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Abstract
We propose a broadband silicon four-mode multi/demultiplexer which consists of three asymmetric directional couplers, and the asymmetric directional couplers were designed by a wavefront matching method to operate as mode multi/demultiplexers for TE1, TE2, and TE3 modes, respectively. Simulated results show that the −0.5-dB bandwidths of normalized transmission of the couplers designed by a wavefront matching method are 112, 114, and 134 nm, respectively. Those for the conventional couplers are 80, 72, 65 nm, respectively. The superiority of asymmetric directional couplers designed by a wavefront matching method are experimentally demonstrated. In the additional investigation, ultrabroadband tapered asymmetric directional couplers are theoretically demonstrated.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the increasing demand for data communication, enhancing the transmission capacity and reducing the power consumption are desired for optical interconnects. Silicon photonics is a promising technology because silicon chips are inexpensive to fabricate via complementary metal–oxide–semiconductor (CMOS) production methods [1]. So far, several types of multiplexing technologies, such as polarization division multiplexing, wavelength division multiplexing (WDM), and mode division multiplexing (MDM), have attracted much attention to increase the capacity [2,3]. Although WDM systems require multiple laser sources, MDM systems do not require additional laser sources. Furthermore, dramatic enlargement of capacity can be realized by the combined use of WDM and MDM technologies [4–7]. Many silicon photonics mode-controlling devices have been proposed enthusiastically. Mode multi/demultiplexers (MUX/DEMUXs) play a key role in MDM systems. To date, various types of mode MUX/DEMUXs have been proposed based on asymmetric directional couplers (ADCs) [4,6–9], multimode interference couplers [5,10], and asymmetric Y-junctions [11,12]. Among them, ADCs are most frequently used to design mode MUX/DEMUXs because ADCs are easy to design and increase the number of channels. However, they have relatively large wavelength dependence, which is not preferable for mode MUX/DEMUXs when they are used in WDM-MDM systems. One of the effective approaches to overcome this problem is the use of an optimization algorithm. Recently, silicon waveguide devices automatically designed using an optimization algorithm, such as direct binary search [13], topology optimization [14], and wavefront matching (WFM) method [15–21], have been reported. We have developed a full-vector WFM method and proposed WFM-designed polarization-controlling and mode-controlling devices [17–21] recently. We presented the design of a broadband four-mode MUX/DEMUX using cascaded WFM-designed ADCs [20], and we presented experimental demonstration of the four-mode MUX/DEMUX at an international conference [21].
In this paper, we propose a silicon photonics four-mode MUX/DEMUX for MDM systems. Although preliminary reports of this work were presented at international conferences [20,21], detailed theoretical design together with experimental data of the proposed mode MUX/DEMUX are described to demonstrate comprehensive results of this work. The device includes three WFM-designed ADCs operating as a MUX/DEMUX for TE1, TE2, and TE3 modes, respectively. In order to demonstrate the effectiveness of the WFM method, we also designed a four-mode MUX/DEMUX which includes three conventional (manually designed) ADCs operating as a MUX/DEMUX for TE1, TE2, and TE3 modes, respectively. The designed devices were fabricated on a silicon-on-insulator platform with 210-nm thick silicon layer. A photolithography-based standard CMOS technology was used. Simulated results show that the −0.5-dB bandwidths normalized by each maximum transmission are 112, 114, and 134 nm for WFM-designed TE0-TE1, TE0-TE2, and TE0-TE3 ADCs, respectively, whereas those for conventional ADCs are 80, 72, and 65 nm, respectively. Characteristics of the WFM-designed ADCs were greatly improved compared with the conventional ADCs in long-wavelength range. We confirmed that the four-mode MUX/DEMUX consists of the WFM-designed ADCs also realized broadband operation from measurement results. In addition, we conducted further investigation on the design of broadband ADCs. A tapered ADC was used as an initial waveguide structure, and ultrabroadband transmission spectra were obtained.
