDFA can replace several parallel single-mode EDFAs, thus reducing the overall cost of SMF trunk transmission lines or networks.
Multicore EDFA is one typical type of the SDM amplifiers that can be realized by using fan-in/fan-out devices as the signal combiner. With cladding pump configuration, it offers lower cost solution through components integration and the use of single high-power pump diode [7–10]. But the pump conversion efficiencies were low for this type of EDFAs. Few-mode EDFA (FM-EDFA) is another option. It could be made by free space optics, to convert the signal into high-order modes by using phase plates, and combine them through beam splitters [11–13]. But the combining loss would be large in this case. In the recent few years, all-fiber photonic lantern (PL) based FM-EDFA has attracted more interests due to its low-loss feature. This type of amplifiers supporting 6–10 spatial channels have been experimentally demonstrated [14,15]. However, the crosstalk between different channels is inevitable even with a mode-selective photonic lantern (MSPL), because of the high crosstalk (around −3 dB) between degenerate modes.
In this paper, we propose and experimentally demonstrate a low-crosstalk FM-EDFA exploiting the unitary property of the coupling matrix of the PL. We show theoretically that mode crosstalks can be suppressed in a retro-reflection configuration even if a non-mode-selective PLs are used for (de)multiplexing. Experimentally, we demonstrate a low-crosstalk 3-mode EDFA even though a high-crosstalk 3-port symmetric PL was used as the spatial (de)multiplexer. The small signal gain of all three channels are greater than 25 dB and the crosstalk of each channel is lower than –10 dB.
2. Principle and theoretical analysis
The schematic setup of the proposed FM-EDFA with low crosstalk is shown in Fig. 1. Each input signal is launched into one port of a symmetric PL through a circulator. At the output of the PL, the signal is amplified by the erbium-doped few-mode fiber (ED-FMF). The resulting signal is reflected back by a dichroic mirror (DM) and amplified by the ED-FMF again in the reverse direction before being coupled out through the PL and the circulator. The relationship between the input signal amplitudes ${{\boldsymbol A}_{in}}$ and output signal amplitudes ${{\boldsymbol A}_{out}}$ can be expressed as following:
Fig. 1. Schematic setup of the low-crosstalk FM-EDFA based on the retro-reflection of a symmetric PL.
Where the matrix ${{\boldsymbol M}_{MUX}}$ is the mode transfer matrix of the symmetric PL. For a lossless PL, it is real and unitary [16]. For example, the matrix for a 3-to-1 symmetric PL can be written as [17]:
However, because of differential modal gain (DMG) and modal dispersion, both amplitude and phase of the elements in matrix ${\boldsymbol G}$ are not always equal. We simulated the effect of DMG on the crosstalk for a three channel system, and the result is shown in Fig. 2(a). We can see that the crosstalk increases as the DMG grows. In order to suppress the crosstalk to below −20 dB, the DMG needs to be less than 1 dB. We also investigated the effect of phase difference between the first two mode groups on the crosstalk, as shown in Fig. 2(b). It indicated that in order to suppress the crosstalk to below −20 dB, the phase difference ${\Delta }\varphi $ should be within $m\pi \pm \pi /25$.
Fig. 2. (a) Calculated channel crosstalk with the increase of DMG between the first two LP modes, (b) crosstalk vs. phase difference between the first two mode groups in the ED-FMF.
3. Proof-of-concept experiment
3.1 Components and experimental setup
The active fiber used in our proof-of-concept experiment was an ED-FMF fabricated in house. Figure 3(a) shows the measured refractive index profile of this fiber, and its cross-sectional microscope image is shown in Fig. 3(b). It is a step-index fiber with a core and cladding diameter of 10 µm and 125 µm, respectively. The numerical aperture (NA) of this ED-FMF was measured to be 0.24, ensuring it supports 3 linearly-polarized (LP) modes at the signal wavelength, and supports one more mode group at the pump wavelength. The core area was doped with pure erbium ions at a concentration of ∼4.5×1025 m−3, that can provide a maximum gain of nearly 10 dB/m for each spatial mode at 1550 nm [15].
Fig. 3. (a) Measured refractive index profile, and (b) cross-sectional microscope image of the 3-mode ED-FMF used in our low-crosstalk FM-EDFA experiment.
The modal gain of a FM-EDFA is essentially determined by the degree of overlap between the doping profile, and the pump and signal mode intensity profiles [20,21], which can be expressed as:
Table 1. Overlap integrals of the normalized intensity profile of the ED-FMF.
