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We propose a novel silicon-on-insulator (SOI) wavelength diplexer design based on an adiabatic bent taper and an unconventional multimode waveguide. The geometry of the device is optimized using particle swarm optimization (PSO). The device has an ultra-short length of 15 μm. Simulated insertion loss at peak wavelength is less than 0.25 dB with 1-dB bandwidth around 100 nm for both O band and C band. The device is fabrication tolerant as demonstrated by simulated yield estimates. The reported design targets 1310 and 1550 nm as peak wavelengths; the design methodology is easily applicable to other wavelengths of interest.
© 2014 Optical Society of America
1. Introduction
Silicon photonics [1,2] has great potential for integration in fiber communication systems with the potential to further reduce costs. The O-band and C-band are of interest for any fiber-based transmission due to the low loss of glass in those bands. But commercially, operation in both bands on a single fiber is chiefly found in passive optical networks (PON) for fiber-to-the-X (FTTX) applications (where X can be “home,” “building,” “curb,” etc.). Many C-band designs for integrated, silicon-on-insulator (SOI) optical components have been demonstrated, including all kinds of basic passive building blocks [3–7], high-speed modulators [8,9] and photodetectors [10,11]. Hybrid evanescent coupled lasers [12] as well as silicon external cavity lasers [13] have also been developed for system integration. Although O-band designs are less frequently reported [14–16], there is no inherent obstacle to extending C-band designs to the O-band on the SOI platform. However to integrate PON optics, an integrable high-performance SOI wavelength diplexer that can combine/split these two bands is desperately needed.
In previous work, three typical structures are involved in the design of an SOI O/C band diplexer: diffractive grating coupler, a resonator-based structure and a multimode interference (MMI) coupler. Grating-coupler based diplexer designs were reported [17,18] but the insertion loss is high, 2.6 dB in Ref [17]. and 5 dB in Ref [18]. Another drawback of this structure is that it is designed for coupling light on/off chip, it cannot deal with an on-chip interconnect. A silicon microring-resonator based diplexer was reported for a PON optical network unit (ONU) [19]. The insertion loss for such a design is small but the bandwidth is limited. Different ring geometries are required to deal with different wavelengths across a band. Extra control systems are needed since silicon microrings are quite temperature sensitive. These two factors limit the microring diplexer designs from practical PON applications. Alternatively, MMI-coupler-based diplexer designs have relatively low insertion loss and wide bandwidth. But the footprint usually exceeds hundreds of microns from the results reported in both SOI and III-V materials [20–22]. Currently a truly passive, low-loss, broadband integrated diplexer design with compact footprint and good fabrication tolerance is needed.
In this paper, we propose a novel SOI diplexer design for O-/C-band wavelength multiplex/de-multiplex applications. The fundamental principle of the proposed device is based on the design of the MMI coupler. This device is very efficient, wideband, ultra- compact and fabrication tolerant. An efficiency higher than 94.4% (i.e., insertion loss < 0.25 dB) is achieved for both bands from 3D finite difference time domain (FDTD) simulation with a device less than 15 μm long. The 1-dB bandwidth is about 100 nm. Yield analysis shows a fabrication tolerance of ± 20 nm deviation in the critical dimensions.
2. Design and optimization
The fundamental operating principle of a conventional MMI diplexer is the self-imaging effect; one or multiple images of the input field profile is periodically reproduced as the light propagates along a multimode waveguide region [23]. This effect has been widely applied to designing M × N couplers, such as coherent hybrid mixers (2 × 2, 2 × 4, 4 × 4 MMI coupler) [5,24]. Furthermore, due to geometry dispersion of the waveguide (i.e., the effective index, neff , is a function of waveguide width), the self-imaging spots in the coupler deviate laterally for different wavelengths. As a result, a 2 × 2 MMI can achieve wavelength diplexing, as illustrated in Fig. 1(a).
Fig. 1 (a) Schematic of a conventional MMI-based diplexer. (b) Schematic of a novel MMI-based diplexer using a combined bent taper and multimode waveguide.
