We present the novel design of a spot-size converter (SSC) for high efficiency coupling between a conventional single-mode fiber (SMF) and a standard silicon nanowire. Our design involves evanescent coupling between a stack of Si3N4/SiO2 alternating layers and a standard silicon nanowire. The proposed SSC coupler demonstrates highly broadband performance with a polarization dependence of less than 0.62 dB and an expected taper loss of less than 1.0 dB, over 100 nm bandwidth ranging from 1.5 to 1.6 µm. To the best of our knowledge, the proposed SSC achieves the highest broadband coupling for both polarizations between a fiber with a large mode-field diameter (i.e., SMF-28) and a standard silicon nanowire.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Silicon photonics has attracted a lot of attention in recent years. The main motivation behind it is its compatibility with the well-established microelectronics industry. Moreover, due to the high refractive index contrast between silicon and silicon dioxide, the dimensions of the waveguides can be on the order of sub-micrometers. Therefore, higher confinement, sharp bends and dense integration can be obtained [1,2]. Silicon based Optical Integrated circuits (OICs), hence, can be mass-produced. However, an efficient and cost-effective solution to interface between a silicon nanowire waveguide on the OIC and a conventional single-mode fiber (SMF) has yet to be presented. Currently, the two most frequently used approaches are grating couplers and edge couplers.
Grating couplers provide out of plane coupling with a fiber placed vertically on top of the grating (usually at a small angle) enabling testing at the wafer-level. In general the efficiencies of grating couplers are not very high [3,4], and they are polarization sensitive. Moreover, by principle, grating couplers have limited bandwidths. However, various broadband [5,6] polarization insensitive [7,8] and high efficiency  designs have been presented recently. Edge couplers, on the other hand, are butt-coupled to the fiber at the side of the chip. Intensive research has been carried out in the field of inverted tapered edge-couplers [10–24]. Most of the inverted tapers studied previously are designed for coupling with lensed or tapered fibers that have a smaller mode-field diameter than conventional SMF [13–15,19–24] and coupling loses lower than 1 dB [10–14] have been reported. These are generally broadband [15–18] and polarization insensitive couplers [14–15,18–19]. Inverted tapers using subwavelength grating (SWG)  have gained popularity in recent years due to their efficient broadband coupling. However, these couplers are designed to mode match with a small mode-field diameter (MFD) of ∼3 µm. To couple these inverted tapers to SMF-28 (with an MFD ∼10.4 µm), local substrate removal is mandatory to prevent leakage to the substrate. In addition, even though one lithographic step is enough to define the SWG pattern, the minimum grating features of 194 nm in the longitudinal direction will require high precision fabrication. In our work, the proposed edge coupler proposed is designed to target an MFD of ∼10.4 µm without the need for local substrate removal but at the cost of a longer device. Moreover, the lithography pattern in our design does not have small features in the direction of propagation. It is noted that there are specific fabrication challenges associated with our proposed design, which are discussed in details in section 4 along with fabrication tolerances. For edge couplers to achieve better alignment tolerance, a spot-size converter (SSC) is usually used to match the MFD of an edge coupler to that of a conventional SMF (of 4.2 µm core radius or mode diameter of ∼10.4 µm) [17–18,25]. An SSC optimized for coupling with SMF of MFD ∼10.4 µm [17–18,25] can more than double the alignment tolerance in comparison to an SSC coupled with a HNA fiber with a MFD ∼6 µm .
In fact, an optimal mode-field matching with high alignment tolerance at the coupling interface is beneficial for high-volume manufacturing and minimizing the packaging costs. Papes et al.  presented a broadband SSC design using three Si3N4 layers. However, this design is only effective for the TE mode. Previous broadband and polarization insensitive SSC designs for coupling between a conventional SMF and a nanowire reported in literature have stringent fabrication requirements [17,18]. One of the designs is based on a double stage taper with a minimum simulated coupling loss of 1.4 dB for both polarizations; however, it requires a nanowire taper tip of less than 150 nm . The second design is based on SiN inverse taper combined with an etch-based substrate removal process to prevent leakage into the substrate. A coupling efficiency of −3 dB for both polarizations has been demonstrated for this design .
