We demonstrate a robust 3-dB directional coupler which has a narrow silicon wire core and a wide gap. Sensitivity to the gap variation is decreased to one tenth that of a conventional directional coupler. Better spectral stability due to the enhanced robustness to waveguide geometrical fluctuations was experimentally verified.
© 2014 Optical Society of America
Generally, performances of devices based on silicon wire waveguides are affected sensitively by a small deviation of a real dimension from design [1,2]. One of the most sensitive components is a 3-dB directional coupler (DC), consisting of two parallel silicon wire cores separated by a gap. A DC is widely used to form a 2 × 2 Mach-Zehnder (MZ) switch [3,4]. A specific application we hold in mind is a matrix switch for circuit switch applications, in which a 2 × 2 MZ switch serves as an element of the matrix [5,6]. In this application, a small deviation in the gap width will severely deteriorate crosstalk performance; therefore, it is necessary to design a DC with enhanced robustness to gap variations. Another common 3-dB coupler is a 2 × 2 multi-mode interference (MMI) waveguide [7,8]. For applications such as the matrix switch , the DC is preferred for its negligibly low loss to the MMI that has insertion loss of typically 0.3 − 0.5 dB. In this study, we present a novel 3-dB directional coupler with greatly enhanced gap tolerance. This will allow high performance of silicon wire waveguide devices to be compatible with their volume production.
2. Design of robust 3-dB directional coupler
A conventional directional coupler (CDC) as shown in Fig. 1(a) consists of two parallel silicon wires which usually are in the same width (~500 nm) with outer connecting waveguides and separated by a gap as narrow as ~200 − 250 nm to keep a realistic 3-dB coupling length. Such a narrow gap is very sensitive to the fabrication process and the power splitting ratio in two waveguides is consequently influenced. The idea to make the directional coupler less sensitive to the gap is to decrease the waveguide width to ~230 nm and to increase the gap to ~850 − 1000 nm. This robust directional coupler (RDC) shown in the bottom of Fig. 1(a) is expected with less gap sensitivity. For CDC, only increasing the gap would make the 3-dB coupling length too long. Even though the gap is as large as >800 nm for RDC, the narrow waveguide width will guarantee the short coupling length due to the spatial mode expansion effect.
The 3-dB directional coupler is featured by the 3-dB coupling length (L3dB), and the sensitivity figure we use in this study is ∆L3dB/∆g, where ∆g is the gap change. The smaller the figure of ∆L3dB/∆g is, the less sensitive the directional coupler is to the gap. Since L3dB is proportional to the reciprocal of index difference (∆n) between the odd and even modes, we first show the dependence of 1/∆n on the gap for both CDC and RDC in Fig. 1(b) which was calculated using a mode solver based on finite element method (FEMSim). By assuming a cross-section of silicon wire in oxide media, the mode solver enabled us to calculate the odd and even mode index. This simulation considered only the straight waveguide as shown in Fig. 1(a). Figure 1(b) was calculated at 1550 nm. As seen here, for both CDC and RDC, the logarithm of 1/∆n is linearly proportional to the gap, described by the relationship of log(1/∆n) = α⋅g + β, where g is the gap width and α and β are coefficients. Table 1 lists the values of α. With L3dB = λ/(4 × ∆n) where λ is the wavelength, we obtained ∆L3dB/∆g = α⋅L3dB, which indicates that the increase in either of the coefficient α and L3dB will cause an increase in the sensitivity figure ∆L3dB/∆g. Thus, a small coefficient α and a small 1/∆n with a larger gap are preferred to decrease sensitivity to the gap.