Without loss of generality, both wavelengths, λ1 and λ2, are launched into the lower left port in Fig. 1(a). Note that for real applications, two wavelengths may travel contra-directionally but the performance is guaranteed by the reciprocity of a two port passive optical system. In conventional 2 × 2 MMI duplex design where a multimode straight waveguide is applied, the length of MMI, LMMI, must satisfy the following mode matching condition [22] in order to efficiently split two wavelengths:
where p is a positive integer, q is an odd integer (usually set to 1), andis the beat length of two lowest modes at wavelength λ. neff0 and neff1 are the effective index of these two modes. To slightly relax the mode matching condition and to improve splitting efficiency of the targeted peak wavelengths, an asymmetric structure is usually introduced at the output side of diplexer (right side in Fig. 1(a)) [20,21].A different way to reduce LMMI is to consider the reciprocal property of a passive silicon photonic device. The middle of Fig. 1(a) indicates an arbitrary intermediate E-field of the MMI when launching TE0 field at the left side. If one can initially launch an exactly same field profile at the same spot to the MMI coupler, one can imagine that same output profile can be obtained. But the device working distance is greatly reduced now since the MMI effectively starts working from the middle.
Following this idea, here we introduce a novel design to realize both a highly efficient wavelength separation and ultra-compact device size. The schematic is shown in Fig. 1 (b). The device can be divided into two seamlessly jointed parts:
Part 1: An asymmetric S-bend like taper that adiabatically transits from single mode region to multimode region. We refer to it as a bent taper. The bent taper is used to excite a well-defined initial field profile as indicated in Fig. 1(b).
Part 2: A symmetric MMI region. The MMI geometry is engineered with particle swarm optimization (PSO), similar to the ones reported to realize highly efficient Y-junction and waveguide crossing [6,7]. We refer to it as a PSO MMI.
The first advantage of this design is the compact device size. Compact device size calls for small beat length Lπ(λ) as well as p, q numbers from Eq. (1). And from Eq. (2), one finds small Lπ(λ) requires large effective index difference between the lowest two modes, i.e., [neff0(λ) − neff1(λ)]. From calculations of the effective index versus waveguide width, shown in Fig. 2(a), [neff0(λ) − neff1(λ)] decreases dramatically as waveguide width increases from single mode region to multi-mode region. The material here is chose to be 220 nm Si on 2 μm buried oxide (BOX). The top cladding is also SiO2. A similar relationship applies to other SOI thicknesses. The resulting beat length is depicted in Fig. 2(b). At a 3 μm wide region, Lπ (1550) ≈22 μm, which is about 10 times larger than that of a 1 μm-wide region. Similar results can be obtained at 1310 nm. Small waveguide width, WMMI, is chosen for Part 2 of Fig. 1(b), in order to shrink the footprint of the MMI coupler-based diplexer.
As observed from Fig. 2(a), [neff0(λ) − neff1(λ)] is more sensitive to the change of waveguide width at smaller widths, which means a narrower MMI coupler is less tolerant of fabrication variation. In order to keep the design within a decent fabrication tolerance regime, the device length must be short if we choose small WMMI. Since q is usually set to 1, p must be small. But p cannot be easily controlled in a conventional geometry like Fig. 1(a). To relax the rigorous restraint of p value, we introduce a bent taper (Part 1) before the MMI (Part 2), as shown in Fig. 1(b). The bent taper here, like a short non-adiabatic linear taper, serves as a multimode excitation tool to provide an initial field profile to Part 2. The multimode excitation can happen in a very short distance. However, different from linear tapers, bent taper is asymmetric and has more complicated geometry, thus offers us more freedom to engineer the multimode mixing for different wavelengths. Regardless of bent taper or MMI, any field profile in a multimode waveguide is a superposition of the supported eigenmodes of the waveguide. In this sense, a well-engineered bent taper can thus provide a well-defined initial field (more complicated than a TE0 profile) for the MMI to reduce the its working distance. By introducing the bent-taper, the device length can be reduced and hence, the fabrication tolerance is increased.
Another feature of this design is the high efficiency. A narrower MMI usually has more scattering loss and crosstalk at the output ports due to that fact that the E-field is less confined and separated. We use a PSO MMI coupler in Part 2 instead of a conventional straight MMI coupler to optimize the device performance after cascading the bent taper with a PSO MMI coupler.
The overall schematic geometry of the diplexer design is shown in Fig. 3(a). Light enters the left end to the bent taper, propagates in the PSO MMI region, and splits at the right end. The upper and lower ports are marked as Port 1 and Port 2 respectively. Note for both ports, a 0.8um long taper is used to connect the S-bend with the right end of PSO MMI. The input waveguide width at left end and the starting width of the tapers at the right are all 500 nm. In this paper, S-bend width of port1 is maintained 500nm and the width of port2 is tapered to 420nm to guide single mode 1310 nm signal. One can set other widths of interests for different target wavelengths.
