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Abstract
We proposed a new type of vertical grating couplers (VGCs) with a compact footprint on the 220-nm silicon-on-insulator platform. The overall size of the device containing the L-shaped coupling grating and the taper with achromatic in-plane metalens is only 45 × 15 µm2, and the measured coupling efficiency at 1550 nm is -5.2 dB with a 1 dB bandwidth of 38 nm, around 1.6 dB higher than the VGC without metalens. The incidence angle mismatch has a 1 dB bandwidth of roughly 4°, whereas the displacement mismatch along the x-/y- axis has a bandwidth of around 3/4 µm. Furthermore, we experimentally show that such a design is compatible with VGCs operating in the S, C, and L bands.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Grating couplers (GCs) [1–3] provide an important solution for coupling light in and out the integrated photonic circuits. It can significantly reduce the mode mismatch between waveguides on chip and single-mode fibers (SMF) in free space [1], resulting in a high coupling efficiency (CE). When compared with another typical approach, edge couplers (ECs) [4,5], it has numerous significant benefits, including none requirement for polishing, high mismatch tolerance, and compatibility with high density integration, making it more suitable for chip layout testing [6–8]. However, in order to meet the Bloch condition [9], most GCs require a certain incidence angle, which creates an undesirable limitation for high-speed testing. To solve this problem, vertical grating couplers (VGCs) haven been proposed and demonstrated in silicon-on-insulator (SOI) platform [10–12]. The fundamental idea of the VGCs is to increase the effective index contrast between upward and downward radiation, and thus enhance the vertical coupling efficiency. People have constructed a bottom metal layer [13] or DBR layer [14] to reflect the light in order to capture the energy that has escaped to the substrate. Other studies have attempted to improve the radiation directionality by utilizing the blazing grating construction [15,16]. However, such architectures need a separate fabrication technique that is not compatible with CMOS processes. In recent years, an L-shaped grating coupler [17,18] has been included to the VGCs design to replicate the index distribution in blazing gratings and achieve high efficiency with a typical silicon photonic (SiP) production method. However, to meet the adiabatic requirement [19,20] and achieve high coupling efficiency, such design requires a long coupling taper, resulting in a huge footprint and lower integration density. Some researchers have utilized focusing coupling grating to demonstrate compact VGCs in a 340 nm SOI platform [12]. However, till now CMOS compatible VGCs with a compact footprint on a typical 220 nm SOI platform have not yet been reported.
Metasurfaces [21–23], also known as two-dimensional metamaterials [24], are composed of ultrathin subwavelength artificial nanostructures that have exceptional abilities in modulating the phase, amplitude, and polarization of light. In the past decades, metasurfaces have been used in a variety of applications, including beam deflection [25], color display [26,27], holograms [28,29], and so on. Metalens [30–33], as one typical example, have piqued people's interest due to their enormous potential for developing an imaging system in a compact and planar manner. When compared with traditional refractive lenses, metalenses have exhibited various unique properties, such as broadband achromatic response [34,35], multiplexed focusing [36,37], and so on. In addition to light in free-space, metalenses have been achieved in various wave systems, such as surface plasmas [38] and acoustics [39]. Recently, researchers discovered that light in waveguides can also be modulated efficiently using metalenses [40,41], providing a novel platform for achieving wave-front shaping on a chip.
In this work, through combining the design of L-shaped grating and achromatic metalens, we experimentally demonstrate a new type of VGC working at 1550 nm (C band) with a compact footprint on the 220-nm silicon-on-insulator platform. Due to the efficient phase modulation of in-plane metalens, the length of taper can be shortened while the coupling efficiency remains relatively high. We fabricate the device with a minimum feature size of 130 nm, which is suitable for most commercial CMOS SiP processes. The overall size of the sample is only 45 ${\times} $ 15 µm2. The measured coupling efficiency was −5.2 dB at 1550 nm with a 1 dB bandwidth of 38 nm. In comparison, the measured coupling efficiency of VGC without metalens is only −6.8 dB. Furthermore, the device has a relatively good tolerance for incident angle (1 dB bandwidth approximately $4^\circ $) and displacement mismatch along x-/y- axis (1 dB bandwidth around 3 µm and 4 µm). Finally, we also experimentally demonstrate that the achromatic characteristic of metalens allows us to develop VGCs that function at various wavelengths, such as 1500 nm (S band) and 1600 nm (L band).
