1. Introduction

The rapid growth of the bandwidth-rich internet applications has driven the research in maximizing the capacity of optical transport. Meanwhile, tremendous breakthrough in high-speed optical transmission networks has been made by utilizing polarization multiplexing, high-order modulation format and coherent optical detection, in both coherent single carrier and CO-OFDM formats [1,2]. As the spectral efficiency (SE) in single-mode fiber (SMF) is ultimately limited by the fiber nonlinearity [3], the natural solution is to use large effective-area SMF [4], or even multimode fiber (MMF) with center launch technique to excite only the fundamental (LP₀₁) mode [5,6] to mitigate the nonlinearity penalty. Most importantly, MMF or few-mode fiber (FMF) supports many spatial modes, and therefore the fiber capacity can be increased in theory by taking advantage of this additional degree of freedom in the form of multiple-input multiple-output (MIMO) transmission [7]. So far a few proof-of-principle demonstrations have been reported such as 2x2 MIMO transmission over 2.8 kms of 62.5-µm MMF at 0.8 Gb/s in [8], direct-detection MIMO 40-Gb/s transmission over 1.1 kms of 62.5 µm-core MMF in [9], and 8-Gb/s transmission over 5 kms of GI-MMF (2x4 MIMO) in [10]. A laudable goal will be to demonstrate the use of all the degrees of freedom simultaneously.

Compared to the MMF solution, FMF can have three advantages: first, with FMF, mode selective coupling/splitting can be controlled more accurately by fiber-based or free-space optics [11], and therefore the performance of mode multiplexer and de-multiplexer of FMF can be improved over MMF. Second, in spatial-mode multiplexed systems with MIMO setup, the group delay between selectively launched propagation modes has to be equalized either by a time or frequency domain filter, or by a large cyclic prefix (CP) overhead in the case of OFDM, and this computation complexity directly scales with number of modes involved. Utilizing only a few modes can reduce the computation complexity to a manageable level. Third, existence of only few modes can result in negligible modal mixing in the FMF due to large mismatch of modal effective indices [4]. Subsequently we could achieve simple capacity improvement by having an efficient method of individually exciting and selectively detecting the orthogonal modes in a FMF. In this work, we present proof-of-principle demonstration of mode- and polarization-multiplexed transmission in a customized two-mode fiber (TMF) at 1550nm, using a periodic pressure-based LP₀₁-LP₁₁ mode converter [12] for mode-selective detection. To the best knowledge of the authors, this is the first demonstration of simultaneous spatial mode- and polarization-multiplexed transmission in TMF.

2. Mode multiplexed transmission

Recent works [9], [10] have relied on butt-coupling like splitting of the mode field pattern at the end of a MMF into SMF-made receivers. But in this way it is difficult to have good modal selectivity and polarization independence. Similar to conventional dual-polarization coherent system, an efficient way to map the single mode transmitters/receivers (Tx/Rx) onto LP₀₁ and LP₁₁ modes of the TMF would be a LP₀₁-LP₁₁ mode coupler [11] as shown in Fig. 1 . At the receiver, a LP₀₁-LP₁₁ mode demultiplexer is used along with polarization beam splitter, so that a dual-mode and dual-polarization transmission can be achieved. In this paper we demonstrate that the 4x4 channel matrix is reduced to 2 sets of 2x2 channels due to limited modal mixing, therefore a simplified MIMO digital signal processing (DSP) can be used to recover the 4 independent signals. For this purpose, a customized TMF is designed to ensure negligible mode mixing by enhancing modal dispersion. Furthermore, we apply a mode converter with a high mode extinction ratio (ER) at the end of the TMF to allow simultaneous dual-mode, dual-polarization transmission. In principle, this doubles the total capacity and spectral efficiency compared to a SMF dual-polarization transmission without additional MIMO overheads.

 

Fig. 1 Schematic of mode and polarization multiplexed TMF transmission between 4 pairs of transmitters and receivers.

