1. INTRODUCTION

Mode division multiplexing (MDM) transmission is an attractive technique for expanding the transmission capacity per fiber. Further increase of capacity could be considered by utilizing multi-mode multi-core fiber (MM-MCF), and Refs. [1,2] demonstrated over 10 Pbit/s transmission using MM-MCFs. Here, it is well known that mode dependent loss (MDL) in MDM transmission severely degrades the transmission performance and distance [3]. MDL is induced by differential modal attenuation among propagation modes. Several MDL suppression techniques have been proposed. Mode permutation was used in Ref. [4], and they realized 3200-km-long MDM transmission by using a six-mode fiber. References [5,6] investigated the applicability of mode scrambling. In addition to reducing MDL in a few-mode fiber (FMF), it is important to control the MDL in few-mode (FM) amplifiers that is induced by differential modal gain (DMG).

Generally speaking, the difference in overlap between electric fields and erbium dopant distribution among transmission modes causes DMG in a FM erbium-doped fiber amplifier (EDFA). There are three well-known techniques for compensating for DMG in FM-EDFAs. The first is tailoring the erbium dopant profile in a FM-EDFA directly [7]. The second utilizes higher-order mode pumping [8]. This enables the content of pump light in each mode to be controlled and thus minimizes the overlap difference. The final technique optimizes the refractive index profile of the FM erbium-doped fiber (EDF). For example, Ref. [9] used a ring profile so that the overlap difference can be minimized. By utilizing the second technique, a DMG of less than 1 dB with an average gain of more than 20 dB is achieved [8]. However, these approaches need additional optical components or complex configurations.

Femtosecond laser inscription is one of the well-known techniques for modulating glass materials [10,11]. The nonlinear nature of ultrafast light interaction at the focal volume causes non-thermal micro modulation in glass. By focusing laser pulses from any direction, refractive index modulation can be caused at arbitrary positions in glass. The results of the fabrication are classified into three types: smooth refractive index change, birefringent modulation, and empty void. The difference depends on the peak intensity of the pulse energy. An empty void enables a larger index change and directly attenuates the transmission signal. In Ref. [12], it is reported that laser inscription enabled a particular core in a multi-core fiber to be attenuated. Thus, we suppose that a laser-inscribed void can be used to manage the attenuation difference between different transmission modes in small processing areas.

In this paper, we propose a novel technique for reducing DMG between the linearly polarized (LP), ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$, modes that use a two-mode EDF (2M-EDF) with a laser-inscribed void [13]. First, we show the concept of our proposed technique in Section 2. We show that the attenuation of the ${{\rm LP}_{01}}$ mode can be selectively controlled by adding an empty void to the core center of the 2M-EDF. We also show that the DMG can be controlled by changing the void diameter. In Section 3, we investigate differential modal attenuation characteristics and two-mode amplification properties obtained with the proposed technique. We experimentally investigate the longitudinal void position dependence on both DMG and noise figure (NF) characteristics. We finally achieve a DMG of less than 0.5 dB in the full C-band while maintaining a sufficiently high gain of more than 24 dB by optimizing the void diameter and its inscribed position.

2. CONCEPT OF DMG REDUCTION TECHNIQUE WITH VOID-INSCRIBED 2M-EDF

Figure 1 shows a conceptual diagram of our proposed technique. In general, the gain of the fundamental mode (${{\rm LP}_{01}}$ mode) is higher than that of other higher-order modes in an FM-EDF when utilizing fundamental mode pumping. We considered an empty void at the core center of a 2M-EDF. The right figures in Fig. 1 show the calculated electric field distribution of the ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes at a wavelength of 1550 nm. The two upper figures show the electric field of the conventional step index profile, and the two bottom figures show when we assumed a sphere void with a 5.0 µm diameter. By making a void at the center of the core, the electric field of the ${{\rm LP}_{01}}$ mode is dramatically changed at the void region. In comparison, it can be seen that the electric field of the ${{\rm LP}_{11}}$ mode has a much smaller change with the void. Thus, it can be considered that an imposed void attenuates the ${{\rm LP}_{01}}$ mode selectively while minimizing the influence on the ${{\rm LP}_{11}}$ mode. Increasing the void size enables the attenuation to the ${{\rm LP}_{01}}$ mode to be made larger; however, too large of a void would cause there to be excess loss for the ${{\rm LP}_{11}}$ mode. We then investigated the relationship between void diameter and the attenuation of each transmission mode.

