We describe a coherent optical MIMO transmission experiment that employs a digital coherent receiver with a mode convergence unit, which converges higher-order mode light into the fundamental mode while maintaining the phase and amplitude information of the higher-order mode. The coherent optical MIMO transmission of two 10 Gbit/s BPSK signals over 20 km of graded-index multi-mode fiber was successfully achieved by using this mode convergence unit. We also show numerically that multi channel signals for a coherent optical MIMO transmission can be recovered by employing sufficient mode diversity, even if mode conversion occurs in the transmission fiber.
© 2011 OSA
Internet traffic is increasing rapidly, and considerable attention has been paid to the construction of high-speed networks such as a 100 G Ethernet. The capacity of wavelength-division multiplexed (WDM) transmission systems has been increased by improving frequency usage efficiency with techniques such as higher-order modulation and polarization-division multiplexing (PDM). Recently, a new approach for realizing a much higher transmission capacity has been developed that utilizes higher-order modes in multi-mode fiber (MMF) . Although the higher-order modes in MMF are thought to cause serious signal degradation as a result of inter-symbol interference (ISI), we can actively utilize the higher-order modes to increase the transmission capacity. With mode-division multiplexing (MDM) transmission, each of the multiple propagation modes in MMF transmits different signal channel [2,3]. At the transmitter, each of multiple signals is converted into different propagation mode and the signals are combined using a combiner. The combined signals are coupled into the transmission MMF, and after the transmission, the MDM signals are divided using a splitter. High mode-extinction-ratios of combiner and splitter at the transmitter and the receiver are indispensable to avoid the crosstalk of other channels. Moreover, we need to suppress the ISI caused by mode conversion in the transmission fiber. On the other hand, by using optical multiple-input multiple-output (MIMO) transmission technique, we can avoid the difficulty of such high mode-extinction-ratio and we can also compensate for the mode conversion [4–8]. With optical MIMO transmission technique, each of the signal channels can contain multiple propagation modes. Namely, we do not need high mode-extinction-ratio, instead, we only need mode diversity at the transmitter and the receiver. In other words, the coupling ratio of the modes should be different in each port of the combiner, thus resulting in a different mode power distribution in each signal channel. Additionally, the coupling ratio of the modes should be also different in each port of the splitter so that each photo detector receives a signal light with a unique mode power distribution. With coherent optical MIMO transmission, to realize such mode diversity, the phase and amplitude information of all modes must be preserved until the signal light is detected by a coherent receiver. Moreover, single-mode operation is required in the coherent receiver, especially in the 90-degree optical hybrid, because the multi-mode operation of the local signal degrades the coherent detection. Therefore, we must converge the higher-order mode of the transmitted signal into the fundamental mode before injecting the signal into the coherent receiver.
In this paper, we describe a coherent optical MIMO transmission experiment that employs a digital coherent receiver with a mode convergence unit (MCU), where two 10 Gbit/s BPSK signals were transmitted over 20 km of graded-index (GI) MMF. We also show numerically that the multi channel signals used for a coherent optical MIMO transmission can be recovered by employing sufficient mode diversity, even if mode conversion occurs in the transmission fiber.
