Abstract
We propose a simple two-channel mode-group-division-multiplexing (MGDM) system operating in the 0.8 µm region over the standard single-mode fiber (SSMF). For the cost-effectiveness, we implement its receiver by using only two photodetectors (PDs) [instead of three PDs required for the detection of the ${{\rm{LP}}_{01}},\;{{\rm{LP}}_{11a}}$, and ${{\rm{LP}}_{11b}}$ modes]. We then detect the signal carried by the ${{\rm{LP}}_{01}}$ mode by using a PD and a mode filter. On the other hand, the other signal carried by the ${{\rm{LP}}_{11}}$ mode group is detected by using another PD and a multiple-input single-output equalizer (i.e., by subtracting the signal carried by the ${{\rm{LP}}_{01}}$ mode from the multiplexed signal). For a demonstration, we transmit ${{2}} \times {{28}}\;{\rm{Gb}}/{\rm{s}}$ MGDM on-off keying signal operating at 852.6 nm over 2.2 km of the SSMF by using the proposed technique. The results show that we can achieve the bit-error rate of ${\lt}{3.8} \times {{10}^{- 3}}$ for both the ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{11}}$ modes.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Recently, there has been much interest in utilizing the polarization-division-multiplexing (PDM) technique, even in the short-reach optical interconnects implemented with direct-detection (DD) receivers [1,2]. This is because we can double the transmission capacity of the standard single-mode fiber (SSMF) by using this technique. However, it appears that this technique is not cost-effective enough for use in such short-reach applications due to the expensive Stokes vector receiver, which is typically made of a polarization beam splitter, a 90° optical hybrid, and four photodetectors (PDs). We note that, in the case of using the 0.8 µm region, the transmission capacity of the SSMF can also be doubled by using the mode-group-division-multiplexing (MGDM) technique [3,4]. This is of course because the SSMF can support two mode groups (i.e., ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{11}}$) in this wavelength region. In fact, the SSMF-based two-channel MGDM system seems to be well suited for the use in the short-reach optical interconnects, since it can be implemented by using the DD receivers instead of the complicate coherent receivers [3–7]. This is due to the small crosstalk between the ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{11}}$ mode groups. However, in the conventional (i.e., previously reported) MGDM technique, three PDs are used for the detection of two modes to avoid the large power fluctuation caused by the intra-mode group coupling (between the ${{\rm{LP}}_{11a}}$ and ${{\rm{LP}}_{11b}}$ modes) [7].
In this Letter, we implement the SSMF-based two-channel MGDM system operating in the 0.8 µm region by using only two PDs. At the receiver, these two PDs are used for the detection of the signal carried by the ${{\rm{LP}}_{01}}$ mode and the multiplexed signal (i.e., the combined signal carried by both ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{11}}$ modes), respectively. We then extract the signal carried by the ${{\rm{LP}}_{11}}$ mode by using a ${{2}} \times {{1}}$ multiple-input single-output (MISO) equalizer. To point out the advantages of the proposed MGDM system, we first compare its performances with those of the conventional MGDM system implemented by utilizing three PDs [7] by numerical simulations. Despite the enhanced simplicity of the proposed MGDM system, no significant difference is observed in their estimated performances. We then experimentally demonstrate the transmission of the ${{2}} \times {{28}}\;{\rm{Gb}}/{\rm{s}}$ MGDM on-off keying (OOK) signal operating at 852.6 nm over 2.2 km of the SSMF by using the proposed technique. The results show that we can achieve the bit-error rate (BER) of ${\lt}{3.8} \times {{10}^{- 3}}$, even after the transmission over 2.2 km of the SSMF.
Figure 1(a) shows a schematic diagram of the SSMF-based two-channel MGDM system implemented by using the proposed technique (i.e., with only two PDs). We utilize two transmitters operating in the 0.8 µm region (i.e., TX1 and TX2) for the generation of two independent signals. These two signals are transmitted through the SSMF link via the ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{11}}$ modes, after being multiplexed by using a mode-multiplexer (M-MUX). At the receiver, in principle, it may be possible to extract the signal carried by the ${{\rm{LP}}_{01}}$ mode from the fiber (for example, by coupling with a propagation-constant-matched waveguide), so that only the signal carried by the ${{\rm{LP}}_{11}}$ mode group remains in the fiber. In this case, we can detect those two transmitted signals by using only two PDs. However, such a convenient mode-demultiplexer (M-DMUX) is not available yet. Thus, we assume implementation of the receiver by using a simple 3 dB coupler and two PDs. Accordingly, at the receiver, the transmitted MGDM signal is split into two parts by using a 3 dB coupler. One part is sent to the PD after passing through the mode filter (which is used to filter out the signal carried by the ${{\rm{LP}}_{11}}$ mode) for the detection of the signal carried by the ${{\rm{LP}}_{01}}$ mode. On the other hand, the other part is directed to PD2 for the detection of the still multiplexed signal. The output signals from PD1 and PD2 are then processed by the MISO equalizer for the extraction of the signal carried by the ${{\rm{LP}}_{11}}$ mode. Since the signal detected by PD2 can be considered as a linear combination of the two signals carried by the ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{11}}$ modes (due to the small crosstalk between two mode groups), the signal carried by the ${{\rm{LP}}_{11}}$ mode can be extracted by using a simple MISO equalizer (which is used to subtract the signal detected by PD1 from that detected by PD2). The MISO equalizer is implemented by utilizing a decision unit for the signal detected by PD1 (DEC1), a symbol-spaced feed-forward equalizer (FFE), ${h_{21}}$, and a half-symbol-spaced FFE, ${h_{22}}$. It should be noted that, due to the use of DEC1 in this MISO equalizer, the signal carried by the ${{\rm{LP}}_{11}}$ mode can be extracted without the effects of the noises of PD1 (which, in turn, improves the receiver sensitivity of the signal carried by the ${{\rm{LP}}_{11}}$ mode). The FFEs (i.e., ${h_{21}}$ and ${h_{22}}$) are used for the synchronization and power adjustment between the signals detected by PD1 and PD2. Thus, in the case of transmitting the signals over a long distance, it would be necessary to increase the tap length of ${h_{22}}$ to cope with the increased differential group delay (DGD) between the ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{11}}$ modes. However, we can minimize this increase of the tap length of ${h_{22}}$ by roughly adjusting the optical and electrical path lengths of PD1 and PD2. It should be noted that, if necessary, we can also utilize an additional FFE, ${h_{11}}$, between PD1 and DEC1 to mitigate the effects of the bandwidth limitations. In comparison, Fig. 1(b)