For CDC, the transverse-magnetic (TM) mode has a smaller α than the transverse-electric (TE) mode. On the contrary, for RDC, the TE mode has a smaller α than the TM mode. The gap range of 350 − 450 nm was also calculated in Fig. 1(b) to clearly show this difference between CDC and RDC under different polarizations. For the TE mode, CDC is often designed using a gap around 200 − 250 nm to keep a short coupling length. For the TM mode, the gap could be designed to ~400 nm because L3dB at the gap of 400 nm is still shorter than that at the gap of 200 nm for the TE mode. Thus, for CDC, the TM mode has a smaller ∆L3dB/∆g than the TE mode, which means that the TM mode is less sensitive than the TE mode. RDC is just on the contrary. For RDC, the TE mode not only has a smaller α, but also a smaller 1/∆n; therefore, the TE mode is less sensitive than the TM mode. Which mode is more sensitive depends on how strong this mode is confined in the waveguides. Due to the waveguide geometrical features, the confinement of TE mode is stronger than that of TM mode in CDC, whereas the situation is adverse in RDC. Thus, throughout this study, we focus on the TE mode which is the most sensitive case for CDC and show the effectiveness of RDC in decreasing the gap sensitivity for the TE mode. We can see that both the coefficient α and 1/∆n of RDC at TE mode are much smaller than those of CDC, which indicates that RDC has much smaller ∆L3dB/∆g than CDC, as seen in Fig. 2(a).
To be more helpful to understand the robustness of RDC, we show the splitting ratio as a function of the gap for a ± 20 nm gap variation in Fig. 2(b). The reference gaps are 230 and 900 nm for CDC and RDC, respectively, at which an ideal 3dB DC is assumed (splitting ratio = 0.5). Both Figs. 2(a) and 2(b) were calculated at 1550 nm. As seen, the slope of splitting ratio of RDC is much smaller than that of CDC, indicating the robustness to gap variation. The wavelength dependences of ∆L3dB/∆g are compared between CDC and RDC in Fig. 2(c). In Figs. 2(a) and 2(c), the figure ∆L3dB/∆g of RDC is less than one-tenth of that of CDC. In addition, ∆L3dB/∆g shows a much weaker gap dependence and wavelength dependence for RDC. For a 10 nm gap change at 1550 nm, L3dB increases by ~2.7 μm in CDC, but it only increases by ~0.22 μm in RDC. Sensitivity to the gap variation is greatly decreased in this robust design within a wide range of wavelength.
An important precondition to decrease the gap sensitivity is that the sensitivities from other waveguide geometries should not be increased. The other two important geometrical parameters are the waveguide width (w) and the height (h). Different from the width that depends on fabrication process, the height is determined by the silicon layer thickness of silicon-on-insulator (SOI) wafer, which usually has a uniformity issue of thickness variation . Similarly, we define ∆L3dB/∆w and ∆L3dB/∆h to examine the sensitivities to the waveguide width and height changes. As seen in Fig. 2(d), ∆L3dB/∆w of RDC was decreased to about a half at 1500 nm and at least one tenth at 1600 nm of that of CDC. In Fig. 2(e), ∆L3dB/∆h of RDC is just about one fifth of that of CDC at 1500 nm and a negligible percent at 1600 nm. The decrease in the height sensitivity is beneficial for the 3-dB directional coupler to endure SOI thickness variations. Thus, we have not sacrificed other dimensional parameters to win the gap robustness; on the contrary, the other waveguide geometries also show the improvement in robustness to the size change. The following experiment is to verify the gap robustness within a certain range of variations in other geometries.
The waveguide was fabricated on a 250-nm-thick SOI wafer with a ~3-μm-thick buried oxide layer. This buried oxide naturally serves as the bottom cladding layer for the waveguide and the top cladding layer was the oxide deposited by plasma-enhanced chemical vapor deposition. The determination of the waveguide width in RDC is related to the thickness of cladding around the core. We fabricated a 2 × 2 asymmetric Mach-Zehnder interferometer (AMZI) based on two RDCs or two CDCs. The optical microscope picture of the AMZI consisting of two RDCs is shown in Fig. 3(a). The arm length difference ∆Larm is designed to 200 μm. The schematic of RDC is shown in Fig. 3(b). RDC uses 10-μm-long horizontal tapers on both sides to tune the waveguide width from 230 to 500 nm. These tapers were not considered in the simulation in Section 2 and kept unchanged for all chips in this study. The 3-μm-long straight waveguides are used to connect these tapers with a bend of 20-μm radius. The AMZI of CDC is different from that of RDC only in the directional coupler parts. CDC is directly connected to a bend of 20-μm radius without a taper. The scanning electron microscope (SEM) pictures at the central parts of directional couplers are shown in Figs. 3(c) and 3(d) for RDC and CDC, respectively.