 

Fig. 1. Conceptual diagram of our proposed technique.

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Figure 2(a) shows the result of calculating the attenuation of the ${{\rm LP}_{01}}$ (red) and ${{\rm LP}_{11}}$ (green) modes as a function of void diameter, where the core diameter and the relative refractive index difference were 14.0 µm and 0.48%, respectively. We calculated the attenuation by considering the overlap between electric fields with and without a void. Here, we used the two-dimensional finite element method [14] for calculating the electric field, and we set the wavelength at 1550 nm. By enlarging the void diameter, the attenuation for both the ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes was monotonically increased. However, the attenuation of the ${{\rm LP}_{11}}$ mode was relatively small, and an excessive loss of less than 1 dB was expected up to a 5.8 µm void diameter. The solid line in Fig. 2(b) shows the attenuation difference between the ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes (${\Delta _{{\rm att}}}$) when the void is at the core center. ${\Delta _{{\rm att}}}$ increased with the void diameter almost linearly. With a void diameter of 5.8 µm as the maximum, ${\Delta _{{\rm att}}}$ is expected to be controlled in the range of  0–2.1 dB when considering one void. The dashed line in Fig. 2(b) shows the calculated ${\Delta _{{\rm att}}}$ when the void deviated 0.5 µm from the center of the core. Although the average calculation results of the four ${{\rm LP}_{11}}$ modes $({{{{\rm LP}}_{11{ax}}},{{{\rm LP}}_{11{ay}}},{{{\rm LP}}_{11{bx}}},{{{\rm LP}}_{11{by}}}})$ are shown here, the void position displacement may have caused the difference in ${\Delta _{{\rm att}}}$ between the degenerate ${{\rm LP}_{11}}$ modes. As shown in Fig. 2(b), the max deviation of ${\Delta _{{\rm att}}}$ is 0.05 dB with a void diameter of 5.8 µm or less, so we considered the influence of position deviation to be small enough.

 

Fig. 2. Result of calculating (a) attenuation of ${{\rm LP}_{01}}$ (red) and ${{\rm LP}_{11}}$ (green) modes, and (b) attenuation difference between ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes (${\Delta _{{\rm att}}}$) as a function of void diameter (at 1550 nm) when the void is at the center of the core (solid) and the void deviated 0.5 µm from the center of the core (dashed).

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Fig. 3. Void diameter as a function of pulse energy.

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Here, the void diameter can be managed by means of pulse energy. Figure 3 shows an experimental result with a void diameter as a function of pulse energy. In this experiment, we fabricated a void at one end-face of a 2M-EDF whose refractive index and erbium dopant profile were a step index with a depression in the core center [8]. The inscription position accuracy degraded when we inscribed from the vertical direction against the side face of the 2M-EDF since we could not use the refractive index matched inscription scheme [15]. Moreover, end-face inscription can reduce the influence of the non-circularity of the void. The diameter and relative refractive index difference of the 2M-EDF were 14 µm and 0.5%, respectively. The duration, repetition rate, and wavelength of our femtosecond laser were 300 fs, 200 kHz, and 515 nm, respectively. The inscription light was tightly converged by an objective lens (Mitutoyo, $\times$100, 0.5NA) onto the end-face of the 2M-EDF along the light propagation axis. We changed the output power from 135 to 604 mW for adjusting the pulse energy while the repetition rate was constant. We observed a void with a 2 µm diameter at minimum, and the void diameter exceeded 6 µm at a pulse energy of 3 µJ. There was a variation of $\pm0.3\; {\unicode{x00B5}{\rm m}}$ at the same pulse energy of 3 µJ. Thus, it is supposed that the void diameter was controllable with a step of $\pm0.3\; {\unicode{x00B5}{\rm m}}$ from 2 to 6 µm. As a result, Figs. 2(b) and 3 show that we can expect to control ${\Delta _{{\rm att}}}$ from 0.6 to 2.2 dB with a step of $\pm0.1\;{\rm dB} $.

