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Ultra-broadband on-chip multimode power splitter with an arbitrary splitting ratio

Hongnan Xu, Daoxin Dai, and Yaocheng Shi

Open Access Open Access

Abstract

The multimode power splitter is a basic component in mode-division multiplexing systems. In this paper, we propose an ultra-broadband silicon multimode power splitter enabling arbitrary power splitting ratios. The proposed multimode splitter is designed based on a waveguide crossing with an obliquely embedded subwavelength grating (SWG) transflector. The incident multiple guided-modes can be split into two beams with low excess losses and low crosstalk by the SWG transflector where the thin-film interference effect happens. As an example, a silicon multimode power splitter is designed to work with the three lowest-order modes of TE polarization. Any desired splitting ratio ranging from 0% to 100% can be achieved by engineering the structural parameters of the SWG. Moreover, the desired splitting ratio can be very uniform over an extremely broad bandwidth of ≥ 415 nm, covering O-, E-, S-, C-, L- and U-bands. The intermodal crosstalk is < −20 dB for all the input modes in theory. To the best of our knowledge, the proposed structure is the first multimode power splitter enabling any desired power splitting ratios in all the optical communication bands.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The mode-division multiplexing (MDM) has been regarded as a promising approach to expand the communication capacity in a single-wavelength carrier [1]. Over the recent years, a series of key elements have been reported in the MDM systems, including mode (de)multiplexer [2–6], mode switch [7–10], multimode bend [11–13], multimode crossing [14–17] and multimode power splitter [18–20]. Among them, the multimode power splitter is a basic component to simultaneously split all the input modes with the same splitting ratio. It should be noted that the single-mode power splitter cannot be directly applied in the multimode realm due to the significant intermodal crosstalk. To realize the multimode power splitting, one can optimize the structural parameters of the directional coupler (DC) to ensure that the coupling length is the common multiple of the beat lengths for all the input modes [18]. However, such structure can only work for two modes since it’s challenging to manipulate the beat lengths for a large number of higher-order modes. In ref. [19], the input TMi mode is firstly converted to be TM2i+1 mode by the cascaded asymmetric directional couplers (ADCs), the TM2i+1 mode is then split into two beams and reverted to be TMi mode by the Y-branch. Such scheme can be exploited to realize the power splitting for any higher-order modes. However, the mode conversion process is quite wavelength-sensitive [21–23], leading to the limited working bandwidth for the ADC-assisted Y-branch. Moreover, such structure can only support the 50:50 splitting since the eigen modes are either symmetric or anti-symmetric. The adiabatic coupler (AC) can be utilized to convert the input modes into the corresponding super-modes and realize the multimode power splitting with an enhanced bandwidth [20]. However, the adiabatic mode conversion process requires an extremely long coupling length (> 800 µm), and the working bandwidth is still restricted to ∼ 180 nm. Moreover, the splitting ratio is also fixed to 50:50 for such structure since the super mode always has a symmetric or anti-symmetric profile. It should be noted that the arbitrary splitting ratio is commonly required for various applications such as power monitor [24], power distribution [25] and box-like filter [26]. However, for all the reported multimode power splitters, the power splitting ratio is fixed to 50:50. In general, it’s still challenging to realize the multimode power splitter with broad bandwidth, large mode capacity and arbitrary splitting ratio.

The subwavelength grating (SWG) is a one-dimensional array of dielectric nano-islands in a deep-subwavelength scale [27–29], which has been employed in a wide range of applications, e.g., refractive index sensing [30–32], high-speed modulation [33], polarization handling [34–38] and mode manipulation [13,17]. In this paper, we propose and theoretically demonstrate an on-chip multimode power splitter based on the waveguide-integrated SWG transflector. Arbitrary splitting ratio can be achieved by engineering the structural parameters of the SWG. Moreover, the multimode splitting can be obtained over an ultra-broad bandwidth > 415 nm, which covers O-, E-, S-, C-, L- and U-bands. To the best of our knowledge, the proposed structure is the first multimode power splitter with arbitrary splitting ratio working for all the optical communication bands.

