Abstract

Two-dimensional grating couplers are important components for silicon photonic circuits to achieve light coupling from/to a fiber for both polarizations. A two-dimensional grating coupler structure with a high coupling efficiency and a low polarization dependent loss is demonstrated. Using two crossing ellipses as the grating scatter and a diamond-like grating lattice, the polarization dependent loss of the grating coupler can be reduced. The coupling loss is further decreased with a metal mirror, which reaches −1.73 dB theoretically at 1310 nm wavelength. Experimentally, −2.37 dB coupling loss is achieved with an 1 dB coupling bandwidth of 29 nm. The corresponding PDL was measured lower than 0.2 dB in a wavelength range of 78 nm. The proposed configuration for the metal mirror also facilitates a robust wafer-scale post-processing as well as an easy fiber alignment.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Silicon-on-Insulator (SOI) has been considered as a promising platform for future photonic integrated circuits (PICs), which benefits from its high refractive index contrast as well as complementary metal-oxide-semiconductor compatibility. One challenging problem for SOI based PICs is the coupling between a fiber and a silicon waveguide due to the significant mismatch of their geometry sizes [1,2]. Grating couplers have already been proposed to overcome this problem with advantages of wafer-scale testing, alleviated alignment tolerance, and avoidance of facet polishing [3]. Using one-dimensional grating couplers (1D GCs), an efficiency close to unity has been achieved theoretically for light coupling between a normal single mode fiber and an SOI wire waveguide [4,5], and experimentally better than −1dB has also been demonstrated [68]. Despite its great success, 1D GC normally works for only one polarization. On the other hand, two-dimensional grating couplers (2D GCs), consisting of two orthogonal-positioned 1D GCs, can accept both polarizations from a fiber, which also serves as a polarization splitter-rotator for polarization diversity circuits [912]. Although some specially designed 1D GC can also couple both transverse-electrical and transverse-magnetic modes of an SOI waveguide, they are not as straightforward as the 2D GC for polarization diversity applications [1317]. Same as 1D GCs, off-vertical coupling is adopted to suppress the second-order back reflection in 2D GCs, which, meanwhile, raises an issue of polarization dependent losses (PDLs). As showed in Fig. 1(a), the electric field of the P-polarized input light is slightly tilted out from the device plane, while that of the S-polarized light lies within the plane. This leads to different coupling spectra for the two polarizations, and hence a large PDL. During these years, many efforts were made to eliminate the PDL in a 2D GC. An active scheme including a phase shifter in the silicon PIC has been proposed, but this increases the complexity as well as the power consumption [18]. Adjusting the shape of the scatters in the grating cell can also reduce the PDL in a wide wavelength range [1922]. Another important figure for a GC is the coupling loss. For 2D GCs, a coupling loss of −0.95 dB has been achieved theoretically with a broad parameter optimization [23]. Experimentally, a 2D GC with a coupling loss of −1.8 dB has been demonstrated with the help of a metal mirror [24]. However, the PDL in this case is still larger, i.e., > 1 dB, and the transferring process imposes some constraints on its application.

 figure: Fig. 1.

Fig. 1. (a) Schematic structure of the proposed 2D GC. (b) Cross-sectional view of the 2D GC and the access fiber.

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In this paper, we demonstrate a high-efficiency and polarization-insensitivity 2D GC on a conventional 220 nm SOI platform, whose grating cells consist of two crossing ellipses arranged in a diamond-like lattice. A feasible configuration for a reflection metal mirror to enhance the coupling efficiency is also introduced, which facilitates a wafer-scale and robust post-processing as well as an easy fiber alignment. Theoretically, the proposed 2D GC exhibits a coupling loss of −1.73 dB with an 1 dB coupling bandwidth of 29 nm at O-band. Experimentally, −2.37 dB coupling loss is demonstrated, and the PDL is below 0.2 dB in a wavelength range of 78 nm.

2. Design and simulation

Figure 1 shows a schematic structure of the proposed 2D GC and its cross-section for fiber coupling. Unlike conventional 2D GCs with circular grating scatters, the present grating pattern consists of two crossing ellipses which are orthogonal to each other. This type of structure is later verified helpful for improving the PDL. Moreover, instead of using a square lattice for the scatter array, a diamond-like lattice with a certain slanted angle is adopted here. The proposed device is designed for a conventional SOI wafer with a 220 nm top silicon layer and a 2 µm buried oxide layer (BOX). To enhance the directionality of the 2D GC, a metal mirror, made of Au, and a SiO2 over-cladding layer with an optimized thickness are introduced. The fiber is accessed from the substrate side through a hole opened in the silicon substrate as shown in Fig. 1(b). Prior to the hole opening, a quartz plate, which could be slightly larger than the opened hole, is bonded above the structure to enhance the mechanical strength of the coupling structure.

