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For Si wire waveguides, we designed a highly efficient fiber coupling structure consisting of a Si inverted taper waveguide and a CMOS-compatible thin SiN waveguide with an SiO2 spacer inserted between them. By using a small SiN waveguide with a 310 nm-square core, the optical field can be expanded to correspond to a fiber with a 4.0-μm mode field diameter. A coupled waveguide system with the SiN waveguide and Si taper waveguide can provide low-loss and low-polarization-dependent mode conversion. Both losses in fiber-SiN waveguide coupling and SiN-Si waveguide mode conversion are no more than 1 dB in a wide wavelength bandwidth from 1.36 μm to 1.65 μm. Through a detailed analysis of the effective refractive indices in the coupled waveguide system, we can understand mode conversion accurately and also derive guidelines for reducing the polarization dependence and for shortening device length.
© 2016 Optical Society of America
1. Introduction
Si photonics technology is attracting attention for promoting developments in high-density photonic and photonic-electronic integrations [1,2]. With this technology, it is possible to form various ultra-compact photonic components as well as electric components on a base with a top Si layer on silicon-on-insulator (SOI) substrate [3–5]. The photonic components are generally constructed by using Si wire waveguides, which can strongly confine an optical field in a sub-micrometer core. Thus, Si-based photonic integrated circuits can be miniaturized to one-hundredth the size of silica-based ones. Moreover, the fabrication process is highly compatible with complementary metal-oxide semiconductor (CMOS) and applicable to a high-volume production technology with superior cost performance [6,7].
As an issue that should be solved in implementing Si photonic integrated circuit, there is a large coupling loss due to mode field mismatching between a Si wire waveguide and optical fiber. The mode field size in a Si wire waveguide is on the order of sub-micrometers, whereas the mode field diameter in an optical fiber is several micrometers. As a solution for this fiber-waveguide coupling issue, an inverted taper-based double-core fiber coupling structures has been proposed, and it has already provided highly efficient, low-polarization-dependent and wide-bandwidth optical coupling [8–13]. The conventional coupling structure consists of an adiabatic Si inverted taper overlaid with a secondary waveguide made of low-refractive-index materials such as silicon-rich silica (SiOx) [8,9] and silicon oxynitride (SiON) [10,11]. Depending on the mode field diameter of the optical fiber, the optimum core dimensions of the secondary waveguide are determined and formed to a level of several micrometers. However, fabricating a waveguide with such a large core requires thick-film processes, which are not supported in CMOS fabrication systems and reduce producibility. Recently, a silicon-nitride (SiN) waveguide-based edge coupler with an interlayer transition to Si waveguide was demonstrated [14–16]. The thickness of the SiN waveguide is 400 nm in this device and is CMOS-compatible. However, further improvement in fiber coupling performance would be required because optical field at the edge is still tightly confined in the SiN core. In the practical application of Si photonics technology, it is therefore very important to construct low-loss fiber coupling structures by using thin-film processes, which are suitable for standard CMOS fabrication systems.
In this paper, we propose a novel fiber coupling structure for a Si wire waveguide, in which CMOS-compatible thin-film processes are applied for the fabrication of the secondary waveguide. In this fiber coupling structure, as an alternative to the SiOx/SiON waveguide, an SiN waveguide with a very small core is used as the secondary waveguide.