We use a 3-to-1 symmetric PL as the signal combiner. To fabricate a PL device, multiple SMFs were inserted into a fluorine-doped capillary tube whose refractive index is lower than that of the SMF cladding. The tube was adiabatically tapered down to create a FMF output at the taper waist, and the modes were guided inside the SMF cladding area [22]. The schematic cross-sectional view of the input of a 3-to-1 symmetric PL is shown in Fig. 4(a). It contains three identical graded-index SMFs whose core and cladding diameter is 14/125 µm. After tapering, the resulting FMF has a core and cladding diameter of 18/90 µm. We measured the output mode profiles of each port of the symmetric PL at the signal wavelength by a CCD camera, the results are shown in Fig. 4(b). All of them are superpositions of the LP01 and LP11s modes. The insertion losses of three channels were measured to be −1.2 dB, −0.9 dB and −0.7 dB, respectively. The insertion losses of the PL mainly come from the imperfection of the tapering process. If the loss for each mode are equal, it will not affect the crosstalk performance. However, the mode-dependent loss is always inevitable. This will cause the mode coupling matrix slightly off from a unitary matrix, and further affect the crosstalk performance.
Fig. 4. (a) Cross-sectional view of the input fiber distribution for the 3-to-1 symmetric PL, (b) output mode profiles of the 3-mode symmetric PL measured at 1550 nm, (c) cross-sectional view of the input fiber distribution for the 6-mode MSPL, (d) mode profiles of the 6-mode MSPL measured at 976 nm.
We also fabricated a 6-mode MSPL for the spatial pump mode control. To achieve mode selective feature, one needs to use dissimilar SMFs at the input. Each input fundamental mode evolves into a particular LP mode at the output FMF based on the propagation constant matching condition [23–25]. The cross-sectional profile of a 6-mode MSPL is shown in Fig. 4(c). It contains 6 graded-index fibers with core diameters of 23, 18, 18, 15, 15, and 11µm, that map to the LP01, LP11a, LP11b, LP21a, LP21b, and LP02 mode, respectively. At the output side, the resulting FMF’s core diameter is 20 µm. We also measured the output mode profiles of the MSPL at the pump wavelength, as shown in Fig. 4(d). The mode patterns of the 6 lowest LP modes were clearly observed.
The experimental setup of the low-crosstalk FM-EDFA is shown in Fig. 5. The signal emitted from the tunable laser source (TLS) was launched into the port 1 of the circulator, and further went into the 3-to-1 symmetric PL from port 2. The input signal power was set to be -20 dBm at the wavelength of 1550 nm. The pump light from a 976 nm pump diode was launched in to a 6-mode MSPL for the pump mode control. Here we used LP11 mode as the pump for the gain equalization. The output of the two PLs were spliced with a 980/1550 nm FM-WDM coupler. The FM-WDM was made of 6-LP mode FMFs whose core and cladding diameter is 16/125 µm based on free space optics. It contains three fiber collimators that fixed at the FMF ends and a DM inside a 3-cm long tube. The output of the FM-WDM was further spliced to the ED-FMF. The length of the gain fiber is 2.5 meters, which was angle cleaved. We slightly stretched the ED-FMF to adjust the phase difference in order to suppress the channel crosstalk, as discussed above. The amplified signal at the output of the ED-FMF was reflected by another DM, and coupled back into the ED-FMF and amplified again in the reverse direction. The resulting signal was coupled out from the three single-mode ports of the symmetric PL. The port under test is detected through port 3 of the circulator. An optical spectrum analyzer (OSA) was used to measure the output optical powers and spectrums of all 3 ports of the PL.
Fig. 5. Experimental setup of the FM-EDFA with reduced channel crosstalk in a 3-mode symmetric PL. DM: dichroic mirror; TLS: tunable laser source; OSA: optical spectrum analyzer.
3.2 Results and discussions
We characterized the net gain of each channel of the amplifier system. The results of all the three channels are shown in Fig. 6(a). We can see that the small signal gain of all the three channels are larger than 25 dB when the pump power of the LP11 mode is larger than 140 mW. At the absorbed pump power of 157 mW, the gain of the three channels are 26.6 dB, 26.1 dB and 26.9 dB, respectively. The gain difference between the three channels are always less than 1 dB. When the pump power exceeds 170 mW, the system starts lasing because there is a cavity formed between the DM and the end of the FMF inside the FM-WDM. To suppress this effect, we can add an AR coating on the FMF end.
Fig. 6. Experimental results (a) small signal gain of each channel vs. pump power, (b) transfer matrix of the FM-EDFA with retro-reflection at a pump power of 157mW, (c) transfer matrix of a pair of 3-mode symmetric PL.