2. Design principle
The design of the VGCs is shown in Fig. 1(a), which contains mainly two components, the L-shaped subwavelength coupling grating and the taper with achromatic in-plane metalens. For the achromatic in-plane metalens design, we etch a gradient rectangular hole array in the taper along the y- axis as shown in Fig. 1(c). To optimize the geometric parameters, we use finite-difference time-domain (FDTD) simulations to calculate the transmission (Fig. 1(d)) and phase (Fig. 1(e)) for the rectangular holes with different widths and lengths. Here, the period along the y-axis is fixed at 600 nm. When the width increases above 300 nm, we can see that the transmission will decrease to a low value, which thus increases the insertion loss. Based on this consideration, we fix the width as 150 nm and change the length of the rectangular hole only (marked by the white dashed lines). The results are extracted and replotted in Fig. 1(f), which shows the transmitted phase has a near-linear relationship with the length while the transmitted amplitude remains constant, resulting in a highly effective modulation of the in-plane wave-front. The phase modulation $\varphi $, which is followed by the metalens design, should meet the Eqs.1 condition.
where $n_{eff}^{slab}$ is the effective refractive index of the slab waveguide; $\lambda ,\textrm{}f\; \textrm{and}\; r$ represent the wavelength, focal length, and coordinate, respectively. To satisfy this 1D phase profile, we can determine the lengths of the slots along the y-axis based on simulated results in Fig. 1(f), resulting in the whole in-plane metalens.
Fig. 1. Device design principle of the VGCs. (a) The schematic of the VGC with metalens. (b) The L-shaped grating. (c) The achromatic metalens. (d) The transmitted amplitude and (e) phase at 1550 nm as a function of the slot width and length. (f) The transmitted phase and amplitude at different lengths with a fixed width of 150 nm. (g) Simulated field distribution showing the in-plane focusing effect with the metalens design.
Figure 1(g) depicts the light's in-plane propagation with the total metalens. The scattering may be regulated due to the concentrating effect, allowing for a relatively high coupling efficiency with a short taper length. Furthermore, due to the phase shift is based on effective index modulation in this system, it can be written as the relationship of Eqs.2 [40]
where ${n_{eff}}$ is the effective refractive index of the nanostructure; $\lambda $ is the working wavelength; L is the lengths of the rectangular holes. When ${\varphi _1}(\lambda )$ equals ${\varphi _2}(\lambda )$, the focal length in Eqs.1 can be expressed as:Through appropriately designing the geometrics of the nanostructure, K could be dispersionless. In this case, we can see that the focal length keeps a constant for different wavelengths and thus realizes a broadband achromatic response.
For the L-shaped grating design, there are six geometric parameters need to be optimized as illustrated in Fig. 1(b), including the width of SWG (${W_1}$), the width of blank area (${W_2}$), the width of rib layer (${W_3}$), the width of ridge layer (${W_4}$), the period (${L_1}$) and length (${L_2}$) of SWG. The top silicon layer in our design is 220 nm thick, while the etched depth is set to 130 nm. The buried oxide layer is 3 µm thick, whereas the overlying oxide coating is 1.7 µm thick. The working wavelength is set as 1550 nm at C band. We use the Particle Swarm Optimization (PSO) algorithm based on full 3D-FDTD simulations to identify the optimized design within the six-dimensional design space, in which a single-mode fiber with a diameter of 9 µm is located at 1.7 µm above the grating surface and a fundamental TE mode is incident from the fiber to the grating coupler. The boundary conditions along the x- and y-axis are set as perfect matched layer and periodic condition, respectively. The power transmitted into the slab silicon waveguide is measured using mode expansion analysis to determine the device CE. More importantly, we define a minimum feature size of 130 nm for the PSO algorithm, which is adequate for most commercial CMOS SiP processes. And for the design space $\textrm{X} = [{{W_1},\; {W_2},\; {W_3},\; {W_4},\; {L_1},\; {L_2}} ]$, the iteration process of PSO method is shown in Fig. 2, with a final optimized results of $[{275\; \textrm{nm},130\; \textrm{nm},235\; \textrm{nm},130\; \textrm{nm},450\; \textrm{nm},300\; \textrm{nm}} ]$. This result shows that the optimized CE at 1550 nm will reach -1.4 dB with an infinite grating region and infinite taper length, demonstrating the high-efficient coupling design.