2. Design and analysis

Figures 1(a) shows the schematic for the proposed multimode power splitter. The structure is a multimode waveguide crossing with an obliquely embedded SWG that partially reflects all the input modes [see Fig. 1(b)]. The SWG is formed by a one dimensional array of fully etched nano-holes [see Fig. 1(c)]. In this paper, the device is design based on the silicon-on-insulator (SOI) platform with a 340-nm silicon (nSi ≈ 3.46) top layer and a 2-µm silica (nSiO2 ≈ 1.45) buffer layer. The cladding is chosen to be a 2-µm SU8 (nSU8 ≈ 1.58) polymer layer [39]. Here, we mainly consider the first three transverse-electric modes (TE0-TE2). The incident TE0-TE2 modes can propagate over the intersection region with negligible scattering losses and intermodal crosstalk when the waveguide width w0 is chosen to be large enough to reduce the diffraction-induced divergence [40]. The embedded SWG structure can be regarded as a transflector formed by an effective-medium thin film, thus, light launched from port #1 will be partially reflected into port #2 due to the thin-film interference effect, while the residual part of light will transmit into port #3, as shown in Fig. 1(d). Moreover, the reflectance should be almost the same for all the input modes since the TE0-TE2 effective indices are quite close if w0 >> λ/ns, where λ is the working wavelength, ns is the effective index of the slab mode [2]. Thus, one can engineer the splitting ratio by controlling the reflectance caused by the SWG transflector. The splitting ratio SR can be obtained according to the thin-film interference principle [41]:

$$SR = \frac{{{T_{21}}}}{{{T_{21}} + {T_{31}}}} = \frac{{2{r^2}(1 + \cos \delta )}}{{1 + {r^4} + 2{r^2}\cos \delta }}.$$
where T21 and T31 are the transmittances at ports #2 and #3 [see Fig. 1(a)], r is the reflection coefficient at the interfaces A and A’ [see Fig. 1(d)], δ is the phase shift within the effective-medium thin film. According to the Fresnel’s law, the reflection coefficient r is dependent on the effective-medium index nswg of the SWG, which can be obtained by using the Rytov’s formulas [42]:
$$n_{swg}^2 = n_{/{/}}^2n_ \bot ^2/(n_{/{/}}^2{\sin ^2}\theta + n_ \bot ^2{\cos ^2}\theta ),$$
$$1/n_{/{/}}^2 = {f_{swg}}/n_{Si}^2 + (1 - {f_{swg}})/n_{SU8}^2,$$
$$n_ \bot ^2 = {f_{swg}}n_{Si}^2 + (1 - {f_{swg}})n_{SU8}^2,$$
where nswg is the effective medium index for the SWG, n///n⊥ are the extraordinary/ordinary effective medium indices, θ is the beam inclination angle within the effective medium [see Fig. 1(d)], fswg is the SWG duty cycle. Additionally, the phase shift δ within the effective-medium thin film can be written as:
$$\delta = 2{k_{eff}}{w_{swg}}\cos \theta ,$$
where keff is the effective wave vector, wswg is the SWG width [see Fig. 1(c)]. Thus, the splitting ratio can be efficiently tuned by modifying fswg and wswg according to Eqs. (1)–(5).

 figure: Fig. 1.

Fig. 1. (a) The 3D view and (b) top view of the proposed on-chip multimode power splitter with some key parameters labeled. (c) The enlarged top view of the SWG transflector with some key parameters labeled. The red arrow shows the optical axis orientation for the SWG. (d) The working principle for the SWG-based splitter. The SWG structure can be regarded as an effective-medium thin film, which partially reflects the input TE0-TE2 modes due to the thin-film interference effect, leading to the multimode splitting.