 

Fig. 4. Measured results of (a) attenuation of ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes and (b) attenuation difference between ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes (${\Delta _{{\rm att}}}$) as a function of void diameter (at 1550 nm).

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3. EXPERIMENTS AND DISCUSSION

A. Optical Property of Void-inscribed 2M-EDF

We fabricated a void at one end-face of a 30-cm-long 2M-EDF and spliced another 2M-EDF that was 30 cm long by conventional fusion splicing. The input end of the 2M-EDF was connected to a three-dimensional (3D)-inscribed waveguide-based mode multiplexer (MUX), and the other end was connected to a power meter directly. We input the ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes separately and measured the power of each mode.

Figure 4 shows the attenuation characteristics as a function of void diameter measured at a wavelength of 1550 nm. Figure 4(a) is the measured attenuation of the ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes, and Fig. 4(b) is the ${\Delta _{{\rm att}}}$. The inset in Fig. 4(a) shows the end-face of the void-inscribed 2M-EDF. The black region shows the void. It was confirmed that a circular void was fabricated at the center of the core and that its diameter was 5.6 µm. It was also confirmed from Fig. 4(a) that the attenuation of the ${{\rm LP}_{01}}$ mode monotonically increased from 0.8 to 3.4 dB as the void diameters increased. Also, the ${{\rm LP}_{11}}$ mode had a relatively small attenuation of less than 1 dB, as expected in Fig. 2. Moreover, we confirmed that the ${\Delta _{{\rm att}}}$ monotonically increased the same as the numerical results. It varied from 0.7 to 2.5 dB for void diameters from 4.4 to 6.4 µm. However, it was also found that the measured attenuation and ${\Delta _{{\rm att}}}$ were relatively smaller than the calculated results. In this measurement, we measured the void position and diameter with a microscope, and the error of the measured void diameter and position was less than $\pm0.2$ and $\pm0.5\;\unicode {x00B5}{\rm m}$, respectively. As shown in Fig. 2(b), the ${\Delta _{{\rm att}}}$ deviation due to these errors can be expected to be small. Although further investigation is necessary, we can consider that the fusion splice in our experimental procedure might have affected the void diameter and that the slightly reduced void diameter resulted in smaller attenuation. These results confirmed that one laser-inscribed void in a 2M-EDF can realize a change of a few decibels (dB) in ${\Delta _{{\rm att}}}$, which can be managed by means of void diameter as expected in the numerical model.