Fig. 2. (a) Simulated efficiency at 1550 nm during the iteration process of PSO method. (b) Simulated coupling efficiency with the optimized parameters.
Next, we combine L-shaped subwavelength coupling grating and the taper with achromatic in-plane metalens, resulting in the whole compact VGC. The simulation results are shown in Fig. 3, where the 3D-FDTD simulations are performed with a coupling area of 15 ${\times} $ 15 µm2 and a linear taper of 30 µm. The incident position and angle of the single-mode fiber is set as 3 µm and $0^\circ $, respectively. And the displacement between the metalens and L-shaped grating is set as 1 µm. To demonstrate the function of metalens, here we run the simulation for the devices with (Fig. 3(a)) and without (Fig. 3(b)) the metalens, respectively. When a metalens with a proper focal length is incorporated into the device, the coupling light may be focused first, and the size of the mode profile can be reduced near to the single-mode silicon waveguide with a width of 500 nm. Figure 3(c) shows the simulated electric filed distributions in the y-x plane at $z = 0.11\mathrm{\;\ \mu m}$ for a metalens with a focal length 30 µm, revealing that the majority of the coupled light transmits into the silicon waveguide. When no metalens is present, however, propagating light is scattered outside of the waveguide due to the significant mode mismatch, as seen in Fig. 3(d).
Fig. 3. Schematic of the device (a) with and (b) without metalens. Simulated electric field distribution in the y-x plane for the device (c) with and (d) without metalens. (e) Simulated efficiency at 1550 nm for the VGCs with different taper length.
It should be mentioned that this metalens design works well throughout a wide range of taper lengths. The simulated CEs for VGCs with and without metalens are displayed in Fig. 3(e) when we sweep the taper length from 20 to 80 µm. The CE for VGC without metalens rapidly declines as the taper length decreases, leading to a low efficiency within a small footprint. However, the CE for the VGC with metalens almost remains the same, demonstrating the good performance of in-plane focusing effect. The difference between Fig. 2(b) and Fig. 3(e) is mainly induced from the size difference of VGCs, which also indicates that our design strikes a balance between the high efficiency and compact footprint. When the taper length is less than 20 µm, the CE for this novel design decreases below -3 dB. In light of this, we fix the taper length as 30 µm in our following research, as marked by the black dashed line in Fig. 3(e).
Figure 4(a) displays the simulated transmitted spectra for these two examples in Fig. 3(c) and Fig. 3(d). For VGC with metalens, a peak coupling efficiency of −2.6 dB is obtained at 1550 nm with a 1 dB bandwidth of 52 nm. In comparison, the coupling efficiency of the VGC without metalens at 1550 nm is just -4.6 dB, which is substantially lower. The small blue shift of the peak wavelength is mainly due to the change of effective index induced from the metalens. Then we investigate the influence of some geometric errors of L-shaped grating on the coupling efficiency and the results are shown in Fig. 4(b) and Fig. 4(c), from which we can see that the 1 dB tolerance for ${W_3}$ and etched depth is around ${\pm} 25\textrm{nm}$ and ${\pm} 10\textrm{nm}$, respectively. The insets define the positive and negative misalignment direction.
Fig. 4. (a) Simulated coupling efficiency for the VGCs with and without metalens. Influence of (b) misalignment error and (c) etched error on the coupling efficiency at 1550 nm.