2. Conceptual structure for fiber coupling
Figure 1 shows the proposed fiber coupling structure. The Si wire waveguide is formed on a sufficiently thick buried oxide (BOX) layer of the SOI wafer. The core of the Si wire waveguide is a rectangle and satisfies the single-mode condition for 1.55-μm wavelength. The width of the inverted taper with the Si wire waveguide narrows towards the tip, while its height is fixed. A silica-based spacer layer is inserted between the Si inverted taper waveguide and the SiN secondary waveguide. The SiN waveguide is straight and located parallel to the Si wire waveguide, and it is covered by a silica-based upper cladding. SiN has a relatively high refractive index of around 2.0, and the cross-sectional size of single-mode SiN waveguides is typically around a micrometer. The optical field guided into a typical single-mode SiN waveguide is tightly confined in the SiN core and cannot expand. In our proposed structure, we therefore apply a SiN waveguide with a very small core, which can expand the optical field enough for efficient fiber coupling. The core size can be determined so that the expanded optical field should match the field of the external optical fiber to be coupled. Such a large optical field in the SiN waveguide can be adiabatically converted to that in Si wire waveguide efficiently through a Si inverted-taper waveguide. In other words, the weak-confinement SiN waveguide with the small core plays the same role as a low-refractive-index SiOx/SiON waveguide with a large core. Hence, the standard CMOS fabrication process can be applied to the fiber coupling structure owing to the thin-film SiN waveguide of several hundred nanometers.
Fig. 1 Schematic drawing of fiber coupling structure consisting of a Si wire waveguide with an inverted taper and the SiN secondary waveguide. A silica-based spacer layer is inserted between them.
3. Design optimization and performance estimation
3.1 Structural model for device design
Figure 2 shows the structural model for device design. The structure consists of an SiN waveguide for fiber coupling and a Si wire waveguide for a photonic integrated circuit, respectively. The Si wire waveguide is formed on SOI substrate with a 3-μm-thick BOX layer. The width and height of the Si wire waveguide core are 420 and 220 nm, respectively. The refractive indices of the Si and BOX are 3.5 and 1.45, respectively. In addition, because of restrictions on fabrication techniques, the tip width of the Si inverted taper is defined as 80 nm, which is consistent with that of the conventional structure [17]. A planarized silicon dioxide (SiO2) spacer layer with a thickness Sspacer is inserted between the Si waveguide and the SiN secondary waveguide. The refractive indices of the spacer layer and SiN are 1.47 and 2.0. Since we assume low-temperature plasma-enhanced chemical vaper deposition methods will be used for the spacer film formation, the refractive index of the spacer is set a bit higher than that of the thermal oxide in the BOX. In order to reduce both polarization dependence and the number of design parameters, the square core is applied to the SiN waveguide and optimized so that coupling efficiency to the fiber should be maximized. The length of the Si inverted taper is denoted as Ltaper. For the launching sections at both ends, a 20-μm-long SiN waveguide and 20-μm-long SiN and untapered Si wire waveguides are assumed. The cross-sectional structure at the interface of the fiber coupling is shown in Fig. 2. The thickness of the SiO2 layer inserted between the SiN waveguide and BOX layer is equivalent to the sum of Sspacer and the height of the Si wire waveguide.
The mode field profiles and the effective refractive indices were calculated by using the finite difference method (FDM) and light propagation performance was simulated by using the eigen-mode expansion method (EME). The edge coupling performance between a fiber and a SiN waveguide was obtained by calculating the overlap integral of optical fields of the fiber and SiN waveguide. These calculations were performed by using commercially available software (Photon Design, FIMMWAVE/FIMMPROP) [18].
3.2 SiN waveguide
First, we designed the SiN secondary waveguide to provide efficient optical coupling with an external fiber. As an optical simulation model, we assumed that the SiN waveguide with a square core is surrounded by a sufficient thick SiO2 cladding and BOX layer whose refractive indices are 1.47 and 1.45, respectively. An ultra-high NA single-mode fiber with a mode-field diameter of 4.0 μm and is assumed for external guiding devices. The ultra-high NA fiber is widely used for the external optical coupling of silicon photonic chip with conventional spot size converters, and it can connect to an ordinary single-mode fiber with an optical loss less than 0.1 dB by applying a thermal expanded core (TEC) technology [17]. The wavelength of the guided light is 1.55 μm. Coupling efficiency between fiber and SiN waveguide was obtained by calculating the overlap integral of optical fields of fundamental modes of these two guiding devices. Figure 3 shows the coupling efficiency as a function of Sspacer and the core size of the SiN waveguide. The interlayer transition is not included in this calculation. The vertical asymmetry of the SiO2 cladding and BOX layer causes the coupling loss, and the coupling efficiency increases with increasing spacer thickness. The SiN waveguide with a 310-nm-square core provides the highest coupling efficiency for the quasi-TE and TM modes. This coupling efficiency is acceptable for practical applications. We therefore fixed this core size as the optimized one. The alignment tolerance between the fiber and SiN waveguide was estimated to be approximately ± 1 μm for an 1-dB excess loss in both horizontal and vertical directions.
