Spatial mode is one of the fundamental properties of light propagating in few-mode fibers (FMFs) or multimode fibers (MMFs). The manipulation of light to support independent propagation through one or multiple modes in optical-fiber-based systems could find wide applications such as optical and quantum communications, optical fiber lasers, optical fiber sensors, and all-optical signal processing. For example, maneuvering the light to emit only from a specific transverse mode in FMF or MMF laser cavities could achieve large core size while maintaining high beam quality [1,2]; mode-division-multiplexing (MDM) transmission over FMF link utilizing multiple modes with low modal crosstalk could multiply single-fiber capacity while avoiding inter-modal multiple-input multiple-output digital signal processing (MIMO-DSP) with huge computation complexity [3–5]; the mode coupling effect between linearly polarized (LP) modes could be utilized as a distributed optical fiber sensor for transverse stress or vibration [6,7].

However, all kinds of modal crosstalk have stalled the drive towards independent light propagation in complex FMF- or MMF-based systems composed of passive fibers, doped fibers, and various optical components, which includes both distributed modal crosstalk (DMC) during light propagation over the fibers [8], and all kinds of discrete modal crosstalk among intrinsic mode channels of optical components [9], at non-ideal splicing points between fibers [10], or at the coupling points between fibers/components induced by mode field mismatch [11].

Recent studies have shown that simple transmission links consisting of FMFs and mode multiplexers/demultiplexers (MMUXs/MDEMUXs) could support independent light propagation through multiple LP modes if the modal crosstalk could be effectively suppressed [3–5]. Because the effective index difference is the dominant factor of DMC between LP modes in weakly guided FMFs, step-index FMF with a high core/cladding index difference and multiple-ring-core (MRC) FMF utilizing ring index perturbations to enlarge relative index differences among LP modes have been proposed for DMC suppression [3,4]. Different kinds of MMUXs/MDEMUXs with low intrinsic channel crosstalk and coupling crosstalk have been adopted such as photonic lanterns [12,13], multiple plane light converters [14,15], and cascaded mode-selective couplers (MSCs) [16,17].

When it is extended to the case of inserting a doped-fiber amplifier into an optical-fiber-based system, an effective solution to sustain low modal crosstalk for the whole system has not been demonstrated yet, so far as we know. For example, inter-modal MIMO-DSP has to be adopted to combat modal crosstalk in experimental investigations of few-mode erbium-doped-fiber amplifiers (FM-EDFAs) in FMF transmission systems [18–24]; likewise, filtering higher-order modes by bending or tapering the optical fibers is always required to improve beam quality in typical high-power fiber lasers with master oscillator power amplifier (MOPA) configurations for not being able to ensure independent fundamental-mode light propagation [25,26].

In this paper, we propose the design of low-modal-crosstalk doped-fiber amplifiers in FMF-based systems by employing identical MRC index profiles for both passive and doped fibers to effectively suppress both distributed and mode-field-mismatch-induced modal crosstalk. However, the mainstream modified chemical vapor deposition (MCVD) methods are not suitable for the fabrication of doped-fiber preform with MRC structures. To achieve this, we develop new direct-glass-transition (DGT) MCVD for precise control of both the refractive index profile and rare-earth ion distribution. Then, a few-mode erbium-doped fiber (FM-EDF) matched with a four-LP-mode transmission FMF is designed and fabricated using the DGT-MCVD. The fabricated FM-EDFA has a maximum gain of 26.08 dB and differential modal gain (DMG) of 2.3 dB. With the insertion of the FM-EDFA, 60 + 60 km simultaneous LP01/LP11/LP21/LP02 transmission without inter-modal MIMO-DSP is successfully demonstrated. The proposed design of low-modal-crosstalk doped fiber in an MRC-FMF-based system represents a breakthrough for mode manipulation methods and offers great potential for wide applications.