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We firstly calculate the effective indices neff for the TE0-TE2 modes in the multimode waveguide with varied w0, as shown in Fig. 2(a). The calculations are carried out by using the finite-element method (FEM). It can be found that the index differences can be negligible between TE0-TE2 modes and slab mode in the multimode waveguide with a relatively large w0. Thus, the waveguide width is chosen to be w0 = 15 µm to ensure the weak diffraction over the intersection region. The SWG pitch is chosen to be Λswg = 200 nm to meet the subwavelength requirement [see Fig. 1(c)]. We then calculate the splitting ratio at 1.55-µm wavelength with varied fswg and wswg by using the finite-difference time-domain (FDTD) method, as shown in the left column of Fig. 2(b). Here, the calculations are carried out for the full SWG structure without effective-medium equivalence. The mesh grid size is set to be dx = dy = dz = 10 nm to fulfill the simulation accuracy requirement. Here, SRTEi denotes the splitting ratio when TEi mode is launched. It can be observed that the splitting ratio varies with both wswg and fswg. Moreover, the splitting ratios are almost the same between TE0-TE2 modes regardless of wswg and fswg. However, the tuning range is quite limited by changing wswg, since the phase shift is relatively weak in the effective-medium thin film with wswg ∼ λ/2ns. In contrast, the splitting ratio can be efficiently tuned from 0 to 1 by changing fswg since the effective-medium index is directly modified. Thus, one can fix wswg and change fswg to obtain the arbitrary SR. Moreover, the fswg-SR curve slope can be reduced with a smaller wswg. The SR dispersion can also be suppressed by choosing a relatively small wswg to inhibit the δ variation at different wavelengths [see Eqs. (1) and (5)]. Thus, the SWG width is chosen to be wswg = 300 nm to relax the parametric sensitivity and enhance the working bandwidth. We then calculate the SR spectra with varied fswg and fixed wswg = 300 nm, as shown in the right column of Fig. 2(b). From the spectra, one can find that variable splitting ratios can be obtained from ∼0.1 to ∼0.9 as fswg varying from 0.44 to 0.18. Moreover, the required splitting ratios can be maintained over an ultra-broad wavelength range from 1.26 µm to 1.675 µm, which covers all the optical communication bands. The SWG duty cycle is then chosen to be fswg = 0.34 to achieve the 50:50 splitting (SR ≈ 0.5), which is the most commonly used splitting ratio. The 10:90 power splitting (SR ≈ 0.1) can also be obtained with fswg = 0.44 to show the utility for power-monitoring applications [24].

 figure: Fig. 2.

Fig. 2. (a) The calculated effective indices neff for the TE0-TE2 modes in the multimode waveguide with varied w0. The dash line shows the effective index ns for the slab mode. (b) The calculated splitting ratio SR for the TE0-TE2 modes. The left column shows the calculated SR at 1.55-µm wavelength with varied fswg when wswg = 300 nm, 400 nm, 500 nm. The right column shows the calculated SR spectra with varied fswg and fixed wswg = 300 nm.

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The optimized parameters are summarized as following: w0 = 15 µm, Λswg = 200 nm, wswg = 300 nm, fswg = 0.34 (50:50 splitting) and fswg = 0.44 (90:10 splitting). To verify the above analysis, we then calculate the light propagation profiles for the optimized multimode power splitter when TE0-TE2 modes are launched, as shown in Fig. 3. For the SWG-based 50:50 splitter with fswg = 0.34, the incident TE0-TE2 modes can be evenly split and coupled into ports #2/#3 with low losses. Moreover, it can be observed that the mode conversion is negligible in the power splitting process, indicating the low intermodal crosstalk. For the SWG-based 90:10 splitter with fswg = 0.44, most part of the incident TE0-TE2 modes directly propagate into port #3, while a small part of light is reflected by the SWG transflector and coupled into port #2.

 figure: Fig. 3.

Fig. 3. The calculated light propagation profiles for the multimode power splitters optimized for 50:50 splitting (left column) and 90:10 splitting (right column).