Fig. 3 Coupling efficiency between the fiber and SiN waveguide as a function of Sspacer and the core size of the SiN waveguide for each mode. Interlayer transition region is not included in calculations.
Next, we took into account the optical leakage to the Si substrate under the BOX layer. The optical field in the optimized SiN waveguide is expanded to about a few micrometers so that fiber coupling efficiency should be maximized. The thickness of the BOX layer is typically not more than 3 μm. The distance between the SiN waveguide and Si substrate is the sum of Sspacer, the 220-nm-high Si waveguide, and the 3-μm-thick BOX layer. Therefore, the tail of the field might touch the Si substrate under the BOX layer and the optical power would leak into the substrate. The substrate-leakage loss is very sensitive to the distance between the waveguide and substrate. We calculated the substrate-leakage loss as a function of Sspacer. To quantitatively calculate optical leakage, we used a complex mode solver and set a perfectly matched layer (PML) for the Si substrate.
Figure 4 shows the calculated substrate-leakage loss for each polarization mode as functions of Sspacer. The substrate-leakage loss becomes lower with increasing Sspacer for both modes. In order to reduce the substrate-leakage loss, the distance between the SiN waveguide and substrate should be large. Since the mode field of the SiN waveguide for the quasi-TM mode is expanded in the vertical direction, the quasi-TM mode causes much larger substrate-leakage than the quasi-TE mode. For example, the substrate-leakage losses with Sspacer = 1.0 μm are 0.2 and 1.1 dB/cm for the quasi-TE and TM modes, respectively. Since the total length of the fiber coupling structure is no more than several hundred micrometers, these substrate-leakage losses are negligible.
3.3 Mode conversion efficiency
Figure 5 shows calculated mode conversion efficiency between the optimized SiN waveguide and Si wire waveguide as functions of Sspacer and Ltaper. In our proposed structure, to provide high mode-conversion efficiency, Sspacer and Ltaper should be thicker and longer, respectively. The spacer thickness required for high conversion efficiency is larger for the quasi-TM mode than for the quasi-TE mode, while the taper length required is longer for the quasi-TE mode. Therefore, the conditions for obtaining the high mode-conversion efficiency for both modes were restricted by the spacer thickness for the quasi-TM mode and the taper length for the quasi-TE mode. In Fig. 5, regions providing conversion efficiency of over 95% for both polarizations are indicated by dashed lines. This mode-conversion structure can provide high conversion efficiency in a wide area of Sspacer and Ltaper. Thus, the design and fabrication margins are very large. Figure 6 shows the simulation results for optical field propagating through the mode conversion structure with Sspacer = 1.0 μm and Ltaper = 500 μm. The optical field is adiabatically converted from the SiN waveguide to the Si wire waveguide through the Si inverted taper. Our proposed structure provides a low-loss and low-polarization-dependent mode conversion.
Fig. 5 Color-plotted mode-conversion efficiency as a function of the Sspacer and Ltaper for each mode. The dashed lines denote mode conversion efficiency above 95% for both modes.
Fig. 6 Simulated optical field propagating through the mode-conversion structure with design parameters, Sspacer = 1.0 μm and Ltaper = 500 μm for each mode.
