A general design rule of scrambling-type mode (de)multiplexers (mode scramblers) based on silica planar lightwave circuit (PLC) with small mode-dependent-loss (MDL) is presented for a mode-division multiplexing (MDM) system. First, we consider four- and eight-mode scramblers and demonstrate that if the number of modes is 2N, it is possible to construct small-MDL mode scramblers by using Y-branch waveguides and mode rotators. Next, a 6-mode scrambler, which can be used for four linearly polarized (LP) mode transmission in MDM system, is considered, and the MDL is large if Y-branch waveguides are cascaded simply, originating from the radiation loss of unwanted modes at the Y-branch. We propose a 2 + 4-type mode scrambler by combining 2- and 4-mode scramblers and demonstrate that it is possible to design a small MDL 6-mode scrambler.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
In recent years, Internet traffic has been increasing rapidly, and it is important to expand the communication capacity per optical fiber. However, in conventional single-mode fibers, it is difficult to expand the transmission capacity because the optical power that can be input is limited . Therefore, an attention is aimed to MDM transmission , which is one of the space division multiplexing techniques. To realize MDM transmission, a mode multiplexer/demultiplexers (MUX/DEMUX) that excites, multiplexes, and separates multiple modes is required. There are various mode MUXs on various platforms. So far, mode MUXs based on free space optics using phase plates and beam splitter [3–5], fiber devices such as photonic lantern and directional coupler [6–9], and waveguide type devices using silicon waveguide or silica based planar lightwave circuits (PLCs) [10–13] have been proposed. Among them, PLCs have various advantages such as low loss and easy connection with fiber. Recently, a 6-mode MUX  has been realized, in which asymmetric directional couplers (ADCs) are cascaded.
The ADC mode MUX is composed of a narrow waveguide (add waveguide) and a wide waveguide (bus waveguide). The mode conversion is achieved by using a phase-matching between the lower order mode of the add waveguide and the desired higher-order mode of the bus waveguide. However, according to the principle, the transmission spectrum is parabolic, and the transmittance is degraded as it deviates from the central wavelength. Also, the waveguide width of the add waveguide becomes narrower for exciting the higher order modes with large mode order, such as LP21 mode. For example, in a PLC with a height of 10 µm and a relative refractive index difference Δ = 1.0%, there exists six modes in the bus waveguide with the width of 10 µm (LP01, LP11, LP21, and LP02 modes) . For this bus waveguide, the widths of the add waveguides for achieving the phase matching with LP11a, LP21a, and LP02 modes, are 4.0, 2.0, and 1.8 µm, respectively. Therefore, the aspect ratio of the waveguide becomes very large. High aspect ratio waveguides generally have high loss and if it is too large, it is difficult to manufacture. Furthermore, the narrow waveguide width leads to weak fabrication tolerance. Therefore, ADC type mode MUX has a problem for increasing the number of modes for multiplexing.
Recently, considering these problems, PLC-based scrambling-type mode MUX (mode scrambler)  has been proposed. The mode scrambler does not aim at combining the desired mode with high inter-mode extinction ratio as in the conventional ADC mode MUX. Instead, on the premise of multi-input multi-output (MIMO) reception at the receiver, multiple modes are intentionally generated for one input. Therefore, each input signal (usually, fundamental mode) is outputted as a sum of multiple modes with an appropriate ratio. By doing this, it is possible to make all the width of the input waveguides the same, and to avoid the problem of the waveguide width in the ADC type mode MUX mentioned above. In , three mode MUX was demonstrated for the proof-of-concept device. It was also pointed out in  that not only simple insertion loss but also MDL obtained by singular value decomposition of the transfer function of the device is important. For future MDM system, although the number of modes should be increased, the design methodology is unknown for mode scramblers.
In this paper, a general design rule of the small-MDL mode scramblers based on silica PLC is presented. We designed the mode scrambler with 4, 6, and 8 modes to increase the number of modes. First, a 4- and 8-mode scramblers were designed by combining a Y-branch waveguide and a mode rotator. We demonstrate that when the number of modes is 2N, it is always possible to construct small MDL mode scramblers. Next, a 6-mode scrambler, which can be used for four linearly polarized (LP) mode transmission in MDM system, is considered and the MDL is large if Y-branch waveguides are cascaded simply, originating from the radiation loss of unwanted modes at the Y-branch. We propose a 2 + 4 - type mode scrambler by combining 2 and 4 mode scramblers and demonstrate that it is possible to design small MDL 6-mode scrambler.
