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Abstract
We demonstrate and optimize a tri-layer vertical coupler for a silicon nitride (Si3N4) multilayer platform operating at a 2 µm band. The large spacing between the topmost and bottommost layers of a gradient structure enables ultra-low crossing loss and interlayer crosstalk without affecting the efficiency interlayer transition. We achieve a 0.31 dB transition loss, ultra-low multi-layer crosstalk of -59.3 dB at a crossing angle of 90° with an interlayer gap of 2300 nm at 1950nm. With width optimization of this structure, the fabrication tolerances toward lateral misalignment of two stages in this coupler have increased 61% and 56%, respectively. We also propose a vertical coupler, based on this design, with mode selectivity and achieve an extinction ratio of < 15 dB for wavelengths in the 1910-1990 range. Meanwhile, a multi-layer interlaced AWGs centered at 1950nm and based on vertical coupler has been demonstrated. The proposed vertical couplers exhibit potential for application in large-scale photonic-integrated circuits and broadly in photonic devices.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Large-scale photonic integrated circuits (PICs) have gradually replaced pure electronic circuits for complex chip architectures [1]. Meanwhile, the increase in optical devices on a limited chip area causes the optical waveguide to cross frequently, resulting in severe waveguide cross-loss. The three-dimensional (3D) optical integrated structure [2] is intended for the fabrication of various optical devices in different photonic layers in the vertical direction of the optical chip. The two-dimensional (2D) limit is then exceeded, which can physically prevent cross-loss and conduct information transfer in the vertical direction of the chip, ultimately constituting a multilayer silicon photonic interconnection network [3]. Meanwhile, compared with single-layer waveguide crossing structure [4], the multi-layer structure is more flexible in crossing angle. Cornell University has proposed a 3D optical integrated network and an electronic integrated chip model [5]. The lower layer of the chip is a microelectronic chip with multiple layers of copper interconnects. Vertically above is a 3D optical integrated structure. The optical waveguides carrying different information are located vertically. In different layers, the ring resonator is responsible for uploading and downloading information. After the 3D integrated structure is adopted, the integration of photonic devices considerably improves, the complexity of the optical chip design is enhanced, and additional on-chip functions can be realized [6].
A 3D vertical coupler is intended to solve the problem of light coupling between different layers when photonic integration transforms from 2D to 3D. Numerous vertical couplers have been recently proposed to achieve an interlayer interconnection, such as directional couplers [7], grating couplers [8,9], reflector mirrors [10], waveguide overpasses [11] and inverted taper couplers [12,13]. Transition loss, crossing loss and coupler length are three important parameters of a vertical coupler. Using slow-varying inverted tapers had reported the minimum transition loss of 0.01 dB [13] when the layer spacing is 700 nm for TE0 mode in C-Band. Specifically, a compact vertical coupler, combining gratings with a gradient index meta-material [14] was only 20 µm in length, with a transition loss of 0.6 dB on a Si/SiNx platform when the layer spacing is about 720 nm. A grating-assisted-cylindrical-resonant-cavity interlayer coupler [15] realized coupling with a large gap and high tolerance.
The trade-off between vertical coupling and multilayer crossing loss is a crucial problem in the design of a vertical coupler. A large interlayer gap increases transition loss; mean, the interlayer distance is considerably short, introducing significant crossing loss and increasing the interlayer crosstalk. This challenge can be effectively addressed using three waveguide layers [16]. Meanwhile, the modification of the center layer which provides an intermediary transition can also obtain a vertical coupler with special functions. In the current study, we design and optimize a tri-layer 3D vertical coupler, based on a Si3N4/SiO2 platform, for ultra-low-loss crossings and inter-layer transitions. Coupling loss equal to 0.31 dB at a large gap of 2300 nm is achieved at 1950nm after the taper width is optimized. We further demonstrate a vertical coupler, based on the tri-layer structure, with TM0 mode filtering on the basis of the tri-layer structure, and achieve an extinction ratio of 25.6 dB, which is useful for future 3D photonic integrated devices. Finally, the demonstrated multi-layer interlaced AWGs based on the tri-layer vertical coupler centered at 1950nm has only one-half of the layout of the single-layer one, which is of important reference value for the miniaturization and on-chip integration of the 2-µm band spectrometers [17] and optical communication [18,19,20] devices.