3.2 Spectrum measurement
An example of the AMZI spectra of RDC is shown in Fig. 4(a). The spectrum was recorded with a resolution of 0.05 nm using an optical spectrum analyzer and a wide band optical source. The spectral fringe spacing (between two minimums) is ~2.8 nm around 1.55 μm which matches the theoretical value of 2.86 nm calculated using a ∆Larm of 200 μm and a group index of 4.2. An AMZI does not have a phase-shifter that an MZ switch would have. Tracing the extremes in Fig. 4(a), we can obtain, in Fig. 4(b), the extinction ratio that a symmetric MZ switch is supposed to have. The maximum of the cross port and the minimum of the bar port in Fig. 4(a) corresponds to the cross state (switching off) and the reverse situation corresponds to the bar state (switching on). Figure 4(b) allows us to evaluate the performance of 3-dB couplers including the 3-dB wavelength, bandwidth, and crosstalk. As seen in Fig. 4(b), a 20-dB bandwidth is ~35 nm and a 3-dB wavelength is 1572 nm. The minimum of the bar port reflects how the two directional couplers consisting one MZ structure deviate from an ideal 3-dB splitter and the minimum of the cross port reflects how equalized in the power splitting ratio these two directional couplers are. This explains why we always observe a better crosstalk within a wider bandwidth at the cross port than at the bar port. In the present study, we used the spectra of the bar port to obtain the 3-dB wavelength and 20-dB bandwidth for the directional couplers.
3.3 Method to obtain ∆L3dB/∆g
We obtain the sensitivity figure ∆L3dB/∆g by plotting L versus g and then finding its slope by a linear fit. In this section, we show the procedure by using Figs. 5(a)-5(h). Figure 5(a) illustrates a group of chips that have the same gap, which was verified by observing with SEM. In each chip, we put several AMZIs. The coupling length is intentionally varied from one AMZI to another with a step of 1 μm. Figure 5(b) is a schematic illustration of transmission spectra at the bar port. We specify one wavelength λa in Fig. 5(b). From the data of all the AMZIs on two or more chips, we choose AMZIs, the extinction of which is good enough at λa. The criterion is −20 dB or lower from the maximum transmission level. We plot the coupling lengths of these qualified AMZIs, L and L′, for this gap, as shown in Fig. 5(c). Repeating this on chips with other gaps, we obtain a plot of candidates of L as a function of g, as shown in Fig. 5(d). The slope of the linear fit in Fig. 5(d) is ∆L3dB/∆g for λa. Again, repeating the whole process while specifying different wavelengths, we obtain L3dB-g relation at respective wavelengths and the corresponding ∆L3dB/∆g. This procedure is illustrated using the experimental spectra of RDC for a specified wavelength λa at 1542.3 nm. Spectra in Figs. 5(e)-5(h) correspond to the gaps of 850 nm, 895 nm, 942 nm, and 995 nm, respectively, and λa is indicated by a green dashed line. It is to be noticed that two or more coupling lengths at which the spectra satisfy the abovementioned criterion are chosen for each gap. To explain this procedure in a different way, we could consider an ideal case of Fig. 5(d) where only one point occurs at one gap. In other words, for one specified wavelength, this L3dB-g relation is unique in the ideal case. However, actually, due to unavoidable fluctuations, we could not explicitly guarantee the spectral minimum is always exactly at this wavelength from one pair of L3dB-g to another. Thus, by performing the procedure above, we can obtain the L3dB-g relation for a specified wavelength.