Figure 5 shows the measured wavelength dependence of the output power of the void-inscribed 2M-EDF. Figures 5(a)–5(d) show the results from when the input and output mode conditions were set at (${{\rm LP}_{01}}$ and ${{\rm LP}_{01}}$), (${{\rm LP}_{11}}$ and ${{\rm LP}_{11}}$), (${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$), and (${{\rm LP}_{11}}$ and ${{\rm LP}_{01}}$), respectively. The red plots show the results from when the mode MUX and demultiplexer (DEMUX) were directly connected. The MUX and DEMUX had an almost 6 dB insertion loss. The green plots show the results from when we inserted a 60-cm-long 2M-EDF without a void between the MUX and DEMUX. The difference in wavelength dependence from the red plots is due to erbium absorption [16], and we observed an attenuation coefficient of 4.3 dB/m at 1550 nm. The blue and magenta plots show the results from when we induced voids with diameters of 4.9 and 5.6 µm. Figure 5(a) shows that the ${{\rm LP}_{01}}$ mode was attenuated in the entire measured wavelength region according to the void diameter. The average attenuation for a wavelength of 1500–1630 nm was 1.17 and 2.08 dB with void diameters of 4.9 and 5.6 µm, respectively. Figure 5(b) also confirms that the ${{\rm LP}_{11}}$ mode had no remarkable increase in loss in the entire wavelength region. The excess loss of the ${{\rm LP}_{11}}$ mode was less than 1 dB with both diameters. Figure 5(c) also confirms that there was no unique crosstalk when the ${{\rm LP}_{01}}$ mode was launched. It can be seen, however, that Fig. 5(d) contained noticeable crosstalk variation around 1550 nm when the ${{\rm LP}_{11}}$ mode was launched. We supposed that it was caused by the polarization and degenerative mode dependence in our MUX/DEMUX. We observed a modal crosstalk variation of about 3 dB in the entire 1500–1630 nm wavelength when we directly connected the MUX and DEMUX and rotated the polarization state of the input light. Thus, we can consider the void-inscribed 2M-EDF to have negligible influence on modal crosstalk and its wavelength dependence. From these results, it was confirmed that we can control the ${\Delta _{{\rm att}}}$ with low wavelength dependence from 1500–1630 nm.

 

Fig. 5. Wavelength dependence of output power. (a), (b), (c), and (d) correspond to results when input and output mode combinations were set at (${{\rm LP}_{01}}$ and ${{\rm LP}_{01}}$), (${{\rm LP}_{11}}$ and ${{\rm LP}_{11}}$), (${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$), and (${{\rm LP}_{11}}$ and ${{\rm LP}_{01}}$), respectively.

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Fig. 6. Void diameter dependence of return loss (at 1550 nm).

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Next, we investigated the return loss (RL) of the void in a 2M-EDF since a void may induce undesired reflection, which degrades the amplification performance. It was supposed that the ${{\rm LP}_{01}}$ mode would have a greater RL than the ${{\rm LP}_{11}}$ mode because of the large overlap with the void. Therefore, we measured the RL for the ${{\rm LP}_{01}}$ mode by splicing the single-mode fiber (SMF) with the void-inscribed 2M-EDF at the input side. We used the optical continuous-wave reflectometer method [17]. A light source and power meter were connected to the input side of a 3 dB coupler, and the output side was connected to the void-inscribed 2M-EDF via a conventional SMF. The other side of the void-inscribed 2M-EDF was inserted in index matching oil to avoid reflection at the end-face. The RL can be obtained by measuring the relative power via the power meter with the input power of the light source. Here, the RL of this setup was sufficiently small at 60 dB when we measured the RL without the void-inscribed 2M-EDF. Figure 6 shows the measured RL normalized by the input power of the ${{\rm LP}_{01}}$ mode. The red symbols and black line show the measured results and best fitted line, respectively. The RL degraded as the void diameter increased, and a 6.5 µm void diameter resulted in a RL of 23 dB. According to Ref. [18], reflection has a catastrophic impact upon amplifier spontaneous emission (ASE) and gain. In Ref. [18], a 21 dB RL caused the NF to degrade more than 4 dB. We then experimentally investigated the amplification property of the void-inscribed 2M-EDF.