3. Experimental demonstration
We fabricated the device on a 220 nm SOI wafer with standard EBL and ICP technology. Figure 5 shows the scanning electron microscopy (SEM) images of the device with different magnifications. The L-shaped structure is realized through double-exposure and double-etch process. The grating couplers has a size of 15 ${\times} $ 15 µm2 and the single-mode waveguide is 30 µm long, the same as the parameters in simulation. Finally, a 1.7 µm silicon dioxide layer is deposited above the device with PECVD as its top cladding layer.
A SANTEC TSL-550 tunable laser and a YOKOGAWA AQ2211 optical power meter was used to measure the coupling of VGC with two single-mode fibers at 0°. To control the input light to the TE mode, a polarization controller was used. A wavelength scan was performed from 1510 to 1590 nm with a 0.5 nm step. The measured results of the VGC are plotted in Fig. 6, which shows a peak coupling efficiency of −5.2 dB at 1550 nm with a 1 dB bandwidth of around 38 nm. We also fabricate and test the VGC without metalens. The measured result shows that the coupling efficiency is only −6.8 dB at 1550 nm (the blue line in Fig. 6). The difference is around 1.6 dB, which is quite close to the simulated value (2 dB). Based on this analysis, the decrease in coupling efficiency compared to the simulation results are mostly due to fabrication error of L-shaped grating during the double-exposure and double-etch process, as discussed in Fig. 4(b) and Fig. 4(c). Next, Table. 1 show the comparison of Figures of Merits of our design with the reported VGCs, from which we can see that our device is the first experimental demonstration for the compact VGC on 220-nm silicon-on-insulator platform.
Table 1. Comparison of Figures of Merits of the VGCs
4. Alignment tolerance for the incident angle and displacement
Incident angle tolerance is a critical feature of VGC for applications in wafer-scale testing. Figure 7(a) shows the simulated spectra after changing the incidence angle from -2° to 3° in a 1° step. As the incident angle increases, the peak wavelength shifts blue from 1586 nm to 1529 nm, which is mostly due to the Bloch condition constraint. The coupling efficiency at 1550 nm is then extracted for each scenario and shown in Fig. 7(b). The results reveal that in our system, 1 dB bandwidth is about 4°, which is easy to manage and displays the good incidence angle tolerance. Figure 7(c) and Fig. 7(d) show the measured results, which agree well with the simulated results.
Fig. 7. Angle tolerance of the VGC. (a) Simulated and (c) measured coupling efficiency for the VGCs at different incident angles from -2° to 3°. (b) Simulated and (d) measured influence of the incident angle for CE at 1550 nm.
Another significant feature of VGC for high-speed testing is displacement tolerance. The x- and y-axis displacement tolerances are both evaluated here. Due to the structural symmetry along y- axis, we only analyze the positive displacement in Fig. 8(a). As the displacement rises, the peak wavelength remains nearly the same while CE slowly decreases. The coupling efficiency at 1550 nm for various displacements is then extracted and shown in Fig. 8(b). According to the findings, 1 dB bandwidth is roughly 4 µm along the y-axis. Figure 8(c) and Fig. 8(d) show the measured results, which further supports the simulation. Figure 9 illustrates the simulated and measured results for the alignment tolerance along the x-axis in a similar way, and we can see that 1 dB bandwidth is roughly 3 µm. It's worth noting that the coupling grating region is only 15 ${\times} $ 15 µm2, implying that our device's displacement tolerance ratio is 20% and 26% along the x- and y- axes, respectively.
Fig. 8. Displacement tolerance of the VGC along the y- axis. (a) Simulated and (c) measured coupling efficiency for the VGCs with different displacement from 0 to 3 $\mathrm{\mu m}$. (b) Simulated and (c) measured influence of the displacement error for CE at 1550 nm.
Fig. 9. Displacement tolerance of the VGC along the x- axis. (a) Simulated and (c) measured coupling efficiency for the VGCs with different displacement error from -3 to 3 $\mathrm{\mu m}$. (b) Simulated and (d) measured influence of the displacement error for CE at 1550 nm.