4. Experimental 3-dB coupling length versus the gap
As explained in Section 3.3, Figs. 6(a) and 6(b) show the coupling length as a function of the gap for RDC and CDC, respectively. All gaps are real dimensions measured with SEM. For one gap at one wavelength in Figs. 6(a) and 6(b), the variation of coupling length is due to unavoidable fluctuations of waveguide width from one chip to another. For the criterion mentioned in Section 3.3, the fluctuation in the waveguide width between different chips is ± 10 nm for RDC and ± 5 nm for CDC, which we confirmed by evaluation with SEM. For RDC as shown in Fig. 6(a), the 150-nm increase in the gap only results in a ~4 μm increase in L3dB at the wavelength of 1542.3 nm, which yields a slope of 26.7 nm/nm. This slope is the sensitivity figure ∆L3dB/∆g, which agrees with the calculation in Fig. 2(a). In contrast, L3dB of CDC is very sensitive to the gap, as seen in Fig. 6(b). When the gap increases by 15 nm around 1549.7 nm, L3dB increases by ~7 μm, indicating a slope larger than 400 nm/nm. This explains why it is difficult for us to design a CDC for a specific wavelength. The deviation of 3-dB coupling length caused by the gap variation is the origin of the sensitivity of CDC. The wavelength dependence of the slopes obtained by a linear fit in Figs. 6(a) and 6(b) is shown in Fig. 6(c), which is in good agreement with the calculation in Fig. 2(c). Figure 6(c) verifies that the value ∆L3dB/∆g of RDC is less than one tenth that of CDC. For a same gap deviation from the design, the coupling length of RDC for a specific wavelength is much less sensitive; thus, RDC is more robust than CDC to gap fluctuation from the fabrication point of view. In addition, RDC does not show an obvious wavelength dependence of ∆L3dB/∆g, whereas CDC shows a strong one. The performance degradation of CDC due to the gap variation becomes significant in the shorter wavelength.
It is also instructive to show the evolution of 3-dB wavelength with the gap at a constant coupling length in Fig. 7(a). The spectral stability could be known from the slopes in Fig. 7(a). RDC has smaller slopes than CDC, indicating a better spectral stability. The slope of RDC is about 0.6 nm/nm, and that of CDC about 2 nm/nm. This slope means the shift of 3-dB wavelength for a certain gap change. Comparing the 3-dB wavelengths between two gaps at the same coupling length, we can obtain the shift of 3-dB wavelength (∆λ3dB) per 10-nm gap change for other coupling lengths. For example, in Fig. 6(a), we compare 3-dB wavelengths between the red circle (1542.3 nm) and the green triangle (1568.6 nm). Figure 7(b) shows statistic ∆λ3dB per 10-nm gap change. ∆λ3dB does not depend on the gap change only and includes contributions from all geometrical changes. Another important change is the change of waveguide width as explained above, ± 5 nm for CDC and ± 10 nm for RDC. If normalized to equal width change, ∆λ3dB of RDC in average is only about 14% of that of CDC (the ratio of the half of 6.4 nm to 22.4 nm). Thus, RDC has better spectral stability due to the enhanced robustness to geometrical fluctuations.
Figure 7(c) shows the 20-dB bandwidth evolution with the gap to clarify the statistic feature. The bandwidth did not exhibit clear dependence on the gap variations. Both RDC and CDC show a ~15 nm variation in bandwidth. In average, the bandwidth of RDC is about 35 nm and that of CDC is about 15 nm. The former is nearly two times wider than the latter. This bandwidth could be further enlarged by using the wavelength-insensitive design . Figure 7(d) compares the spectral feature of RDC and CDC. From the maximum transmission at both bar and cross ports, no obvious excess loss was observed for RDC in comparison to CDC. Even for the cross port, RDC shows a better crosstalk and a larger bandwidth than CDC as indicated by a 30-dB line in Fig. 7(b). Not only the RDC is more robust to the gap variation than CDC, but also its performance is improved in bandwidth and crosstalk.