B. Amplification Property of Void-inscribed 2M-EDF

Figure 7 shows the experimental setup used to evaluate the gain and NF. Four reference lights at 1532, 1545, 1555, and 1565 nm, used to lock the population inversion state of ${{\rm Er}^{3 +}}$, were injected with test light. We can suppress fluctuations in gain and NF caused by insufficient input power when the signal light has only one wavelength. Here, we called these reference lights “saturated lights.” Their input power was ${-}15\;{\rm dBm} $, and they were combined with test light from a tunable wavelength laser diode (TWLD) via a 4:1 coupler. Here, the test light was modulated with a 2.5 Gbaud/s quasi-phase-shift keying (QPSK) format. The modulated test light was divided into three ports of the MUX, corresponding to ${{\rm LP}_{01}}$, ${{\rm LP}_{11a}}$, and ${{\rm LP}_{11b}}$ modes, and the saturated lights were input to the ${{\rm LP}_{01}}$ port of the MUX with the test light. The input power of each was adjusted to ${-}25\;{\rm dBm} $ by variable attenuators (ATTs). The mode-multiplexed signals were injected into a 19-m-long 2M-EDF through a three-mode isolator and signal/pump combiner. The pump light was operated at 980 nm and input as the ${{\rm LP}_{01}}$ mode, and we utilized a core pumping system. After the 2M-EDF, the signal output from the DEMUX was individually detected with an optical spectral analyzer (OSA) via an optical switch. When we evaluated the amplification property with the void, we added a 5.6 µm diameter void at positions A, B, or C. In this experiment, we input ${{\rm LP}_{01}}$, ${{\rm LP}_{11a}}$, and ${{\rm LP}_{11b}}$ modes simultaneously, so we could not measure characteristic differences between the degenerate ${{\rm LP}_{11}}$ modes (${{\rm LP}_{11a}}$ and ${{\rm LP}_{11b}}$).

 

Fig. 7. Experimental setup.

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Fig. 8. Measured modal gain and gain difference $\Delta {{G}_{01 - 11}}$ as a function of pump power. Circles, squares, and triangles correspond to ${{\rm LP}_{01}}$-, ${{\rm LP}_{11}}$-gain, and $\Delta {{G}_{01 - 11}}$, respectively. (a) Results when the 2M-EDF without void was used. (b) Results when a 5.6 µm diameter void was inscribed in the 2M-EDF.

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Fig. 9. Measured NF of ${{\rm LP}_{01}}$ (red) and ${{\rm LP}_{11}}$ (green) modes as a function of pump power. Filled and open symbols correspond to with and without void.

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Fig. 10. Wavelength dependence of $\Delta {{G}_{01 - 11}}$ measured at 690 mW pump power. Filled and open symbols correspond to 2M-EDF with and without void.

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Figure 8 shows the gain and its difference between two-mode $\Delta {{G}_{01 - 11}}$ as a function of the pump power measured at 1550 nm. The circles, squares, and triangles correspond to the ${{\rm LP}_{01}}$-, ${{\rm LP}_{11}}$-gain, and $\Delta {{G}_{01 - 11}}$, respectively. Figure 8(a) was measured with a 2M-EDF with no void. Figure 8(b) was measured when a 5.6 µm diameter void was added at position B. It can be seen from Fig. 8(a) that the test EDFA had a gain of more than 25 dB, and $\Delta {{G}_{01 - 11}}$ reached 2 dB when the pump power was 625 mW. Figure 8(b) reveals that $\Delta {{G}_{01 - 11}}$ was successfully reduced to 0.5 dB through the introduction of a void with the optimum diameter. Although there was gain degradation of 3.0 and 1.3 dB for the ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes, respectively, a sufficient gain of more than 20 dB was maintained in this experiment. However, larger gain reduction is expected if a higher MDL needs to be controlled. In that case, additional techniques such as bi-directional pumping should be considered for compensating gain reduction. Figure 9 shows the NF of the ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes measured at 1550 nm. The circles and squares correspond to the ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes, respectively. The filled and open symbols show the results when a 2M-EDF with and without a void was used, respectively. Figure 9 reveals that there was no remarkable degradation in the NF even when we utilized a void. Here, the back reflection at a void may degrade the optical amplification stability, as discussed in Fig. 6. In this experiment, we confirmed that there was no remarkable change for the output power and ASE properties, including their time dependence, even when we removed the isolator placed before the mode MUX. Therefore, the influence of reflection degradation caused by a void could be neglected in our experiments.

 

Fig. 11. Influence of void position on (a) modal gain and (b) NF measured at 1550 nm with 690 mW pump power.