Fig. 3 (a) Design of a diplexer consists of a bent taper cascaded with a PSO MMI. Light enters from the left end and splits at the right end into two S-bends with bend radius of 6 μm. (b). Detailed design parameters of a bent taper. (c). Detailed design parameters of the PSO MMI.
Geometry detail of the proposed bent taper is shown in Fig. 3(b). The geometry engineering of the bent taper starts from a normal S-bend. Universally, an S-bend waveguide can be defined by three factors: center radius R0, vertical offset dy, and waveguide width. In waveguide routing, it is common practice to avoid using multimode S-bend to eliminate multimode mixing. However, such multimode mixing can be of use if its behavior can be tailored. Instead of fixing the waveguide width as a constant, we choose to vary it at different angles. As seen in Fig. 3(b), we break the S-bend into 8 segments of equal angles, dθ, and do interpolation between each segment to make the transitions smooth. The waveguide width of a S-bend is relative to the center radius R0. The center radius R0 divides the S-bend into the up side and the down side. We choose asymmetric widths to increase the optimization freedom. Therefore, we have two sets of independent width parameters: {U1, U2, U3, …, U9} and {D1, D2, D3, …, D9}, as indicated in Fig. 3(b).
The bent taper is then connected with the PSO MMI coupler, as depicted in Fig. 3(c). Similar to Ref [6], the PSO MMI is symmetric and evenly divided into 8 parts by defining {W1, W2, W3, …., W9}; interpolation is used to smooth the geometry. The simulations are carried out by Lumerical 3D FDTD Solutions. Material dispersion is a built-in property of the simulation tool.
Optimization is divided into two phases. First, we optimize the bent taper. In this phase we take the PSO MMI as a normal MMI with constant width, i.e., W1 = W2 = W3 = …. = W9 = W. Here W is chosen to be 1.25 µm so after connecting the MMI with two lead out waveguides, it still leaves a 250 nm gap in between S-bends to avoid violating the minimum feature size rule of a CMOS-compatible fabrication process. We also fix LMMI to be 8 µm. Note that {Wi} and LMMI may change in the second optimization phase. The vertical offset, dy, of the bent taper is set to be 1.1 µm. We then optimize the center radius R0 as well as the S-bend width parameters {Ui} and {Di}. Since the design goal is to reach a highly-efficient wavelength diplexer, the design figure of merit (FOM) in this step was chosen to be the average transmittance of the two-targeted wavelengths, i.e., FOM = [T(λ1) + T(λ2)]/2. Here we set λ1 = 1550 nm, and λ2 = 1310 nm. To make seamless connections, U1 and D1 at the narrow end are both fixed to be 0.25 µm to connect with the input single mode waveguide while U9 and D9 at the wide end are fixed to be 0.625 µm to connect with the MMI coupler. By only optimizing the R0 and the first two segments (U2, U3 and D2, D3), a FOM = 88% can be reached. The rest of the parameters are kept the same for the wide end. Optimizing all the eight segments actually does not increase the FOM but forms sharp wavy geometries that are unwanted for fabrication. R0 is found to be 6 µm after the first step of optimization. The length of the bent taper can thus be calculated to be 5.02 μm. The final width parameters {Ui} and {Di} of the bent taper are listed in Table 1. Note the nm resolution in Table1 is rather the simulation accuracy than the required fabrication accuracy. Fabrication tolerance will be discussed at section 3.
Table 1. Bent taper geometry parameters (μm)
The second phase is to optimize the MMI part to further increase the diplexing efficiency and to balance the performance of each port. By taking the degree of unbalance of the two ports into consideration, we modify the FOM to be [T(λ1) + T(λ2)]/2 − | T(λ1) − T(λ2)|. In this step we optimize W2 to W9 as well as LMMI. W1 is fixed to be 1.25 µm to make the connection with the bent taper. With LMMI = 9.173 µm and {Wi} as listed in Table 2, the best FOM is found to be 95.3%. Note the slowly-varying geometry of the final PSO MMI shown in Fig. 3(c) is suitable for fabrication.