2. Operation principle and device design
Before going to the design, we define the labelling of modes treated here. Figure 1 shows the field distributions of (a) rectangular waveguide modes, and (b) fiber modes. In the rectangular waveguide mode, when the waveguide cross-section is square (H = W), the E31 and E13 modes are degenerated and the field distributions are like the LP21b and LP02 modes of the fiber mode  due to the hybridization of E31 and E13 modes. Here, we call E31 and E13 modes as LP21b and LP02 modes for H = W although they are not fiber modes.
2.1 4-mode scrambler
Figure 2 shows the structure of the Y cascade 4-mode scrambler. Two Y-branch waveguides are placed in parallel and they are cascaded another Y-branch waveguide. There are four input ports and one output port. When the E11 mode is incident on each input port, the E11 mode and the E21 mode are equally excited (50% : 50%) in the first Y-branch waveguide. The excited E21 mode is 100% converted to the E12 mode by the mode rotator and the inputted E11 mode pass through without conversion . The cross section of the mode rotator is shown in Fig. 2 and (a) trench is formed on top of the waveguide to convert E21, 12 mode. In the second Y-branch waveguide, the E11 mode couples equally to the E11 mode and the E21 mode. The E12 mode couples to the E12 mode and the E22 mode, respectively. These mode transitions are depicted in the bottom panel of Fig. 2. Therefore, it is possible to mix and emit 4 modes with a uniform ratio of 25% at the exit port. The relative refractive index difference is Δ, the width of the Y-branch waveguide of the input port is W1, the width of the mode rotator is W2, the length of the mode rotator is Lr, the length of the Y-branch waveguide is Lb1, Lb2, respectively, the length of the tapered waveguide is Lt, and the parameters of the S-branch waveguide are Sep and Sep2, as shown in Fig. 2. Table 1 shows the structural parameters of the Y cascade 4-mode scrambler. The bending radius of Y1 and Y2 is 25.0 mm. These structural parameters were optimized to obtain low-loss structure, using the 3D scalar finite element beam propagation method (3D-SFE-BPM) .
Here, the general characteristics of the Y-branch waveguide are explained. Figure 3 shows the operations of the Y-branch waveguide, when (a) E11, (b) E12, and (c) E21 are inputted to the Y-branch waveguide. Figure 4 shows dispersion curves of the PLC waveguide. Figure 4 shows input waveguide (w1 = 5.1 µm) supports E11, E12, E21, E13 modes, and the output waveguide (w2 = 10.1 µm) supports E11, E12, E21, E13, E22, E31 modes. When the E11 mode is inputted to one of the input waveguides, as shown in Fig. 3(a), the E11 mode and the E21 mode are excited at a ratio of 1:1 [18,19]. Next, when the E12 mode is inputted (Fig. 3(b)), the E12 mode and the E22 mode are excited at a ratio of 1:1 as in the E11 mode [18,19]. Finally, when the E21 mode is inputted (Fig. 3(c)), E31 and E41 modes are equally excited. However, in the case of a 4-mode scrambler, E41 modes is not supported by the output waveguide, resulting in loss. For this reason, in the 4-mode scrambler, the loss is reduced by converting the E21 mode to the E12 mode in the mode rotator before the second Y-branch waveguide.
Figure 5 shows the calculated field distribution when the E11 mode is inputted to Port4. From Fig. 5, it can be confirmed that the incident E11 mode excites the E21 mode at the junction of Y1, and the E21 mode is converted to the E12 mode in the rotator. At Y2, four modes are excited. Figure 6 shows the calculated transmission of each mode in the output port when the E11 mode is incident on each port. From Fig. 6, it can be confirmed that the four modes are excited with almost equally and low loss, regardless of the input port. Also, calculated MDL  from the transfer matrix of the device is 0.18 dB and very small. Here, MDL is calculated as follows. The transmission matrix is defined as
2.2 8-mode scrambler
Next, we designed an 8-mode scrambler (E11, E21, E12, E31, E22, E41, E32, and E42 mode), in which two 4-mode scramblers are placed in parallel and cascaded to a Y-branch waveguide. Figure 7 shows the schematic of the 8-mode scrambler. The E11, E21, E12, and E22 modes are outputted from the 4-mode scrambler, and they are inputted to the Y-branch waveguide. From the operation principle of the Y-branch waveguide shown in Fig. 3, the E31, E41, E32, and E42 mode are newly excited. The mode transitions at second Y-branch waveguide is shown in the right panel of Fig. 7. As a result, 8 modes are mixed and outputted. Table 2 shows the structural parameters of the 8-mode scrambler optimized by BPM. The height, Δ, bending radius of Y branch waveguide, and other parameters of the waveguide are the same as for the 4-mode scrambler. In this case, the E21 mode output from one of the 4-mode scramblers excites the E31 mode and the E41 mode in the last Y branch waveguide as shown in Fig. 3(c). But it is not lost because it is supported by the output waveguide. The same is true for the other modes. Figure 8 shows the field distribution when E11 mode is launched to Port 1. The same is true for the other modes. Figure 9 shows the calculated transmission of each mode in the output port when the E11 mode is incident on each port of the 8-mode scrambler. The loss of each port is about − 0.91 dB, and all 8 modes are mixed almost equally with low loss. The calculated MDL is 1.15 dB, and again, the value is small.