2. Structural design
The slowly-varying inverted taper is a practical structure for an inter-layer coupler based on the Si3N4/SiO2 platform, which effectively solves the refractive index matching between upper and lower waveguides. As shown in Fig. 1, it can almost reach 100% coupling efficiency under certain conditions [21]. The entire coupling process, as indicated in the x direction shown in Fig. 1(a), is divided into three stages: in the first stage, the effective refractive index n1 of Waveguide A is much larger than the effective refractive index n2 (n1> n2) of Waveguide B, and no light transmission occurs; in the second stage, the effective refractive indices of Waveguides A and B are close (n1≈n2), optical power transfer occurs, and light is transmitted from A to B; in the third stage, as the width of Waveguide A continues to decrease, n1 also decreases accordingly. At this time, the effective refractive index n1 of Waveguide A is much smaller than n2 of B (n1<n2), and light is prevented from being transmitted again. Therefore, in the entire process, light is transmitted from Waveguide A to Waveguide B only when the effective refractive indices of the two waveguides are equal; in addition, light is always confined in Waveguide B without being transmitted back. Figure 1(b) illustrates the transition of the TE0 mode field in the x-direction. The cross-sectional cutting diagram of the yellow-dotted box shows the specific process.
Fig. 1. (a) A schematic of the inverted taper vertical coupler, with the light vertically coupled from the lower Waveguide A to the upper Waveguide B; (b) Transition of the TE0 mode field in the x-direction.
In this study, we aim to design and optimize a tri-layer Si3N4/SiO2 photonic platform and ultimately apply the output to our design of compact arrayed waveguide gratings (AWGs). As the interconnection of the upper and lower layers, a suitable structure of the waveguides needs to be selected to match the device. The input waveguide measures 1.5 µm × 0.15 µm Si3N4, and the output waveguide measures is 4 µm × 0.05 µm [22], with SiO2 as the cladding. The upper and lower waveguides largely vary in width; consequently, we insert a layer of the Si3N4 waveguide measuring 2.5 µm × 0.10 µm as an intermediary transition to achieve improved refractive index matching while balancing losses, to reduce further loss. Cross-sections of the proposed tri-layer gradient waveguides are present in Fig. 2(a). Figures 2(b)–2(e) illustrate the intuitive spatial structure and the TE0 mode field of each layer. Optical signals are input from the lowest layer and are gradually coupled to the uppermost layer, achieving a signal exchange between the two layers. The use of a tri-layer structure can effectively increase the gap between the bottom layer and the top layer, to reduce the crossing loss under the condition of a considerable transition performance.
Fig. 2. (a) Cross-sections of the proposed tri-layer gradient waveguides and structural parameters; (b) Spatial structure of the tri-layer vertical coupler; (c), (d), (e) the TE0 mode field of each layer.
