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Abstract
We propose the design of a broadband grating coupler using full-etched subwavelength gratings (SWGs) on a silicon-on-insulator platform efficiently coupling both TE and TM polarizations. Due to SWG’s unique property of refractive index engineering, our design achieves a simulated 3 dB operating bandwidth of 105 nm and 121 nm for the TE and TM polarizations, respectively. Our proposed device reaches a maximum coupling efficiency of –4.88 dB at 1550 nm, exhibiting near zero polarization dependent loss at 1550 nm. Although the results are obtained from the identical SWGC design, the optimized incident angle for TE and TM are 39° and 16°, respectively. The back-reflections from the proposed grating coupler are suppressed to as low as −20 dB. To the best of our knowledge, our design offers the best reported performance in bandwidth and polarization sensitivity.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Silicon Photonics has attracted tremendous research interest in the past decades. Although with many outstanding optical and electrical properties, there are still many challenges in silicon photonics that are yet to be addressed. One of the key challenges is efficient coupling of light from a fiber into and out of photonics integrated circuits (PICs). A conventional silicon waveguide has a cross-sectional area on the order of 10−1 µm2, while a single mode fiber has a core diameter of ∼8.2 µm. A low-loss and practical solution to couple light from the SMF fiber into a 500 nm wide silicon nanowire is yet to be presented. With the increasing demand for higher data capacity at a faster speed, the optical network for data communication and telecommunication are now adopting Dense Wavelength Division Multiplexing (DWDM) which can presently carry up to 96 data channels per fiber with a standard channel spacing of 0.8 nm or 0.4 nm [15], leading to a bandwidth requirement of ∼80 nm. As the technology advances, the number of channels in a DWDM signal can be as high as 128, increasing the minimum bandwidth limit to about 100 nm [14]. Thus, it is highly desirable to utilize an optical coupler that is efficient and broadband. Data capacity can be improved by either increasing the number of data channels, or introducing polarization diversity, where TE and TM polarization operate independently. By establishing polarization insensitivity to the optical couplers, the data rate of PICs effectively doubles.
The current solutions that offer strong optical coupling are edge couplers and grating couplers. Experimental demonstrations of edge couplers reported a minimum coupling loss of less than −0.25 dB at 1550 nm with a 1-dB coupling bandwidth of approximately 100 nm for both TE and TM polarizations and 3-dB bandwidth of almost 300 nm [19,21]. However, edge couplers have their own challenges. To begin with, they require highly polished lensed fibers to couple light from the fiber into an inverse taper of lateral widths as small as 80 nm [20]; secondly, they require long tapers with lengths on the order of hundreds of microns that occupy precious real-estate on the SOI wafer for the adiabatic conversion of a micrometric mode to a nano-sized mode [16–18]; and thirdly, they require high-resolution optical alignment, which increases the packaging cost [13]. Furthermore, the edge couplers can only be placed along the edges of a PIC, which adds additional complexity to their post-fabrication facet preparation and testing.
In contrast, grating couplers (GC) have greater alignment and fabrication tolerance with the flexibility of placement on the wafer. GC are also well suited for wafer-scale testing. But they also have their set of limitations: 1) they are good polarization filters as a result of the grating properties and normally allow only one polarization type to be coupled in; 2) they have low operating bandwidths as compared to edge couplers due to the directionality of the radiated mode related to the operating wavelength(s); 3) they have lower coupling efficiency (CE) than edge couplers owing to the power lost downwards towards the buried oxide (BOX) layer and silicon substrate. Further decrease in CE is caused by the mismatch in the Gaussian profile of the fiber mode and the radiated mode of the grating. While a typical 1-dB bandwidth of ∼30–40 nm is sufficient for single-channel silicon photonics, it prevents the usage of the conventional grating couplers in multi-channel ICT systems that rely on Coarse Wavelength Division Multiplexing (CWDM) or DWDM, where a bandwidth up to 80-100 nm is required [5]. Hence, it is necessary to come up with an optical coupler which exhibits large bandwidth and polarization insensitivity, as well as being practical with ease of fabrication and integration, to accommodate for the high data capacities in DWDM applications.