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Figure 10 shows the wavelength dependence of $\Delta {{G}_{01 - 11}}$ measured at a 690 mW pump power. The open and filled symbols show the results when we used the 2M-EDF without and with a void at position B, respectively. Figure 10 confirms that the max $\Delta {{G}_{01 - 11}}$ in the 1530 nm to 1560 nm wavelength region was 2.1 dB when we used the 2M-EDF with no void. It was also confirmed that a sufficiently low DMG of 0.5 dB or less could be realized over the entire C-band. Moreover, there was no noticeable change in the wavelength dependence, even when we utilized a void as expected in Fig. 5.

Finally, we investigated the impact of the longitudinal position of a void in the 2M-EDF on the amplification characteristics. Figure 11 shows the gain and NF characteristics measured with three different void positions, shown as A, B, and C in Fig. 7. A, B, and C, respectively, correspond to the input side, middle, and output sides of the 2M-EDF. Figure 11(a) shows the modal gain at 1550 nm with a 690 mW pump power. The circles and squares correspond to the ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes, respectively. When we imposed the void at the input side of the 2M-EDF (position A), the signal light was attenuated before amplification, so the gain received in the EDF was not compensated for, and the apparent $\Delta {{G}_{01 - 11}}$ was not improved. When the void was imposed in the middle of the 2M-EDF (position B), the $\Delta {{G}_{01 - 11}}$ was compensated for at the middle point. $\Delta {{G}_{01 - 11}}$ was degraded in the rest of the EDF; however, the influence of the void was relatively small since the signal gain was almost saturated before the void. Since attenuated light could be amplified within the remaining 9 m EDF, sufficient gain was obtained. Finally, the void at the output side (position C) enabled full compensation, but the gain was directly affected by the insertion loss of the void. Figure 11(b) shows the modal NF measured at 1550 nm with a 690 mW pump power. It is also seen from Fig. 11(b) that the void at the input side of the 2M-EDF (position A) clearly degraded the NF, and the NF of the ${{\rm LP}_{01}}$ mode became larger than that of the ${{\rm LP}_{11}}$ mode. This is because the input power of the ${{\rm LP}_{01}}$ mode degraded more than the ${{\rm LP}_{11}}$ mode or ASE.

From these results, it was revealed that we can reduce $\Delta {{G}_{01 - 11}}$ by inducing a void at the middle of the 2M-EDF (position B) while maintaining enough gain, NF, and its flatness.

4. CONCLUSION

We proposed a technique for reducing DMG that uses a void-inscribed 2M-EDF. We revealed that the output power of the ${{\rm LP}_{01}}$ mode can be attenuated selectively by simply inscribing an empty void at the core center of the 2M-EDF by utilizing a femtosecond laser. By changing the void diameter with pulse energy in laser inscription, we can manage the attenuation difference between the ${{\rm LP}_{01}}$ and ${{\rm LP}_{11}}$ modes from 0.7 to 2.5 dB at 1550 nm with less than a 1 dB excess loss for the ${{\rm LP}_{11}}$ mode. The proposed technique reduced $\Delta {{G}_{01 - 11}}$ from 2.1 to 0.5 dB in the wavelength region of 1530–1560 nm. We also clarified that the optimum gain and NF properties could be maintained by introducing a void in the middle of the 2M-EDF. Moreover, there was no noticeable influence on both wavelength characteristics, including modal crosstalk and operation stability, when introducing a void in the 2M-EDF. These results show that the proposed technique enables us to minimize the modal difference in an MDM transmission link by simply introducing an empty void in a discrete FM-EDFA. Although the proposed technique is effective in attenuating the ${{\rm LP}_{0m}}$ modes where the electric field is at the center of the core, it is difficult to control the DMG when using three or more modes by utilizing only this technique. To expand the mode number in controlling DMG, we need to consider more complex configurations, for example, combinations of void inscription and mode MUX. Thus, we expect that our proposed technique will contribute to realizing long-distance and MDM transmission links in a simple and cost-effective manner.