2. Experimental set-up and results of coherent optical 2 × 2 MIMO transmission
Figure 1 shows the set-up of a coherent optical MIMO transmission experiment that employs a single-mode digital coherent receiver with an MCU. The CW light emitted from an external cavity laser operating at 1550 nm was split with a single-mode coupler (SMC) and coupled into two LiNbO3 modulators, and two independent 10 Gbit/s BPSK signals (x 1, x 2) were generated. The two signals were coupled into a multi-mode coupler (MMC). We used a 2 × 1 MMF filter coupler that is commercially available. The filter coupler contains a half mirror and it has two input and one output ports with MMFs. Half of the light coupled into one of the input port was reflected by the mirror, and half of the light coupled into the other input port was transmitted through the mirror. The reflected and transmitted lights were coupled into the output port. Higher-order modes were efficiently excited at the output port because the spot size of the light was expanded before being coupled into the output port. Different mode power distributions were generated between the reflected and the transmitted lights because the two lights were injected into slightly different places of the output multi-mode fiber. As a result, mode diversity was realized at the transmitter. Then the mixed two-channel signals were coupled into a 20 km-long 50 μm-core GI-MMF. We used the GI-MMF based on ITU-T G.651. The numerical aperture (NA) is 0.2. After a 20 km transmission, the mixed two-channel signals were split with an MMC. The 1 × 2 MMC at the receiver had the reverse function as that in the transmitter, and mode diversity was realized at the receiver. Then each of the two divided signals was coupled into a MCU. The configuration of the MCU is also shown in Fig. 1. The signal light emitted from the end of the GI-MMF passed through two optical lenses, and the light was coupled into a single-mode fiber (SMF). The focal length and NA of the lens at the MMF side are 11.0 mm and 0.25 respectively. On the other hand, the focal length and NA of the lens at the SMF side are 18.4 mm and 0.15. In the MCU, almost whole of the end facet of the MMF is mapped to the SMF core. We place the cleaved ends of the two optical fibers to the fine adjustment stages and we adjusted each fine adjustment stage so that the received optical power becomes maximum. Since the optical devices at the receiver in our experiment are single-mode devices, we need this MCU, which acts as an interface between the multi-mode and single-mode devices. Information regarding the amplitude and the phase of the higher-order modes is required for a coherent optical MIMO transmission. We can preserve the information by using the MCU. The received signal was combined with the CW light from a local oscillator in each 90-degree optical hybrid. Each of the two 90-degree optical hybrids contains a polarization beam splitter and we utilized only one of the two orthogonal polarizations. We adjusted the polarization controllers at the receiver so that the optical power at the output of each 90-degree optical hybrid becomes maximum. The in-phase and quadrature parts were fed to two balanced photo detectors and digitized using a real time oscilloscope (y 1, y 2). During digital signal processing, the collected data were processed offline for symbol recovery with adaptive MIMO equalization realized by a decision feedback equalizer (DFE). Because the DFE uses the recovered signal after the decision, the recovery accuracy can be high for a signal with a large ISI. The adaptive MIMO equalizer is shown in Fig. 2 . We used information about the amplitude and phase of both y 1 and y 2 to recover x 1 or x 2. By using adaptive MIMO equalization realized with the DFE, we obtained the recovered signals (xr 1 = y 1*w 11 + y 2*w 12, xr 2 = y 1*w 21 + y 2*w 22) where w ij represents the tap weight of the DFE derived using the recursive least squares (RLS) algorithm.
Figure 3 shows the impulse responses of part of the transmission system. Figure 3 shows the impulse responses of paths (1) and (2) in Fig. 1, in which we can see that two distinctive higher-order modes were excited, and their mode delays were 2.5 and 4.7 ns. And the differences between the two impulse responses shown in Fig. 3 reveal that mode diversity is realized at the transmitter. Figures 4(a) and 4(b) show the impulse responses of paths (3) and (4) in Fig. 1 without and with an MCU, respectively. The impulse responses without an MCU (Fig. 4(a)) are obtained when we connected the MMF directly to the SMF. In this case, the higher-order modes are lost, and we could not recover the signal. On the other hand, the impulse responses with an MCU (Fig. 4(b)) show that the higher-order mode information is preserved in the SMF by inserting the MCU before coupling the transmitted light into the SMF. And the difference between the two impulse responses shown in Fig. 4(b) shows that mode diversity is realized at the receiver.
The tap number of the feed-forward (FF) filter and the feed-back (FB) filter of the DFE were set at 5 and 60, respectively. The number of taps was determined depending on impulse response of MMF. And a training sequence of 800 for a total of 4096 transmitted symbols was used for adaptive MIMO equalization. Tracking mode of the DFE was utilized to compensate for the small time variation of the impulse response in a short time range. For a large time variation of the impulse response in a long time range, statistical variation of the recovery accuracy has been reported [6,7]. Figures 5(a) and 5(b) show constellation maps of the received (y 1, y 2) and recovered (xr 1, xr 2) signals, respectively. The received signals are distorted owing to the mixing of the two-channel signals with ISI caused by mode dispersion. On the other hand, the two states are clearly separated on a complex plane after adaptive MIMO equalization in the two recovered signal channels. The two recovered signal channels were error free and the Q2-factors were 16.5 and 17.9 dB, respectively. The recovery accuracy was lowered when the training sequence was fewer than 800, and even if we increase the number of training sequence over 800, the improvement of the recovery accuracy was small. The recovery accuracy was changed greatly depending on the tap number of the DFE. We varied the FB filter tap number from 10 to 80 to estimate the required equalizer length. Figure 6 shows the tap number characteristics of the Q2-factor. The recovery accuracy improved steeply after the 25th tap, which corresponds to a mode delay of 2.5 ns in the first higher-order mode. And the recovery accuracy improved after the 47th and 58th taps, which correspond to mode delays of the second and the third higher-order modes. We can see that the FB filter tap number of the DFE reflects the mode delay of the impulse response of the GI-MMF shown in Fig. 4(b).