Most of the existing broadband grating coupler are polarization sensitive and rely on only one polarization. The broadband coupler designs reported in literature all exploited the benefits of SWGs to engineer the grating index to achieve the characteristic broadband behavior [6–10]. One such design was reported in [8] by Y. Wang et al. using 1-D SWG for TE polarization. They reported a simulated 1-dB bandwidth of 90 nm and a CE of −5.5 dB. Zhong et al. reported the design and characterization of a focusing-curved 2-D SWGC in [7], where a 1dB-bandwidth of ∼ 100 nm and a maximum CE of −4.7 dB for TE polarization were achieved. They used anti-reflective structures to reduce back reflections by tapering the connections between the high and low refractive index regions. In order to compete with edge couplers in performance, a grating coupler needs to exhibit high operating bandwidth as well as polarization insensitivity. Substantial amount of work has been carried out, focusing on designing polarization insensitive grating couplers. Almost all polarization independent designs reported in the literature exhibited very limited coupling bandwidths. Zhang et al. [2] designed and analyzed a 1D-GC for coupling the incident TE0 and TM1 polarizations into the planar silicon waveguide. The TM1 polarization that was coupled into the silicon waveguide, was then converted into TM0. At 1550 nm, they reported a maximum CE of −2.2 dB (60%) for both TE and TM, with a limited 1-dB bandwidth of 30 nm for TE0 and 40 nm for TM1. This design also required an additional device for the conversion of TM1 to TM0. A polarization splitter grating based on partially etched silicon was proposed in [3] that obtained almost −3.00 dB CE for both TE and TM polarization at 1550 nm with a 3-dB bandwidth of 70 nm. Polarization diverse grating couplers have also been designed using apodized focusing SWGs. The grating coupler fabricated in [4] uses a suspended SWGC to couple both the polarizations into the same waveguide. This design achieved a maximum CE of −3.2 dB for the TM polarization with a 1-dB bandwidth of 28 nm, while a maximum CE of −4.3 dB and 1 dB bandwidth of 58 nm were demonstrated for TE. The coupling peaks for the two polarizations differed by a minimum of ∼32 nm. The group claims a polarization insensitive behavior with a CE of −6.5 dB at 1525 nm for the same design. Apart from the limited operating bandwidths, none of the aforementioned designs are based upon the industry standard 220 nm SOI wafer.
Until now, no previous design has addressed the problems of bandwidth and polarization diversity of grating coupler simultaneously. In this work, we introduce a novel grating design which addresses both of the aforementioned limitations. To the best of our knowledge, this is the first design that is both polarization flexible as well as broadband (>100 nm).
2. Background
The coupling of the input light from the incident fiber to the planar waveguide is governed by the well-established Bragg phase match condition given in $(1 )$:
where ${k_0}$ is the wave-vector of the light in free space, ${n_{eff}}$ is the effective index of the propagating mode in the silicon waveguide, ${n_c}$ is the index of the cladding. $\theta $ is the angle of the incident fiber with respect to the surface normal, the order of diffraction is given by m, and ${\Lambda}$ is the grating period or pitch. In a rectangular waveguide, the effective index of TE $({n_{avg}}_{eff}^{TE})$ does not equal the effective index of TM $({{n_{avg}}_{eff}^{TM}} )$. Therefore, to obtain the polarization independence in a grating coupler the phase match condition given by (1) must be satisfied for both TE and TM. The grating coupler structure that we propose satisfies the phase match condition for both the TE and TM polarization.To further estimate the bandwidth of the grating coupler, Eq. (1) is re-arranged for |m| = 1 to obtain (2), followed by taking a derivative with respect to θ (See Eq. (4)). The term, ${\eta _{1dB}}$ in (4) is the constant of proportionality, which depends on the fiber and grating parameters, was given as 0.07 based on simulation and experimental data [1]. From (4), it is evident that the 1-dB bandwidth is directly proportional to the grating period of the coupler and the dispersion $\frac{{d{n_{eff}}(\lambda )}}{{d\lambda }}$. The dispersion term is negative for silicon implying that the effective index decreases as wavelength increases.
Sub-wavelength structures, where segments of silicon have dimensions on the order of $\lambda /10$ in the direction of mode propagation, allow precise engineering of the effective index of the grating. Beyond the diffraction limit, the propagating mode perceives SWGs as a homogeneous medium along the propagation direction, therefore, it does not experience the abrupt change in refractive index. The effective index of a sub-wavelength structure is calculated using the Effective Medium Theory (EMT). EMT is widely exploited to tailor the effective index for the guided mode of the GC, edge couplers, crossings etc. If the grating extends indefinitely in the $x$ and $y$ directions and $> \Lambda $ , the refractive index of the equivalent homogeneous medium is given by Rytov’s formulas (5) and (6) [11].
