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We propose a planar lightwave circuit (PLC)-based mode multi/demultiplexer (MUX/DEMUX) with an asymmetric parallel waveguide for mode division multiplexed (MDM) transmission. The PLC-based mode MUX/DEMUX has advantage of selectively exciting higher-order mode. We realize three-mode (LP01, LP11a, and LP21a) multiplexing by using an asymmetric parallel waveguide. We then design and fabricate a PLC-based mode MUX/DEMUX on one chip by using our proposed LP11 mode rotator to allow us to utilize the LP11b mode. We successfully multiplex the LP01, LP11a, and LP11b modes and achieve a relatively low insertion loss over the C-band using our fabricated mode MUX/DEMUX. Our results indicate that the PLC-based mode MUX/DEMUX with a uniform height has the potential to increase the mode number by using an LP11b mode.
© 2014 Optical Society of America
1. Introduction
The transmission capacity in standard single-mode fiber (SMF) is limited to around 100 Tbps because an input power limitation is imposed by fiber nonlinearity or the fiber fuse phenomenon [1]. Therefore, space-division multiplexing (SDM) and mode-division multiplexing (MDM) have attracted increasing attention as a way of realizing a much larger capacity. Recently, a transmission exceeding 1 Pbps has been achieved by using a 12-core fiber [2], and a capacity-distance exceeding 1 Exabit/s∙km has been realized with a multi-core fiber [3, 4].
As regards MDM transmission, a transmission capacity exceeding 70 Tbps has been realized by using two linearly polarized (LP) modes with a few-mode fiber [5]. Various types of mode multi/demultiplexer (MUX/DEMUX) and few-mode fiber have been proposed [6–21]. The free-space optics based mode MUX/DEMUX requires precise alignment to realize a low insertion loss [6–13]. In addition, this MUX/DEMUX has a problem that the mode dependent loss increases as the mode number increases [12]. In contrast, a mode MUX/DEMUX using a fiber or a waveguide must realize a low insertion loss [14–17]. Planar lightwave circuit (PLC)-based devices offer the advantages of compactness, low loss and mass-producibility because of their mature manufacturing technology. Recently, several types mode MUX/DEMUXs with selectively exciting higher-order mode have been proposed with a view to realizing MDM transmission [14–21].
In this paper, we design and fabricate a three-mode (LP01, LP11a, and LP21a) MUX/DEMUX by using an asymmetric parallel waveguide. The fabricated three-mode MUX/DEMUX achieved the mode conversion of the LP01 mode to the LP11a and LP21a modes over the conventional band (C-band). We also report that a mode MUX/DEMUX with two degenerate LP11 modes can be realized by using an LP11 mode rotator [22]. Finally, we demonstrate the mode multiplexing of the LP01, LP11a, and LP11b modes by using our fabricated PLC-based mode MUX/DEMUX with an LP11 mode rotator on one chip.
2. Mode multi/demultiplexing using asymmetric mode coupler with uniform height
We propose mode multiplexing that uses an asymmetric mode coupler (AMC) with two different waveguide widths. Figure 1 shows the concept and a summary of mode coupling between two waveguides. For mode coupling between the LP01 and LP11a modes we must match the effective index of the LP11a mode in waveguide 1 to that of the LP01 mode in waveguide 2 as shown in Fig. 1(a) [23]. The effective indices of the LP01 and LP11a modes increase as the waveguide width increases when the relative refractive index difference (Δ) and height are constant. Here, the Δ is determined by when the ncore and nclad are core and clad indices, respectively. Thus, the LP01 mode in waveguide 2 can be coupled to the LP11a mode in waveguide 1 by increasing w1 appropriately compared with w2 as shown in Fig. 1(a). The AMC has two waveguides with widths of w1 and w2 (w1 > w2) as shown in Fig. 1(b). Here, G, L and h are the waveguide gap, interaction length and waveguide height, respectively, and h is the same as w2. Mode multi/demultiplexing can be realized by the AMC when the L value is appropriate for a certain G with matching effective indices for the LP01 and LP11a modes. In addition, the coupling of other propagation modes can also be realized using the same concept. However, mode coupling between even and odd modes on a vertical axis cannot be realized simply by matching the effective indices in an AMC with a uniform height. Figure 1(c) shows an image of the overlapping field between two waveguides. The mode coupling of the LP01 mode to the LP11a mode was possible as shown in the first row of Fig. 1(c). On the other hand, since the coupling coefficients of the LP01 mode to the LP11b mode with vertical field distribution was zero between the two waveguides, the mode coupling of the LP01 mode to the LP11b mode was impossible as shown in the second row of Fig. 1(c).