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3. Characteristics of the two-mode fiber and mode converter

3.1 Two-mode fiber

The TMF we use in this work is a 4.5-km customized Ge-doped step-index fiber with a core diameter of 11.9 µm, nominal refractive index step (Δn) of 5.4x10⁻³, LP₁₁ mode cutoff wavelength of 2323 nm and loss of 0.26 dB/km. Figure 2(a) shows the simulated modal index vs. wavelength profile based on the parameters of the TMF we designed. The three images to the bottom of Fig. 2(a) are measured modal profiles for LP₀₁ mode and two degenerate LP₁₁ modes. It can be seen that TMF fiber in fact supports three spatial modes: one LP₀₁ mode and two degenerate LP₁₁ modes [13]. The modal dispersion between the LP₀₁ and LP₁₁ modes is first estimated by inserting a broadband light source (black line in Fig. 2(b)) into a 1-m-long TMF with core-position offset such that both modes are excited, and then measuring the coherent mode beating period from output of the TMF (green line in Fig. 2(b)) [5]. The beating period of 2.7 nm observed on the OSA is inversely proportional to the modal delay, which is 3.0 ps in this case. This measured modal dispersion (3.0 ps/m) of the TMF corresponds to a group index difference of 8.8x10⁻⁴. The LP₀₁/LP₁₁ mode beat length L_B = 2π/(β₀- β₁) is inversely proportional to the difference of modal indices between the two modes, and is found to be 520 µm at the wavelength of 1.55 µm. The corresponding effective modal index difference is 2.98x10⁻³, which agrees with the calculation in Fig. 2(a). The zoomed-in modal indices at 1.55 µm are also shown as the inset to the right of Fig. 2(a). Since our TMF has much larger effective index difference than that between the two polarization modes of a polarization-maintaining fiber, and also several times larger than the FMF used in [5], we can expect that the TMF used in our experiments will have negligible coupling between the two supported modes LP₀₁ and LP₁₁ during transmission, which is an important condition to the proposed transmission method.

 

Fig. 2 (a) Effective modal indices for the LP₀₁ and LP₁₁ modes of the designed TMF. The insets at the bottom are the measured mode profiles of LP₀₁ mode and two degenerate LP₁₁ modes at the end of TMF. The inset at the right is the zoom-in modal index at 1.5µm. (b) Optical spectrum before (black line) and after (green line) a 1-m-long TMF fiber measured with an OSA. The spectral power before TMF was scaled to be in the same region as after TMF and does not reflect the real power level.

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3.2 LP₀₁-LP₁₁ mode converter

The critical part of dual-mode transmission depends on excitation and selective detection of the LP₀₁/LP₁₁ mode in the TMF, and the proposed concept to achieve this is shown in Fig. 3 . The mode multiplexing and de-multiplexing are done with two mode converters (MC). The MCs are constructed by pressing the TMF against a metallic slab with a surface grating of 500 µm nominal pitch. The actual fiber deformation pitch is then adjusted to the modal beat length of TMF (~520 µm) by optimizing the orientation angle of the slab with reference to the TMF. In order to achieve this, the TMF is first pulled straight and fixed onto a 6cm x 1.9cm x 1.9cm aluminum slab. The TMF and grating together with slabs are then loaded onto two 3-axis translation stages. The effective grating length (interaction length) and force are controlled by moving the stages and/or slabs, eventually optimized for targeted efficiency. MC1 has a nominal conversion ratio of 50%, exciting both the LP₀₁ and LP₁₁ mode equally in the transmission fiber to emulate mode-multiplexing coupler, as shown in Fig. 3(a). Note that only one of the LP₁₁ modes along the direction of the mechanical pressure is excited [12]. The MC2 converts LP₀₁ mode into LP₁₁ and vice versa with high conversion ratio and extinction ratio (ER). After an LP₁₁ mode stripper (MS), only the LP₀₁ component, which is in fact the LP₁₁ during transmission, passes to the receiver. A simple MS eliminates the interference of LP₁₁ component with a rejection ratio of ≥30 dB and allows detection of the transmitted LP₀₁ mode. The MSs used in this experiment are made by wrapping 20 turns of the fiber around a 0.9-cm diameter post [14]. The excess losses of all the MSs are measured to be within 0.2~0.4 dB. The measured excess losses of MC1 and MC2 are 0.4 and 1.5 dB, respectively. For MC2, an ER (or rejection ratio if used at the receiver) of 22dB/17dB is achieved for the best/worst polarizations, respectively. The inset to the top of Fig. 3(b) shows far field pattern of LP₀₁-to-LP₁₁ conversion case, from which high ER of MC2 can be confirmed.

