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Abstract
A design of a 1 × 2 multimode 3 dB optical power splitter using tapered couplers is proposed and investigated in this paper. As an example, a 1 × 2 splitter processing five-lowest order transverse-electric-polarized modes is designed and optimized by utilizing finite difference time domain method and particle swarm optimization algorithm. To verify the feasibility of this novel design, the optimized device is fabricated on a silicon-on-insulator platform. The coupling lengths of tapered couplers are respectively 6.5 µm, 6.0 µm, 3.5 µm, 5.0 µm, 5.0 µm, 7.5 µm, 6.0 µm, 5.0 µm, and 8.0 µm. Measurement results reveal that, for the fabricated splitter, the power uniformity varies from 0.041 to 0.88 dB, the crosstalk ranges from -23.96 to -14.12 dB, and the insertion loss changes from 0.089 to 1.50 dB within a bandwidth from 1520 to 1600 nm.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Owing to the advantage of broad bandwidth, high speed, excellent CMOS compatibility, and high-density integration, silicon-based optical interconnects provide a promising solution to satisfy the ever-increasing traffic demands [1–3]. In order to expand the capacity of on-chip optical links, several kinds of techniques have been deeply explored, such as mode-division multiplexing (MDM), polarization division multiplexing (PDM), and wavelength-division multiplexing (WDM). Among them, MDM in which each mode is regarded as an independent data carrier has attracted much attentions for offering a new dimension to further increase the capacity in a single wavelength channel [4–6].
In order to achieve on-chip MDM transmission, a wide range of components have been presented, such as mode (de)multiplexers, multimode optical switches, multimode optical filters, multimode waveguide bends, and multimode waveguide crossings. However, splitting or combining eigen modes is also a fundamental operation in MDM transmission. Thus, multimode optical power splitters (MOPSs) are gradually attracting research interest. Previously, MOPSs based on various structures have been experimentally demonstrated, including asymmetrical directional couplers and a Y-branch [7], multimode interference coupler [8,9], subwavelength grating structure [10], and photonic crystal like structure [11–13]. However, most of the reported MOPSs only support two or three modes and are not easily scalable. Although an ultra-compact MOPS using a photonic crystal like structure is proposed to handle two-lowest guided modes with dual polarizations (TE0, TE1, TM0, and TM1) [13], the measured insertion loss is relatively high. The presented MOPS using an adiabatic coupler and a Y-branch can process four-lowest guided modes (TE0, TE1, TE2, and TM0) with high performance [14], but its footprint is rather large. To the best of our knowledge, a compact and high-performance MOPS supporting more than three transverse-electric (TE)-polarized modes or transverse-magnetic (TM)-polarized modes is still absent.
In this paper, we propose a novel design of a 1 × 2 multimode optical power splitters using tapered couplers (TC-MOPS), which is easily scalable and can support more than three TE-polarized modes or TM-polarized modes. To realize a relatively small size, a low crosstalk (CT), a broad bandwidth (BW), a low insertion loss (IL), and an excellent power uniformity (PU), the finite difference time domain (FDTD) method and particle swarm optimization (PSO) algorithm are adopted to optimize tapered couplers. The coupling lengths of tapered couplers in the proposed 1 × 2 TC-MOPS processing five-lowest order TE-polarized modes are 6.5 µm, 6.0 µm, 3.5 µm, 5.0 µm, 5.0 µm, 7.5 µm, 6.0 µm, 5.0 µm, and 8.0 µm. For the designed 1 × 2 TC-MOPS processing five-lowest order TE-polarized modes, within a bandwidth from 1500 to 1600 nm, the CT < -23.16 dB, the IL < 0.46 dB, and the PU < 0.0036 dB can be obtained. To confirm the practicability of our design, the optimized 1 × 2 TC-MOPS is experimentally demonstrated on a silicon-on-insulator (SOI) platform. For the fabricated 1 × 2 TC-MOPS, within a bandwidth from 1520 to 1600 nm, the power uniformity changes from 0.041 to 0.88 dB, the crosstalk varies from -23.96 to -14.12 dB, and the insertion loss ranges from 0.089 to 1.50 dB.
2. Design and analysis
Figure 1(a) shows the schematic structure of the proposed 1 × 2 TC-MOPS. As depicted in Fig. 1(a), it can be seen that, the structure is symmetrical and there are three types of tapered couplers. The corresponding detailed drawings of these tapered couplers are respectively illustrated in Figs. 1(b) –1(d). The cross-sectional view of the coupling region for a tapered coupler is shown in Fig. 1(e). Figure 1(f) describes calculated effective refractive indices of eigenmodes in a silicon strip waveguide with a thickness of Hs = 220 nm as a function of the waveguide width at 1550 nm. For the tapered coupler shown in Fig. 1(b), when the effective refractive index of the k-th-order (k = 1, 2 …) mode in the bus waveguide is equal to the ones of the fundamental modes in the two tapered waveguides on both sides, the k-th-order mode in the bus waveguide would be transformed into the fundamental mode in the tapered waveguide and the remaining modes in the bus waveguide keep forward modal propagation. For the tapered coupler shown in Fig. 1(c), the coupling region is composed of an inverted taper waveguide and two adjacent taper waveguides. When the fundamental mode is input, this tapered coupler is served as a 3 dB power splitter. For the tapered coupler shown in Fig. 1(d), similar to the one in Fig. 1(b), as the effective refractive index of the fundamental mode in the taper waveguide is equal to the one of the k-th-order mode in the bus waveguide, the mutual conversion between the k-th-order mode and the fundamental mode is achieved. By cascading these three types of tapered couplers, uniform splitting of the power for multiple input modes can be obtained. In order to realize compactness, reduce the insertion loss, expand the bandwidth, improve the crosstalk, and enhance the power uniformity, the design of each tapered coupler is optimized by using FDTD method and PSO algorithm.
