Applications of weakly-coupled few-mode fibers [Invited] Download: 1102次
1. INTRODUCTION
As the transmission capacity worldwide continues to grow exponentially and single-mode fiber-optic communication systems approach their capacity limit[1,2], space-division multiplexing (SDM) has attracted significant attention in recent years[3,4]. With more spatial modes in few-mode fibers (FMFs) or multicore fibers (MCFs), SDM enables a larger transmission capacity[5], improved signal transmission performance, or enhanced signal processing ability compared with single mode fibers (SMFs)[6] due to more degrees of freedom (DOFs)[3].
Spatial modes in FMFs are orthogonal to each other ideally, so they can deliver different signals in independent channels. However, in practical fibers, there are unavoidable defects due to a limited fabrication accuracy or surrounding environment change, such as index profile fluctuation, geometry deviation, and microbending, leading to cross talk between different modes[79" target="_self" style="display: inline;">–
To recover independent information from mode cross talk, digital signal processing (DSP) with multiple-input-multiple-output (MIMO) is usually needed to retrieve both amplitude and phase information of the received optical signal with the help of mature coherent detection techniques[10]. However, due to the modal dispersion of FMFs, equalizers with a long memory are required in DSP[11], which increases the complexity and cost of the whole system. Even with optimized fiber index profiles, equalization schemes, and algorithms, some transmission systems still suffer from the cost and power consumption of DSP components, especially those short-reach systems such as datacenter transmission systems[12].
Weakly-coupled FMFs offer a cost-effective solution to address the above issues, since there is no need of MIMO DSP at the receiver end[13]. Recently, there have been many references of designing weakly coupled FMFs[1416" target="_self" style="display: inline;">–
2. CONSIDERATIONS OF WEAKLY-COUPLED FMFs
Weakly-coupled FMFs can increase the fiber capacity without DSP, since different modes can carry different information with negligible cross talk. To study how to make FMFs weakly coupled, the coupling between different modes is analyzed here.
In an ideal FMF, spatial modes are orthogonal to each other, so there is no cross talk between different spatial modes, which can be seen from the coupling coefficient
To achieve that and ensure the same number of modes is supported in the fiber, both a large index contrast between the core and cladding and a small core diameter are needed[27]. However, a small core diameter will reduce the effective areas of modes, which would increase nonlinearities in FMFs[28], so here we study the trade-off between the large mode effective area and the large effective index difference between neighboring modes by theoretical analysis and numerical simulation.
Usually, effective areas of higher-order modes are larger than that of the fundamental mode, since they are less confined by the core[29]. Nonlinearity is more concerned when the optical power is large in long-haul systems, where quasi-single-mode (QSM) transmission plays an important role. QSM usually transmits the fundamental mode, since it is easily launched and compatible with other single-mode components in the system[18]. So the effective area of the fundamental mode is calculated here. In QSM transmission, the index difference between the fundamental mode and the first higher-order mode is a very important evaluator of the mode cross talk. For other applications with graded-index (GRIN) FMFs, there are almost equal index differences between neighboring mode groups[30], so the effective index difference between the first two modes is computed here.
Figure
Fig. 1. Effective index difference between the first two modes, as a function of the effective area of the fundamental mode, with varying core radius for each core index, in (a) two-mode step-index fiber and (b) two-mode graded-index fiber. Step-index fiber with a 1.45 core index and a large range of core radius is plotted as the reference curve.
The multiplication of effective index difference and effective area seems to be a constant value for different fiber index profiles, which can be verified analytically for GRIN fibers. The Helmholtz equation for electrical field
From Eq. (
The fundamental solution of the electrical field can be approximated as the Gaussian function
The multiplication of the effective area and index difference thus leads to the relation below:
It is a constant at a fixed core index and wavelength. When the constant is divided by the wavelength, the formula is only related to the core index in the following form:
The value would be 0.1098 for a 1.45 core index. The fitting curve is plotted in Fig.
Fig. 2. (a) Effective index difference vs. effective area curve fitting for graded-index fiber. (b) The multiplication constant as a function of wavelength for SI or GRIN fibers with two or ten modes.
To verify that the formula
The previous simulation shows that the multiplication of the effective index difference and the effective area of the fundamental mode is always a constant for common SI and GRIN FMFs. To generalize the conclusion, fibers with various index profiles shown in Fig.