From these results, if the number of modes is 2N, we can always construct small-MDL mode scrambler by cascading Y-branch waveguides with the help of the mode rotator. The widths of the input waveguides are all the same and the problem of ADC mode MUX can be avoided.
2.3 3×2 = 6-mode scrambler
In the fiber-based MDM transmission system, the communication is performed using few-mode fiber (FMF). Due to the degeneracy of the high-order mode in the fiber, the number of modes in the fiber without considering the polarization changes discontinuously as 1, 3, 6, and 10 (1, 2, 4, and 6LP modes). Naturally, the same multiplexing number is required for the MUX. Therefore, for example, for the 6-mode scrambler, it is impossible to use the mode scrambler configuration described in the previous section. In this section, we try to design a 6-mode scrambler by using two 3-mode scramblers proposed in  cascaded with a Y-branch waveguide. Figure 10 shows the schematic of (a) the 3×2 = 6-mode scrambler and (b) the 3-mode scrambler section. The 3-mode scrambler proposed in  is placed parallel and joined by an S-shaped Y-branch waveguide. It should be noted that the output powers of three modes are not uniform in the 3-mode scrambler. At the output, the tapered waveguide is placed to convert waveguide Epq mode to fiber LP mode as described follows.
In the 3-mode scrambler, the input E11 mode is converted to the sum of E11, E21, and E12 modes. At the junction of the S-shaped Y-branch waveguide, the E21 mode is coupled to E31 and E41 modes as shown in Fig. 3, and the E41 mode is lost in this case. In the last tapered waveguide at the output port, the E31 mode is coupled to the LP21b and LP02 modes , and the 6 modes (E11, E21, E12, E22, LP21b like, LP02 like modes) are mixed and outputted. W4 and W5 are the widths of the input and output ports of the S-shaped branch waveguide, W6 is the width of the tapered waveguide at the edge of the chip, Ls is the length of the S-shaped branch waveguide, and lengths of the tapered waveguides are Ltp1 and Ltp2. Table 3 shows the optimized structural parameters of the 3×2 = 6-mode scrambler designed by BPM. The bending radius of last Y branch waveguide is 28.8 mm. Figure 11 shows the field distribution when E11 mode is launched to Port 1. The radiated fields at S-shaped Y-junction can be seen. Figure 12 shows the transmission of each mode of the 3×2 = 6-mode scrambler for different input ports. From Fig. 12, it can be confirmed that 6 modes are mixed and emitted, however, the loss and the mode excitation ratio for each input port are not uniform. This comes from the fact that the output powers of three modes are not uniform in the 3-mode scrambler. Especially, LP21b and LP02 modes are hardly excited for Port 3 and 6 input. The calculated MDL is 19.8 dB, which is very large compared to the 4-, 8-mode scramblers. It is considered that this is caused by the fact that the transfer matrix of the device is quite different from the unitary matrix due to the loss and the nonuniformity of the output mode power.