3. Design and simulations
The proposed grating coupler is schematically illustrated in Fig. 1. The structure consists of alternating regions of high and low refractive index as seen in Fig. 1(c). A top-view of the proposed grating is presented in Fig. 1(a) where the grating period is denoted by $\Lambda $. The length of the high-index regions and the low-index region are ${\Lambda _H}$ and ${\Lambda _L}$, respectively, such that ${{\Lambda }_\textrm{L}} + {{\Lambda }_\textrm{H}} = {\Lambda}$. The duty cycle or the fill-factor, denoted by $f{f_1} = \frac{{{\Lambda _H}}}{\Lambda }$ , is described as the ratio of the lengths of high-index region to the total grating period. The high index region is made up of one single silicon segment ($f{f_H}$) and the index of the low-index region is engineered using SWGs. The low-index region has periodic regions of Si and SiO2 with a fill-factor of $f{f_L}$. The fill-factor of low index region is calculated as the sum of the lengths of all the silicon SWG divided by ΛL. The approximate value of effective index of low and high index regions, ${n_L}$ and ${n_H}$ as calculated using Rytov’s Formula for $T{E_0}$ and equals $1.7855\; and\; 2.845$, whereas for TM0, the values are 1.5295 and 2.0643, respectively. The number of gratings in the low-index region is selected by considering the minimum feature size allowed for fabrication and is optimized for both TE and TM transmission. Figure 1(c) illustrates the arrangement of the sub-wavelength gratings in a single pitch of the SWGC.
Fig. 1. Schematic diagrams for the sub-wavelength grating coupler (SWGC) (a) Top View (b) Cross-section view with effective index approximation (c) 3D representation.
This SWGC is designed for a 220 nm SOI wafer with a 3 µm thick BOX layer. The Si wafer is assumed to have a SiO2 cladding, with a background index of 1.45. The fiber is incident on the grating coupler at an angle $\theta ^\circ $ with respect to the surface normal. The design is simulated using the 2D-FDTD method with a resolution of 1 nm from 1.45–1.65 µm. The mode source calculates and injects the TE0 and TM0 mode-profiles from the fiber to the straight waveguide. The transmissions and reflections of the 2-port device are measured through the S-parameters. Optiwave’s OptiFDTD simulation software was used for the design and simulations of our proposed device. Similar results were also obtained using Lumerical FDTD Solutions. The design problem was broken down into two parts: first to realize a polarization flexible design; and second to make it broadband. The initial polarization flexible design was realized by partially etching silicon with ${t_{Si}} = 220nm$. Optimization of the shallow-etched grating resulted in a grating period of 675 nm with an etch depth of 70 nm and fill-factor $f{f_1} = 0.5$ to attain the lowest PDL of 0.8 dB at 1550 nm with a SMF fiber incident at 17.4˚. The initial polarization flexible shallow etched grating design offered a maximum CE of −3.0 dB and −3.6 dB for TE0 and TM0, respectively, at 1550 nm. This design had a typical 1-dB coupling bandwidth of 40 nm and a 3dB-bandwidth of approximately 65 nm for both TE0 and TM0.
The next step towards obtaining a larger bandwidth was to engineer the etch depth and the grating period. This was accomplished by first equating the refractive index of the shallow-etched grating to the same as that of a full-etched grating for the TM0 polarization (Eq. (6)), and therefore obtaining the approximate values of the fill-factors nH and nL. The conversion of the shallow etched grating was done for TM0, since it was the second highest mode in the silicon waveguide and the presence of TM0 indicated the fundamental guiding mode TE0 was supported. Therefore, the initial shallow etched grating, discussed above was converted into SWGs followed by an increase in the grating period to further reduce the grating index. This optimized SWG based broadband and polarization flexible design demonstrated un-equal angle of incidence for TE and TM transmission.
Optimizations for both polarizations resulted in the final device parameters listed in Table 1, where both the TE0 and TM0 polarizations co-propagate in the same silicon waveguide. The optimized fill factor is $f{f_1} = 0.5$ with the high and low index region having duty cycle of $f{f_L} = 0.2$ and $f{f_H} = 1.0$ respectively. For this design the number of SWG periods in the low index region were optimized to ${n_L} = 4$, offering the smallest feature size of Si to be 29.375 nm. It is noted that, although the designed grating coupler is identical for both polarizations, the fiber is set to incident at an angle of 39° and 16° for the TE0 and TM0, respectively, for achieving the maximum coupling efficiency.