Fig. 1. (a) Schematic structure of the proposed 1 × 2 TC-MOPS (b)-(d) A detailed drawing of the tapered coupler in each stage (e) Cross-sectional view of the coupling region for a tapered coupler (f) Calculated effective refractive indices of eigenmodes in a 220-nm-thick silicon strip waveguide.
Here, we take a 1 × 2 TC-MOPS handling five-lowest order TE-polarized modes for example. As depicted in Figs. 1(b)–1(d), the tapered waveguides in Stage i (i = 1, 2, 3…9) are divided into m equilong segments. The value of m can be different in different stage. LM represents the length of each segment and Wix (x = 0, 1, 2,…, m) stands for the width of the segment in the tapered waveguide. In the optimization process, the definitions of the figure of merit (FoM) for three types of tapered couplers can be written as:
In the simulation, the widths WB0, WB1, WB2, WB3, and WB4 are selected to guarantee the supported modes can propagate stably. As seen in Fig. 1(f), the widths WB0, WB1, WB2, WB3, and WB4 are respectively chosen to be 0.40 µm, 0.82 µm, 1.14 µm, 1.50 µm, and 2.00 µm in this work. For the widths of the tapered waveguides on both side in each stage, the corresponding variation range belongs to [0.15, 0.70], which is also shown in Fig. 1(f). Considering the minimum feature size of the adopted foundry process, the gap GP is chosen as Gp = 150 nm. The length LM is selected to be 0.5 µm. wI, r1, and r2 are respectively set to be 1, 2, and 2. The specific optimization steps are described in Fig. 2. Figure 3 describes FoM1, FoM2, and FoM3 changing with the number of iterations for particle-swarm-optimized tapered coupler in each stage. As shown in Fig. 3(a), it can be seen that, the value of FoM1 for the tapered coupler in Stage 1, Stage 2, Stage 3, or Stage 4 reaches the maximum when the corresponding number of iterations is up to 89, 98, 98 or 99. Similarly, for the tapered coupler in Stage 5, as the number of iterations increases to 66, FoM2 achieves its maximum. When the number of iterations comes up to 83, 86, 85 or 90, the corresponding maximum value of FoM3 for the tapered coupler in Stage 6, Stage 7, Stage 8, or Stage 9 can be realized. The optimal segments’ widths for the tapered coupler in each stage are listed in Table 1. Thus, the corresponding optimal coupling lengths of tapered couplers are 6.5 µm, 6.0 µm, 3.5 µm, 5.0 µm, 5.0 µm, 7.5 µm, 6.0 µm, 5.0 µm, and 8.0 µm, respectively. Figure 4 describes the insertion loss or crosstalk of the tapered coupler in each stage changing with the corresponding coupling length at 1550 nm. From Fig. 4, it can be found that, when the optimal coupling lengths are realized, the minimum insertion loss and the best crosstalk can be obtained. Here, the insertion loss and crosstalk of the tapered coupler in each stage are defined as:
Fig. 3. FoM1, FoM2, and FoM3 changing with the number of iterations for particle-swarm-optimized tapered coupler in each stage.
Fig. 4. Insertion loss or crosstalk of the tapered coupler in (a) Stage 1, (b) Stage 2, (c) Stage 3, (d) Stage 4, (e) Stage 5, (f) Stage 6, (g) Stage 7, (h) Stage 8, or (g) Stage 9 changing with the corresponding coupling length at 1550 nm
Table 1. Optimal widths of each particle-swarm-optimized tapered coupler in the proposed 1 × 2 TC-MOPS
FDTD simulations of light propagation in the designed 1 × 2 TC-MOPS at 1550 nm are shown in Fig. 5. As shown in Figs. 5(a)–5(e), it can be seen that, due to the symmetrical structure, two images with the same intensities are formed at the two output ports, when the corresponding TE0 mode, TE1 mode, TE2 mode, TE3 mode, or TE4 mode is injected into the port I0. The functionality of the proposed MOPS can be well performed.
Fig. 5. Simulated light propagation in the designed 1 × 2 TC-MOPS at 1550 nm, when (a)TE0 mode, (b)TE1 mode, (c) TE2 mode, (d) TE3 mode, or (e) TE4 mode is launched into the port I0
Here, the definitions of the insertion loss, crosstalk, and power uniformity for the proposed 1 × 2 TC-MOPS are given by:
Fig. 6. (a)-(e) Insertion loss, (f)-(j) crosstalk, and (k)-(o) power uniformity of the designed 1 × 2 TC-MOPS changing with the wavelength for various values of ΔW, when the input modes are TE0, TE1, TE2, TE3, and TE4 modes.