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We then calculate the transmittance spectra for the optimized multimode power splitters, as shown in Fig. 4. The transmittance at port #4 is negligible (< −50 dB), so we only consider the transmission responses at ports #2 and #3. Here, T21,TEi and T31,TEi denote the TEi transmittances at ports #2 and #3. The grey dash lines show the target power levels. From the spectra, one can find that the TE0-TE2 transmittances are quite close to the required values over the 1.26-1.675 µm wavelength range. Moreover, one can find that the intermodal crosstalk is as low as IMC < -20 dB for all the input modes over the whole bandwidth. Here, the intermodal crosstalk is defined as:

$$IM{C_{21,TEi}} = 10{\log _{10}}(\max \{ {T_{21,TEj}}\} )\textrm{ }i \ne j,$$
$$IM{C_{31,TEi}} = 10{\log _{10}}(\max \{ {T_{31,TEj}}\} )\textrm{ }i \ne j,$$
where IMC21,TEi and IMC31,TEi are the intermodal crosstalk at ports #2 and #3 when TEi mode is launched. Furthermore, the excess losses are calculated to be as low as ELsp < 0.1 dB for all the input modes. Here, the excess loss is defined as:
$$E{L_{sp,TEi}} ={-} 10{\log _{10}}({T_{21,TEi}} + {T_{31,TEi}}),$$
where ELsp,TEi is the excess loss for the multimode power splitter when TEi mode is launched. For the 50:50 splitter, the imbalance is calculated to be lower than 0.2 dB at the central wavelength. Moreover, the imbalance can be lower than 1 dB over the 1.26-1.675 µm wavelength range. Further simulations also show that the weak imbalance ≤ 1 dB, low IMC ≤ −20 dB, low EL ≤0.1 dB and large bandwidth ≥ 415 nm can still be maintained for the 50:50 splitter even with some parametric deviations of dw0 = ±0.5 µm, dwswg = ±10 nm and dfswgΛswg = ±10 nm. As a comparison, we also calculate the transmittance spectra for the multimode power splitter with a smaller w0 = 5 µm (see Appendix). It can be found that the transmittances deviate from the required values and the intermodal crosstalk is also significantly increased, since the smaller w0 will give rise to the light divergence when propagating over the intersection region, leading to the stronger scattering at ports #2 and #3. Hence, one has to choose a relatively large w0 = 15 µm to achieve the lower EL and IMC. One can utilize the adiabatic linear tapers to connect the multimode power splitter with the conventional multimode waveguides with a relatively small width, .e.g. win = 3.5 µm, as shown in Fig. 5(a). We calculate the excess loss for the adiabatic taper with varied taper length ltp, as shown in Fig. 5(b). Here, the excess loss is defined as:
$$E{L_{tp,TEi}} ={-} 10{\log _{10}}({T_{tp,TEi}}),$$
where ELtp,TEi is the excess loss for the adiabatic taper when TEi mode is launched, Ttp,TEi is the transmittance for the TEi mode propagating through the adiabatic taper. The excess losses are optimized to be ELtp < 0.2 dB for the adiabatic taper with ltp = 150 µm. Thus, the excess loss for the total structure should be EL = ELsp + 2ELtp < 0.5 dB. Further simulations show that such low losses can be maintained over the 1.26-1.675 µm wavelength range, since the adiabatic mode-size conversion process is naturally wavelength-insensitive [43]. Figure 5(c) shows the calculated light propagation profiles for the optimized taper when TE0-TE2 modes are launched. It can be seen from the profiles that mode size can be efficiently expanded in the adiabatic taper. Further simulations also show that the intermodal power coupling is lower than −25 dB for the optimized taper, leading to the negligible IMC.

 figure: Fig. 4.

Fig. 4. The calculated transmittance spectra for (a) 50:50 splitting and (b) 90:10 splitting. The grey dash lines show the target power levels. The shaded regions show the intermodal crosstalk levels.

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 figure: Fig. 5.

Fig. 5. (a) The top view of the multimode power splitter connected with the adiabatic tapers. (b) The calculated excess loss ELtp for the adiabatic taper with varied ltp. (c) The calculated light propagation profiles for the optimized adiabatic taper.

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We have compared the performances of several reported on-chip multimode power splitter in Table 1. It can be found that all the previous structures can only achieve the 50:50 splitting (SR = 0.5) and the working bandwidth is limited to 180 nm, while for the SWG-based splitter, the arbitrary splitting ratio can be achieved over an extremely broad bandwidth >415 nm. It should be noted the long linear waveguide taper could be replaced by some special short waveguide taper [44] or the subwavelength-structured lenses [45,46], in which way the footprint of the whole device can be shrunk greatly.