Figure 1(a) shows an MRC-FMF-based system model consisting of mode control components, passive FMFs, doped FMFs, and other optical functional components, which could be widely employed in various applications such as optical fiber transmission links and optical fiber lasers. The mode control components implement different operations to light propagating in different modes of the FMF-based system such as mode conversion, filtering, excitation, multiplexing/demultiplexing, or add/drop. For the existence of different kinds of FMFs in the system, the major challenge comes from the suppression of not only DMC in both FMFs but also mode-field-mismatch-induced crosstalk at their coupling points. In a weakly guided MRC-FMF, multiple-ring-area perturbations could be applied to the core of FMF to adjust the effective index distribution among all the degenerate or non-degenerate LP modes to suppress the overall DMC levels [4,5]. Moreover, the management of DMG is always required for multiple-mode amplification in various applications, which could be solved by non-uniform erbium ion doping [22,27–29]. So, a few-mode-doped fiber with double MRC profiles of both index and rare-earth ion distribution could address both issues. However, current fabrication processing for doped fibers could not precisely modulate such MRC profiles. We analyze the limitations and present new MCVD processing in the next section.

Besides, other kinds of modal crosstalk in the MRC-FMF-based system model should also be addressed. For example, both high selectivity among different channels and high mode field match with fibers should be achieved for the mode control components; the fusion splicing between FMFs should be properly handled to avoid extra modal crosstalk; especially, various optical functional components such as optical power splitters, optical isolators, or signal/pump wavelength multiplexers (WMUXs) should not break the low-modal-crosstalk condition for the whole system. If micro-structured free-space optical elements are utilized for mode-insensitive light operations, the length of the light path between each pair of input/output FMF collimators should be greatly shortened to avoid significant modal crosstalk. As an example, we describe the realization of a few-mode signal/pump WMUX in the principle of low-modal-crosstalk FM-EDFA, which is employed in this paper.

The fabrication of fiber preforms is essential to the realization of doped fibers. Although some deposition methods such as plasma chemical vapor deposition (PCVD) are proved to be effective for precise fabrication of passive fiber preforms with gradual or MRC index profiles [30,31], they are incompetent for complex deposition of multiple-material composition including rare-earth ion dopants and metallic ion co-dopants. Currently, two kinds of MCVD approaches are widely adopted for preform fabrication of doped fibers [32,33], for both of which the transitional soot is first deposited and then transformed into a glass-phase fiber preform by a secondary sinter. In the MCVD with a solution doping technique (SDT) [32], porous soot without doping rare-earth ions is first deposited in the deposition tube utilizing MCVD, and then impregnated with rare-earth salt solution. After the solution is drained, the soot is dried and sintered. On the other hand, in the all-gaseous-phase MCVD with chelate doping [33], the soot is deposited in the deposition tube by heating all the gaseous-phase materials including the dopants and co-dopants at the same time, for which organic chelate precursors of rare-earth ions with low sublimating temperature are heated and blown into the deposition tube by inert gas flow. We can see that neither of two MCVD approaches are suitable for the fabrication of doped fibers with MRC profiles of index or rear-earth ion distribution.

The schematic structure of our developed DGT-MCVD processing with erbium-ion chelate doping is shown in Fig. 1(b). Compared with previous MCVD approaches, three key improvements have been made for precise fabrication of FM-EDF with MRC structures. First, higher temperature ranges of 1800°C–1900°C at multiple temperature areas are adopted, which are determined through a lot of trials, so that glass-state deposition could be obtained directly instead of the transitional soot. Second, although the doping of an aluminum ion could slightly raise the refractive index to form a weakly guided core/cladding structure in addition to suppression of the erbium-ion clustering effect, we add the doping of germanium ion to precisely modulate the index profile. Thus, all the gaseous-phase materials including SiCl4, GeCl4, C2F6, the chelate of Er(thmd)3 and AlCl3, and O2 participate in the chemical reaction. The co-dopant of a fluoride ion is used to adjust the viscosity of the glass. Finally, stratified deposition is employed for the realization of MRC structures. For each ring area, the doping concentration of the erbium ion could be adjusted by regulating the velocity of helium flow, while the refractive index could be adjusted by the injecting speed of GeCl4. The rest of the processing for the fabrication of doped fiber could be the same as previous methods [33].