A three-dimensional finite difference time-domain algorithm is employed to optimized the proposed GC. A Gaussian beam with a waist radius of 4.6 µm and tilted by 10° to the surface normal of the SOI chip along the symmetrical axis is used as the incident light, which simulates the mode field of a conventional single-mode fiber at 1310 nm wavelength. The grating holes are shallowly etched by 70 nm. First, a conventional 2D GC with a square lattice of circular holes was considered [9], where the thickness of the BOX is assumed infinite. The hole radius, the pitch P of the array, and the optimal position of the incident fiber was optimized for a maximal coupling power to the transverse electrical modes of the two SOI waveguides. The coupling loss is therefore defined as the ratio between the total power coupled to these two waveguides and the input power of the Gaussian beam. Normally, the coupling spectra of the P-polarized and S-polarized incident light for this conventional 2D GCs may have different peak coupling efficiencies, center wavelengths, and bandwidths [9]. This will consequently result in a large PDL in the working wavelength range. PDL here is defined as the absolute difference between the coupling losses of P-polarized and S-polarized input light. To overcome these problems, two strategies are adopted here. First, the conventional square lattice of the scatter holes is replaced by a diamond-like lattice, which has been demonstrated helpful for more balanced spectra [21]. Here, the slanted angle θ was swept, and θ  = 3.3° was found optimal, where a similar peak coupling efficiency and bandwidth can be obtained for the two polarizations. However, their peak coupling wavelengths still exhibit a large difference in this case, i.e., 11 nm as shown in Fig. 2. The second strategies adopted is to replace the circular scatter holes into two orthogonally crossed ellipses. Here, we further swept the semi-minor axis RS and the semi-major axis RL of the ellipses while keeping the area of each scatter unchanged. The evolution of the coupling spectra for the two polarizations is shown in Fig. 2. One can find that the coupling spectra of the S-polarized light exhibits a red shift, while, on the contrary, that of the P-polarized light exhibits a blue shift, when increasing RS. The spectra of the two polarizations tend to coincide when RS = 100 nm. The final optimized parameters for the 2D GC structures are chosen as RS = 98.8 nm, RL = 225 nm, and P = 487 nm.

 figure: Fig. 2.

Fig. 2. Coupling loss spectra of the P-polarized and S-polarized light at different RS while the area of each scatter is unchanged. The right most figure is with circular scatters when θ  = 3.3°.

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To improve the coupling efficiency, a reflection Au mirror was added on top of the SiO2 over-cladding, and the coupling fiber is also moved to the substrate side as shown in Fig. 1(b). The thickness of the SiO2 over-cladding h was then optimized to produce a constructive interference between the downward diffracted light and the light reflected by the mirror. The coupling loss at 1310 nm wavelength for the two polarizations are plotted in Fig. 3(a), when the over-cladding thickness h was swept from 0.5 µm to 1.3 µm. One can find that these two curves almost overlap and periodic maximums are presented. The PDLs, as shown in Fig. 3(b) in these cases, are all small, less than 0.34 dB, within the simulated range of h, which indicates a high tolerance for the PDL about the over-cladding thickness. Here, we adopted h = 600 nm, i.e., the first intersection point of the two coupling curves shown in Fig. 3(a), since in this case both polarizations show a low coupling loss and the PDL is zero. It is worthwhile to note that the Au mirror introduced here would result in a blue shift of center wavelength of the coupling spectra for about 20 nm away from 1310 nm, and we adjusted the pitch P to 496 nm to compensate this shift. As shown in Fig. 4, the coupling loss of this improved 2D GC reaches −1.73 dB, and the 1dB coupling bandwidth is 29 nm (from 1298 nm to 1327 nm). The PDL is less than 0.2 dB among a wavelength range of 63 nm. For comparison, the coupling spectra of a conventional 2D GC (square lattice of circular holes without metal mirror) is plotted. It exhibits a low coupling loss of −2.87 dB only for the S-polarized light and a much larger PDL. Obviously, the proposed structure significantly improves the performances of a 2D GC on silicon.

 figure: Fig. 3.

Fig. 3. (a) Simulated coupling losses of P-polarized and S-polarized light as a function of over-cladding thickness h at 1310 nm wavelength, and (b) the corresponding PDLs.

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 figure: Fig. 4.

Fig. 4. (a) Simulated spectra of the coupling losses for the proposed 2D GC and a conventional 2D GC, and (b) the corresponding PDLs.

