William Shieh ,An Li ,Abdullah Al Amin ,Xi Chen ,Simin Chen ,and Guanjun Gao ,2

(1.Department of Electrical and Electronic Engineering,The University of Melbourne,3010 Parkville,VIC,Australia;

2.State Key Laboratory of Information Photonics and Optical Communications(Beijing),Beijing University of Posts and Telecommunications,100876,China)

Abstract Spatial mode-division multiplexing is emerging as a potential solution to further increasing optical fiber capacity and spectral efficiency.We report a dual-mode,dual-polarization transmission method based on mode-selective excitation and detection over a two-mode fiber.In particular,we present 107 Gbit/s coherent optical OFDM(CO-OFDM)transmission over a 4.5 km two-mode fiber using LP01 and LP11 modes in which mode separation is performed optically.

Keyw ordscoherent communications;few-mode fiber;mode converter;fiber optic components

1 Introduction

T he fast advance of high-speed opticaltransport systems has spurred the use of dense wavelength division multiplexing(DWDM),polarization multiplexing,coherent detection,and multilevelmodulation schemes in optical fiber transmission.However,higher required optical signal-to-noise ratio(OSNR)causes higher transmission power per channel,and this may give rise to impairments caused by fiber nonlinearity[1],[2].Recently,there has been increasing interest in few-mode fiber(FMF)as the next-generation fiber for achieving capacity beyond that of standard single-mode fiber(SSMF)[3]-[7].One of the advantages of FMF,for example,two-mode fiber(TMF),is that spacial modes are multiplexed,and this doubles or triples fiber capacity without exponentially increasing SNR(as is the case with SSMFfiber)[4]-[7].By adding another degree of freedom(here,the spatialmodes with respect to the wavelength,polarization,and higher-order modulation),the information data coding can also be made more efficient[8].Compared with previous approaches based on conventional multimode fiber(MMF)[9]-[12],FMFhas better mode selectivity and can more easily manage mode impairments.Recently,a number of groups have mode-division multiplexed(MDM)LP01and LP11modes[4],[5],two degenerate LP11modes(LP11a+LP11b)[6],and even all three modes(LP01+LP11a+LP11b)[7]over FMFs or TMFs.The advance to FMFtransmission requires new research on topics ranging from device to system level,including TMFdesign,TMF-compatible component design,and TMFtransmission.In mode-multiplexed transmission systems,mode-selective components are critical.All the mode-selective devices proposed in[4]and[5]fall into two main categories:free-space based and fiber based.The former uses phase masks that are based on liquid crystal on silicon(LCoS)spatial light modulator(SLM)[6]or specially fabricated glass plate[7].Free-space components are often bulky whereas a fiber-based one is compact and can be easily integrated.The coupler proposed in[13]could be a promising solution for future MDM systems even though fabrication of the coupler involves sophisticated fiber etching,fusion,and tapering.Asimple,tunable mechanical pressure-induced long-period fiber grating(LPFG)is an efficient mode converter[14].An LPFG mode converter has been applied in a 2×10 Gb/s non-return-to-zero(NRZ)MDM system[5]and a 107 Gb/s mode-multiplexed OFDM transmission system[4].We propose 107 Gbit/s coherent optical OFDM(CO-OFDM)transmission over a 4.5 km TMFusing LP01and LP11modes in which mode separation is performed optically.

2 Mode-Selective Component Design

2.1 LPFG-Based Mode Converter

The main purpose of the mode converter is to convert optical signals from LP01to LP11and vice versa.There are various methods for performing this conversion on an FMFor TMF.These include microbending[14],periodic mechanical pressure[15],and refractive index modulation induced by lasers[16].Resonant coupling occurs when the grating pitch,Λ,equals the beating length,given by LB=2π/(β01-β11),whereβ01andβ11are the propagation constants of LP01and LP11[17].Fig.1 shows the physical design of the mode converter.The TMFwe use is a 4.5 km germanium-doped step-index fiber with a core diameter of 11.9μm and nominal refractive index step,Δn,of 5.4×10-3.The LP11mode cutoff wavelength is 2323 nm,and the loss is 0.26 d B/km.The modal group delay is 3.0 ns/km,and the mode beat length,LB,is approximately 524μm.The large differential group delay(DGD)results in very small modal mixing in our TMFbecause of the large mismatch of modal effective indices[18].To simplify our analysis,we only consider the deformation effect in a mode converter.The simulation is based on the beam propagation method[19],and the core deformation is assumed to have an s-bend shape(Fig.1).The coupling efficiency depends on the coupling length,and core deformations are defined for s-bend arc radiuses of 0.08,0.1,and 0.2μm(Fig.2).The optimum coupling length is inversely proportional to the core deformation radius r,and for a 0.2μm deformation,the optimum coupling length is 8.1 mm,which means our mode converter is very compact.Fig.3 shows the wavelength dependence of coupling efficiency at a coupling length of 8.1 mm(approximately 15.5 ridges)and core deformation of 0.2μm.Fig.4 shows the extinction ratio(ER)versus wavelength using the same coupling length and core deformation.The ERis the power ratio between LP11and LP01after mode conversion.Theoretically,the ERcan be very high,around 1550 nm,and remain above 20 d B for a wavelength range of more than 10 nm.In light of the simulation result,we fabricated four metal gratings with 20 evenly spaced grooves on one polished surface.The groove pitch is given byΛ0=510±5μm.To fabricate the four mode converters,first we place a 0.9 mm jacketed TMFonto an aluminum slab with tape.The TMFand grating are then mounted between a three-axis stage and L-shaped steel.The angle between grating and fiber,and the applied pressure can be controlled by the stage and position of the fiber.The angle between the grating and fiber determines the effective pitch,given byΛ=Λ0/sinθ,whereΛ0is the original pitch of the grating,andθis the angle.After appropriate adjustment of the stage and position of the fiber,the maximum coupling ratio and ERfor allmode converters occurs at around 1550 nm.From the measured and simulated ERs shown in Fig.4,the ERcan be maintained beyond 20 d B for a 13 nm wavelength range.The best ERs are 26.8,22.8,24.6,and 24.3 d B and occur at 1551 nm for mode cnoverters one to four.