3. Simulation and optimization of the Si3N4 platform
3.1 Tri-layer gradient coupler
The taper length, width, and inter-layer gap are three import factors of a low-loss vertical coupler. A sufficient taper length can provide increased coupling efficiency but can also lead to an enlarged device and unnecessary transmission losses. The taper width should also be controlled within a certain range to ensure sufficient coupling and minimize return-loss. We divide the bottom-up optical transmission of the entire platform into two processes: the transmission from the bottom layer to the middle layer and the transmission from the middle layer to the top layer. The taper length, width, and gap between the bottom layer and the middle layer are Length_A, Width_A, and Gap_A, whereas those between the middle layer and the top layer are Length_B, Width_B, and Gap_B, respectively. The taper widths are the first set to be 1/10th of the input waveguides, only 0.15 µm (Width_A) and 0.25 µm (Width_B), and the simulation of the taper lengths and gaps are shown in Fig. 3. Figure 3(a) shows the variation of the two processes with the couple lengths when the gap is 500 nm. With the transition -0.2 dB as the standard, Length_A is set to be 60 µm, and Length_B is 130 µm. As shown in Fig. 3(b), with Length_A = 60 µm and Length_B = 130 µm, when the gap gradually increases, the transition gradually decreases. Setting -0.3 dB as the standard, the gaps are set as 800 nm and 1500 nm, respectively.
Fig. 3. Selections of the coupling length and the layer gap of two processes. (a) The transition of the two processes varies with the couple lengths; (b) the transition of the two processes varies with the layer gaps.
Each layer of waveguide varies in width and thickness; consequently, the width of each taper has to be optimized to achieve the best refractive index matching and the highest coupling efficiency. Figure 4(a) presents the optimization of the two tapers of the first process. The transition gradually increases, as the width of the input taper increases; when Width_in is 0.5 µm, the maximum value is achieved and then it decreases with an increase in taper width. The reason is that only when the effective refractive index is close to that of the upper and lower waveguides can effective energy exchange occur. If the taper width is too small, the two sections of the tapers do not have a sufficient effective coupling length; if the width is too large, the end reflection is increased, and the transmission is decreased. After the input taper width is optimized, the output taper width is also optimized. Therefore, according to the simulation results in Fig. 4, for the first process, Width_in is 0.5 µm and Width_out is 0.3 µm, and the transition is about -0.185 dB; for the second part, Width_in is 0.9 µm and Width_out is 0.3 µm, and the transition is about -0.044 dB.
Fig. 4. Width optimization of the two processes. (a) The transition for the first process (b) and the second process. The black curve is the width optimization of the input inverse taper, whereas the red curve is the width optimization of the output inverse taper.
We specifically use a neural network [23,24] to predict the width optimization, with the lower and upper tapers as the input and the transition loss as the output. The 49 groups of data simulated by changing the width of the upper and lower tapers are used as learning samples. After debugging, the root-mean-square error (loss value) of the model decreases to 10−5, and the transition loss can be accurately estimated. With the change in the 100 nm taper width as the step length, we draw the predicted results into a two-dimensional contour map, as shown in Fig. 5. The optimal matches are 0.5 µm (input) - 0.3 µm (output) and 0.9 µm (input) - 0.5 µm (output), which are consistent with our optimization results when the subtle errors are ignored.
Fig. 5. The two-dimensional contour map of the transition loss predicted results, and the intersecting positions of the dotted lines in the figure indicate the optimal width matching (a) for the first process and (b) for the second process.
3.2 Polarization-selective coupler
Owning to the particularity of the tri-layer structure, specific functions can be achieved using the special design of the middle layer. Figure 6(a) shows the proposed TM0 mode filter structure. On the basis of the theory of pattern evolution [25], we transform the TM0 mode into the TE1 mode and then filter the TE1 mode to achieve polarization selection. The entire middle layer is divided into four parts, and 220 nm × 600 nm Si is used as the waveguide instead of Si3N4 because it has a greater difference in refractive index to achieve a better mode conversion performance. The inter-layer gaps are also adjusted to 500 nm to better verify the device. The first part is an inverted taper coupled to the lower Si3N4 input layer, with its taper width and length measuring 50 nm and 70 µm, respectively. The second part is a polarization converter using an adiabatic T-waveguide. Figure 6(b) shows the cross-sections of the T-waveguide, which comprises a 130 nm × 600 nm ridge waveguide and a 90 nm slab waveguide. As the width of the slab waveguide (W) increasing (Fig. 6(c)), a mode-mixing zone appears, and two modes with similar Ex and Ey components are coupled and transformed to the other. We use Si as the waveguide of the second layer; thus to achieve the refractive index matched with the third layer, a coupling structure is necessary to perform the transition and filter the TE1 mode simultaneously, as shown in Fig. 6(a). This part uses a 320 nm × 2000nm Si3N4 waveguide to wrap the Si inverse taper. The TE0 mode can be transferred to the Si3N4 waveguide without loss; meanwhile, the TE1 mode gradually dissipates because it is in the cut-off region of the taper waveguide. Finally, an inverse taper is used to couple with the third layer, which measures 300 nm in taper width and 125 µm in taper length.