In this article, we propose a novel tapered multilayer SSC design for edge-coupling between a single-mode nanowire in an OIC and a conventional SMF, which provides a higher simulated coupling efficiency than the previous designs. Moreover, the width of the taper tip of the nanowire is 150 nm, which can be fabricated without advanced e-beam lithography. The coupler has been optimized to achieve the best coupling efficiency while minimizing the polarization dependent loss. The design presented is highly broadband and its fabrication tolerances are also been studied in details.
2. Taper design optimization
Our previous work on spot-size converter proposed a configuration with a multilayer stack of dielectrics [26,27]. Although the previous two designs work well for mode conversion at 1550 nm, they are both sensitive to fabrication variations, wavelength and polarization. In this work, we propose a new design which is broadband and polarization independent. The advantage of using a multilayer stack of dielectrics instead of using a large core of homogenous material [17,20] is that an arbitrary effective index can be readily implemented with common fabrication materials. The initial optimization for this design is discussed in . Figure 1 shows the proposed SSC design with a tapered stack of Si3N4/SiO2 layers forming the input waveguide and a silicon nanowire (NW).
For maximum modal overlap between a SMF and the stack layers, the width of the stack is set to W = 14 µm. The total thickness of the stack is 12.3 µm, with seventeen layers of alternating 300 nm (ts) Si3N4 and sixteen layers of 450 nm (ti) SiO2. The top cladding of SiO2 has a thickness of 1 µm. The single-mode NW has a cross-sectional geometry of 420 nm × 220 nm, with a tapered tip at the facet edge of 150 nm × 220 nm. The spacing between the stack and the NW is designed to be 500 nm for optimal coupling from the supermodes in the stack down to the NW. The buried oxide layer (BOX) is set to 3 µm. The refractive indices at λ = 1.55 µm for Si, SiO2 and Si3N4 are assumed to be 3.476, 1.444 and 1.996, respectively.
All the geometrical dimensions W, ti, ts and the number of layers in the stack have been optimized to reach the maximum modal overlap with a conventional SMF. The overlap between the first TE mode of the multimoded SSC and the fiber TE mode was found to be 94%. Similarly, the mode overlap between the first TM mode of the SSC and the fiber TM mode was 99%. Furthermore, we found that seventeen layered stack offers optimal mode matching between the fiber and the stack. Increasing the number of layers beyond seventeen provides very slight improvement to the modal overlap for both polarizations.
The number of layers in the stack can be reduced to simplify fabrication; however, this comes at the cost of a reduction in the overlap between the mode of the fiber and the one of the SSC. Therefore, we investigate the overlap of the TE0 and TM0 supermodes of the stack with the fundamental mode of the fiber for different numbers of layers in the stack. It was observed that the maximum overlap with the fundamental fiber mode is obtained when the thickness of the Si3N4 layers is minimized. Therefore, we fixed the Si3N4 layer thickness to 225 nm since it is the minimum value for which the mode remains confined. We then decreased the number of layers in the stack and optimized the spacing between the stack layers to get the maximum overlap with the fiber as shown in Table 1. For the seventeen-layer stack, the overlap shown in Table 1 with these slightly different optimized thicknesses is the same as the one obtained with our design. It can be seen that by decreasing the number of layers in the stack, the overlap of modal fields at the interface falls off more rapidly for the TE mode than the TM mode. For eleven layers the overlap is ∼90%-97% whereas for seven layers it is 80%-92% for the TE and TM modes.
The stack taper has been divided into three tapered sections, with a total length of L1 along the propagation direction, as shown in Fig. 1. The stack is first tapered from W = 14 µm to a width of 757 nm (taper tip) while the tip of the NW remains at WNW = 150 nm. A stack taper tip of 757 nm is chosen because for this width the birefringence of the stack is zero. In the next tapered region of total length L2 along the propagation direction, the stack width is kept fixed at 757 nm and the NW width is increased from 150 nm to its final width of 420 nm. The stack of W = 757 nm and the NW, when analyzed separately, become phase-matched at a NW width of WNW = 216.5 nm. The modes of the SSC or the supermodes of the overall structure are a linear combination of the modes of the NW and of the stack waveguide. The relationship between the effective indices of the supermodes in the SSC and the variations in NW widths is shown in Fig. 2. The solid curves represent the TE0 and TM0 modes of the NW. The horizontal dotted line represents the fundamental stack mode for a width 757 nm. The dash double-dotted and dashed curves represent the TE and TM supermodes of the SSC, respectively.
