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Abstract
In this work, an ultra-sharp multimode waveguide bend (MWB) based on gradient shallowly etched grooves is proposed and demonstrated. With a bending radius of only 5.6 μm, our shallowly-etched-groove multimode waveguide bend (SMWB) can enable low excess loss and low-crosstalk propagation with the four lowest-order TE mode-channels, simultaneously. In the simulation, the excess losses of the proposed 90°- SMWB for TE0-TE3 are all below 0.46 dB and the inter-mode crosstalks are lower than −18 dB in 1500 nm-1600 nm. Furthermore, the measured results of the fabricated 90°- SMWB show that the excess losses for TE0-TE3 are less than 1 dB and the inter-mode crosstalks are all below −14 dB in 1510 nm-1580 nm. Such a proposed device thus provides a promising solution for ultra-compact MWBs in multimode silicon photonics.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
On-chip Mode-Division Multiplexing (MDM) [1–4] can transmit independent signals via multiple mode-channels along a multimode bus waveguide [5–7], which has been regarded as one of the main drives to increase the transmission bandwidth of photonics integrated circuits (PICs) [8–11]. Indispensably, to improve the integration of on-chip MDM, compact multimode waveguide bends are of pivotal importance, since they can be used to route the data transmission flexibly [12–14]. However, when multiple mode-channels propagate along multimode waveguides with compact bends, the modal mismatch between multimode straight waveguides (MSWs) and multimode waveguide bends (MWBs) as well as the modal overlap in the MWBs will introduce significant excess losses and inter-mode crosstalks [14], due to the high asymmetry of the modal field along the central axis of the multimode sharp bend. Thus, it is highly desired to achieve compact multimode bends with low excess losses and low inter-mode crosstalks.
Recently, various approaches have been demonstrated to obtain ultra-sharp MWBs with low excess losses and low inter-mode crosstalks. Among the demonstrated approaches, the on-chip transformation optics (TO) method [15] is regarded as an attractive method, in which mode-preserving and low loss transmission can be obtained in MWBs. Based on such method, in 2012, Lipson et al. demonstrated a novel multimode bend with a bending radius of 78.8 μm [16]. However, it is not compatible with the traditional CMOS process since a graded-index device fabrication process is required. Meanwhile, by using the TO method and the shape-optimized approach, a compact multimode bend with a decreased bending radius of 17 μm has been obtained, which can enable low-loss transmission with the four lowest-order TE modes [17]. To further reduce the bending radius, a novel MWB assisted with subwavelength grating waveguide structures has been implemented, which can support the three lowest-order TE modes with a bending radius of 10 μm. Note that, such device can also support the four lowest-order TE mode-channels if the radius is increased to be 20 μm [18]. To obtain ultra-sharp MWB, another feasible method is proposed to utilize mode converters to connect multi-waveguides and multimode waveguide bends. By using mode conversion, inter-mode coupling in the MWB can be eliminated and thus low excess losses and low crosstalks can also be achieved. Recently, by introducing a pair of step-tapered mode converters at the endfacets of an arc-bend, a sharp multimode bend has been demonstrated for two TE mode-channels [19]. In that device, the bending radius (R) of the arc-bend is R = 5 μm and the length (LC) of mode converters is LC = 5 μm. Thus, the effective radius for such device (r) is given as r = 10 μm (= LC + R). To increase the number of supported modes, a multimode bend supporting four TM mode-channels has been demonstrated by using PMMA-coated metamaterial based mode converters (LC = 15.8 μm) [20]. Since that device has a bending radius (R) of 30 μm, the effective bending radius r can then calculate to be ≈ 45.8 μm. Thus, one can find that the radiuses of the abovementioned demonstrated MWBs are still limited to be larger than 10 μm, especially for the devices which can support four-mode operations.