Fig. 1. Schematic diagrams of the SSMF-based two-channel MGDM systems implemented by using (a) the proposed technique and (b) the conventional technique [7].

Fig. 2. Estimated BER curves of the ${{2}} \times {{28}}\;{\rm{Gb}}/{\rm{s}}$ MGDM-OOK and ${{2}} \times {{56}}\;{\rm{Gb}}/{\rm{s}}$ MGDM-PAM4 signals in the proposed and conventional MGDM systems by numerical simulations.

Fig. 3. (a) Experimental setup used to demonstrate the transmission of ${{2}} \times {{28}}\;{\rm{Gb}}/{\rm{s}}$ MGDM-OOK signals in the proposed system. (b) Eye diagram of the 28 Gb/s OOK signal measured at the output of MZM. Measured eye diagrams of the multiplexed signal at the output of the M-MUX when (c) two OOK signals were bit-synchronized and (d) one OOK signal was delayed by one-half of the bit period from the other OOK signal. Measured eye diagrams at the outputs of (e) PD1 and (f) PD2 after the transmission over 2.2 km of the SSMF.
Figure 3(a) shows the experimental setup to demonstrate the proposed two-channel MGDM system. We transmitted a ${{2}} \times {{28}}\;{\rm{Gb}}/{\rm{s}}$ MGDM-OOK signal operating in the 0.8 µm region over 2.2 km of the SSMF (i.e., SMF-28 fiber) by using the proposed MGDM technique. In this experiment, we utilized a single-frequency laser diode operating at 852.6 nm [10]. The output of this laser was coupled to 780HP fiber [11]. We first modulated the output of this laser by using a commercial MZM (designed for the operation in the 0.8 µm region) for the generation of the 28 Gb/s OOK signal, as shown in Fig. 3(b). We believe that the proposed MGDM system can be implemented by using directly modulated vertical-cavity semiconductor lasers (VCSELs). However, an MZM was utilized in this experiment, since we did not have the high-speed (${\gt}{{25}}\;{\rm{Gb}}/{\rm{s}}$) single-mode VCSELs in our laboratory. We split the OOK signal into two parts by using a 3 dB coupler and directed to the M-MUX based on a mode-selective fiber coupler (crosstalk: ${-}{30} \;{\rm{dB}}$) [8]. One part was used to excite the ${{\rm{LP}}_{01}}$ mode of the SSMF (after passing through an optical delay line for the decorrelation between two OOK signals), while the other part was used to excite the ${{\rm{LP}}_{11}}$ mode. Figures 3(c) and 3(d) show the measured eye diagrams of the multiplexed signals at the output of the M-MUX, when two OOK signals are bit-synchronized, and the signal carried by the ${{\rm{LP}}_{01}}$ mode is delayed by one-half of the bit period from the signal carried by the ${{\rm{LP}}_{11}}$ mode, respectively. We transmitted the multiplexed signal over the 2.2 km long SSMF link (including two fiber connectors). The fiber loss was measured to be 2.2 dB/km for both the ${{\rm{LP}}_{01}}$ and the ${{\rm{LP}}_{11}}$ modes. After the transmission, this MGDM signal was split into two parts by using a variable coupler. One output fiber of this coupler was fusion-spliced to the short patch cord made of HI780 fiber (to strip out the ${{\rm{LP}}_{11}}$ mode) [12], which was then connected to PD1 for the detection of the signal carried by the ${{\rm{LP}}_{01}}$ mode. On the other hand, the other output fiber was directed to PD2 for the detection of the multiplexed