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We also investigate the fabrication tolerance of the present 2D GC. First the influence of the etching depth variation ΔE is simulated as shown in Fig. 5(a) and 5(b). When the etching depth increases, the whole coupling spectra blue-shift for both polarizations. Consequently, the PDL spectrum also shifts accordingly. Nevertheless, within the 1 dB coupling bandwidth, the PDL are still kept below 0.25 dB. The peak coupling efficiency remains similar for different etching depths. As the relative positions of the scatters in the array can be rather accurate, the influence of in-plane dimensions of the scatters, defined by RS and RL, is further studied. As shown in Fig. 5(c), the peak coupling wavelength also blue-shifts as RS and RL both increase. This is similar to the case of increasing the etching depth, since the effective volume of the scatters become larger. The peak coupling efficiency does not show a significant variation within the parameter range considered here. The worst PDL within its 1 dB coupling bandwidth for each RS and RL value is plotted in Fig. 5(d). One can find that as RS and RL both increase the PDL maintains small. However, when RS and RL change in different directions, i.e., one increases and the other decreases, the PDL performance gets worse. Nevertheless, compared to that of the conventional 2D GC shown in Fig. 4, the PDL of the proposed structure would maintain low in a large process window.

 figure: Fig. 5.

Fig. 5. Fabrication tolerance analyses of the scatter pattern. (a) Coupling spectra and (b) PDL when the etching depth E deviates from 70nm. The two curves for each ΔE are for two polarizations. Contour maps of the peak coupling wavelength (c) and the worst PDL (d) within the 1 dB coupling bandwidth when RS and RL deviate from the optimal values.

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3. Fabrication and measurement

Test structures of the designed GC were fabricated on an SOI wafer with a 220 nm top silicon layer and a 2 µm BOX layer. First, electron-beam lithography and inductively-coupled-plasma etching were utilized to define the grating and the waveguide. A SiO2 over-cladding of 600 nm was then prepared using plasma-enhanced chemical vapor deposition, on which a patch of metal films, consisting of 5 nm Ti, 100 nm Au, and 5 nm Ti is subsequently deposited only over the GCs using electron-gun evaporation and lift-off process. The Ti layer is employed as an adhesion promoter. In order to achieve a better coupling loss, the thickness of the over-cladding must be finely controlled to achieve the desired constructive interference. Then, a quartz plate of 4 mm × 4 mm in size was bonded above the coupling structures through a UV-curable adhesive. Finally, the part of the silicon substrate underneath the quartz plate was removed for fiber access through optical lithography with back-side alignment and deep-silicon etching. Although the quartz plate is relatively large here, there is no any technique difficulties to reduce its size down to sub-mm scale to cover only the grating coupler region in real applications.

 Figure 6(a) shows the optical micrograph of two back-to-back connected 2D GCs, and the inset depicts the details of fabricated grating cells. The measurement configuration is shown in Fig. 6(b). Here, the access fibers are placed upwards from the bottom of the chip through the hole opened in the substrate. The proposed configuration for fiber access brings some advantages for fabrication, testing, and packaging. First, as compared to the approach using a bottom mirror, i.e., mirror fabricated from the substrate side after the hole opening in the substrate [6,8,14], the present structure is mechanically more stable. The bonded quartz plate can prevent the device layer from wrinkling. The requirement, such as the stress management and the BOX layer thickness, for the SOI structure is released as well [6]. The quartz plate and the hole in the silicon substrate can also be designed with an appropriate size, which was to cover only the necessary coupling structure and leave the rest of the chip free. As compared to the conventional approach of transferring the whole device layer upside down on a new substrate [7,24], this facilitates not only a wafer-scale post-process for the whole structure, but also electrical connections to the chip, if needed. For example, metal pads and bonding wires can be placed on the rest area of the chip which is not covered by the quartz plate as sketched in Fig. 1(b). The alignment of a fiber array or a multicore fiber, can also be made easier. Figure 6(c) is an image captured through a camera mounted on top of the structure. In this case, one can see the device and the fiber simultaneously through the transparent quartz plate, and the alignment of them becomes more straight forward.

 figure: Fig. 6.

Fig. 6. (a) Optical micrograph of back-to-back cascaded 2D GCs, the inset shows a scan-electron microscope image of the fabricated grating cells. (b) Measurement setup for back-side fiber access. (c) Optical micrograph of the GC and the coupling fiber during testing.