In a simple directional coupler between a single-mode waveguide and a NW, the effective index of the second supermode (TE1/TM1) would first increase with WNW and for a WNW higher than the phase-matching width, the index would remain constant (at a value approximately equal to the effective index of the single-mode waveguide). However, in our case, the directional coupler is a combination of a multimoded stack waveguide and a NW. We find that the effective index of the TE1/TM1 supermode coincides with the TE0/TM0 mode of the stack represented by the horizontal dotted line in Fig. 2. This is because for WNW lower than the phase-matching width, 216.5 nm, the second supermode is not the anti-symmetric combination of the fundamental mode of the NW and the stack. The TE1/TM1 mode is actually the second mode of the multimoded stack waveguide. This effective index is very close to the fundamental effective index of the stack; therefore, it almost overlaps with the TE0/TM0 dotted line of the stack. The birefringence of the NW is zero at WNW = 217 nm. Further, we can observe that the intersection point of the effective indices of TE0 and TM0 supermodes in Fig. 2 is very close to the phase-matching condition. Therefore, the birefringence of the SSC is nearly zero around the phase-matching condition and a polarization insensitive behavior is expected from this SSC at the phase-matching condition.
The first cross-over point between TE0 and TM0 supermodes of the SSC (see inset of Fig. 2), while most of the power is still in the stack, is the most sensitive region of the taper. Therefore, an adiabatic transfer of power around this region (between WNW = 150 nm to WNW = 160 nm), requires a long taper length. The adiabatic transformation of the TE0/TM0 supermode of the SSC along the taper length is determined by evaluating the total transmitted power or the square of the S-parameter S21 using the Eigenmode Expansion (EME) method of the MODE Solutions tool from Lumerical. EME simulations are computationally efficient and can provide the same accuracy as 3D-FDTD  but in a much shorter time. First, the stack taper is piecewise analyzed and its length is optimized for the propagation of the first supermode. As shown in Fig. 1(b), the first taper section starts with the stack width, W = 14 µm, which falls rapidly down to 2.4 µm along a taper of length L1a = 275 µm, followed by a taper of length L1b = 10 µm, reducing the width from 2.4 µm down to 800 nm. Finally, the taper width is reduced from 800 nm to 757 nm using a taper of length L1c = 450 µm. The last stack taper section (L1c) is more sensitive to the adiabatic TE mode propagation compared to the TM mode, since in this region the TE0 supermode is the fundamental mode of the SSC. The total optimal length of the stack taper is L1 = 735 µm. In the next taper section, the stack has a fixed width but the NW increases slowly from 150 nm to 180 nm in width along a taper of length L2a = 1035 µm. This L2a region is sensitive to the adiabatic transformation of the TM mode, since in this region the TM0 supermode is the fundamental mode of the SSC. Thus, L2a requires a long length to provide a conversion efficiency as high as that of the TE mode. Figure 3 shows the power transmission through the entire SSC when the taper length of this section is varied and the length of all the other sections are fixed at the optimized values. It is followed by a taper of length L2b = 100 µm where the NW width exponentially increases from 180 nm to 420 nm. The total length of the NW taper is thus L2 = 1135 µm.
The total conversion efficiency obtained for the TE and TM mode is 91.2% (0.4 dB) and 90.4% (0.43 dB), respectively, for a total SSC device length of 1870 µm. It is important to note that the total SSC device length would be much shorter (<63%) if the optimization was carried out for only one polarization. For example, if only the TE polarization is considered, a total SSC length of 1185 µm will achieve a conversion efficiency of 95%.