▲Figure 2.Normalized power of LP11 versus effective coupling length for an LPFG-based mode converter with grating pitchΛ=524μmat wavelengthλ=1550 nm.The three curves correspond to coredeformation radiuses of 0.08,0.1 and 0.2μm.

▲Figure 3.Normalized power of LP11 versus wavelength for anLPFGG-based mode converter with core deformation radius of 0.2μm.

▲Figure 4.Extinction ratio versus wavelength for an LPFG-based MC with core deformation radius of 0.2μm.

▲Figure 5.Schematic of a free-space mode combiner.The precision stages have freedom of two axes,x and y.The light propagation axis is denoted Z.The beams are collimated before entering the BStominimize divergence and distortion.

2.2 Free-Space Mode Combiner/Splitter

The mode combiner/splitter comprises two double-axis precision stages,one beamsplitter(BS),and three collimating lenses(Fig.5).The signalis polarization multiplexed and mode converted before entering the mode combiner.The two input TMFs that carry either LP11aor LP11bgenerated by the mode converters are connected with the two input ports of the mode combiner,whose position can be manually aligned by the precision stages.The output port of the mode combiner is fixed using a fiber collimator and connected with the 4.5 km transmission fiber.The input signal is first collimated to a spot size with 2 mm diameter by one of the movable collimating lenses with numerical aperture(NA)of 0.25 and effective focal length f of 11.0 mm.The collimated beam is subsequently passed through the BSin either transmission or reflection direction and is finally focused onto the core of the output fiber by another lens inside the packaged collimator.The BSis polarization insensitive with less than 5%difference in transmission for s-polarization and p-polarization at 1550 nm.The input and output of the TMFs are connectorized before being mounted onto the stage with an FC-type adapter.The connectors are specially designed with an adjustable key so that the fiber can be axially rotated.By adjusting the key of the connectors,the orientation of the two LP11modes can be changed so that the modes are orthogonal(90 degrees to each other).An infrared camera is placed in the unused path of the BSto monitor the orientation and orthogonality of the two LP11modes(Fig.5).The loss in the reflection path of the BSis approximately 3.5 d B,and the loss in the transmission path of the BSis approximately 4.5 d B.The loss in the focusing system caused by misalignment and Fresnel reflection is approximately 1 d B.The 1 d Bpower difference between the two paths is balanced using an SMFattenuator before mode conversion.It is also possible to upgrade to a 3×1 mode combiner by introducing another precision stage and collimating lens as well as another BS,which we introduce in the triple-mode(LP01+LP11a+LP11b)transmission experiment.The mode splitter has the same structure as the combiner except that it is operated in opposite direction.

3 LP01/LP11 Transmission Setup and Results

▲Figure.6 Experimentsetup for 107 Gb/s dual-mode dualpolarizationtransmission over 4.5 km TMFfiber.The center-spliced controlled couplings between LP01 modes of SMFand TMFare marked×.