Table 2. PSO MMI geometry parameters (μm)
E-field plots in Fig. 4(a) and (b) clearly show the diplexing functionality of the design. Both wavelengths enter from the left end. Within a footprint of less than 15 × 2 μm2, 1550 nm is efficiently routed to port 1 and 1310 nm to port 2 with very weak crosstalk as well as scattering. The performance is plotted in Fig. 4(c). The peaks are closely centered around 1310 nm and 1550 nm, respectively, as indicated by the red lines. Crosstalk is below −20 dB at both ports. Note that for the most common use of a diplexer (in PONs) this crosstalk is not pertinent as the light for the two bands is traveling in opposite directions.
Fig. 4 Simulated performance. (a) E-field at 1550 nm (b) E-field at 1310 nm. (c) Output spectrum of the two ports. The vertical red lines indicate 1310 nm and 1550 nm.
This design also offers a very wide bandwidth as seen from the two insets at the top of Fig. 4 (c), which are magnified plots around the peak wavelengths. Port 1 has a 1dB bandwidth of 110 nm with a peak efficiency of 96.1% (i.e., 0.17 dB insertion loss) and port 2 has a bandwidth of 90 nm with a peak efficiency of 94.4% (i.e., 0.25 dB insertion loss). The numerical simulation results showed that a bent taper can be engineered to be a powerful mode-evolution device. Together with a PSO MMI, a very efficient wavelength diplexer is realized within an ultra-compact footprint. A comparison of the performance of our diplexer to other integrated diplexer designs is shown in Table 3 with the key metrics listed.
Table 3. Comparison to other integrated diplexer designs
3. Yield analysis
Fabrication robustness is one of the key considerations for any devices aimed for real CMOS-compatible production. For MMI-type silicon photonics devices, the uncertainty of lateral dimension (width, W) and the vertical dimension (thickness, H) are two main factors, as been tested in Ref [25].
As discussed before, an MMI-coupler-based diplexer with smaller WMMI is more vulnerable to fabrication uncertainty since Lπ is more sensitive to the change of WMMI. Such a device must have a compact footprint to maintain its robustness. We first performed yield analysis by sweeping the deviation of WMMI,written as ΔW, to exam the fabrication tolerance of our design. It is worth noting that for the bent taper, ΔW needs to be distributed on both sides since it is asymmetric, i.e., {Ui + ΔW /2} and {Di + ΔW /2}. But for PSO MMI, the width is defined by {Wi + ΔW}. Although the real fabrication situation might be more complex, this analysis is a good approximation to examine the robustness of the design. The insertion loss and crosstalk at 1310 nm and 1550 nm are plotted in Fig. 5(a) and (b), respectively. Within a deviation of ± 20 nm in WMMI, the insertion loss degradation is smaller than 0.6 dB for both wavelengths. The worst case for the crosstalk across the ± 20 nm deviation happens at ΔW = −20 nm, but the value is still below −15 dB for both wavelengths, as seen in Fig. 5(b).
Fig. 5 Yield analysis. (a) and (b). Sweep of width deviation. (c) and (d) Sweep of thickness deviation.
We then swept the deviation of Si thickness, written as ΔH, since the thickness of SOI wafers is less well controlled than epitaxial grown III-V wafers. Within a range of 220 +/ - 20nm, both insertion loss and crosstalk are insensitive to the change of thickness, as shown in Fig. 5(c) and (d). The worst-case insertion loss is still smaller than 0.5 dB and crosstalk is below −18 dB. The yield analysis at both dimensions verifies that this design has high fabrication tolerance.
4. Conclusion
We proposed and designed an ultra-compact, low-loss and broadband O-/C-band diplexer using a novel bent taper cascaded with a PSO MMI. The footprint of the proposed device is smaller than 15 × 2 μm2. For both 1550 and 1310 nm center wavelengths, the insertion loss is about 0.25 dB with crosstalk lower than −20 dB. The 1dB bandwidth is around 100 nm at both output ports. Yield analysis shows the design is fabrication tolerant.
Acknowledgment
The authors would like to thank Gernot Pomrenke, of AFOSR, for his support of the OpSIS effort, through both a PECASE award (FA9550-13-1-0027) and ongoing funding for OpSIS (FA9550-10-l-0439). The authors are grateful to Portage Bay Photonics and Mentor Graphics, particularly Juan Rey and Michael Buehler, for their continuing support of the OPSIS effort. The authors would also like to gratefully acknowledge Lumerical for the use of their software, which made this work possible.
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