Figures 4(a) and 4(b) show the side-view and the top-view of the absolute value of electric field distributions along the center of the SSC, respectively when the TE0 mode is input from the facet edge. The cross-sectional mode profiles of the TE0 mode along the SSC at the edge and center positions along the tapered region (marked as (i) to (iv) in Fig. 1(b)) are compared in Fig. 5 (a) to (d). At the facet edge in position (i), the supermode TE profile closely matches to that of the fiber mode with a 94% mode overlap. As the mode propagates along the taper, the TE mode is squeezed out of the stack block and enters into the NW. By the end of the taper section in position (iv), the mode is transferred entirely from the stack block into the TE0 mode of the NW. The transition of the TM0 supermode has a similar trend as what is observed in Figs. 4 and 5. The modal overlap of the TM0 mode of the SSC with the fiber TM mode is greater than 99%.
The wavelength dependence of the TE and TM modes of the SSC is shown in Fig. 6. It can be seen that the 1 dB bandwidth of the device is more than 100 nm over the wavelength range from 1.5 µm to 1.6 µm for both polarizations. Therefore, the designed SSC not only has a very small polarization dependence but is also highly broadband. The total coupling efficiency including facet edge coupling for the TE and TM mode is 0.71 dB and 0.48 dB, respectively at λ = 1.55 µm. The Fresnel reflection due to effective index mismatch at the input/output interfaces between the SMF and SSC is taken into account in the total loss calculations. It should be noted that the efficiency is much higher than the previously reported value of 1.4 dB for coupling to SMF . We also believe that the substrate leakage loss is minimal as the supermodes in the stack block are highly confined within the layers, far away from the substrate [16,25]. We would like to point out that the scattering and propagation loss in the waveguides are not taken into account as it is difficult to predict the experimental values.
4. Fabrication tolerances
Next we investigate the fabrication tolerances of our design. The fabrication steps and the material considered in the SSC are completely compatible with CMOS processes, requiring CVD growth of alternating Si3N4 and SiO2 layers. It is also noted that the fabrication difficulties can increase with the number of layers due to mechanical stress. However, the deposition of low stress Si3N4 films reported in [29–31] offers a promising opportunity for successful fabrication of the multilayer stack structure. In fact, multilayer Si3N4 devices having comparable and even higher thickness compared to the stack proposed here have already been successfully demonstrated [30,31]. Moreover, only one mask would be required for etching all the layers of the stack.
Considering that fabrication errors can produce variations in the widths of the tapers, we simulate the transmission efficiency of the SSC after introducing variations in the widths of both the stack and NW taper tips either simultaneously, or independently. Figure 7 shows the loss in response to width variations of both the stack and NW taper tip. Overall, the taper loss for both TE and TM is below 0.6 dB for variations of −40 nm to +10 nm. The taper loss for the TM mode increases rapidly when the NW width is increased by 20 nm, which corresponds to over 13% of error in the NW width. It is important to note that the width of the stack might vary by a large amount after the etching step if the walls of the stack are slanted and not as vertical as assumed initially in the design. The NW width should not vary as much as the stack width since the silicon layer is assumed to be 220 nm—much thinner than the stack. Hence, we calculate the taper loss by varying the stack width independently. In this case, the total loss is below 1 dB for a 60 nm deviation in the stack taper tip width as shown by the blue solid and dotted curves in Fig. 7. The overall performance of the SSC is sensitive to the stack width. Before fabricating the final design, short-loops of the experimental processes will be required to analyze the achievable sidewall angles with respect to a given aspect ratio of the stack, offering statistically estimated fabrication variations from the process sequence. Development of device fabrication processes and process sequences, along with adjustments in the initial design based on the prediction of the sidewall angles can help achieve the initial design performance. For example, assuming that the sidewalls have an 80° angle, a transmission of 97% is obtained for the TE mode when the NW taper tip width is increased from 180 nm to 250 nm and the taper lengths are L1a = 400 µm, L1b = 200 µm, L1c = 100 µm, L2a = 10 µm and L2b = 1000 µm, respectively. The total length is even smaller than the initial design and can be reduced by further optimizing the shape of the tapers.