We design an FM-EDF matched with a transmission MRC-FMF supporting LP01, LP11, LP21, and LP02 modes, and then fabricate it using the DGT-MCVD processing. Figure 2(a) shows the index profiles of designed (blue line) and fabricated (magenta line) transmission MRC-FMFs. The effective indexes of all LP modes for the fabricated MRC-FMF are also plotted. The designed transmission MRC-FMF has a normalized frequency V of 4.8 and an index difference (Δn) between the fiber core and cladding of 0.6%. Three ring index perturbations are applied to enlarge the minimum effective index difference (min|Δneff|) as much as possible to suppress the modal crosstalk among all LP modes [4]. The refractive indexes are 1.451267, 1.454767, and 1.452767 for the three ring areas from inner to outer, respectively, while the radii of the outer border are 2.629, 5.7044, and 7.4406 μm, respectively. The depressed-index fluorine-doped trench is employed in the cladding to reduce the bending sensitivity of high-order LP modes. The characteristics of fabricated transmission FMF are measured at 1550 nm. The min|Δneff| of the fabricated MRC-FMF is 1.89×10−3, lying between LP21 and LP02 modes. The attenuation of four LP modes is all lower than 0.227 dB/km. The effective mode field areas (Aeff) of four LP modes from low-order to high-order are 134.85, 107.27, 122.743, and 129.65μm2, respectively. The picture of the cross-section of fabricated MRC-FMF is shown in Fig. 2(c).

The MRC profiles of index and erbium ion distribution of the designed FM-EDF are plotted in Fig. 2(b) with blue lines and orange blocks, respectively. The index profiles of the designed FM-EDF are the same as those of the designed transmission MRC-FMF, while the erbium-ion distribution is calculated by a parameter scanning method utilizing MATLAB and COMSOL [28]. To simplify the pump configuration, only 980-nm pump light being launched into the LP01 mode of the FMF is adopted. The intensity overlap integrals between 980-nm pump light and signal light in the four LP modes of the FMF from low-order to high-order are calculated to be 6.14, 5.38, 4.13, and 3.42×109m−2, respectively. For each group of concentration parameters at different ring areas, gain spectra for each mode are calculated considering the influence of intensity overlap integrals. In the simulation, the input signal power is set to be −15dBm for non-degenerate LP01 and LP02 modes, while it is −12dBm for degenerate LP11 and LP21 modes. With the pump power of 500 mW, the optimized erbium-ion concentrations for the three ring areas from inner to outer are 1.5, 1.1, and 4.1×1025m−3 at the FM-EDF length of 2 m, respectively. The simulated maximum gain and DMG are 34.75 and 1.73 dB, respectively.

The index profiles and the effective indexes for different LP modes of the fabricated FM-EDF are plotted in Fig. 2(b) with magenta curves and black lines, respectively. We can see that the fabricated FM-EDF has a similar index profile to that of the fabricated transmission FMF. The fabricated FM-EDF supports six LP modes. The min|Δneff| among LP01, LP11, LP21, and LP02 modes is 1.61×10−3, lying between LP21 and LP02 modes, while the Aeff are 160.45, 128.64, 150.97, and 176.84μm2, respectively. Compared with the fabricated transmission FMF, the Aeff differences range from 15.93% to 26.69% for all four LP modes. The cross section of fabricated FM-EDF is shown in Fig. 2(d). The measured absorption spectrum of the FM-EDF is shown in Fig. 2(e), in which the peak absorption coefficients at 980 and 1530 nm are 19.5 and 44.1 dB/m, respectively. The radial distributions of erbium-ion doping concentration in the core of FM-EDF are measured by an electron probe microanalyzer (EPMA, JEOL JXA-8230), and the normalized distributions of erbium ion are shown in Fig. 2(f). Although there is large noise for the measured results limited by the low detection sensitivity of the equipment, the red fitting curve indicates that stratified erbium-ion doping in the core is feasible.

The mode-field-mismatch-induced crosstalk versus different misalignments for the case of light propagation from fabricated transmission FMF to fabricated FM-EDF is simulatively investigated utilizing semivector 3D-BPM [28], and the results are shown in Fig. 2(g). In the simulation, the probe signal is launched from each mode of the fabricated transmission FMF one by one with the power of 0 dBm at the wavelength of 1550 nm, and the total crosstalk in all the other LP modes is calculated. Here, the crosstalk is defined by the ratio between the total power in all the crosstalk modes and the remaining signal power in the target mode. The simulated results show that the total modal crosstalk is less than −16.63dB when the two fibers are centrally aligned.