Table 1. Optimized device parameters for broadband & polarization flexible grating coupler
The coupling efficiency was calculated as the normalized ratio of the power coupled into the waveguide and the power in the fiber, CE = $10 \cdot \textrm{lo}{\textrm{g}_{10}}\left( {\frac{{{P_{fiber}}}}{{{P_{waveguide}}}}} \right)$. With our design, the maximum CE of −4.86 dB and −4.88 dB were obtained for the TE and TM polarization with 2D-FDTD, respectively, with back reflections suppressed to −20 dB at 1550 nm. The 3D-FDTD simulations conformed well with the 2D results as can be seen in Fig. 2, with a slightly lower maximum CE, owing to the losses incurred by the taper. As illustrated in Fig. 2(a), for TE polarization a 1-dB coupling bandwidth of 57.73 nm and a 3-dB bandwidth of 105 nm were achieved by simulations. The bandwidth performance of TM polarization is superior than that of the TE: with a 1-dB bandwidth reaching up to 70 nm and a 3-dB bandwidth of 121 nm for the same grating design, as shown in Fig. 2(b). 3D-FDTD simulations also depicted an increase in the 1dB-bandwidth for TE by 5 nm.
Fig. 2. Coupling efficiency (dB) of the optimized SWGC as a function of wavelength for (a) TE polarization (b) TM polarization for both 2D and 3D-FDTD.
In comparison to the coupling bandwidths reported for the polarization independent design in [2] our design offers an increase of 1-dB coupling bandwidth by a factor of 1.9 and 1.72 times for TE and TM polarization, respectively. The 3-dB bandwidths obtained from our design also show an enormous improvement over the previously published results. The FOM obtained with the optimized structure are listed in Table 2. At 1550 nm, the CE of −4.88 dB was achieved for both the polarization, resulting in a PDL of 0.00376 dB at 1550 nm, the lowest ever reported so far in literature. It should be noted that the minimum feature size and the number of the SWG segments play a crucial role in the coupling efficiency and bandwidth performance in both polarizations. For a fixed grating period and fill-factors, an increase in the minimum feature size can be realized by reducing the number of SWG segments in the low-index region. Wider SWG causes reduction in both CE and bandwidth, although the effect on bandwidth is much more pronounced. For instance, doubling the minimum feature size from 30 to 60 nm, the 3-dB bandwidth reduces by approx. 20%. Further increase in the feature size to 120 nm leads to a CE of −8.08 dB with 60% reduction in bandwidth. Due to the higher refractive index contrast between TE polarized mode and the cladding, the effect of SWG size is more evident for TE than for TM. With the currently available lithography, a minimum feature size of ∼ 30 nm may be difficult to fabricate. Though, it is feasible to achieve an increased dimension sizes for the SWG segments, however, the trade-off of a more relaxed feature size is a reduction in CE and bandwidth.
Table 2. Simulation results
4. Conclusion
In this paper, we presented a methodology and proposed a grating coupler design which is polarization flexible and broadband with the lowest ever reported PDL of 0.00376 dB at 1550 nm. The maximum CE of −4.86 dB and −4.88 dB were obtained for the TE and TM polarization, respectively with back reflection as low as −20 dB. Compared to the existing polarization insensitive grating coupler designs, our device demonstrates a much superior broadband performance. Instead of the typical 60–70 nm bandwidth range [2,3,4], we achieved the 3-dB coupling bandwidths of 105 nm (for TE) and 121 nm (for TM). The relatively large operating bandwidth makes our design useful for polarization diverse DWDM applications. The coupling efficiency and bandwidth performance could further be improved by apodization, where the silicon subwavelength segments vary in width along the length of the grating. In addition to the excellent potential for delivering high performance light coupling, one other major advantage of our proposed design lies in the simplicity of the fabrication: only one full-etch step is required, which can be done at the same etch step as defining the silicon waveguides. This makes our design highly desirable for commercial applications. Owing to the performance characteristics and ease of fabrication, this polarization flexible and broadband grating coupler design has a wide range of potential practical applications.
Acknowledgment
The authors would like to acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC).
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