signal. However, we noted that, due to the limited resources in our laboratory, a PIN PD with no transimpedance amplifier (TIA) was used for PD1, while a PIN-TIA receiver was utilized for PD2. The 3 dB bandwidths of PD1 and PD2 were 25 and 22 GHz, respectively. Figure 3(e) shows the binary signal measured at the output of PD1. However, the eye diagram measured at the output of PD2 indicated a ternary signal, as shown in Fig. 3(f). Thus, we concluded that the signals carried by the ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{11}}$ modes were linearly combined due to the low crosstalk. For example, Fig. 4 shows

Fig. 4. Measured mode crosstalk after the M-MUX and variable coupler (with and without inserting the 2.2 km long SSMF).

Fig. 5. Measured BER curves of the ${{2}} \times {{28}}\;{\rm{Gb}}/{\rm{s}}$ MGDM-OOK signals carried by the (a) ${{\rm{LP}}_{01}}$ and (b) ${{\rm{LP}}_{11}}$ modes in the back-to-back condition and after the transmission over 2.2 km of the SSMF.
We have proposed a simple SSMF-based two-channel MGDM system operating in the 0.8 µm wavelength region. In this system, the receiver was implemented by using a 3 dB coupler, a mode filter, two PDs, and a ${{2}} \times {{1}}$ MISO equalizer. One PD (i.e., PD1) was used for the detection of the signal carried by the ${{\rm{LP}}_{01}}$ mode after stripping out the signal carried by the ${{\rm{LP}}_{11}}$ mode simply by using a short length of HI780 fiber. The other PD (i.e., PD2) was used for the detection of the multiplexed signal (i.e., carried by both the ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{11}}$ modes). We then extracted the signal carried by the ${{\rm{LP}}_{11}}$ mode by using a simple ${{2}} \times {{1}}$ MISO equalizer consisting of a decision unit (used for the signal carried by the ${{\rm{LP}}_{01}}$ mode), a symbol-spaced FFE (used to process the output of this decision unit), and a half-symbol-spaced FFE (used for the equalization of the multiplexed signal). Due to this decision unit included in the MISO equalizer, we could detect the signal carried by the ${{\rm{LP}}_{11}}$ mode without the effects of the noises of PD1 (used to detect the signal carried by the ${{\rm{LP}}_{11}}$ mode). We confirmed by numerical simulations that the proposed MGDM technique could be used for the PAM4 signals, as well as the OOK signals. For a demonstration, we transmitted ${{2}} \times {{28}}\;{\rm{Gb}}/{\rm{s}}$ MGDM-OOK signals operating at 852.6 nm over 2.2 km of the SSMF. In this experiment, we generated the MGDM signal by using a mode-selective coupler as an M-MUX. The results showed that we could achieve the BER better than ${3.8} \times {{10}^{- 3}}$ for both signals carried by the ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{11}}$ modes, even after the transmission over 2.2 km of the SSMF. We believe that, for doubling the transmission capacity of the SSMF in short-haul applications, the proposed technique has a potential to be more cost-effective than the PDM-DD technique.
Funding
Institute for Information and Communications Technology Promotion (2017-0-00702).
Disclosures
The authors declare no conflicts of interest.
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