Fig. 3. (a) Index profiles for two-step SI fibers (high or low index for the inner step), a GRIN fiber with a trench, a triangular-index fiber, and a fiber corresponding to the reversed mode profile. (b) Corresponding curves of effective index difference vs. effective area.
MCFs are also considered, with the first supermode profiles for three-core or six-core fibers shown in Figs.
Fig. 4. Fundamental mode profiles of (a) three-core fiber and (b) six-core fiber. (c) Corresponding curves of effective index difference vs. effective area.
For FMFs and MCFs with various index profiles, the multiplication of effective index difference and effective area cannot bypass the limit. However, in a three-core MCF, if the first three supermodes have similar effective indices, the effective index difference between them and the 4th supermode may be larger than that limit, for certain effective areas of the 1st supermode. The simulated index differences between the 1st supermode and 4th supermode or 2nd supermode with different core-to-core distances, are plotted in Figs.
Fig. 5. (a) Effective index difference of the 1st and 4th supermodes, and (b) the effective index difference of the first two supermodes vs. the effective area of 1st supermode, for different core distances.
3. WEAKLY-COUPLED FMFs FOR QUASI-SINGLE-MODE TRANSMISSION
Weakly-coupled FMFs can have larger effective areas than SMFs, benefiting a large SNR in advanced modulation systems. QSM transmission can use the fundamental mode in FMFs with a large effective area, while keeping other components untouched in the system[18]. However, if the effective area is too large, an FMF would suffer from a mode cross talk induced multipath interference (MPI) problem, due to the trade-off between a large effective area and a large effective index difference as well as modal dispersion, and the higher splicing loss to SMF, due to the unmatched mode area. In practical QSM transmission, with proper effective area, the low nonlinearity advantage will outperform the modal cross talk and splicing loss penalties.
To verify that, we demonstrated a QSM transmission over a two-mode fiber, with ten polarization division multiplexed (PDM) WDM channels at 28 Gbaud with QPSK modulation[17]. Figure
Fig. 6. Setup for the PDM QPSK WDM transmission experiment through the fundamental mode of FMFs. (a), (b), and (c) are the transmitter, fiber loop, and coherent detection parts. DFB: distributed feedback laser, PMC: polarization maintaining coupler, PBC: polarization beam combiner, VOA: variable optical attenuator, IL: interleaver, SW: optical switch, FMF: few-mode fiber, WSS: wavelength selective switch, PM-EDFA: polarization-maintaining erbium-doped fiber amplifier, LO: local oscillator, PD: photodiode. Reprinted from Ref. [35].
The transmission loop consists of an optical switch, EDFAs, two spans of FMFs with lengths of 76 km and 72 km, and a wavelength selective switch (WSS). The FMF has an attenuation coefficient of 0.2 dB/km, and an effective area of
At the receiver, a signal channel is selected by the WSS and mixed with an LO in a polarization diversity 90 deg hybrid and detected by PDs. A real time oscilloscope with a 16 GHz analog bandwidth working at 40 GSa/s is used to acquire the output signals from the PDs. The received signals are processed offline to calculate the Q factor by several digital signal processing (DSP) modules, including chromatic dispersion compensation, frequency offset estimation, phase noise estimation, and polarization-mode dispersion compensation based on a time-domain equalizer with the constant modulus algorithm (CMA).
Figure
Fig. 7. -factor for the center channel as a function of the launched power per channel after 3100 km for FMFs, and after 3040 km for SMFs. The constellation diagrams for X polarization at the optimal power for both cases are shown in the insets. Reprinted from Ref. [35].
4. WEAKLY-COUPLED FMFs FOR MODE-GROUP-MULTIPLEXED TRANSMISSION
Benefiting from a large effective area of the fundamental mode, QSM transmission allows for higher launched power and has a better performance without replacing components except fibers, compared with SMF transmission. To also use higher-order modes as independent channels in weakly-coupled FMFs, some other components are required. Like wavelength multiplexers in WDM, mode multiplexers are used to project different channels to different spatial modes in weakly-coupled FMFs[36,37]. With low-cross-talk FMFs and mode multiplexers, MIMO-less mode-group multiplexing (MGM) becomes feasible in short-reach applications[38].