2. Device design
Figure 1(a) shows the schematic configuration of the four-mode MUX. It includes three ADCs and two adiabatic tapers. They are cascaded to multiplex four channels as TE0, TE1, TE2, and TE3 modes in the bus waveguide. The core width of the access waveguides was set to 400 nm. The core widths of the bus waveguides of the three ADCs were set to 840, 1280, 1710 nm, respectively. The widths of the bus waveguides were determined to roughly match the effective index of the TE0 mode in the access waveguides and desired higher-order modes in the bus waveguides, respectively. The bending radius of the 90° bends was set to 5 µm. Figure 1(b) shows the initial waveguide structure of an ADC before using the WFM method. The WFM method was used to optimize the waveguide outline of the access waveguide in the coupling region. Note that only the sides of the access waveguide are changed by the WFM optimization, whereas the coupling length is fixed. The principle of the WFM method is described in [15–18]. In the optimization using a WFM method, a refractive-index distribution is changed according to the following function:
Fig. 1. (a) Schematic configuration of the four-mode MUX. (b) Initial waveguide structure of an ADC before using the WFM method.
Figure 2 shows the improvement of the (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 ADCs as a function of the WFM iteration count. Performance of each ADC was almost improved in the first several iterations. Optimum waveguide structures were selected according to the average transmission of the five wavelengths, and those were obtained after 19, 30, and 17 iterations for TE0-TE1, TE0-TE2, and TE0-TE3 ADCs, respectively. Figure 3 shows the optimum waveguide outlines of the WFM-designed (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 ADCs. The average gap widths of the WFM-designed TE0-TE1, TE0-TE2, and TE0-TE3 ADCs were 244, 247, and 247 nm, respectively. The minimum gap widths of the WFM-designed TE0-TE1, TE0-TE2, and TE0-TE3 ADCs were 190, 200, and 190 nm, respectively. Please note that the lengths with the gap width of 190 nm is 0.6 µm out of 66.6 µm for the WFM-designed TE0-TE1 ADC, and 0.4 µm out of 108.2 µm for the WFM-designed TE0-TE3 ADC.
Fig. 2. Improvement of the (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 ADCs as a function of the WFM iteration count.
Fig. 3. Optimum waveguide outlines of the WFM-designed (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 ADCs.
In order to demonstrate the effectiveness of the WFM method, we manually designed conventional ADCs for comparison. The core widths of the bus waveguides of the conventional TE0-TE1, TE0-TE2, and TE0-TE3 ADCs were set to 837, 1275, 1713nm, respectively. The lengths of coupling region of the conventional TE0-TE1, TE0-TE2, and TE0-TE3 ADCs were set to 18.2, 22.0, 25.2 µm, respectively. The lengths were smaller than those of the WFM-designed ADCs. If the coupling lengths become large, mode coupling between access and bus waveguides are repeated. This results in the narrow band operation of the conventional ADCs. Therefore, the lengths are optimal for the broadband operation of the conventional ADCs. The gap widths of the conventional ADCs were set to 200 nm. In terms of operation wavelength range, the narrower gap width is preferable for the conventional ADCs. In order to make a fair comparison, the WFM-designed ADCs should not have the advantage for the gap width, which affect to the operation wavelengths. Therefore, the gap width of 250 nm was used for the initial waveguide structure of the WFM-designed ADCs, and the gap width of 200 nm was used for the conventional ADCs. In this condition, the comparison between the WFM-designed and conventional ADCs is disadvantageous for the WFM-designed ADCs.
3. Device fabrication and measured results
The WFM-designed ADCs, four-mode MUX/DEMUX consists of the WFM-designed ADCs, conventional ADCs, and four-mode MUX/DEMUX consists of the conventional ADCs were fabricated by a standard CMOS technology. A photolithography (KrF, 248 nm) was used in the lithography process. Figure 4 shows our measurement setup. The TE0 mode is launched into a silicon chip through an inverse taper spot size converter [22], and the output TE0 mode is measured by an optical spectrum analyzer. We used two tunable lasers (1450–1500 nm and 1500–1650 nm). Since a finite time is necessary to tune the fiber position, measured spectra shown in paper have some discontinuities at the wavelength of 1500 nm. Figure 5 shows the microscope pictures of the fabricated four-mode MUX/DEMUX consists of the WFM-designed ADCs. The four-mode MUX/DEMUX consists of the conventional ADCs were also fabricated in the same layout.
Fig. 5. Microscope pictures of the fabricated four-mode MUX/DEMUX consists of the WFM-designed ADCs.