Tables Icon

Table 1. Performance comparison of several on-chip multimode power splitters.

View Table

3. Conclusion

In conclusion, we have proposed and theoretically demonstrated a multimode power splitter on the SOI platform by using an embedded SWG transflector. With this design, the incident TE0-TE2 modes can be split with mode-insensitive splitting ratios. Moreover, any desired splitting ratio can be achieved by optimizing the SWG duty cycle. Such multimode splitting can be achieved over an extremely broad wavelength band from 1.26 µm to 1.675 µm with low excess losses EL < 0.5 dB and low intermodal crosstalk IMC < −20 dB. The proposed SWG-based splitter is a four-port structure with a symmetric configuration, so it can also be used as a 2×2 coupler, which can be usefully in the multimode switches or box-like filters [47–50]. To the best our knowledge, the proposed structure is first multimode power splitter that can provide arbitrary splitting ratio over all the optical communication bands, which expands the toolbox for the MDM systems.

Appendix: analysis for multimode power splitting with a smaller waveguide width

We also calculate the transmittance spectra for the multimode power splitter with w0 = 5 µm, as shown in Fig. 6. From the spectra, one can find that the excess losses and intermodal crosstalk are much higher compared with the results shown in Fig. 4. Such phenomenon is mainly induced by the diffraction effect. The smaller w0 will increase the light divergence over the intersection region, which will enhance the scattering at the output ports, leading to the higher EL and IMC.

 figure: Fig. 6.

Fig. 6. The calculated transmittance spectra with w0 = 5 µm for (a) 50:50 splitting and (b) 90:10 splitting. The grey dash lines show the target power levels. The shaded regions show the intermodal crosstalk levels.

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Funding

National Key Research and Development Program of China (2019YFB2203603); National Natural Science Foundation of China (11861121002, 61922070, 61961146003).

Disclosures

The authors declare no conflicts of interest.

References

1. C. Li, D. Liu, and D. Dai, “Multimode silicon photonics,” Nanophotonics 8(2), 227–247 (2018). [CrossRef]  

2. D. Dai, J. Wang, and Y. Shi, “Silicon mode (de)multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light,” Opt. Lett. 38(9), 1422–1424 (2013). [CrossRef]  

3. J. Wang, S. He, and D. Dai, “On-chip silicon 8-channel hybrid (de)multiplexer enabling simultaneous mode- and polarization-division- multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014). [CrossRef]  

4. D. Dai, C. Li, S. Wang, H. Wu, Y. Shi, Z. Wu, S. Gao, T. Dai, H. Yu, and H.-K. Tsang, “10-channel mode (de)multiplexer with dual polarizations,” Laser Photonics Rev. 12(1), 1700109 (2018). [CrossRef]  

5. H. Xu and Y. Shi, “Broadband nine-channel mode-division (de)multiplexer based on densely packed multimode waveguide arrays,” J. Lightwave Technol. 35(22), 4949–4953 (2017). [CrossRef]  

6. H. Xu and Y. Shi, “Ultra-broadband 16-channel mode division (de)multiplexer utilizing densely packed bent waveguide arrays,” Opt. Lett. 41(20), 4815–4818 (2016). [CrossRef]  

7. S. Wang, H. Wu, H.-K. Tsang, and D. Dai, “Monolithically integrated reconfigurable add-drop multiplexer for mode-division-multiplexing systems,” Opt. Lett. 41(22), 5298–5301 (2016). [CrossRef]  

8. S. Wang, X. Feng, S. Gao, Y. Shi, T. Dai, H. Yu, H.-K. Tsang, and D. Dai, “On-chip reconfigurable optical add-drop multiplexer for hybrid wavelength/mode-division-multiplexing systems,” Opt. Lett. 42(14), 2802–2805 (2017). [CrossRef]  

9. B. Stern, X. Zhu, C. P. Chen, L. D. Tzuang, J. Cardenas, K. Bergman, and M. Lipson, “On-chip mode-division multiplexing switch,” Optica 2(6), 530–535 (2015). [CrossRef]  