Finally, it is necessary to estimate the increase in device footprint caused by using RDC instead of CDC. The RDC length is 36 μm at most, including connecting waveguides, tapers, and the central coupling length. The CDC length is about 24 μm. Compared to the great benefit in robustness, this degree of length increase is acceptable for photonic devices.
We designed a robust 3-dB directional coupler which is featured by a narrow (220 − 240 nm) silicon wire and a wide (>850 nm) gap. It was experimentally verified that the robustness described by the change in the 3-dB coupling length per-unit gap variation was >10 times better than the standard directional coupler. This design will greatly tolerate a dimension error in the fabrication and will enable volume production of complicated circuits including many 3-dB couplers.
The authors are grateful to Mr. K. Tashiro for his technical assistance in device fabrication. This study was supported in part by Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
References and links
1. K. Yamada, “Silicon photonic wire waveguides: fundamentals and applications,” in Silicon Photonics II. Topics in Applied Physics119, 1−29 (2011), D. J. Lockwood and L. Pavesi, eds. (Springer-Verlag Berlin Heidelberg, 2011).
2. M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrications of low-loss photonic wires in silicon-on-insulator using hydrogen silsesquioxane electron-beam resist,” Electron. Lett. 44(2), 115–116 (2008). [CrossRef]
3. T. Shoji, K. Kintaka, S. Suda, H. Kawashima, T. Hasama, and H. Ishikawa, “Low-crosstalk 2 x 2 thermo-optic switch with silicon wire waveguides,” Opt. Express 18(9), 9071–9075 (2010). [CrossRef] [PubMed]
4. J. Van Campenhout, W. M. Green, and Y. A. Vlasov, “Design of a digital, ultra-broadband electro-optic switch for reconfigurable optical networks-on-chip,” Opt. Express 17(26), 23793–23808 (2009). [CrossRef] [PubMed]
5. K. Suzuki, K. Tanizawa, T. Matsukawa, G. W. Cong, S. H. Kim, S. Suda, M. Ohno, T. Chiba, H. Tadokoro, M. Yanagihara, Y. Igarashi, M. Masahara, and H. Kawashima, “Ultra-compact Si-wire 8×8 PILOSS Switch,” PD2.D.2, ECOC2013 (London, 2013).
6. S. Nakamura, S. Takahashi, M. Sakauchi, T. Hino, M-B. Yu, and G-Q. Lo, “Wavelength selective switching with one chip silicon photonic circuit including 8×8 matrix switch,” OFC/NFOEC 2011, OTuM2.
7. S. Sekiguchi, T. Kurahashi, L. Zhu, K. Kawaguchi, and K. Morito, “Compact and low power operation optical switch using silicon-germanium/silicon hetero-structure waveguide,” Opt. Express 20(8), 8949–8958 (2012). [CrossRef] [PubMed]
8. K. Voigt, L. Zimmermann, G. Winzer, and K. Petermann, “SOI based 2×2 and 4×4 waveguide couplers – evolution from DPSK to DQPSK,” The 5th IEEE International Conference on Group IV photonics, pp. 209–211 (2008).
9. S. Selvaraja, L. Fernandez, M. Vanslembrouck, J.-L. Everaert, P. Dumon, J. Van Campenhout, W. Bogaerts, and P. Absil, “Si photonic device uniformity improvement using wafer-scale location specific processing,” IEEE Photonics Conference 2012, pp. 725−726 (2012). [CrossRef]
10. J. Van Campenhout, W. M. Green, S. Assefa, and Y. A. Vlasov, “Low-power, 2 x 2 silicon electro-optic switch with 110-nm bandwidth for broadband reconfigurable optical networks,” Opt. Express 17(26), 24020–24029 (2009). [CrossRef] [PubMed]