5. Broadband achromatic response
Our proposed in-plane metalens can provide a broadband achromatic response, as specified in the design concept. To exemplify this concept, we adjust the silicon slab waveguide width to 14 µm and incident a basic TE mode from the bottom to the top, as shown in Fig. 10. As can be seen, there is a clear focusing effect in the broadband region of 1500 nm to 1600 nm. Furthermore, with a value of roughly 25 µm, the focal length stays practically constant, illustrating the good achromatic in-plane focusing effect in the communication band.
Fig. 10. The achromatic in-plane focusing effect. The focal length of the in-plane metalens remains nearly the same from 1500 nm to 1600 nm.
Due to the achromatic property of the metalens, this design is compatible to VGCs working at various working wavelengths. To illustrate such performance, we design two VGCs with the same metalens that operate at 1500 nm (S band) and 1600 nm (L band). The optimum parameters based on PSO method at the design space $\textrm{X} = [{{W_1},\; {W_2},\; {W_3},\; {W_4},\; {L_1},\; {L_2}} ]$ is $[{250\; \textrm{nm},130\; \textrm{nm},220\; \textrm{nm},130\; \textrm{nm},450\; \textrm{nm},300\; \textrm{nm}} ]$ for 1500 nm and $[300\; \textrm{nm},130\; \textrm{nm},250\;\textrm{nm},$ $130\; \textrm{nm},450\; \textrm{nm},300\; \textrm{nm} ]$ for 1600 nm. The simulated electric filed distributions of the y-x plane for the two devices are shown in Fig. 11(a) and 11(b), respectively, from which we can see that the majority of the energy is coupled into the single mode silicon waveguide. Then we fabricate the VGCs with the same process in Section 3 and the SEM images of the devices are shown in Fig. 11(c) and 11(d). The simulated (Fig. 11(e)) and measured (Fig. 11(f)) transmitted spectra show that a peak of -3.2 dB/-5.1 dB and -2.8 dB/-4.3 dB can be achieved at the desired wavelengths. Due to the bandwidth limit of tunable laser, here the measured spectra can only cover the range from 1500 to 1600 nm.
Fig. 11. The vertical coupling effect of VGCs working at (a) 1500 nm and (b) 1600 nm, respectively. SEM images of the VGCs working at (c) 1500 nm and (d) 1600 nm, respectively. (e) Simulated and (f) measured coupling efficiency for the VGCs.
6. Conclusion
In conclusion, we propose a novel type of VGC with a compact footprint on the 220-nm silicon-on-insulator platform. The L-shaped coupling grating and the taper with achromatic in-plane metalens make up this innovative VGC. The in-plane scattering of light may be greatly reduced with this design, and a coupling efficiency (-2.6 dB simulated at 1550 nm) can be accomplished with only a 30 µm taper. The measured result at 1550 nm was −5.2 dB with 1 dB bandwidth of 38 nm. In comparison, the measured coupling efficiency of VGC without the metalens is just −6.8 dB. We further show that such a device has a good tolerance for incidence angle mismatch (1 dB bandwidth around 4°) and displacement mismatch (1 dB bandwidth around 3/4 µm along x-/y- axis). Moreover, due to the broadband achromatic property, we experimentally demonstrate that such design can be compatible with VGCs operating at various working wavelengths, including the S, C, and L bands. We think that our work offers a novel approach to efficient and mismatch-tolerant VGCs, and that it will find extensive use in SiP.
Funding
China Postdoctoral Science Foundation (2021M702869, 2022T150563); Fundamental Research Funds for the Central Universities (2021QNA5006); National Natural Science Foundation of China (61635011, 62105285); National Ministry of Science and Technology Key Research and Development Program (2018YFB2201200).
Acknowledgments
The authors acknowledge Zhejiang University Micro and Nano Processing Platform for providing the facility support. The authors thank Mr. Xiangyu Luo, Mr. Chenguang Li, Mrs. Ying Huang and Mrs. Yating Wu for their fruitful discussions on the experiments conducted in this study and revisions made in the manuscript.
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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