A pair of MMUX and MDEMUX supporting four LP modes has been adopted in the experiment, which consists of multiple MSCs fabricated by side-polishing processing [16]. Figure 3(a) depicts their schematic structures. We adopt the transmission MRC-FMF for the fabrication of the MSCs, which can effectively eliminate the modal crosstalk at the connection points between the components and the FMFs. To achieve low modal crosstalk, different custom single-mode fibers (SMFs) are designed and fabricated to realize a precise phase match with multiple modes in the transmission MRC-FMF [16]. The FMF and SMF are respectively embedded in quartz blocks with groves for polishing and then mated together. The MSCs for LP01, LP11, LP21, and LP02 modes are designed and fabricated to form the whole MMUX/MDEMUX by fusion splicing. The output mode fields of the MMUX captured by a charge-coupled device (CCD) camera (Newport, LBP2-IR2) at 1550 nm are shown in Fig. 3(b). The output mode fields after amplification are shown in Fig. 3(c).

A few-mode signal/pump WMUX is utilized to combine both pump and signal lights. Here, we adopt the micro-structured free-space thin film filters for its realization [34], which is mode-insensitive, and the length of four light paths between a pair of FMF collimators could be very short. The schematic structure of the few-mode wavelength multiplexer (FM-WMUX) is shown in Fig. 3(d). Because the beam divergence angles are different for the LP modes when light propagates from the FMF to the free space or vice versa, the numerical aperture (NA) of the FMF collimators should be optimized to reduce insertion loss (IL) and modal crosstalk.

The FM-EDFA supporting four LP modes is fabricated, and its characteristics are measured. Figure 4(a) shows the experimental setup for characterization of the fabricated FM-EDFA, and its picture is shown in Fig. 4(b). First, the single-mode signals are multiplexed into different LP modes in the transmission MRC-FMF by the MMUX and then are launched into the FM-EDFA. The 980-nm single-mode pump lights and few-mode signal lights are combined by an FM-WMUX. Then, the amplified few-mode signals after the FM-EDFA are demultiplexed into multiple single-mode signals by the MDEMUX. The characteristics of the fabricated FM-EDFA are measured with six external cavity lasers (ECLs) and an optical spectrum analyzer (OSA, Yokogawa, AQ6390C). With the pump power of 500 mW, the length of FM-EDF is optimized to be 2.5 m by balancing the gain levels and DMG levels. The measured modal crosstalk is shown in Fig. 4(c). The input power of each mode is set to −15dBm and the pump power is 500 mW. We can see that the largest modal crosstalk is −12.45dB for the case of LP01 input and LP11 output.

The gains for all four LP modes versus different pump powers are measured, as shown in Fig. 4(d). To exclude the influence of modal crosstalk for accurate measurement of gain [22], the signal wavelengths with 1-nm spacing at 1550 nm are simultaneously sent into each spatial mode. For the input light power of −15dBm, the gains are no less than 23.62 dB at the pump power of 500 mW, while the measured DMG is 1.64 dB. The gain spectra and noise figures (NFs) over the C-band are measured, as shown in Figs. 4(e) and 4(f). It can be seen that the gain for each mode is above 22.48 dB and the DMG is lower than 2.3 dB. The NFs range from about 3.37 to 4.88 dB.

The experimental setup to investigate the transmission performance of the fabricated FM-EDFA is shown in Fig. 5(a). At the transmitter side, the continuous-wave (CW) lights are generated by four wavelength-tunable ECLs with a linewidth of about 100 kHz, which are combined by a polarization-maintaining optical coupler (PM-OC) to emulate different wavelength division multiplexing (WDM) channels. The 28-GBaud differential quadrature phase-shift keying (DQPSK) baseband signal is generated by a two-channel arbitrary waveform generator (AWG, Keysight M8195A), which drives a single-polarization optical IQ modulator (IQM) to generate optical DQPSK signal. The polarization division multiplexing is emulated by an emulator consisting of a PM-OC, a tunable optical delay line (TODL), and a polarization beam combiner (PBC). The dual-polarization (DP) DQPSK signal is further split into six branches, which are time-decorrelated by optical fiber delay lines with lengths of 30, 60, 90, 120, and 150 m, respectively. The SM-EDFA in each individual branch is utilized to adjust the launched power of each mode.