Fig. 1 Basic concept of AMC with mode conversion. (a) Image of effective index for mode coupling between LP01 and LP11 modes. (b) Cross-sectional view of AMC. (c) Image of mode coupling between even and odd modes at vertical axis in waveguide with uniform height.
Thus three-mode (LP01, LP11, LP21 modes) multiplexing cannot be realized using only the mode coupling of the LP01 mode to other modes in a parallel waveguide with a uniform height since the LP21a mode has a vertical field distribution. We proposed realizing the mode coupling of the LP21a mode by using the LP11b mode since the mode coupling of the LP11b mode to the LP21a mode is possible [18]. The LP11b mode can be generated by rotating the LP11a mode after LP01 to LP11a mode coupling with the AMC. Therefore, three-mode multi/demultiplexing can be realized with the LP11b mode.
Figure 2 shows the structure of our proposed three-mode MUX/DEMUX. The inset in Fig. 2 is the electrical field transition from each input port. The mode coupling of the LP01 to LP11a and LP11b to LP21a modes can be realized by matching the effective index. The LP11b mode is generated by rotating the LP11a mode 90 degrees. The LP01 mode from port 1 is directly output at the output port. The LP01 mode from port 2 is converted to the LP11a mode. The LP01 mode from port 3 is converted to the LP11a mode, and the LP11b mode is generated from this LP11a mode by rotating the waveguide 90 degrees, and is converted to the LP21a mode. Table 1 shows the waveguide parameters we used to realize three-mode multi/demultiplexing. We then calculated the mode coupling ratios of the LP01 mode to the LP11a mode and the LP11b mode to the LP21a mode. Figure 3(a) and (b) show the wavelength dependence of the coupling ratios from port 1 or 2 to port 2’ and from port 3′ or 5′ to port 5. The solid and dashed lines, respectively, show the coupling ratios of the LP01 and LP11a modes in Fig. 3(a) and of the LP11a and LP21a modes in Fig. 3(b). The coupling ratios of the LP11a and LP21a modes were higher than 98% and 92%, respectively, between 1530 ~1560 nm. We consider the mode crosstalk to be relatively small since the coupling ratios of the LP01 and LP11a modes in a straight port exceeded 99%. Moreover, we believe that the polarization dependence of the coupling ratio is a sufficiently small because the two-mode MUX/DEMUX has a low polarization dependence [16].
Table 1. Waveguide parameters of three-mode MUX/DEMUX
Fig. 3 (a) LP11a mode coupling ratio dependence on wavelength. (b) LP21a mode coupling ratio dependence on wavelength.
3. Characteristics of fabricated three-mode MUX/DEMUX
We fabricated three-mode MUX/DEMUXs using the waveguide parameters in Table 1 and evaluated their optical characteristics. We realized the excitation of the LP11b mode by using two chips with a rotation of 90 degrees in this mode MUX/DEMUX. In the experiment, a four-LP-mode fiber with a core diameter of 12 μm and Δ of 0.6% supporting the LP01, LP11, LP21, and LP02 modes in the C-band was connected to the output port of the PLC, and a conventional SMF was connected to ports 1, 2, and 3. Figure 4 shows near field patterns (NFPs) measured at the connecting fiber of output port when a continuous wave (CW) light of the LP01 mode at a wavelength of 1530 to 1565 nm was input into ports 1, 2, and 3. The LP01 mode in the three-mode MUX was purity because the LP02 mode was cutoff. Since we thought that the mode coupling of the LP01 and LP02 mode was sufficiently small between the waveguide and connecting fiber, we considered that the LP01 mode from port 1 was almost the true LP01 mode. The LP11a and LP21a mode patterns were clearly observed by converting the LP01 mode from ports 2 and 3 to the LP11a and LP21a modes in the waveguide. As a result, we confirmed that the three modes were multiplexed by the fabricated MUX/DEMUX.