In FMFs, degenerate modes are easily coupled to each other along transmission[39], so they are treated as one channel and it is essential to collect power from all the degenerate modes to maintain a stable signal-to-noise ratio (SNR) or bit error ratio (BER). Stable
The FMF was specifically designed to increase the effective index difference between mode groups, leading to reduced coupling between them. The FMF we used in this work supports six spatial modes at 1550 nm[36,38], and we used the first five modes in the first three mode groups to perform the transmission experiment. Figure
Fig. 8. (a) Refractive index profile of FMF, and effective indices of LP modes. Measured impulse response for (b) PL 1, (c) PL 2, and (d) PL 3. Each PL is spliced to a 20 km FMF. Reprinted from Ref. [19].
Low-cross-talk-mode multiplexers and mode demultiplexers are required to launch and receive different modes in the FMFs. A few components can be used as mode (de)multiplexers, among which the PL is lossless in theory and has been shown to achieve excellent mode selectivity[37]. SMFs with different core sizes are used to fabricate a mode-selective PL, and the propagation constant of each SMF is matched to the corresponding mode in the FMF through an adiabatic taper.
Three PLs were used in the experiment: one as the mode multiplexer, the second one as the mode demultiplexer, and the last one as the degenerate mode combiner at the receiver. The impulse responses of the PL spliced with the FMF were measured, as shown in Figs.
Fig. 9. Experiment setup for MGM transmission. BERT: bit error ratio tester; EDFA: erbium-doped fiber amplifier; VOA: variable optical attenuator; PC: polarization controller; PL: photonic lantern; PD: photodetector. Reprinted from Ref. [19].
The setup for the stable
The advantages of combining degenerate modes can be seen in the comparison of BERs in Figs.
Fig. 10. (a) Measured BERs as functions of transmitted power for detecting only one of the degenerate modes or both degenerate modes of the and group. (b) The measured BERs as functions of received power for detecting only one of degenerate modes or both degenerate modes of the group for two different transmitting polarizations ( and ). (c) The measured BERs as functions of transmitted power for three mode groups. The hollow symbols represent separate mode-group transmissions, and solid symbols represent MGM transmissions. Reprinted from Ref. [19].
Figure
These results demonstrate that MGM with direct detection can play a role in intra-datacenter networks and other short-reach applications. Better PLs or other mode multiplexers with low modal cross talk are expected to improve the performance further.
5. WEAKLY-COUPLED FMFs FOR OTHER APPLICATIONS
In weakly-coupled FMFs, spatial DOFs can also help to improve the performance of the systems already using other DOFs, such as eliminating the combining loss in the upstream transmission of the TDM PON system, and alleviating nonlinearities in the WDM microwave photonic links.
5.2 A. Spatial DOF Assisted TDM PON with Low Combining Loss
In the TDM PON system, the combining ratio is a problem for the upstream transmission to exhaust the power budget. Using a mode multiplexer instead of a power splitter can eliminate the combining loss, in theory[42]. As shown in Fig.
Fig. 11. PON architectures using (a) an SMF with a power splitter and (b) an FMF with a mode multiplexer.
Because the upstream signals are time-division multiplexed for different users, they will not cross talk with each other at the beginning of the FMF attributed to non-overlapping in time. However, due to the MGD of the FMF, the mode cross talk coming from the mode multiplexer results in inter-symbol interference in the signal from the same optical networking unit (ONU), leading to an increased BER and packet loss. It is impossible to reduce the MGD too much by careful fiber index profile optimization, so weakly-coupled FMFs combined with low-cross-talk PL are required to alleviate the cross talk problem.
Before insertion into the real PON system, the weakly-coupled FMFs combined with the low-cross-talk-mode multiplexer are evaluated by a bit-error ratio tester (BERT). BER results for separate mode transmissions are shown in Fig.
Fig. 12. Measured BERs of the six-mode optical link at 1 Gb/s. Reprinted from Ref. [21].
Figure
Fig. 13. Schematic of the six-mode-GPON system using a PL spliced to 20 km FMF for upstream transmission with commercial OLT and ONUs. OLT: optical line terminal; ONU: optical networking unit; PL: photonic lantern. Red line: 1490 nm transport; blue line: 1310 nm transport; gray line: bidirectional transmission. Reprinted from Ref. [21].
