PLC-based LP 11 mode rotator for mode-division multiplexing transmission

: A PLC-based LP 11 mode rotator is proposed. The proposed mode rotator is composed of a waveguide with a trench that provides asymmetry of the waveguide. Numerical simulations show that converting LP 11a (LP 11b ) mode to LP 11b (LP 11a ) mode can be achieved with high conversion efficiency (more than 90%) and little polarization dependence over a wide wavelength range from 1450 nm to 1650 nm. In addition, we fabricate the proposed LP 11 mode rotator using silica-based PLC. It is confirmed that the fabricated mode rotator can convert LP 11a mode to LP 11b mode over a wide wavelength range.


Introduction
An expansion of the transmission capacity per fiber is needed because of the rapid growth of Internet traffic in the optical fiber network. Mode-division multiplexing (MDM) has attracted attention to obtain a much larger transmission capacity. The mode (de)multiplexer is an important component to realize MDM transmission. Various mode (de)multiplexers based on free-space optics [1][2][3], fiber coupler and a long-period fiber bragg grating (LPFBG) [4,5], photonic lantern [6], adiabatically-tapered fiber [7], and planar lightwave circuit (PLC) [8,9] have been demonstrated. PLC-based mode (de)multiplexer has unique advantages including a low insertion loss, relatively low wavelength dependence, a small size, and high mass productivity due to the adoption of mature semiconductor manufacturing technologies such as photolithography and ion etching. The PLC-based mode (de)multiplexer is one of the promising mode (de)multiplexers for the purpose of mass production. We have proposed the PLC-based threemode multiplexer which can multiplex and excite LP 01 , LP 11a , and LP 21 modes [10]. The PLC-based mode multiplexer which can excite LP 11b mode is required to realize a mode (de)multiplexer which can multiplex LP 01 , LP 11a , LP 11b , and LP 21 modes. However, the PLCtype mode multiplexer which can excite LP 11b mode has not been presented because it is difficult to excite electronic waveguide modes E mn (n ≥ 2) like LP 11b mode in the same plane.
In this paper, we design and fabricate a PLC-based LP 11 mode rotator for the excitation of LP 11b mode [11]. Numerical simulations show that converting LP 11a mode to LP 11b mode can be achieved with high conversion efficiency (more than 90%) over a wide wavelength range from 1450 nm to 1650 nm. Numerical simulations also show that the LP 11 mode rotator can convert LP 11b mode to LP 11a mode, has little polarization dependence, and has a good fabrication tolerance. We finally fabricate the proposed LP 11 mode rotator using silica-based PLC and confirm that the fabricated LP 11 mode rotator can convert LP 11a mode to LP 11b mode over a wide wavelength range. Figure 1 shows the structure of the PLC-based LP 11 mode rotator. The proposed mode rotator is composed of a waveguide with a trench that provides asymmetry of the waveguide as shown in Fig. 1. The degree of the asymmetry can be controlled by changing the trench position t, the trench width s, and the trench depth d. By properly designing the trench parameters, two orthogonal LP 11 modes whose optical axes are rotated by around 45° with respect to the x-and y-axes propagate in the waveguide with the trench as shown in Figs. 2(a) and 2(b), and the two orthogonal LP 11 modes are equally excited and propagated with different propagation constants, β 1 and β 2 , in the waveguide with the trench when LP 11a (LP 11b ) mode is launched. By setting the length of the waveguide with the trench to a half beat-length, π/(β 1 -β 2 ), LP 11a (LP 11b ) mode is rotated into LP 11b (LP 11a ) mode.  In this paper, we assume that the proposed mode rotator is based on silica-based PLC with a relative refractive index difference Δ between the core and cladding of 0.45% [10], and the waveguide width w and height h are respectively set to w = 11.3 μm and h = 11.0 μm in order to reduce the coupling loss between PLC waveguide and a two-mode fiber to be connected. One can choose other values for Δ, w, and h as you desire.

Principle and design
Next, we choose design parameters related to the trench such as the trench position t, width s, and depth d. When t, d, and s are chosen to large values, the device length tends to be short because the difference of the propagation constants, β 1 and β 2 , between two orthogonal LP 11 modes becomes larger. However, crosstalk to undesired modes such as LP 01 mode and undesired back reflections become higher when t, d, and s are chosen to large values due to the mode field mismatch at the boundary between the waveguides with and without the trench. Thus, t, d, and s should be chosen to small values in order to suppress the crosstalk to undesired modes. In this paper, we chose target parameters of t = 2.0 μm and s = 1.5 μm for easy fabrication.  Fig. 2 to be equivalent. Figure 3(b) shows t dependence of the normalized overlap integral of LP 11a mode with 1st and 2nd LP 11 modes at a wavelength of 1550 nm with d = 5.4 μm and s = 1.5 μm, and Fig. 3(c) shows s dependence of the normalized overlap integral of LP 11a mode with 1st and 2nd LP 11 modes at a wavelength of 1550 nm with d = 5.4 μm and t = 2.0 μm. It can be seen that the normalized overlap integral of LP 11a mode with 1st and 2nd LP 11 modes can be controlled by changing t, d, and s. Finally, the length of the mode rotator L is set to L = 1.46 mm, which equals the half beat-length of the two orthogonal LP 11 modes shown in Fig. 2. The designed parameters are shown in Table 1. It has been numerically confirmed that the undesired back reflection at the boundary between the waveguides with and without the trench is lower than −30 dB when the designed parameters in Table 1 Fig. 4, we can see that LP 11a (LP 11b ) mode is converted into LP 11b (LP 11a ) when L equals 1.46 mm, and there is little polarization dependence because two lines for x-and y-polarization almost overlap each other. The polarization dependence in the PLC-based mode rotator with small index difference between core and cladding is negligibly small, however, it may become large if the core-cladding index difference increases.   Figure 5 shows the calculated wavelength dependence of the LP 11 mode rotator when (a) LP 11a mode or (b) LP 11b mode is launched into the mode rotator with the design parameters shown in Table 1. From Fig. 5, the wavelength dependence of the conversion efficiency is negligible (more than 90% over a wavelength range from 1.45 μm to 1.65 μm), and the crosstalk to the input LP 11 mode is less than −20 dB over a wavelength range from 1.5 μm to 1.6 μm for both polarizations. Figure 6 shows the fabrication tolerance of the LP 11 mode rotator when LP 11a mode is launched at a wavelength of 1550 nm. The conversion efficiency is insensitive to fabrication errors and the crosstalk to the input LP 11 mode is less than −20 dB when t, d, and s change by ± 0.3 μm, ± 0.4 μm, and ± 0.1 μm, respectively. The actual fluctuation through PLC fabrication will depend on a fabrication process and it is usually in the order of submicron. Next, we consider reducing the crosstalk to undesired modes such as LP 01 mode and the input LP 11 mode. Figure 7 shows the calculated wavelength dependence of the normalized output power of LP 01 , LP 11a , and LP 11b modes when (a) LP 01 mode, (b) LP 11a mode, or (c) LP 11b mode is launched into the mode rotator with the design parameters shown in Table 1. From Fig. 7(a), LP 01 mode is output (without polarization conversion) when LP 01 mode is input. This is because the optical axis for the LP 01 mode is not rotated by the small trench. As shown in Fig. 7, the crosstalk to the undesired modes is less than −16 dB over a wavelength range from 1.45 μm to 1.65 μm.