Figure 5(a) shows the insertion loss of the fabricated PLC. Here, our measured insertion losses were including the splicing loss between the waveguide and connecting fiber. The open and filled circles, and open triangle in Fig. 5(a) show the insertion losses of the LP01, LP11a, and LP21a modes, respectively. The insertion losses of the LP01 and LP11a modes were less than 0.5 and 1.5 dB, respectively, throughout the C-band. The insertion loss of the LP11 mode was higher than 0.8 dB [16]. We supposed that the insertion loss of the LP11 mode was increased by increasing the waveguide height because the fabrication process didn’t optimize in the height of 9.0 μm. The measured insertion loss of the LP21a mode was higher than that of the LP01 and LP11a modes, and increased with wavelength. The measured insertion losses included the mode-field mismatching loss between the spliced fiber and the waveguide and the macro-bending loss in the waveguide. We consider that this results from the coupling loss at port 3′ and can be reduced by minimizing the field mismatch between the LP11a and LP11b modes. Since the insertion loss of the LP21a mode increased with the wavelength as shown in Fig. 5(a), we considered that the main factor of this loss was the macro-bending loss of the LP11b mode at waveguide 4. We then calculated the macro-bending loss of the LP11b mode before the LP21a mode-coupling region. The solid, dashed, and dotted lines in Fig. 5(b) show the simulated bending loss of the LP11b mode with three different sets of waveguide parameters. The bending loss of the LP11b mode with the parameters used for fabrication (Δ = 0.42% and R = 50 mm) increased with increases in wavelength as found with the measured result. We also calculated the bending loss for (Δ = 0.42%, R = 70 mm) and (Δ = 0.45%, R = 70 mm) as shown in the figure. We believe that the insertion loss of the LP21a mode can be reduced because macro-bending loss of the LP11b mode can be reduced by appropriately designing Δ and the bending radius as shown in Fig. 5(b). Furthermore, we considered that the insertion loss can be realized less than 1.0 dB by optimizing the fabrication process in the waveguide height of 9 μm.
Fig. 5 (a) Insertion loss of fabricated three-mode MUX/DEMUX. (b) Simulated macro-bending loss of waveguide.
We then measured the mode extinction ratio in the fabricated three-mode MUX/DEMUX with a four-mode fiber of about 5 m. Figure 6(a), 6(b), and 6(c) show the mode extinction ratios of the LP01 mode to the LP11a or LP21a mode, the LP11a mode to the LP01 or LP21a mode, and the LP21a mode to the LP01 or LP11a mode, respectively. Here, we measured the mode extinction ratio by connecting two fabricated MUX/DEMUXs. The mode extinction ratios from the LP01 and LP11a modes were higher than 15 dB in the C-band. These values were almost the same as the results for the two-mode MUX/DEMUX described in the reference [16]. The mode extinction ratio of the LP21a mode was higher than 11 dB in the C-band. Figure 7 shows the eye patterns at a wavelength of 1534 nm when the signals of an individual mode and three multiplexed modes were input into the three-mode DEMUX. Here, we used a 10 Gbps non-return-to-zero (NRZ) signal with a 231−1 PRBS. The first, second, and third rows in Fig. 7 are eye patterns of the LP01, LP11a, LP21a modes, respectively. Although the eye patterns of the third row were slightly degraded compared with those when the individual modes were input into the mode DEMUX, we confirmed that we could obtain relatively clear eye patterns with our fabricated three-mode DEMUX when we used the LP01, LP11a, and LP21a modes. We found that the eye opening penalties were about 40% between individual and 3 modes after demultiplexing. We considered that this degradation didn’t include a mode conversion in few-mode fiber because the connecting fiber length was less than 10 m. We believe that the LP21a mode to LP01 and LP11a mode extinction ratios can be improved by optimizing the waveguide parameters when we increase waveguide height.
Fig. 6 (a) Mode extinction ratios of LP01 to LP11a or LP21a mode. (b) Mode extinction ratios of LP11a to LP01 or LP21a mode. (c) Mode extinction ratios of LP21a to LP01 or LP11a mode.
Fig. 7 Eye patterns when inputting signals of individual modes and three multiplexed modes in fabricated DEMUX.
4. Degenerate two-LP11 mode multiplexing in parallel waveguide with mode rotator
We described the mode coupling of the LP11b mode to the LP21a mode with our fabricated three-mode MUX/DEMUX in the previous section. However, the excitation of the LP11b mode in this mode MUX/DEMUX required the 90-degree rotation of a waveguide. We have already proposed a PLC-type LP11 mode rotator with a single-trench waveguide [22]. In this section, we describe our design and fabrication of an LP11a and LP11b mode MUX/DEMUX with an LP11 mode rotator.
Figure 8(a) and (b) show the structures of the LP11 mode MUX/DEMUX and LP11 mode rotator, respectively. This mode rotator is constructed from an asymmetric waveguide with a single trench, where the position (t), width (s), and depth (d) were set as shown in Fig. 8(b). Since the two orthogonal LP11 modes are excited equally and propagated with different propagation constants in this asymmetric waveguide when an LP11a mode is launched, the LP11a mode can be rotated into the LP11b mode by setting the length of this asymmetric waveguide at a half beat-length [22]. Table 2 shows the waveguide parameters for the LP11 mode MUX/DEMUX. We then calculated the wavelength dependence of the coupling ratio to the output port from ports 1, 2, and 3 as a function of wavelength as shown in Fig. 9. The solid, dashed and dotted lines, respectively, show the coupling ratios of the LP01, LP11a, and LP11b modes. These coupling ratios were higher than 90% and exhibited a low wavelength dependence over the C-band. In addition, we consider that the LP11 mode MUX/DEMUX has a low polarization dependence since the LP11 mode rotator has a low polarization dependence [22].