To solve this issue, in this paper, we propose and demonstrate an ultra-compact shallowly-etched-groove multimode waveguide bend (SMWB) with a bending radius of only 5.6 μm. By introducing shallowly-etched-groove multimode waveguides within the bending section, our device can support on-chip low-loss and low-crosstalk propagation with the four lowest-order TE mode-channels. In the simulation, the excess losses of our device are 0.27-0.38 dB, 0.28-0.38 dB, 0.32-0.40 dB, and 0.35-0.46 dB for TE0-TE3, respectively, in a wavelength range from 1500 nm to 1600 nm. And the inter-mode crosstalks are all below −18 dB. Moreover, the experiment results of the fabricated 90°-SMWB show that the measured excess losses of TE0-TE3 are all lower than 1 dB while the inter-mode crosstalks are all below −14 dB in 1510 nm -1580 nm.
2. Design structure, principle, and simulations
Figure 1(a) shows the three-dimensional schematic diagram of our proposed 90°- SMWB. The bending radius R of our proposed device is 5.6 μm and the Si waveguide (n1 = 3.476) core width W is 1.8 μm. Meanwhile, two MSWs with the same core width are connected at the input/output endfacets of our designed SMWB. From the cross-section shown in Fig. 1(b), one can find that the bending section of SMWB can be approximately regarded as a sub-wavelength grating with two periods in the radial direction. Here, the grating periods (Λ) is set to 900 nm while the duty ratios are 88.9% and 16.7% for the two periods, respectively. Thus, the widths of the gradient waveguides are W1 = 800 nm, W2 = 100 nm, W3 = 150 nm, W4 = 750 nm. Meanwhile, the shallowly-etched depth he of the SMWB is 85 nm and the thickness hSi of the core is 220 nm. Moreover, in order to be compatible with traditional on-chip integrated devices, the upper-cladding is selected to be silicon oxide (n2=1.444).
Fig. 1. Schematics of the proposed SMWB. (a) Three-dimensional view. Here, the bending radius R is defined as the distance between the center of the arc and the center of the waveguide core. (b) Cross section of the SMWB along the central axis, which is corresponding to the red dash line in Fig. 1(a).
In this device, the inter-mode crosstalk and the excess loss can be effectively suppressed based on such structure. Note that, to suppress the inter-mode crosstalk, one can reduce the modal overlap between different modes in the bend. Based on the inverse design of TO method [15,16], this can be achieved by modifying the refractive index profile of the waveguide and reducing the refractive index of the waveguide along the radial direction [16,18]. In our work, with proper designed parameters, such effect can also be obtained by using SMWB, which can manipulate the refractive index of the gradient waveguide in the radial direction and decrease the refractive index of the outer side of the bend. Meanwhile, through proper design of the SMWB, the modal mismatch at the interface between the MSWs and SMWB can be reduced. Then, by suppressing the inter-mode crosstalk and minimizing the abovementioned modal mismatch, a low excess loss in our device can also be obtained.
In order to characterize the performance of our proposed device, the transmission property of the 90°- SMWB is then evaluated by the 3D finite-difference time-domain (FDTD) simulations. Here, the Hz component is selected as the parameter to describe the mode channel propagation while the input light wavelength is set to be 1550 nm. Figures 2(a)-(d) show the magnetic field profiles (Hz component) of the device when the TE0, TE1, TE2 and TE3 are launched from the input MSWs, respectively. Meanwhile, the input/output Hz field profiles are shown in the insets. It can be noted that the modal patterns at the output facet match the modal patterns at the input facet, which indicates that the undesired mode coupling between the input/output MSWs and the SMWB is efficiently suppressed.
Fig. 2. 3D-FDTD simulation results of the 90°-SMWB. (a)-(d) The profiles of HZ field components for (a) TE0, (b) TE1, (c) TE2 and (d) TE3 at 1550 nm are shown, respectively. Here, the modes are excited in the MSWs while the interfaces between the MSWs and SMWB are marked as black dash lines. The insets show the input/output Hz field profiles. Note that, the multimode profile in the SMWB region might have a slight difference from that at the input/output facet.