10. Y. Zhang, Y. He, Q. Zhu, C. Qiu, and Y. Su, “On-chip silicon photonic 2 × 2 mode- and polarization-selective switch with low inter-modal crosstalk,” Photonics Res. 5(5), 521–526 (2017). [CrossRef]  

11. C. Sun, Y. Yu, G. Chen, and X. Zhang, “Ultra-compact bent multimode silicon waveguide with ultralow inter-mode crosstalk,” Opt. Lett. 42(15), 3004–3007 (2017). [CrossRef]  

12. L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3(1), 1217 (2012). [CrossRef]  

13. H. Xu and Y. Shi, “Ultra-sharp multi-mode waveguide bending assisted with metamaterial-based mode converters,” Laser Photonics Rev. 12(3), 1700240 (2018). [CrossRef]  

14. H. Xu and Y. Shi, “Dual-mode waveguide crossing utilizing taper-assisted multimode-interference couplers,” Opt. Lett. 41(22), 5381–5384 (2016). [CrossRef]  

15. S. Li, Y. Zhou, J. Dong, X. Zhang, E. Cassan, J. Hou, C. Yang, S. Chen, D. Gao, and H. Chen, “Universal multimode waveguide crossing based on transformation optics,” Optica 5(12), 1549–1556 (2018). [CrossRef]  

16. W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng, D. Liu, and M. Zhang, “Ultracompact dual-mode waveguide crossing based on subwavelength multimode-interference couplers,” Photonics Res. 6(7), 660–665 (2018). [CrossRef]  

17. H. Xu and Y. Shi, “Metamaterial-based Maxwell's fisheye lens for multimode waveguide crossing,” Laser Photonics Rev. 12(10), 1800094 (2018). [CrossRef]  

18. Y. Luo, Y. Yu, M. Ye, C. Sun, and X. Zhang, “Integrated dual-mode 3 dB power coupler based on tapered directional coupler,” Sci. Rep. 6(1), 23516 (2016). [CrossRef]  

19. H. Xu and Y. Shi, “Ultra-broadband dual-mode 3 dB power splitter based on a Y-junction assisted with mode converters,” Opt. Lett. 41(21), 5047–5050 (2016). [CrossRef]  

20. L. Han, B. P.-P. Kuo, N. Alic, and S. Radic, “Ultra-broadband multimode 3 dB optical power splitter using an adiabatic coupler and a Y-branch,” Opt. Express 26(11), 14800–14809 (2018). [CrossRef]  

21. H. Xu and Y. Shi, “Ultra-broadband silicon polarization splitter-rotator based on the multi-mode waveguide,” Opt. Express 25(15), 18485–18491 (2017). [CrossRef]  

22. H. Xu and Y. Shi, “Ultra-compact and highly efficient polarization rotator utilizing multi-mode waveguides,” Opt. Lett. 42(4), 771–774 (2017). [CrossRef]  

23. H. Xu and Y. Shi, “Ultra-compact and broadband silicon polarization rotator,” in 2017 Conference on Lasers and Electro-Optics Pacific Rim, (Optical Society of America, 2017), paper s1544.

24. A. Zanzi, A. Brimont, A. Griol, P. Sanchis, and J. Marti, “Compact and low-loss asymmetrical multimode interference splitter for power monitoring applications,” Opt. Lett. 41(2), 227–229 (2016). [CrossRef]  

25. J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013). [CrossRef]  

26. H. Xu and Y. Shi, “Flat-top CWDM (de)multiplexer based on MZI with bent directional couplers,” IEEE Photonics Technol. Lett. 30(2), 169–172 (2018). [CrossRef]  

27. P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, “Subwavelength integrated photonics,” Nature 560(7720), 565–572 (2018). [CrossRef]  

28. R. Halir, A. Ortega-Moñux, D. Benedikovic, G. Z. Mashanovich, G. J. Wangüemert-Pérez, J. H. Schmid, Í. Molina-Fernández, and P. Cheben, “Subwavelength-grating metamaterial structures for silicon photonic devices,” Proc. IEEE 106(12), 2144–2157 (2018). [CrossRef]  