We also studied the fabrication tolerances of the thickness of the Si3N4 (ts) and of the SiO2 (ti) layers produced by the CVD growth. Figures 8 shows the taper loss as a function of variations in the thicknesses of Si3N4 and SiO2 layers in the stack block, varied both independently and simultaneously. Note that it is assumed that the thickness of all the layers of the same material change by the same amount. Figure 8 (left) shows the taper loss variation for the TE0 supermode and Fig. 8 (right) for the TM0 supermode. The thicknesses ts and ti are changed from their nominal values of 300 nm and 450 nm by ±20 nm. This accounts for 4.5% and 6.7% variations from the optimal thickness of SiO2 and Si3N4 layers, respectively. It can be seen from these figures that the taper loss is most sensitive to the thickness of the Si3N4 layer as shown by the dashed line. A fabrication variation of ±10 nm in the thickness increases the loss by less than 1.0 dB and 0.51 dB for the TE and TM modes, respectively. It can also be observed that for fabrication variations of the same value for both layers (as shown by the solid blue curve), the sensitivity to change of the taper loss reduces. However, as expected, for equal and opposite shifts in thickness of both layers (as shown by solid pink curve), the taper loss sensitivity increases for increases in thickness of the Si3N4 layers in case of the TE mode but for the TM mode the sensitivity increases when this thickness decreases.
Next, we study the effect of the variation in the thickness of the 500 nm buffer layer between the NW and the stack on the taper loss. Figure 9 (left) shows the taper loss variation for both the TE and TM modes when this thickness is varied by ±20 nm. For a ±10 nm variation, the loss increases by less than 0.45 dB and 0.11 dB for the TE and TM mode, respectively.
Lastly, we investigate the effect of lateral misalignment between the NW and stack waveguide, such that the centers of the NW and stack are horizontally displaced with respect to one another. Figure 9 (right) shows the taper loss variation for both the TE and TM modes when this alignment is varied by ±100 nm. For a ±50 nm variation, the loss increases by 0.48 dB and 0.54 dB for TE and TM mode, respectively.
In summary, the proposed SSC design provides a highly efficient and broadband coupling with low polarization dependence between a silicon nanowire and a conventional single-mode fiber. The SSC has a record low total taper loss of 0.40 dB and 0.43 dB for the TE and TM polarizations, respectively, at λ = 1.55 µm. Based on the concept of evanescent coupling between an inverted nanowire taper and a stack taper, the proposed SSC is highly broadband. The design demonstrates a total taper loss variation of less than 0.6 dB for both polarizations over a 100 nm bandwidth in the wavelength range from 1.50 µm to 1.60 µm. The mode overlap between the fundamental mode of the SSC and a conventional single-mode fiber of core radius 4.2 µm is 94-99%. Moreover, the performance of the SSC is affected by less than 1 dB with variations of 60 nm in the width of the stack taper tip or 20 nm in the thickness of the Si3N4 layers (i.e. the most sensitive layer in the stack). For a 20 nm variation in the spacing between the nanowire and the stack, the performance changes by less than 0.45 dB. Similarly, for lateral misalignment of 100 nm between the NW and stack waveguide, the performance changes by less than 0.54 dB. Although precaution is required against stress deformation in the multilayer deposition of the stack block, we believe the proposed SSC design is still practical for fabrication since Si3N4 and SiO2 produce mechanical stress of opposite direction (tensile for Si3N4 and compressive for SiO2) that can partially offset each other. The key advantage of the proposed broadband and low polarization sensitivity SSC lies in its ability to enable direct butt-coupling to a conventional single mode fiber with only minor mode mismatch losses. We believe the proposed design will be useful for silicon photonic circuits due to the significant reduction in packaging costs.
Shastri Indo-Canadian Institute (SICI); Natural Sciences and Engineering Research Council of Canada (NSERC); Canada Research Chairs (CRC).
N. Kohli would like to thank Dr. Vladyslav Vakarin for the fruitful discussions.
The authors declare that there are no conflicts of interest related to this article.
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