3. Simulation of coherent optical 2 × 2 MIMO transmission
Until now, the effects of mode diversity and mode conversion on coherent optical MIMO transmissions in MMF have not been sufficiently investigated. In this section, we show the results of our numerical investigation of these effects in the coherent optical 2 × 2 MIMO transmission system shown in Fig. 7 . The calculation was performed using commercially available simulation software (ModeSYS ). Two 40 Gbit/s QPSK signals were generated by a CW laser source operating at 1550 nm and two QPSK modulators. The two modulators were driven by two independent data sequences (x 1, x 2), each of which had a data length of 4096. The SMF at the output of the modulator was butt-jointed to the MMF of the coupler. Here, to excite higher-order modes with different mode power distributions between the two channels, we applied different offsets at the two joint sections. Thus, we obtained mode diversity at the transmitter. The two QPSK signals were coupled into a 20 km-long 50 μm-core GI-MMF, and the signals were distorted by the mode dispersion of the GI-MMF. In this simulation, we ignored the effect of the loss, chromatic dispersion, polarization mode dispersion, and nonlinearity in the fiber. We simulated mode conversions by providing a + 1 or −1 μm axial deviation at eight randomly selected locations in the 20 km-long transmission fiber. The transmitted signal was equally split using an MMC, and each of the two divided signals was coupled into another MMF via a butt-joint section. Here, we applied different offsets at the two joint sections to obtain mode diversity at the receiver. Each of the received signals (y 1, y 2) contained the two signal channels with different ratios. We used information about the amplitude and phase of both y 1 and y 2 to recover x 1 or x 2. By using adaptive MIMO equalization realized with DFE, we obtained the recovered signals (xr 1, xr 2). The numbers of FF filter tap and FB filter tap were set at 10 and 50, respectively. The number of the training sequences was 800. We set the offsets at joint sections A and C at zero (i.e. center launching), and set the offsets at joint sections B and D at d offset.
Figure 8 shows the constellation maps we obtained before and after adaptive equalization when we ignored the mode conversion in the MMF. When d offset is 0.1 μm, the signals cannot recover even if the numbers of FF filter and FB filter taps were increased sufficiently. When d offset is 5.0 μm, the signals are recovered and the Q2-factors of xr 1 and xr 2 are 22.3 and 21.7 dB, respectively. We can see that sufficient mode diversity is indispensable for signal recovery in a coherent optical MIMO transmission. Figures 9(a) and 9(b) show the impulse responses of the transmission fiber without and with mode conversion, respectively. The upper and the lower curves in Fig. 9 show the impulse responses of paths (1) and (2) in Fig. 7, respectively. We set d offset at 5.0 μm. The upper curve in Fig. 9(a) shows that higher-order modes are excited even with center launching. The difference between the two impulse responses shown in Fig. 9(a) shows that mode diversity is realized at the transmitter. A comparison of Figs. 9(a) and 9(b) shows that mode conversion complicates the impulse response. Figure 10 shows constellation maps obtained before and after adaptive equalization. The numbers of FF filter and FB filter taps were set at 50 and 70, respectively. The number of the training sequences was 800. The Q2-factors of xr 1 and xr 2 were 22.2 and 22.4 dB, respectively. Although we need additional taps, the MIMO equalizer can recover the signal even if mode conversion occurs in the transmission fiber.
We demonstrated experimentally the coherent optical MIMO transmission of two 10 Gbit/s BPSK signals over a 20 km GI-MMF by using a digital coherent receiver with an MCU. The MCU converges the higher-order mode light into the fundamental mode while maintaining the phase and amplitude information of the higher-order mode, which enables us to realize the coherent detection of multi-mode signals with single-mode devices. We also employed optical couplers with a mode-dependent coupling ratio at the transmitter and receiver to realize mode diversity, which is indispensable for signal recovery in optical MIMO transmissions. In addition, we showed numerically that the multi signal channels in a coherent optical MIMO transmission can be recovered by applying sufficient mode diversity at the transmitter and the receiver, even if mode conversion occurs in the transmission fiber.
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