3.4 Wavelength dependence
Figure 7 shows the wavelength dependence of coupling and mode-conversion losses. The wavelength of the guided light was set in the range of 1.25 μm to 1.65 μm, which is the range normally used in optical telecommunications. Figure 7(a) shows coupling loss between the optical fiber and the 310 nm-square SiN waveguide with Sspacer = 1.0 μm in the range from 1.25 μm to 1.65 μm. The SiN waveguide satisfies the single-mode condition in these wavelengths. The coupling loss of less than 1 dB was achieved at over 1.36-μm-wavelength for the quasi-TE and TM modes. Particularly, an excess loss was suppressed less than 0.25 dB in the range from 1.45 μm to 1.65 μm. Figure 7(b) shows the mode-conversion loss between the SiN waveguide and Si wire waveguide. We used Sspacer = 1.0 μm and Ltaper = 500 μm as representative design parameters. The mode-conversion loss of less than 0.5 dB was achieved in almost the entire range for both modes. Therefore, our proposed structure has low wavelength dependence and can operate in a wide wavelength bandwidth from 1.36 μm to 1.65 μm (E-, S-, C- and L-bands).
Fig. 7 Dependence of (a) coupling loss and (b) mode-conversion loss for each mode on calculated wavelength ranging from 1.25 μm to 1.65 μm.
4. Discussion
Here we analyze effective refractive indices in a coupled waveguide system using our proposed structure in detail to gain an understanding of this mode-conversion behavior. Based on our understanding, we discuss guidelines for reducing the polarization dependence and shortening device length.
The mode conversion structure is a coupled waveguide system consisting of an SiN waveguide and Si taper waveguide. The coupling behavior between the two waveguides greatly varies with the width of the Si taper waveguide, namely, the light propagation direction. The coupling behavior can be understood by analyzing effective refractive indices of guided modes of this coupled waveguide system. Figure 8(a) and 8(b) show the models for the effective refractive index calculation. The core width of the Si taper waveguide is adiabatically expanded from 0 to 420 nm, which is the core width of a normal Si waveguide. The core size of the SiN waveguide core is 310-nm-square, which was optimized as described in section 3.2. The coupling between the two waveguides is mainly performed in the region of the upper-cladding whose refractive index is 1.47. Therefore, to simplify the calculation, we define the refractive index of upper- and under-cladding as 1.47. Figure 8(c)–8(h) shows effective refractive indices of the guided modes as a function of the width of the Si taper waveguide for spacer thickness Sspacer = 0.5, 1.0 and 1.5 μm. The fundamental and high-order modes of the coupled waveguide system are indicated by solid lines. In addition, the fundamental modes of isolated SiN and Si waveguides are indicated by dashed lines. In each spacer thickness, effective refractive indices of the coupled waveguide system indicate anti-crossing behavior. They asymptotically approach the indices of the isolated Si and SiN waveguides. The anti-crossing indicates two waveguides are coupled, and the gap between two anti-crossing curves indicates coupling strength. At both ends of the device, the index approaches that of each isolated waveguide; in other words, the light is independently confined in each waveguide. Thus, the coupling strength becomes weaker with increasing spacer thickness and is stronger for the quasi-TM mode than for the quasi-TE mode. Figure 8(c) and 8(d) show the effective refractive indices of the coupled waveguide system in the mode-conversion structure designed with an 0.5-μm-thick spacer. Here, it should be noted that the tip width of the Si taper waveguide is defined as 80 nm from the viewpoint of fabrication techniques. For the quasi-TE mode [Fig. 8(c)], the effective refractive index of the coupled waveguide system with an 80-nm-wide Si waveguide core is almost the same as that of the isolated SiN waveguide. In other words, at the taper tip, the optical field is guided only by the SiN waveguide and is not coupled to the Si waveguide. Then, these two waveguides gradually couple to each other as the width of the Si waveguide core expands to the point where adiabatic mode conversion is performed. In contrast, for the quasi-TM mode [Fig. 8(d)], the effective refractive index of the coupled waveguide system at the taper tip is significantly larger than that of the isolated SiN waveguide. In other words, the two waveguides are already coupled strongly at the taper tip. The mode mismatch occurs at the interface of the isolated SiN and coupled waveguides. This mode mismatch loss in the quasi-TM mode can be eliminated by reducing the coupling of two waveguides at the taper tip. As shown in Figs. 8(e) and 8(g), in the coupled waveguide system with the thicker spacer, the effective refractive index at the taper tip becomes close to that of the isolated SiN waveguide, and the coupling of the two waveguides is significantly reduced. The coupled waveguide system with the thick spacer achieves the high mode-conversion efficiency for both modes. Therefore, the polarization dependence can be reduced by controlling the coupling strength.