Figure 6 shows the (a) layout of the fabricated ADCs, and (b) definition of T and XT in Fig. 7. T denotes the transmission of the ideal higher-order mode in the bus waveguide, and XT denotes the transmission of the TE0 mode in the access waveguide. Figure 7 shows the simulated (dashed lines) and measured (solid lines) transmission spectra of (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 ADCs. The 3D finite-element method (FEM) was used for calculations [23,24]. The calculations were carried out in the layout shown in Fig. 6(b). Measured results were normalized by a transmission spectrum of straight waveguide fabricated in the same chip. For multiplexing operation shown as T, the normalized values were divided by two because the normalized values include both multiplexing and demultiplexing operations. The transmission spectra of the WFM-designed ADCs are very flat in the whole wavelength range (1450–1650 nm), whereas the transmission spectra of the conventional ADCs are parabolic. Although the WFM-designed and conventional ADCs have almost the same performance in the short-wavelength range, the great superiority of the WFM-designed ADCs are observed in long-wavelength range. The maximum transmissions of conventional TE0-TE1, TE0-TE2, and TE0-TE3 ADCs are 0.71, 0.47, and 0.81 dB larger than those of WFM-designed ADCs from the simulated results. In terms of the bandwidth, for the WFM-designed ADCs, the −0.5-dB bandwidths normalized by each maximum transmission are 112, 114, and 134 nm for TE0-TE1, TE0-TE2, and TE0-TE3 ADCs, respectively, whereas those for conventional ADCs are 80, 72, and 65 nm, respectively. XTs are reduced for WFM-designed ADCs. For the WFM-designed TE0-TE3 ADC, the spectrum of operation for TE3 mode (green solid line in Fig. 7(c)) has unexpected ripples from 1550 nm to 1600 nm. The ripples are caused by the interference between TE3 and TE4 modes. It is avoidable by adjusting the width of the multimode waveguide between the 4-mode MUX and 4-mode DEMUX to cut off TE4 mode.
Fig. 7. Simulated (dashed lines) and measured (solid lines) transmission spectra of (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 ADCs.
Figure 8 shows the measured transmission spectra of the four-mode MUX/DEMUX consists of the (a–d) WFM-designed and (e–h) conventional ADCs. TE0 mode was launched from (a, e) I1, (b, f) I2, (c, g) I3, and (d, h) I4, respectively. I1-O4, I2-O3, I3-O2, and I4-O1 correspond to the operations of multiplexing and demultiplexing for TE2, TE0, TE1, and TE3 modes, respectively. Maximum transmission curves in Figs. 8(a, e), (b, f), (c, g), and (d, h) correspond to TE2, TE0, TE1, and TE3 mode operations, respectively. The transmission spectra of the four-mode MUX/DEMUX consists of the WFM-designed ADCs are very flat, especially in the long-wavelength range as simulated, showing the usefulness of the WFM method.
Fig. 8. Measured transmission spectra of the four-mode MUX/DEMUX consists of the (a–d) WFM-designed and (e–h) conventional ADCs.
4. WFM-designed tapered ADC
Tapered ADCs have been used for polarization-controlling and mode-controlling devices to enhance robustness to the fabrication error of waveguide widths, which is the weak point of conventional ADCs [8,25,26]. In addition to such feature, transmission spectra of tapered ADCs are flatter than conventional ADCs. To achieve further broadband operation of ADCs, a tapered ADC was used as an initial waveguide structure. Ultrabroadband multiplexing operation of WFM-designed tapered ADCs are shown in this section.
Figure 9 shows the schematic configuration of a tapered ADC. The access waveguide of the tapered ADC has 90° bends before and behind the coupling region as same as the ADCs shown in Fig. 1(a). The design region is surrounded by the red dashed frame. The WFM optimization was applied to the one side of the access waveguide. Therefore, the gap width between the access and bus waveguides is not changed. The core width of the access waveguide was set to 400 nm. The core widths at the start and end points of the bus waveguides (win and wout) are described in Table 1. The bending radius of the 90° bends was set to 5 µm. The gap width between the access and bus waveguides were set to 200 nm. The lengths of the coupling region were set to 40, 50, and 90 µm for TE0-TE1, TE0-TE2, and TE0-TE3 tapered ADCs, respectively. To achieve broadband operation of tapered ADCs, seven wavelengths (1470, 1490, 1510, 1530, 1550, 1570, and 1590 nm) were considered in the WFM optimization.
Table 1. Core Widths at the Start and End Points of Bus Waveguides.