Fig. 14. Measured packet loss of 9 ONUs in the six-mode PON in 12 h. Reprinted from Ref. [21].
Seven of nine ONUs work well and can achieve a packet loss smaller than 10%, over a continuous duration of 12 h. ONU4 and ONU5 cannot establish upstream traffic due to the strong cross talk of
5.3 B. Spatial DOF Assisted Microwave Photonics Links with High Power Throughput
Optical fiber can be used to deliver radio frequency (RF) and microwave signals, with the advantages of large bandwidth, low loss, and immunity to electromagnetic interference[4446" target="_self" style="display: inline;">–
SMFs or FMFs with a larger effective area can alleviate these nonlinear effects for one-channel microwave transmission[53]. Compared with SMFs, FMFs can have larger effective areas for either fundamental mode or higher-order modes. Higher-order modes in FMFs also have smaller acousto-optic effective areas, benefiting a high SBS threshold.
For multi-channel microwave transmission links[54], spatial modes can be used to carry different wavelength channels to reduce the inter-channel nonlinearities, with spatial orthogonality and phase walk-off among different spatial modes[20]. In theory, channels assigned in two different DOFs (wavelength and space) will encounter smaller cross talk. To better separate WDM channels in different spatial modes, large effective index differences between spatial modes are needed in the weakly-coupled FMFs.
The experimental setup for WDM microwave transmission over an FMF link is shown in Fig.
Fig. 15. Experimental setup for WDM transmission over an FMF link. The inset illustrates the generation of nonlinear cross talk due to four-wave mixing. Reprinted from Ref. [20].
To emulate this, the interfering channel is launched into higher-order modes, and a spool of weakly-coupled 20 km long FMF with a large effective index difference is used to reduce the modal cross talk. Nonlinear cross talk power and spurious-free dynamic range (SFDR) with or without mode diversity for WDM channels versus received optical power are plotted in Fig.
Fig. 16. Experimental results for WDM transmission over an FMF link. (a) Measured microwave power of the nonlinear cross talk caused by the FWM effect. (b) The estimated SFDRs as functions of received optical power. Reprinted from Ref. [20].
From Fig.
6. CONCLUSION AND DISCUSSION
In conclusion, we demonstrated various applications of weakly-coupled FMFs, with deployment of only spatial DOFs or combination with other DOFs. First, the relationship between the effective area of the fundamental mode and the effective index difference between the first two modes is studied to help us understand the trade-off between the reductions of the nonlinear effects and linear modal cross talk. Second, quasi-single-mode transmission in weakly-coupled FMFs is demonstrated, with weaker nonlinear effects due to a larger effective area. Third, mode-group-multiplexed transmission in weakly-coupled FMFs is demonstrated, showing a largely increased fiber capacity by using spatial DOFs to support more channels. To effectively deliver signals in each spatial mode channel, a photonic lantern as a low-cross-talk-mode multiplexer is also needed in the transmission system. Last, assisted by spatial DOFs, performance improvement is demonstrated in the systems using other DOFs, such as time and wavelength. The combining loss of upstream transmission in the TDM PON system is eliminated by replacing SMFs with FMFs because the numbers of DOFs on both sides of the mode multiplexer are matched. The nonlinearities in WDM microwave transmission links are also alleviated, assisted by spatial DOFs, due to spatial orthogonality and phase walk-off between spatial modes. In these two cases, with spatial modes in weakly-coupled FMFs used in systems as well, different channels, either in time slots, or frequency spacing, can be better separated, and thus nonlinear interaction between channels is suppressed a lot. Overall, these applications verify that spatial modes in weakly-coupled FMFs can not only provide more information channels, but also help to reduce the loss or cross talk of/to channels in other DOFs, through a larger power delivery ability, spatial orthogonality, and phase walk-off of spatial modes. Now the weakly-coupled FMFs can achieve a very low cross talk between different spatial modes, and the cross talk’s limiting component is the mode multiplexer. In the future, mode multiplexers with a better mode selectivity and lower loss are required to further improve the system performance.
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Article Outline
Huiyuan Liu, He Wen, Guifang Li. Applications of weakly-coupled few-mode fibers [Invited][J]. Chinese Optics Letters, 2020, 18(4): 040601.