Meanwhile, the simulated transmission spectra for the four lowest-order TE mode-channels are shown in Figs. 3(a)-(d). Based on the transmission simulations, we have calculated the transmission Tij from the ith TE mode at the input port to the jth TE mode at the output port. Then, the excess loss ELii and the inter-mode crosstalk CTij (i ≠j) can be expressed as
Fig. 3. (a)-(d) Transmission spectra of the 90°-SMWB when different modes (TE0-TE3) are launched, separately.
As shown in Fig. 3 (a)-(d), the excess losses for TE0-TE3 are 0.27-0.38 dB, 0.28-0.38 dB, 0.32-0.40 dB, and 0.35-0.46 dB, respectively, in the wavelength range of 1500 nm to 1600 nm. And the inter-mode crosstalks for the four lowest-order TE modes are all lower than −18 dB, Meanwhile, the excess losses of the four lowest-order TE mode-channels at 1550 nm are 0.28, 0.30, 0.35 and 0.36 dB, respectively, while the inter-mode crosstalks are all below −20 dB. Note that, for a typical stripe bend with a same bending radius, the four lowest-order TE mode-channels could have severe optical crosstalks and large excess losses. Thus, the simulation results show that inter-mode crosstalk and the excess loss are both effectively suppressed in our device by using sub-wavelength grating structures. Our device can then support low excess loss and low-crosstalk propagation with the four lowest-order TE modes.
3. Fabrication and measurement
Our device was fabricated on a commercial silicon-on-insulator (SOI) wafer with 220-nm-thick top silicon. The waveguides were firstly fabricated on the top silicon layer, by an electron-beam lithography (EBL) process and an inductively coupled plasma (ICP) dry-etching process. Then, the shallowly etched groove waveguides as well as the grating couplers were defined by another overlay process. Finally, 1-μm-thick SiO2 upper cladding was deposited over the device to protect the top-silicon layer, by using plasma- enhanced chemical vapor deposition (PECVD). Note that, in the fabrication, all these patterns are defined by the e-beam lithography on AR-P6200.09 positive resist. Meanwhile, for testing convenience, we construct a U-shape structure with two cascaded 90°- SMWBs.
Figure 4 shows the fabricated device on the PICs, including the U-shape structure, asymmetric directional couplers (ADCs) (de)multiplexers and grating couplers. The scanning electron microscope (SEM) image of the U-shape structure is show in Fig. 4(b), where the bending radius and the width of the fabricated multimode bend are 5.6 μm and 1.8 μm, respectively. Furthermore, as show in Fig. 4(c), the edge of the device is well-etched from the enlarged SEM image, which is beneficial to the transmission performance of our device. Meanwhile, the ADCs (de)multiplexers with four TE mode-channels are connected at the input/output ends of the MWB, as shown in Fig. 4(a). Then, one can selectively measure the transmission of any mode-channel through launching the light from the selected input/output port. Note that, in this work, we use ADC (de)multiplexers discussed in [21]. Moreover, in our chip, MSW connected with the ADC (de)multiplexers are also fabricated as a reference for the device characterization.
Fig. 4. The fabricated U-shape structure with two cascaded 90°- SMWBs. (a) Microscopic image of the PIC and U-shape device. ADC-Mode (de)MUXer is the ADC-based (de)multiplexer. (b) Scanning electron microscope (SEM) image of the U-shape structure, (c) Enlarged SEM image of the bending section.