Fig. 6. (a) The TM0 mode filter structure of the middle layer in the black dashed box, whereas that in the red dashed box is the part of the Si waveguide that is buried in the Si3N4 waveguide; (b) the cross-sections of the T-waveguide, which consists of a 130 nm × 600 nm ridge waveguide and a 90 nm thick slab waveguide; (c) the relationship between the effective refractive index of the TE0, TE1, TM0, and W. In the green dashed mode-mixing zone, TE1 and TM0 have similar Ex and Ey components.
In order to achieve high conversion efficiency, Finite Different Time Domain (FDTD) is used to calculate the change curve of the mode conversion efficiency with L1 and L2, and the results are shown in Fig. 7. L2 is sent to 5 µm to scan the value of L1 and subsequently determine the best value, L1 is then set to the best value to scan the value of L2 and subsequently determine the best value. With the conversion efficiency and size considered, the lengths L1 and L2 are ultimately selected as 43 and 9 µm, respectively.
We consider the TE0 and TM0 modes as the input of this layer. The simulation results are present in Fig. 8. When the input is the TE0 mode, it can pass through and is then coupled into the upper layer without loss; if the TM0 mode is converted to the TE1 mode during the transmission, it gradually dissipates at the refractive index matcher, unable to enter the inter-layer coupling region. Specifically, the extinction ratio reaches -30 dB at 1950nm.
Fig. 8. (a) Transmission in the mode transformation and filter structure, with TE0 and TM0 as the input at 1950nm; (b) spectral transmission characteristics of the TE0, TM0, and TE1 modes which are transferred from the TM0 mode.
4. Characterization of the vertical couplers
The optimized tri-layer gradient vertical coupler and its parameters are presented in Fig. 9. The total length of the device is 230 µm and each taper has a buffer of 10 µm. After width optimization, our device achieves higher fabrication tolerance toward lateral misalignment, as shown in Fig. 10. The red curve shows the change in transition loss without width optimization with an increase in misalignment, whereas the black curve shows the situation after optimization. With -0.5 dB as the standard, the tolerance of the first layer and the second layer increases by 61% and 56% respectively, after optimization, which largely improving the advantage of using the device.
Fig. 9. The spatial structure of the optimized tri-layer gradient vertical coupler based on the Si3N4/SiO2 platform.
Fig. 10. (a) Schematic of misalignment between two layers; (b), (c) increase in misalignment after width optimization for the first process. The black curve represents the optimized situation.
For the ultra-thin Si3N4 waveguide, the mode-limiting factor is relatively low, resulting in variations in transition loss between the TE0 and TM0 modes. Figure 11(c) shows the spectral characteristics of the tri-layer gradient coupler under two fundamental modes. For the TE0 mode, the transition loss can be controlled to less than -0.5 dB within the 80 nm working bandwidth required within the 1910-1990nm range. Meanwhile, Fig. 11(b) shows the crossing loss and crosstalk for a waveguide crossing with another layer crossing at the angles 0°, 30°, 45°, 60°, 75°, and 90° with an inter-layer gap of 2300 nm. When the upper and lower waveguides are parallel, that is, when the crossing angle is 0°, the inter-layer crosstalk is less than -10.7 dB. This occurrence provides advantages for our devices because of the gradient waveguides and large layer spacing. Moreover, the crossing loss and crosstalk are -0.6 and -59.3 dB when the crossing angle is 90°, respectively.