Fig. 8 (a) LP11a and LP11b modes multi/demultiplexer with mode rotator. (b) Structure of mode rotator.
Table 2. Parameters of LP11 mode MUX/DEMUX
We then fabricated an LP11 mode MUX/DEMUX with the waveguide parameters listed in Table 2. In the experiment, a two-mode fiber with a core diameter of 14 μm and Δ of 0.35% supporting the LP01 and LP11 modes in the C-band was connected to the output port of the PLC, and a conventional SMF was connected to ports 1 and 3. Figure 10(a) shows the NFPs measured at the connecting fiber of output port when a CW light with a wavelength of 1530 to 1560 nm was input into ports 1, 2, and 3. The LP11a mode pattern was clearly observed by converting the LP01 mode from port 1 in the fabricated MUX/DEMUX in the C-band. We also confirmed that the LP11 mode pattern from port 3 rotated by 90 degrees in relation to that of port 1 in this MUX/DEMUX. So we successfully multiplexed the LP11a and LP11b modes by using a waveguide with an LP11 mode rotator. Figure 10(b) shows the insertion loss of the fabricated MUX/DEMUX. The open and filled circles, and open triangle in Fig. 10(b) show the insertion losses of the LP01, LP11a, and LP11b modes, respectively throughout the C-band. As a result, we found that the insertion loss of the fabricated MUX/DEMUX had a low wavelength dependence and was less than 3.5 dB. We considered that the insertion loss difference between the LP11a and LP11b modes due to the structural imperfection. We believe that the insertion loss can be reduced by optimizing the fabrication process. Figure 11(a), (b), and (c), respectively, show the mode extinction ratios of the LP01 mode to the LP11a or LP11b mode, the LP11a mode to the LP01 or LP11b mode, and the LP11b mode to the LP01 or LP11a mode. Here, the LP11 mode MUX/DEMUXs are connected two-mode fiber of 5m. The mode extinction ratios from the LP01 and LP11a modes were higher than 15 dB in the C-band. The mode extinction ratio of the LP11b mode was higher than 13 dB in the C-band. Since the mode extinction ratio of the LP11 mode MUX/DEMUX depend on the LP11 mode rotator, we consider that the LP11 mode MUX/DEMUX can be improved by using optimized parameter of the LP11 mode rotator [22]. Figure 12 shows the eye patterns under the same signal condition as the previous section. The first, second, and third rows in Fig. 12 are the eye patterns of the LP01, LP11a, LP11b modes, respectively. We confirmed that we could obtain relatively clear eye patterns with our fabricated LP11 mode DEMUX. We found that the eye opening penalties were less than 30% between individual and 3 modes after demultiplexing. We believe that the PLC-based mode MUX/DEMUX with more higher-order mode can be realized by using the AMC and LP11 mode rotator.
Fig. 10 (a) NFPs of fabricated LP11 mode MUX. (b) Insertion losses of LP01 (●), LP11a (○), and LP11b (△) in fabricated LP11 mode MUX.
Fig. 11 (a) Mode extinction ratios of LP01 to LP11a or LP11b mode. (b) Mode extinction ratios of LP11a to LP01 or LP11b mode. (c) Mode extinction ratios of LP11b to LP01 or LP11a mode.
Fig. 12 Eye patterns when inputting signals of individual modes and three multiplexed modes in fabricated DEMUX.
5. Conclusion
We demonstrated a PLC-based mode multi/demultiplexer (MUX/DEMUX) for mode division multiplexed transmission by using an asymmetric mode coupler. We designed and fabricated a three-mode (LP01, LP11a, and LP21a) MUX/DEMUX by using the mode coupling of the LP11b mode to the LP21a mode. We then designed and fabricated a mode MUX/DEMUX with an LP11 mode rotator that can multi/demultiplex the LP01, LP11a, and LP11b modes. Additionally, our fabricated mode MUX/DEMUX achieved the multi/demultiplexing of two degenerate LP11 modes over the C-band. We consider a PLC-based mode MUX/DEMUX to be a promising candidate for achieving MDM transmission.
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