Figure 10 shows the improvement of the (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 ADCs as a function of the WFM iteration count. The average and minimum transmissions of the seven wavelengths are shown. The insets show the transmissions of the seven wavelengths. Optimum waveguide structures were selected according to the minimum transmission of the seven wavelengths, those were obtained after 10, 6, and 29 iterations for TE0-TE1, TE0-TE2, and TE0-TE3 tapered ADCs, respectively. Conventional tapered ADCs were also designed for comparison. The core widths at the start and end points of the bus waveguides are the same with the WFM-designed tapered ADCs. The lengths of coupling region were determined to operate around the wavelength of 1550 nm. Then, the lengths of coupling region were 50, 60, and 65 µm for the conventional TE0-TE1, TE0-TE2, and TE0-TE3 tapered ADCs, respectively. Figure 11 shows the optimum waveguide outlines of the WFM-designed (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 tapered ADCs, and Fig. 12 shows the transmission spectra of the conventional and WFM-designed (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 tapered ADCs. The calculations were carried out in the layout shown in Fig. 9. The transmission spectra of the WFM-designed and conventional ADCs shown in Fig. 7 are plotted together for comparison. For T, −0.5-dB operations were observed over 155, 144, 118 nm for the WFM-designed TE0-TE1, TE0-TE2, and TE0-TE3 tapered ADCs, respectively, whereas those for the conventional tapered ADCs were 42, 54, and 79 nm, respectively. Although the WFM-designed ADCs which do not have tapered structures have flat transmission spectra and relatively large insertion losses, the WFM-designed tapered ADCs achieved both low-loss and broadband operations. The WFM-designed tapered ADCs are also superior to the others for XT in the wide wavelength range. Figure 13 shows the field distributions |Hy| of the WFM-designed (a–c) TE0-TE1, (d–f) TE0-TE2, and (g–i) TE0-TE3 tapered ADCs at the wavelengths of 1510, 1550, and 1590 nm. Efficient multiplexing operations were obtained in the wide wavelength range. Finally, comparison of operation wavelength ranges among conventional ADCs, WFM-designed ADCs, conventional tapered ADC, and WFM-designed tapered ADCs are shown in Table 2. We compared in the wavelength range from 1450 to 1650 nm. Low-loss and ultrabroadband operations of the WFM-designed tapered ADCs were achieved for all modes. Comparison of coupling lengths among conventional ADCs, WFM-designed ADCs, conventional tapered ADC, and WFM-designed tapered ADCs are shown in Table 3. The coupling lengths of the WFM-designed tapered ADCs are smaller than the WFM-designed ADCs, whereas operation wavelength ranges of the WFM-designed tapered ADCs are superior to any other ADCs. The use of a tapered ADC as an initial structure is effective to design broadband mode MUX/DEMUXs.
Fig. 10. Improvement of the (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 ADCs as a function of the WFM iteration count. The average and minimum transmissions of the seven wavelengths are shown. The insets show the transmissions of the seven wavelengths.
Fig. 11. Optimum waveguide outlines of the WFM-designed (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 tapered ADCs.
Fig. 12. Transmission spectra of the conventional and WFM-designed (a) TE0-TE1, (b) TE0-TE2, and (c) TE0-TE3 tapered ADCs. The transmission spectra of conventional and WFM-designed ADCs shown in Fig. 7 are plotted together for comparison.
Fig. 13. Field distributions |Hy| of the WFM-designed (a–c) TE0-TE1, (d–f) TE0-TE2, and (g–i) TE0-TE3 tapered ADCs at the wavelengths of 1510, 1550, and 1590 nm.
Table 2. Comparison of Operation Wavelength Ranges Among Conventional ADCs, WFM-designed ADCs, Conventional Tapered ADCs, and WFM-designed tapered ADCs.
Table 3. Comparison of Coupling Lengths Among Conventional ADCs, WFM-designed ADCs, Conventional Tapered ADCs, and WFM-designed Tapered ADCs.
5. Conclusion
We experimentally demonstrated a broadband four-mode MUX/DEMUX including WFM-designed ADCs. The transmission spectra of the WFM-designed ADCs were very flat, and broadband multiplexing and demultiplexing operations were observed. The effectiveness of considering several wavelengths in the WFM optimization were also demonstrated theoretically and experimentally. In addition, low-loss and ultrabroadband ADCs were realized by the use of a tapered ADC as an initial waveguide structure.
Funding
Japan Society for the Promotion of Science (20J11564).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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