Fig. 11. (a) Schematic of waveguide crossing; (b) crossing loss and crosstalk at different angles with an inter-layer gap of 2300 nm; (c) spectral characteristics of the tri-layer gradient coupler under the TE0 and TM0 modes.
Changing the middle layer of the tri-layer coupler so that it has the function of polarization selection has not been reported in previous research, as shown in Fig. 12. The inverted tapers of the uppermost and lowermost waveguides are removed for better refractive index matching. We evaluate the proposed polarization-selective coupler, the polarization characteristics of which are shown in Fig. 13. In the required bandwidth, the transfer loss of the TE0 mode is less than 0.8 dB, and it exerts a good filtering effect on the TM0 mode, given that extinction ratio is less than 15 dB within the 1910-1990nm range and up to 25.6 dB at 1950nm. Meanwhile, the transition of the TE1 mode is realized using the TM0 mode after the transformation structure is also simulated. The TE1 mode is in the cut-off area; thus, the transition is less than -33 dB in the working bandwidth, exerting no effect on the TE0 mode.
Fig. 12. (a) The spatial structure of the polarization-selective vertical coupler. The inverted tapers of the uppermost and lowermost waveguides are removed for better refractive index matching. (b) Parameters of the mode filter structure designed.
Fig. 13. The transition of the polarization-selective vertical coupler with different modes as input, and TE0 mode is specially marked out.
The performance and parameters in this study relative to those of other studies are listed in Table 1. The proposed design achieves a large layer gap and a low crosstalk on the premise of ensuring low transmission loss. On this basis, the vertical coupler with high polarization ER has not been previously reported, rendering the proposed design more advantageous.
Table 1. Performance comparison of vertical couplers
5. Application for interlaced AWGs
The layout of the multi-layer interlaced AWGs using the tri-layer vertical coupler is shown in Fig. 14(a). The overall structure of the AWGs can be divided into three parts. A high resolution AWG with 7 outputs, as the purple device in Fig. 14(a), is used as the first stage and placed at the bottom layer. The second part, where in the black dotted box in Fig. 14(a), are the vertical couplers, discussed in this paper, which connect the upper and lower AWGs. Finally, 7 coarse AWGs with 26 outputs are used and placed at the top layer, as the red part in Fig. 14(a). It can be seen intuitively that the use of a vertical multi-layer structure can reduce the area of the designed interlaced AWGs to one-half of its original size. Figure 14(b) shows the transmission spectrum of the multi-layer interleaved AWGs in the 2-µm band with a spectral resolution of 0.4 nm and crosstalk of about -33 dB.
Fig. 14. (a) The layout of the multi-layer interlaced AWGs, where in the black dotted box are the vertical couplers. (b) Simulation results of the proposed AWGs transmission.
6. Conclusion
We demonstrate a tri-layer gradient vertical coupler for 3D PICs with a large inter-layer gap of 2300 nm and low transfer loss and small multilayer crosstalk of -10.7 dB and -59.3 dB at 0° and 90° crossing angles, respectively. After width optimization, the fabrication tolerances toward lateral misalignment reach 1.45 µm for the first layer and 2.03 µm for the second layer at a transition loss of 0.5 dB. On this basis, we design a vertical coupler with mode selectivity, with the extinction ratio reaching 25.6 dB for the TM0 mode at 1950nm. Finally, we demonstrate the multi-layer interlaced AWGs based on inter-layer couplers, providing a reference for the multi-layer integration of 2-µm spectrum devices and the size of our AWG is only one-half of that using traditional design. The tri-layer inverse taper vertical coupler is expected to overcome the trade-off between transfer loss and multi-layer crossing loss and further develop special devices applied to 3D PICs.
Funding
National major scientific research instrument development project (61627802).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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