 

Fig. 3 (a) Mode converter 1 (MC1) with nominal 50% conversion ratio. (b) Mode converter 2 (MC2) with nominal 100% conversion ratio.

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4. Mode and polarization multiplexed transmission experiment setup at 107 Gb/s

The transmission experiment setup is shown in Fig. 4 . Four transmitters are emulated by polarization and mode multiplexing as follows: first, the transmitted signal is generated off-line with MATLAB program. The total number of OFDM subcarriers is 64, and cyclic prefix (CP) is set to be 1/8 of the observation window. The middle 40 subcarriers out of 64 are filled with data mapped from 2¹⁵-1 PRBS. 500 OFDM symbols are sent for evaluation, out of which 20 symbols with alternative polarization launch are used for channel estimation. The digital time-domain signal is formed after IFFT operation. The real and imaginary components of the time-domain signal are uploaded onto a Tektronix Arbitrary Waveform Generator (AWG). We generate three optical tones spaced at 6.563 GHz by feeding an external cavity laser at 1549.3 nm to two cascaded intensity modulators driven by RF tones at 6.563 GHz. The baseband OFDM signal from AWG is impressed to the three optical tones by a nested Mach-Zehnder modulator. The tone spacing is chosen to be an exact multiple of the OFDM subcarrier spacing to ensure inter-band orthogonality [2]. The orthogonally multiplexed 3-band OFDM signal is then divided and recombined on orthogonal polarizations with one symbol delay to emulate polarization multiplexing. The OFDM symbol length is 7.2 ns. The raw data rate is 150 Gb/s and net data rate after deducting all the overheads is 107 Gb/s for both modes and all 3 bands. The overheads include 7% forward error correction (FEC), 4% training symbol (TS), 12.5% CP and 5 discarded subcarriers around DC. The signal at a power of 5.5 dBm is then coupled into the fiber with mode coupler MC1 to emulate the mode coupler. After a transmission of 4.5-km TMF fiber, the mode delay is 13.5 ns. Since OFDM symbol is 7.2 ns, which is nearly half of the modal delay, the two modes are completely de-correlated at the reception, validating the reception for two independent modes from the same launch data at the transmitter. At the receiver, the mode demultiplexing is performed as follows: For the LP₀₁ mode, an MS is used to remove LP₁₁ mode, and the remaining LP₀₁ is fed into the coherent optical receiver; for the LP₁₁ mode, the second mode converter, MC2 is used to convert the LP₁₁ into LP₀₁, and LP₀₁ into LP₁₁. The original LP₀₁ signal is converted into LP₁₁ and is removed by a subsequent MS. The original LP₁₁ is converted in LP₀₁ and is fed into the coherent receiver. An optical 90° hybrid is used for coherent detection of each mode separately, which is then sampled by a 50 GSa/s oscilloscope and processed offline [2]. We use 2x2 MIMO-OFDM program to process the received dual-polarization signal. Each mode is processed individually. The signal processing consists of the following five steps: 1) FFT window synchronization; 2) frequency offset compensation; 3) channel estimation; 4) phase estimation and 5) constellation recovery and BER computation [2,6].