Fig.6 shows the 107 Gbit/s LP01/LP11dual-mode coherent OFDM transmission setup 0.Four transmitters corresponding to LP01and LP11(both modes have two polarizations,x and y)are implemented as follows:First,the OFDM signal is generated offline with MATLAB.The fast Fourier transform(FFT)size is 64,with the middle 40 subcarriers filled.The Cyclic prefix(CP)is set to 1/8 of the observation window.The OFDM waveform consists of 500 symbols,and an initial 20 symbols with alternative polarization launch are used as training symbol(TS)for channelestimation.After FFT,the real and imaginary components of the time-domain signal are uploaded onto a Tektronix arbitrary waveform generator(AWG).Then,three tones spaced at 6.563 GHz are generated by an external cavity laser operating at 1549.3 nm wavelength and an intensity modulator(IM)driven by a synthesizer.The optical OFDM signal is then modulated on each tone by using the AWG to drive a nested Mach-Zehnder modulator.The orthogonally multiplexed triple-band OFDM signal is divided and recombined on orthogonal polarizations with one symbol delay to emulate polarization multiplexing.The sampling rate of the AWG is 10 GSa/s and as a consequence,the OFDM symbol length is 7.2 ns.The raw data rate is 150 Gb/s,and the net data rate after overheads(7%FEC,4%TS,12.5%CP,and five discarded subcarriers around the DC)is 107 Gb/s.Constant optical power of around 5.5 d Bm is launched into the SMFbefore the MC1 for TMFtransmission.A mode stripper(MS)is used after center splicing to strip off the unwanted LP11,ensuring pure LP01is launched into the TMF.The MSis realized by tightly bending the bare TMFover 7 mm posts of about 20 rounds that provide a rejection ratio of greater than 30 d Bagainst LP11[4].The first mode combiner has a nominal 50:50 conversion ratio on LP01/LP11,with both modes carrying the previously described polarization multiplexed signal.We estimate that after the 4.5 km TMF,the delay between LP01and LP11is 13.5 ns.This delay is nearly double the OFDM symbol length.Therefore,the two modes are completely decorrelated after 4.5 km TMFtransmission,and the signal can be independently received on LP01or LP11.At the receiver,the two modes are detected individually.For LP01,a mode stripper(MS2)is used to strip off LP11,and the remaining LP01is coupled into the SMF.The signal is subsequently detected by a coherent optical receiver.For LP11,a second mode converter(MC2)with nominal100%conversion ratio is used to convert LP11into LP01.Any residual LP11not converted to LP01and any LP01converted to LP11is stripped off by a subsequent MS.The converted LP11(now LP01)is coupled into the SMFand is subsequently fed into the coherent optical receiver.

▲Figure 7.(a)Opticalspectrum and(c)constellations of LP01 after 4.5 km transmission in three bands.(b)Opticalspectrum and(d)constellations for LP11 after 4.5 km transmission in three bands.

The received signal is converted from the optical to electrical domain and sampled by a 50 GSa/s digital oscilloscope.The received signal is processed using a 2×2 MIMO CO-OFDM program.The digitalsignal processing consists of five steps:1)timing synchronization,2)frequency offset compensation,3)channel estimation and phase estimation,4)subcarrier mapping and constellation recovery,5)BERand Q computation.With this setup,the received power of LP01is-0.5 d Bm and that of LP11is-5.3 d Bm.Therefore,the end-to-end loss is 6 d B for LP01and 10.8 d B for LP11.The higher loss for LP11can be attributed to the excessive loss in MSs(0.2-0.4 d B)and loss in the MCs(approximately 0.4 d B in MC1 and approximately 1.5 d Bin MC2).Also,there is random coupling between the degenerate LP11modes inside the 4.5 km TMF,whereas only one of the two orientations can be launched or detected because of the asymmetry of our mode converter.Fig.7(a)shows the high-resolution(0.01 nm)optical spectrum of a signal received from LP01,and Fig.7(b)shows the high-resolution optical spectrum of a signal received from LP11.Good constellations in all three bands and for both modes are shown in Fig.7(c)and(d).We could not detect any errors in the 100,590 bits of any of the 12 possible combinations of signal states(three bands,two polarizations,and two modes).Overall Q factors for all bands,polarizations,and modes are shown in Table 1.The 2 d B relative difference in average Q between LP01and LP11can be attributed to the increased crosstalk in LP11.The ERof the mode converter becomes non-ideal under random perturbation between two LP11spatial modes.The results demonstrate the feasibility of using TMFfor dual-mode and dual-polarization transmission in order to increase fiber capacity and/or SE.In this experiment,we assume negligible mode coupling between LP01and LP11because of the high modal mismatch and relatively short distance.This negligible coupling has been tested in[18].The modes are detected individually without the need for MIMO processing,and this reduces complexity.The main limiting factors for a TMF-based transmission system are 1)mode converter ERand MSrejection ratio;2)dependence of mode converters and free-space components on polarization and mode,which causes mode-dependant loss,polarization-dependant loss,and crosstalk discrepancy in ER;and 3)the intrinsic loss of the fiber because a TMFamplifier is not readily available.For long-haul transmission,MIMO processing is necessary because there is significant accumulation of mode coupling.

4 Conclusion

We have presented a dual-mode,dual-polarization transmission method on a TMFusing a grating-based LP01/LP11mode converter for mode-selective detection.Spectrally efficient transmission over a 4.5 km TMFat 107 Gb/s using CO-OFDM is achieved using a QPSK subcarrier.Spatial mode division multiplexing may be a solution to increasing optical fiber capacity beyond that of SSMF.