Fig. 8 Calculation model. (a) Top view and (b) side view. Effective refractive indices as a function of the width of the Si taper waveguide are shown in (c) and (d) at Sspacer = 0.5 μm, (e) and (f) at Sspacer = 1.0 μm, and (g) and (h) at Sspacer = 1.5 μm for each mode. Red regions denote anti-crossing regions.
Next, we discuss how to shorten the Si taper. The method for shortening it can also be derived from the calculation results of effective refractive indices. In Fig. 8(c)–8(h), typical anti-crossing structures are indicated in the red-shaded regions, where the SiN and Si waveguides are strongly coupled and mode conversion is performed. In the regions outside the anti-crossing regions, these two waveguides are not coupled and mode conversion is not performed. Figure 9 shows field distributions of the guided modes in the coupled waveguide system at various positions (i) – (iv) in Fig. 8(e) and 8(f). In these field distributions, we can confirm that the strong coupling occurs only in the anti-crossing regions. In order to obtain high mode-conversion efficiency, the conversion should be adiabatic and the anti-crossing regions should be long. The region outside the anti-crossing one does not contribute to the mode conversion; therefore, the length of this region can be reduced as much as it is possible to do so and still guarantee optical confinement. Thus, we can employ a two-step taper to shorten the mode-conversion structure. For example, for spacer thickness Sspacer = 1.0 μm, we can achieve high mode-conversion efficiency equal to a 500-μm-long linear taper by using a 195-μm-long two-step taper, where one step is 175-μm long and the other is 20-μm long. The former is a linear taper which gradually slants from 80 nm to 220 nm, whereas the latter steeply slants from 220 nm to 420 nm. Fiber coupling sufficient for practical applications can be provided by controlling the coupling strength between the waveguides and optimizing the taper design. These guidelines based on the analysis of the effective refractive indices are very useful for designing an efficient fiber-coupling structure.
Fig. 9 Simulated electromagnetic field distribution in the coupled waveguide system at various positions (i) – (iv) in Fig. 8(e) and (f).
5. Conclusion
We proposed and designed a CMOS-compatible, highly efficient fiber coupling structure for Si wire waveguides. The coupling structure consists of a Si taper waveguide and a small SiN secondary waveguide. The structure has two functions: low-loss coupling between a fiber and the SiN waveguide, and a low-loss mode conversion between the SiN and Si waveguides. A SiN waveguide with a 310-nm-square core can provide low-loss and polarization-independent fiber coupling with efficiency of over 94% for a fiber with a 4.0-μm mode-field diameter. An optimized SiN-Si coupled waveguide structure can provide low-loss and low-polarization-dependent mode conversion with a conversion efficiency of over 95%. Both the coupling and mode-conversion losses of the optimized structure are no more than 1 dB in a wide wavelength bandwidth from 1.36 μm to 1.65 μm (E-, S-, C- and L-bands). We obtained an accurately understanding of the mode conversion from an analysis of the effective refractive indices of the coupled waveguide systems and demonstrated guidelines for reducing the polarization dependence and for shortening device length.
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