Fig. 7. (a)-(e) Insertion loss, (f)-(j) crosstalk, and (k)-(o) power uniformity of the designed 1 × 2 TC-MOPS changing with the wavelength for various values of Tr, when the input modes are TE0, TE1, TE2, TE3, and TE4 modes.
Table 2. Performances of the designed MOPS with different values of ΔW
Table 3. Performances of the designed MOPS with different values of Tr
3. Fabrication and characterization
The optimum 1 × 2 TC-MOPS was fabricated on an 8-inch SOI wafer at Institute of Microelectronics, Singapore. Figure 8 shows a microscope image of the fabricated devices, including a straight waveguide, a pair of five-channel mode (de)multiplexers using cascaded particle-swarm-optimized counter-tapered couplers [16] and the proposed 1 × 2 TC-MOPS cascaded with three five-channel mode (de)multiplexers.
A tunable semiconductor laser (SANTEC TSL-550) and a multi-port optical powermeter (SANTEC MPM-210) are used for characterizing the fabricated 1 × 2 TC-MOPS. In order to couple optical signals, TE-type grating couplers are adopted. The transmission spectra of a pair of five-channel mode (de)multiplexers are measured first. After that, we measure the transmission spectra of the fabricated 1 × 2 TC-MOPS cascaded with three five-channel mode (de)multiplexers. The normalized transmission spectra can be obtained by subtraction. Figures 9(a)–9(c) shows the measured insertion loss, crosstalk, and power uniformity as a function of the wavelength. Note that in Fig. 9(a), when the wavelength increases from 1520 to 1600 nm, the measured insertion loss changes from 0.089 to 1.50 dB. From Fig. 9(b), it can be found that, the measured crosstalk varies from -23.96 to -14.12 dB within a bandwidth from 1520 to 1600 nm. As illustrated in Fig. 9(c), within a bandwidth from 1520 to 1600 nm, the measured power uniformity ranges from 0.041 to 0.88 dB. Comparing Fig. 9 to Fig. 6 and Table 2, it is found that, the measured bandwidth, insertion loss, crosstalk, and power uniformity are slightly worse than the simulated ones. The main reason is that the actual widths of the fabricated waveguides deviate from the optimal values and the value of the gap Gp is also changed due to the process deviation. And thus, the conversion efficiency or coupling efficiency would get worse, leading to the degradation of device performance. Additionally, owing to the limitation of the light source, the measured bandwidth is not as wide as the simulated one. Table 4 summarizes the performance comparison of our proposed 1 × 2 TC-MOPS and other reported MOPS. As shown in Table 4, only simulation results are given in Refs. 14 and 17. Although some MOPSs can have ultra-compact size with good performance, the corresponding minimum feature size is required to be quite small. Compared with other reported MOPS, our presented 1 × 2 TC-MOPS which is suitable to be fabricated in foundry platforms can handle more modes and have an excellent power uniformity, a small insertion loss, a low crosstalk, and a broad bandwidth in a relatively compact footprint. To further improve the performance of our proposed device, high-quality fabrication processes with finer minimum feature size can be adopted.
Fig. 9. (a) Measured insertion loss, (b) crosstalk, and (c) power uniformity of the fabricated 1 × 2 TC-MOPS changing with the wavelength.
Table 4. Performance comparison of the proposed 1 × 2 TC-MOPS and other reported MOPS
4. Conclusion
In conclusion, a novel design of a 1 × 2 TC-MOPS have been proposed and investigated. We optimize a 1 × 2 TC-MOPS processing five-lowest order TE-polarized modes by using the FDTD method and the PSO algorithm to realize broad bandwidth, small insertion loss, low crosstalk, excellent power uniformity, and relatively compact footprint. To confirm the viability of this design, the optimized 1 × 2 TC-MOPS is fabricated on an SOI platform. The coupling lengths of tapered couplers in Stage 1, Stage 2, Stage 3, Stage 4, Stage 5, Stage 6, Stage 7, Stage 8, and Stage 9 are 6.5 µm, 6.0 µm, 3.5 µm, 5.0 µm, 5.0 µm, 7.5 µm, 6.0 µm, 5.0 µm, and 8.0 µm, respectively. Measurement results show that, within a bandwidth from 1520 to 1600 nm, the power uniformity changes from 0.041 to 0.88 dB, the crosstalk varies from -23.96 to -14.12 dB, and the insertion loss ranges from 0.089 to 1.50 dB. With these characteristic, our presented 1 × 2 TC-MOPS can offer an attractive option for constructing large scale photonic integrated circuits and realizing on-chip mode-division multiplexing transmission.
Funding
National Natural Science Foundation of China (62275134, 62234008, 61875098, 61874078); Natural Science Foundation of Zhejiang Province (LY20F050003, LY20F050001); the K. C. Wong Magna Fund in Ningbo University.
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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