 

Fig. 4 Experimental setup for 107-Gb/s dual-mode and dual-polarization transmission over 4.5-km TMF fiber. ‘X’ indicates controlled coupling between LP₀₁ modes of SMF and TMF by center splicing.

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5. Results and discussion

With this setup, the received power of LP₀₁ mode is −0.5 dBm and of LP₁₁ mode is −5.3 dBm. The end-to-end losses for the LP₀₁/LP₁₁ are measured to be 6 and 10.8 dB, respectively. The higher loss for the LP₁₁ mode can be attributed to the fiber micro-bending loss and polarization/spatial mode dependence of the additional MC2 due to asymmetric deformation [12], combined with the fact that there exists random coupling among the degenerate LP₁₁ modes inside the 4.5-km TMF fiber, although initially at MC1 we launch only one of the two orientations. This can be improved with optimization of the MC. Figures 5(a) and 5(b) show respectively the high-resolution (0.01 nm) optical spectra of LP₀₁ and LP₁₁ modes. It can be seen that the intensity ripple of LP₁₁ is much more severe than LP₀₁ case. These intensity ripples are attributed to the coherent beating between the mode-to-detect and residual unwanted modes, which is related to the rejection ratio of the MC or MS used before receiver as shown in Table 1 . This explains the reason why in the case of LP₁₁ we observe stronger spectral ripple, which is due to the limited ER of the MC2. Nevertheless, despite this level of power variation, we can still receive good constellations in all 3 bands for both LP₀₁ and LP₁₁ modes as shown in Figs. 5(c) and 5(d). Again the constellation of LP₁₁ is noisier than LP₀₁ due to the limited ER of the MC2, leaving the residual LP₀₁ component to act as crosstalk. There are 12 combinations of signal states (3 bands, 2 polarizations and 2 modes). For any given combination, we could not measure any error out of 100,590 bits measured. Overall Q factor for all bands, polarizations and modes are summarized in the Table 2 . The 2-3 dB variation of Q for the three bands can be attributed to the varying crosstalk in the case of LP₁₁, as the MC is sensitive to only one of the spatial orientation of LP₁₁ modes which is randomly perturbed along the 4.5-km TMF span.

 

Fig. 5 Optical spectrum for (a) LP₀₁ and (b) LP₁₁ mode; Constellations for (c) LP₀₁ and (d) LP₁₁ mode after 4.5-km transmission of 3-band 107-Gb/s CO-OFDM signal.

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Table 1. Measured Performance of the Mode Demultiplexer

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Table 2. Measured Q Factor (in dB) for a 107-Gb/s, 3-Band CO-OFDM Dual-Mode, Dual-Polarization Transmission on 4.5-km TMF; ‘Pol-x/y’ Stands for x/y Polarization

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The results demonstrate the feasibility of use of TMF in dual-mode and dual-polarization transmission to increase the fiber capacity. Considering the OFDM signal spectrum width of 19.7 GHz, the achieved net SE is 5.4 b/s/Hz, which can be further improved by reducing overheads. Even though the fiber available to us is limited to 4.5-km length, transmission to longer distances with the present method is not limited by modal dispersion, rather loss of the end-to-end TMF span. In the absence of practical dual-mode amplification as a repeater, modal splitting followed by single-mode amplification and modal recombining can be a solution, and this can be an interesting topic of future research.

6. Summary

We have demonstrated dual-mode and dual-polarization transmission on a two-mode fiber using an LP₀₁/LP₁₁ mode converter for mode selection. Transmission over a 4.5-km TMF fiber at 107 Gb/s using CO-OFDM is achieved at a spectral efficiency of 5.4 b/s/Hz using QPSK modulation. This is the first experimental demonstration of dual-mode and dual-polarization TMF transmission. Even though the performance is limited by the extinction ratio of the mode converter and the dynamic variation of the spatial modes, the proposed method has the potential to achieve double capacity than that of SMF. Our future work will be focused on using mode couplers/splitters and electronic DSP in place of mode converters, enabling dynamic tracking of the spatial mode variations.