We fixed the pump power at 157 mW, and measured the transfer matrix of the retro-reflecting amplifier. To measure the crosstalk matrix, we launched the small signal into one channel, and use three power meters to measure the output power of three output ports simultaneously. Then did the same measurement for the other two channels to create the transfer matrix. The result is shown in Fig. 6(b). As can be seen, the matrix is nearly diagonal, the crosstalks of all three spatial channels are between −10 dB to −15 dB. In comparison, we also measured the transfer matrix of a pair of 3-mode symmetric PL without retro-reflection. The result is shown in Fig. 6(c). There is no obvious one-to-one relationship observed, the selectivity are no more than 3 dB for all the channels. One of the reasons for the residual crosstalk in the retro-reflecting FM-EDFA is the phase difference between the two mode groups is hard to be manually adjusted. The other reason comes from the mode mismatch between the passive and active FMF at the splice point, which will affect the total transfer matrix of the amplifier system. Both are not fundamental problems and can be improved in the future by using electronic feedback control of the stretcher and core size matched ED-FMFs. The mode-dependent loss of the PL is another reason for the crosstalks. The coupling loss of the reflected signal from DM into ED-FMF doesn’t affect the crosstalk matrix. This is equivalent to insert a diagonal matrix between ${{\boldsymbol G}^T}$ and ${\boldsymbol G}$ in Eq. (1). Since the values of this diagonal matrix are equal, it will not introduce additional crosstalk.
We also swept the input signal wavelength across the C-band, and measured the gain and noise figure (NF) for the three channels. The pump power was fixed at 157 mW. The measured gain figure is shown in Fig. 7(a). We can see that the gain of all the three channels are greater than 25 dB for the signal wavelength ranges from 1530 nm to 1560 nm. The highest gain appears at 1530 nm, where the net gain for each channel are 30.3 dB, 29.6 dB, and 30.2 dB, respectively. Figure 7(b) shows the NF of the FM-EDFA. The NF looks flat across the C-band, ranging between 7 dB to 9.4 dB for all three channels. The coupling loss for the signal reflected from the DM coupled into the ED-FMF before the second stage of amplification caused the NF to be slightly higher. In order to further improve the NF, we can either optimize the coupling of the reflected signal, or increase the pump power, to let the amplifier working at pump undepleted region.
Fig. 7. Measured gain (a) and noise figure (b) for each channel at different input signal wavelength across the C-band.
4. Fiber design with large low-crosstalk bandwidth
It is important to make sure the low-crosstalk feature can be achieved for a wide bandwidth, so that our amplifier system is compatible with wavelength-division multiplexing. In that case, the phase difference between LP modes inside the ED-FMF should keep constant at different input signal wavelengths. From Eq. (4) we can find that in order to satisfy this condition, the effective index difference ${\Delta }{n_{eff}}$ must increases linearly with $\lambda $. We designed an ED-FMF with graded-index profile, as shown in Fig. 8(a), that can satisfy the above features [26]. It has a parabolic index profiles with a core radius of 14 µm, and the NA is 0.129, ensuring it supports two mode groups at entire C-band. We calculated the effective indexes of the first two LP modes of this fiber at each wavelength across the C-band, as shown in Fig. 8(b). We can see the effective indexes of both LP modes are decreasing as the wavelength increasing, but the index difference is slightly increasing. We further calculated the phase difference between the two LP modes across the C-band, the result is shown in Fig. 8(c). As we can see, the change of ${\Delta }\varphi $ is very small and its value is confined within ${\pm} \pi /10$ for almost entire C-band, which corresponding to the channel crosstalk less than −10 dB. That means once the phase relationship is aligned well, one can change the input signal wavelength without any other adjustments.
Fig. 8. (a) Designed refractive index profile of the graded-index ED-FMF with large low-crosstalk bandwidth, (b) calculated effective indexes of the two lowest LP modes, (c) phase difference between the first two mode groups across the C-band.
To design such a fiber that supports 3 mode groups, the power-law refractive index profile can be optimized to make ${\Delta }{n_{eff}}$ between successive mode groups the same. This design will scale the operation of the proposed amplifier to six channels (spatial modes) when using a 6-to-1 symmetric PL. For fibers supporting more than three mode groups, special shapes of fiber refractive index profile are needed to minimize the phase differences between mode groups.
5. Conclusion
We proposed a low-crosstalk FM-EDFA by exploiting the unitary property of the coupling matrix of the PL. We experimentally demonstrated a 3-channel FM-EDFA using a high-crosstalk 3-to-1 symmetric PL. The small signal gain for all three channels are larger than 25 dB over the entire C-band and the crosstalks are below −10 dB. We also show that by controlling the ED-FMF’s refractive index profile, the low-crosstalk fashion could be achieved for a broad range of input signal wavelength. With further development and optimization, our multi-channel FM-EDFA could replace multiple single-mode EDFAs in SMF trunk lines and networks.
Funding
Army Research Office (W911NF-12-1-0450, W911NF17-1-0500, W911NF17-1-0553); National Science Foundation (ECCS-1711230, ECCS-1808976).
Acknowledgment
The authors would like to thank Dr. Axel Schülzgen for providing the optical fiber profilometer.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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