29. R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015). [CrossRef]  

30. J. Flueckiger, S. Schmidt, V. Donzella, A. Sherwali, D. M. Ratner, L. Chrostowski, and K. C. Cheung, “Sub-wavelength grating for enhanced ring resonator biosensor,” Opt. Express 24(14), 15672–15686 (2016). [CrossRef]  

31. V. Donzella, A. Sherwali, J. Flueckiger, S. M. Grist, S. T. Fard, and L. Chrostowski, “Design and fabrication of SOI micro-ring resonators based on sub-wavelength grating waveguides,” Opt. Express 23(4), 4791–4803 (2015). [CrossRef]  

32. L. Huang, H. Yan, X. Xu, S. Chakravarty, N. Tang, H. Tian, and R. T. Chen, “Improving the detection limit for on-chip photonic sensors based on subwavelength grating racetrack resonators,” Opt. Express 25(9), 10527–10535 (2017). [CrossRef]  

33. Z. Pan, X. Xu, C.-J. Chung, H. Dalir, H. Yan, K. Chen, Y. Wang, B. Jia, and R. T. Chen, “High-speed modulator based on electro-optic polymer infiltrated subwavelength grating waveguide ring resonator,” Laser Photonics Rev. 12(6), 1700300 (2018). [CrossRef]  

34. H. Xu, D. Dai, and Y. Shi, “Ultra-broadband and ultra-compact on-chip silicon polarization beam splitter by using hetero-anisotropic metamaterials,” Laser Photonics Rev. 13(4), 1800349 (2019). [CrossRef]  

35. H. Xu, D. Dai, and Y. Shi, “Anisotropic metamaterial-assisted all-silicon polarizer with 415-nm bandwidth,” Photonics Res. 7(12), 1432–1439 (2019). [CrossRef]  

36. H. Xu and Y. Shi, “Ultra-compact polarization-independent directional couplers utilizing a subwavelength structure,” Opt. Lett. 42(24), 5202–5205 (2017). [CrossRef]  

37. H. Xu and Y. Shi, “Subwavelength-grating-assisted silicon polarization rotator covering all optical communication bands,” Opt. Express 27(4), 5588–5597 (2019). [CrossRef]  

38. T. Huang, Y. Xie, Y. Wu, Z. Cheng, S. Zeng, and P. S. Ping, “Compact polarization beam splitter assisted by subwavelength grating in triple-waveguide directional coupler,” Appl. Opt. 58(9), 2264–2268 (2019). [CrossRef]  

39. P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D.-X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010). [CrossRef]  

40. W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Low-loss, low-cross-talk crossings for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 32(19), 2801–2803 (2007). [CrossRef]  

41. H. A. Macleod, “Thin-film optical filters,” Adam Hilger Ltd, Bristol (1986).

42. C. Gu and P. Yeh, “Form birefringence dispersion in periodic layered media,” Opt. Lett. 21(7), 504–506 (1996). [CrossRef]  

43. Y. Fu, T. Ye, W. Tang, and T. Chu, “Efficient adiabatic silicon-on-insulator waveguide taper,” Photonics Res. 2(3), A41–A44 (2014). [CrossRef]  

44. P. Sethi, A. Haldar, and S. K. Selvaraja, “Ultra-compact low-loss broadband waveguide taper in silicon-on-insulator,” Opt. Express 25(9), 10196–10203 (2017). [CrossRef]  

45. J. M. Luque-González, R. Halir, J. G. Wangüemert-Pérez, J. de-Oliva-Rubio, J. H. Schmid, P. Cheben, Í. Molina-Fernández, and A. Ortega-Moñux, “An ultracompact GRIN-lens-based spot size converter using subwavelength grating metamaterials,” Laser Photonics Rev. 13(11), 1900172 (2019). [CrossRef]  

46. Z. Wang, T. Li, A. Soman, D. Mao, T. Kananen, and T. Gu, “On-chip wavefront shaping with dielectric metasurface,” Nat. Commun. 10(1), 3547 (2019). [CrossRef]  