The transmission link consists of a pair of MMUX and MDEMUX, two pieces of 60-km transmission MRC-FMF, and the fabricated FM-EDFA. The six signal branches are multiplexed by the MMUX and then launched into the FMF. After FMF transmission, signals are demultiplexed by the MDEMUX. The performance for the back-to-back case is measured by directly connecting the output of the MMUX with the input of the MDEMUX. The fibers are spliced at all connecting points. The DMC coefficients h of the transmission MRC-FMF are calculated with an improved swept-wavelength interferometry (SWI) technique [5], which are shown in Fig. 5(b). We can see that the measured DMC coefficients for all LP modes are lower than −33.82dB/km. Figure 5(c) shows the crosstalk characteristics of the whole link from the MMUX to the MDEMUX at 1550 nm. The input power of each mode for FM-EDF is set as −15dBm and the pump power is 500 mW. We can see that the largest modal crosstalk is −9.15dB for LP01 input and LP11 output.

At the receiver, the reception for non-degenerate LP01 and LP02 modes is similar to that for conventional single-mode polarization division multiplexing (PDM) signals. The demultiplexed signals are received by a polarization-diversity coherent receiver (PD-CRx, u2t CPRV1220A) and then the electrical waveforms are captured by a real-time digital storage oscilloscope (DSO, Keysight DSA-X96204Q) with a sampling rate of 80 GSa/s to be processed offline. A second independent ECL is used as the local oscillator (LO). The optical band-pass filter (OBPF, Yenista Optics XTM-50) is utilized to filter out-of-band noise. Finally, 2×2 MIMO-DSP is performed for polarization demultiplexing and channel equalization.

For the reception of degenerate LP11 and LP21 modes, a time division multiplexing (TDM) reception scheme is adopted to detect both degenerate modes with one coherent receiver [35], in which the demultiplexed optical signals from a pair of degenerate modes are temporally interleaved with a 1.5-km SMF delay and then combined to occupy different time slots. Similarly, the output of the LO laser at the receiver is split into two branches, one of which is exactly delayed with another 1.5-km SMF delay line for phase match. In the offline MIMO-DSP, the initial convergence of 2×2 or 4×4 equalizers is obtained using the data-aided least-mean-square algorithm, and then the constant-modulus algorithm is utilized [5].

The Q2-factor performance after 60-km MDM-WDM transmission is first investigated, as shown in Figs. 5(d) and 5(e). The Q2-factor threshold is set to 6.25 dB for 20% overhead forward error correction (FEC) [36]. Figure 5(d) shows the Q2-factors of each mode with the four wavelengths of 1548.4, 1549.2, 1550.0, and 1550.8 nm, respectively, in which all the six signal branches for the LP01/LP11/LP21/LP02 modes at the transmitter are simultaneously launched into the fiber with four WDM channels in each LP mode. For better comparison, the Q2-factors for the back-to-back case by directly connecting the output of the MMUX with the input of the MDEMUX are also plotted. We can see that Q2-factor penalties for 60-km FMF transmission range from 0.6 to 3.28 dB for all the LP modes. Figure 5(e) shows the Q2-factor performance over C-band for all the modes, in which LP01/LP11/LP21/LP02 modes are simultaneously launched and the wavelengths are tuned from 1530 to 1565 nm with 5-nm spacing. We can see that only slight Q2-factor fluctuation could be observed when the wavelengths are tuned over the C-band.

Then, the Q2-factor performance after 120-km MDM-WDM transmission is investigated, as shown in Figs. 5(f) and 5(g). Figure 5(f) shows the Q2-factors of each mode with the four wavelengths of 1548.4, 1549.2, 1550.0, and 1550.8 nm, respectively, in which all the six signal branches for the LP01/LP11/LP21/LP02 modes at the transmitter are simultaneously launched into the fiber with four WDM channels in each LP mode. We can see that Q2-factor penalties for 120-km FMF transmission range from 1.91 to 5.98 dB for all the LP modes. Figure 5(g) shows the Q2-factor performance over C-band for all the modes, in which LP01/LP11/LP21/LP02 modes are simultaneously launched and the wavelengths are tuned from 1530 to 1565 nm with 5-nm spacing.

In conclusion, the design of a low-crosstalk doped-fiber amplifier by adopting an identical index profile to the passive fiber in FMF-based optical systems is proposed. The new DGT-MCVD processing is developed for the precise fabrication of FM-EDF with MRC profiles of both index and erbium ion distribution. Then, an FM-EDFA is realized based on an FM-EDF, which is fabricated using the DGT-MCVD. The experimental demonstration of 60 + 60 km simultaneous LP01/LP11/LP21/LP02 transmission with inline loss compensation by the FM-EDFA proves the feasibility of the scheme. It is promising to extend the scheme to wide applications.