In the measurement, a tunable continuous wave (CW) laser (Keysight 81960A) with 4 mW output power is used to characterize the device performance. Here, the polarization of light from the laser source is firstly adjusted to be TE polarized by a polarization controller (PC). Then, to characterize ith TE mode channel, light is launched from the selected input port (Ii, i = 0, 1, 2, 3). After passing through the device, the output light power from all the four output ports (O0-O3) was recorded by using an optical power meter. In the experiment, grating couplers are used to couple light in and out of the device. Here, the period and the duty cycle of the grating coupler are set to 630 nm and 50%, respectively. And, the grating coupler has a coupling loss of ≈ 7.5 dB at the central wavelength of 1550 nm and a 3-dB bandwidth of ≈40 nm. Note that, such grating coupler can only support the TE fundamental mode in our coupling system. Meanwhile, the measured insertion losses of ADCs are 0.8 dB, 0.5 dB and 0.7 dB for TE1-TE3, respectively.
The normalized transmission spectra of the presented U-shape structure with two cascaded 90°- SMWBs are shown in Figs. 5(a)-(d). Here, the results indicate the measured spectral responses at the output ports (O0, O1, O2, O3) when one of TE modes (i.e., TE0, TE1, TE2, TE3) is launched from the corresponding input port. It can be seen that the excess losses of the U-shape structure for the TE0-TE3 mode-channels are all lower than 2 dB and the inter-mode crosstalks are all below −11 dB in 1510 nm -1580 nm. Thus, the excess losses of a single 90°-SMWB for TE0-TE3 should be all less than 1 dB while the crosstalks are all lower than −14 dB within the same wavelength range, by using the device cascading relationship. Meanwhile, the operation wavelength bandwidth is ≈70 nm in measurement, which is smaller than that in the simulation. That might be limited by the operational wavelength range (1507 nm to 1600 nm) of the tunable laser and the 3-dB bandwidth (≈ 40 nm) of grating couplers. Furthermore, owing to the fabrication sensitivity of the ADC-based (de)multiplexers, there is some discrepancy between the reference ADC-based (de)multiplexers and the ones employed in our device. Then, the excess losses and the crosstalks of the device may show certain divergence, which could be improved after implementing appropriate reference ADC-based (de)multiplexers. Moreover, one can find an interference pattern in the transmission spectra, which might be due to the reflections at the silicon grating couplers and the ADCs [21].
Fig. 5. Normalized transmission spectra of the designed U-shape structure with two cascaded 90°- SMWBs for (a) TE0, (b) TE1, (c) TE2 and (d) TE3 modes. Here, the coupling loss of the grating couplers and the insertion losses of the ADCs are excluded.
To illustrate the characteristics of our device more intuitively, Table 1 shows the performance of some reported multimode waveguide bends and our SMWB on silicon platform. It should be noted that the SMWB demonstrated in this paper has low excess losses in theory and a very small bending radius, which can also support four TE mode-channels. Furthermore, the designed SMWB can be fabricated just with the normal electron-beam lithography and dry-etching process. Thus, our proposed SMWB provides a potential drive to enable ultra-compact footprint, low-loss and fabrication-compatible in the waveguide bend with multiple mode-channels.
Table 1. Summary of some reported demonstrated waveguide bends and our device.a
4. Conclusion
In conclusion, we propose and demonstrate an ultra-compact SMWB with a bending radius of 5.6 μm, which can support the four lowest-order TE modes. In our SMWB, gradient shallowly-etched-groove waveguides are introduced, which can significantly decrease the influence of asymmetric mode profile and then effectively reduce the inter-mode coupling within the bending section. The simulation results of the designed 90°-SMWB for TE0-TE3 exhibit low excess losses (< 0.46 dB) and low inter-mode crosstalks (< −18 dB) in 1500 nm -1600 nm. Furthermore, for the fabricated device, the measured excess losses for the four TE modes are lower than 1 dB and the crosstalks are all below −14 dB in 1510 nm -1580 nm. With such an ultra-sharp bend and low excess losses as well as low crosstalks, we believe that the SMWB will find its application on high-integrated photonics circuits for optical interconnects.
Funding
National Key R&D Program of China (2019YFB2205204); National Natural Science Foundation of China (61875120); “Shuguang Program“ supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission.
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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