47. K. Chen, Z. Nong, J. Zhang, X. Cai, S. He, and L. Liu, “Multimode 3 dB Coupler Based on Symmetrically Coupled Waveguides for On-Chipbrk Mode Division Multiplexing,” J. Lightwave Technol. 35(19), 4260–4267 (2017). [CrossRef]  

48. K. Chen, J. Yan, S. He, and L. Liu, “Broadband optical switch for multiple spatial modes based on a silicon densely packed waveguide array,” Opt. Lett. 44(4), 907–910 (2019). [CrossRef]  

49. G. Zhang, H. R. Mojaver, A. Das, and O. Liboiron-Ladouceur, “Mode insensitive switch for on-chip interconnect mode division multiplexing systems,” Opt. Lett. 45(4), 811–814 (2020). [CrossRef]  

50. H. Xu, L. Liu, and Y. Shi, “Polarization-insensitive four-channel coarse wavelength-division (de)multiplexer based on Mach–Zehnder interferometers with bent directional couplers and polarization rotators,” Opt. Lett. 43(7), 1483–1486 (2018). [CrossRef]  

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Figures (6)
Fig. 1.
Fig. 1. (a) The 3D view and (b) top view of the proposed on-chip multimode power splitter with some key parameters labeled. (c) The enlarged top view of the SWG transflector with some key parameters labeled. The red arrow shows the optical axis orientation for the SWG. (d) The working principle for the SWG-based splitter. The SWG structure can be regarded as an effective-medium thin film, which partially reflects the input TE0-TE2 modes due to the thin-film interference effect, leading to the multimode splitting.

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Fig. 2.
Fig. 2. (a) The calculated effective indices neff for the TE0-TE2 modes in the multimode waveguide with varied w0. The dash line shows the effective index ns for the slab mode. (b) The calculated splitting ratio SR for the TE0-TE2 modes. The left column shows the calculated SR at 1.55-µm wavelength with varied fswg when wswg = 300 nm, 400 nm, 500 nm. The right column shows the calculated SR spectra with varied fswg and fixed wswg = 300 nm.

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Fig. 3.
Fig. 3. The calculated light propagation profiles for the multimode power splitters optimized for 50:50 splitting (left column) and 90:10 splitting (right column).

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Fig. 4.
Fig. 4. The calculated transmittance spectra for (a) 50:50 splitting and (b) 90:10 splitting. The grey dash lines show the target power levels. The shaded regions show the intermodal crosstalk levels.

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Fig. 5.
Fig. 5. (a) The top view of the multimode power splitter connected with the adiabatic tapers. (b) The calculated excess loss ELtp for the adiabatic taper with varied ltp. (c) The calculated light propagation profiles for the optimized adiabatic taper.

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Fig. 6.
Fig. 6. The calculated transmittance spectra with w0 = 5 µm for (a) 50:50 splitting and (b) 90:10 splitting. The grey dash lines show the target power levels. The shaded regions show the intermodal crosstalk levels.

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Tables (1)

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Table 1. Performance comparison of several on-chip multimode power splitters.

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Equations (9)

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S R = T 21 T 21 + T 31 = 2 r 2 ( 1 + cos ⁡ δ ) 1 + r 4 + 2 r 2 cos ⁡ δ .
n s w g 2 = n / / 2 n ⊥ 2 / ( n / / 2 sin 2 θ + n ⊥ 2 cos 2 θ ) ,
1 / n / / 2 = f s w g / n S i 2 + ( 1 − f s w g ) / n S U 8 2 ,
n ⊥ 2 = f s w g n S i 2 + ( 1 − f s w g ) n S U 8 2 ,
δ = 2 k e f f w s w g cos ⁡ θ ,
I M C 21 , T E i = 10 log 10 ( max { T 21 , T E j } )   i ≠ j ,
I M C 31 , T E i = 10 log 10 ( max { T 31 , T E j } )   i ≠ j ,
E L s p , T E i = − 10 log 10 ( T 21 , T E i + T 31 , T E i ) ,
E L t p , T E i = − 10 log 10 ( T t p , T E i ) ,
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