Characteristics
The crosstalk can be improved by making the parameters related to the trench smaller values. Figure 8 shows the calculated wavelength dependence of the normalized output power of LP 01 , LP 11a , and LP 11b modes for the case of t = 1.0 μm, d = 4.3 μm, and L = 1.92 mm (the other parameters are not changed) when (a) LP 01 mode, (b) LP 11a mode, or (c) LP 11b mode is launched. From Figs. 7 and 8, we can see that the crosstalk to the undesired modes is reduced from −16 dB to −18 dB when the trench parameters are set to be smaller values. Figure 9 shows the calculated wavelength dependence of the normalized output power of LP 01 , LP 11a , and LP 11b modes for the case of t = 0 μm, d = 3.9 μm, and L = 2.99 mm (the other parameters are not changed) when (a) LP 01 mode, (b) LP 11a mode, or (c) LP 11b mode is launched. The crosstalk to the undesired modes is reduced from −16 dB to −23 dB when the trench parameters are set to be smaller values as shown in Figs. 7 and 9.   Figure 10 shows the fabricated LP 11 mode rotator using silica-based PLC with the target structural parameters shown in Table 1. All components shown in Fig. 10 are fabricated on a chip. Figure 11 shows the experimental setup for the LP 11 mode rotator. In the experiment, we observed near field patterns of output light through a waveguide with or without the trench when LP 11a mode is input. LP 11a mode should be output when LP 11a mode is input to the waveguide without the trench. On the other hand, rotated LP 11 mode (ideally LP 11b mode) should be output when LP 11a mode is input to the waveguide with the trench. We used the PLC-based two-mode multiplexer [8] to excite LP 11a mode. Table 2 shows the near field patterns of output light through the waveguide with (the left column of Table 2) or without (the right column of Table 2) the trench when LP 11a mode is input at each wavelength. The reason of rotation of LP 11 mode with the change of wavelength is because the optimum half beat-length for 90 degree rotation is depending on the wavelength. From Table 2, we can confirm that the fabricated LP 11 mode rotator converts LP 11a mode to LP 11b mode over a wide wavelength range from 1460 nm to 1600 nm.

Fabrication
We can obtain PLC-based three-mode (de)multiplexer for LP 01 , LP 11a , and LP 11b modes when we utilize the proposed LP 11 mode rotator and the two-mode (de)multiplexer [8]. Figure  12 illustrates the schematic drawing of the PLC-based three-mode multiplexer that can multiplex and demultiplex LP 01 , LP 11a , and LP 11b modes. The three-mode multiplexer consists of two PLC-based two-mode multiplexers [8] and the proposed LP 11 mode rotator. Two-mode multiplexers are used for excitation of LP 11a mode. All components can be fabricated on a chip. LP 11b , LP 01 , and LP 11a modes are output when LP 01 modes are launched to port 1, port 2, and port3, respectively.  12. Schematic drawing of PLC-based three-mode multiplexer that can multiplex and demultiplex LP 01 , LP 11a , LP 11b modes. The three-mode multiplexer consists of two PLC-based two-mode multiplexers and the proposed LP 11 mode rotator. Two-mode multiplexers are used for excitation of LP 11a mode.

Conclusion
We have designed and fabricated the PLC-based LP 11 mode rotator for the excitation of LP 11b mode. Numerical simulations showed that converting LP 11a mode to LP 11b mode could be achieved with high conversion efficiency (more than 90%) over a wide wavelength range from 1450 nm to 1650 nm. Numerical simulations also showed that the LP 11 mode rotator could convert LP 11b mode to LP 11a mode, had little polarization dependence, and had a good fabrication tolerance. It was clarified that the crosstalk to the undesired modes could be suppressed by making the trench smaller. We finally fabricated the proposed LP 11 mode rotator using silica-based PLC and confirmed that the fabricated LP 11 mode rotator can convert LP 11a mode to LP 11b mode over a wide wavelength range. We can realize the PLCbased three-mode (de)multiplexer for LP 01 , LP 11a , and LP 11b modes when we utilize the proposed LP 11 mode rotator and the two-mode (de)multiplexer [8].