2.4 4 + 2 = 6-mode scrambler
From the discussion in section 2.2, the 2N-mode scrambler can be configured with small MDL. Therefore, to construct a small MDL 6-mode scrambler, we consider the combination of 4-mode and 2-mode scrambler (simple Y-branch waveguide). Figure 13 shows the schematics of (a) the proposed 4 + 2 = 6-mode scrambler, (b) E31 → E13 mode converter, and (c) grating-type E11 → E21 converter. The 4-mode and the 2-mode scramblers are connected by an ADC, and the operating principle of the 4-mode scrambler is the same as in section 2.1. The E11 mode incident on ports 5 and 6 excites the E11 and E21 modes equally at the 2-mode scrambler (lower Y branch). Only the E21 mode is multiplexed to the 4-mode scrambler side as the E31 mode in the ADC-1. The combined E31 mode is converted to the E13 mode by the adiabatic tapered type mode converter  shown in Fig. 13(b). At the same time, the E11 mode left in the lower waveguide is converted to the E21 mode by the grating-type mode converter shown in Fig. 13(c). The converted E21 mode is multiplexed to the 4-mode scrambler side as the E31 mode by the ADC-2, and 6 modes (E11, E21, E12, E22, E31, E13 modes) are multiplexed. Finally, the E31 and E13 modes are converted into the LP21b mode and the LP02 mode by making the shape of the waveguide square by using a steep taper waveguide. As a result, six modes of E11, E21, E12, E22, LP21b, and LP02, which are like the fiber mode, can be multiplexed and outputted from the bus waveguide. Table 4 shows the structural parameters of the 4 + 2 = 6-mode scrambler designed by BPM. The bending radius of the Y branch (port 5, 6) is 25.0 mm, and the structural parameters of ADC-2 are the same as ADC-1.
Figure 14(a) shows a field distribution after 4-mode scrambler part when the light is launched to port 1. It is shown that the signal is propagated without being coupled to the lower waveguide side in the ADC-1. Namely, we do not have to care about the output light from the 4-mode scrambler. Figure 14(b) shows field distribution after 4-mode scrambler part when the light is launched to port 5. E11 and E12 modes are equally excited and only the E21 mode couples to the upper waveguide of the ADC-1, and the E11 mode remains in the lower waveguide. Figure 15 shows the transmission of each mode for each input port of the 4 + 2 = 6-mode scrambler. When E11 mode is input to Ports 1 to 4, the operation is the same as that of 4-mode scrambler. When E11 mode is input to Ports 5 and 6, LP21b mode and LP02 mode are mixed and outputted. The loss is small regardless of the input port, and the difference in total output power is also very small compared to the case of the 3×2 = 6-mode scrambler. The calculated MDL is only 0.48 dB, and the small MDL 6 mode scrambler can be designed by combining the 2N-mode scramblers. Although there is a large difference in the output modes excited by Port 1 to 4 or Port 5 to 6 input, the unitarity of the entire device is maintained, resulting in small MDL. Finally, the tolerance of the Y-junction waveguide is commented. The tolerance to the waveguide width is relatively strong compared with ADC since the Y-junction waveguide is adiabatic device. However, the fabrication imperfection of the Y-junction geometry increases the loss .
2.5 Wavelength dependence
Here, the wavelength dependence of 4 + 2 = 6-mode scrambler is investigated. First, we consider the wavelength dependence of the mode scramblers. Figure 16 shows the MDL spectra of 4-mode, 3×2 = 6-mode, and 4 + 2 = 6-mode scramblers. The MDL of 3×2 = 6-mode scrambler is very large in the wavelength range of 1.5 to 1.6 µm. There is almost no wavelength dependence in 4-mode scrambler. This is because in the 4-mode scrambler, there are no wavelength sensitive components. The spectrum of 4 + 2 = 6-mode scrambler is slightly wavelength dependent. We consider the physical reason of the wavelength dependence. Figure 17 shows the total output power spectra of 4 + 2 = 6-mode scrambler for different input ports. For input port 1 to 4, the losses are very small and almost wavelength insensitive. This is because the input ports 1 to 4 are related to 4-mode scrambler. On the other hand, the output powers for the input ports 5 and 6 are wavelength dependent. Therefore, the wavelength dependences of the components ADC-1,-2, E31 → E13 mode converter, and grating-type E11 → E21 may be large. Figure 18 shows the output power spectra of these components. In these components, the wavelength dependence of grating-type E11 → E21 converter is relatively large. Therefore, by replacing the grating-type converter with more wavelength insensitive components , the wavelength dependence of 4 + 2 = 6-mode scrambler can be reduced further.
We presented a design method of small-MDL mode scramblers aiming at increasing the number of multiplexing modes. From the design results of the 4 and 8 mode scramblers, it was shown that it is possible to construct a mode scrambler, whose MDL is always small when the number of multiplexing modes is 2N. In addition, in the case of 6-mode scrambler, it is clarified that low loss and small MDL mode scrambler can be configured by combining 4 and 2 mode scramblers.
The authors declare no conflicts of interest.
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