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 Figure 7 shows the measured coupling spectra and the derived PDLs of a fabricated 2D GC with and without a metal mirror. The best coupling loss of −2.37 dB at 1310 nm wavelength is obtained for the case with the metal mirror. The 1 dB coupling bandwidth is 29 nm, and the corresponding PDLs is better than 0.2 dB in a wavelength range of 78 nm. The measured coupling loss is about −0.64 dB at the best, which is higher than that of the simulated results. This may attribute to the fabrication error of the over-cladding thickness and the 5 nm Ti layer. As compared to an identical structure on the unmodified SOI wafer, i.e., without the metal mirror and substrate etching, measured from the top side, the coupling loss exhibits an 1.7 dB reduction through the mirror. The PDLs are similar in these two cases. Besides, the spectral curves in Fig. 7 are relatively smooth, which implies low back reflections in the SOI waveguides for the present GC. Simulation results also demonstrate that the reflection is indeed small in the order of 10−5 over a wavelength range of 100 nm. We owe this to the off-vertical coupling scheme and a shallowly etched grating. Table 1 shows the performances of some recent demonstrations of 2D GCs on silicon. Clearly, the coupling loss of the present structure is the best, and the PDL maintains the lowest in a wide wavelength range.

 figure: Fig. 7.

Fig. 7. (a) Measured coupling losses and (b) derived PDLs at different wavelengths for the proposed 2D GC with and without a metal mirror.

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Tables Icon

Table 1. Performances of 2D GCs on silicon.

4. Conclusion

In summary, we have introduced a 2D GC on silicon with a high coupling efficiency and a low PDLs. Using two crossing ellipses as the grating scatter and a diamond-like grating lattice, the PDL can be effectively reduced with nearly a coinciding coupling spectra for the P-polarized and S-polarized light. The coupling loss was further reduced using a metal mirror. The coupling loss of −1.73dB theoretically and −2.37dB experimentally at 1310nm wavelength has been obtained. The corresponding PDL was measured lower than 0.2dB in a wavelength range of 78nm. To the best of our knowledge, the present structure demonstrates the best coupling loss with a low PDL for 2D GCs fabricated on a conventional SOI wafer. In addition, the configuration for the reflection metal mirror facilitates a wafer-scale and robust post-processing, as well as easy testing and packaging for access fibers.

Funding

National Major Research and Development Program (2018YFB2200200); Guangzhou Science and Technology Program (201707010444); Special Funds for the Cultivation of Guangdong College Students’ Scientific and Technological Innovation; National Natural Science Foundation of China (61675069).

Disclosures

The authors declare no conflicts of interest.

References

1. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luysseart, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]  

2. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006). [CrossRef]  

3. R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photonics Res. 7(2), 201–239 (2019). [CrossRef]  

4. A. Michaels and E. Yablonovitch, “Inverse design of near unity efficiency perfectly vertical grating couplers,” Opt. Express 26(4), 4766–4779 (2018). [CrossRef]  

5. D. Benedikovic, C. Alonso-Ramos, S. Guerber, X. Le Roux, P. Cheben, C. Dupré, B. Szelag, D. Fowler, É Cassan, D. Marris-Morini, C. Baudot, F. Boeuf, and L. Vivien, “Sub-decibel silicon grating couplers based on L-shaped waveguides and engineered subwavelength metamaterials,” Opt. Express 27(18), 26239–26250 (2019). [CrossRef]  

6. W. S. Zaoui, M. F. Rosa, W. Vogel, M. Berroth, J. Butschke, and F. Letzkus, “Cost-effective CMOS-compatible grating couplers with backside metal mirror and 69% coupling efficiency,” Opt. Express 20(26), B238–B243 (2012). [CrossRef]  

7. Y. Ding, C. Peucheret, H. Ou, and K. Yvind, “Fully etched apodized grating coupler on the SOI platform with −0.58 dB coupling efficiency,” Opt. Lett. 39(18), 5348–5350 (2014). [CrossRef]  

8. D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015). [CrossRef]  

9. W. Bogaerts, D. Taillaert, P. Dumon, D. Van Thourhout, R. Baets, and E. Pluk, “A polarization-diversity wavelength duplexer circuit in silicon-on-insulator photonic wires,” Opt. Express 15(4), 1567–1578 (2007). [CrossRef]  

10. D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. DeLa Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photonics Technol. Lett. 15(9), 1249–1251 (2003). [CrossRef]  

11. J. Zou, Y. Yu, and X. Zhang, “Single step etched two dimensional grating coupler based on the SOI platform,” Opt. Express 23(25), 32490–32495 (2015). [CrossRef]  

12. T. Watanabe, Y. Fedoryshyn, and J. Leuthold, “2-D Grating Couplers for Vertical Fiber Coupling in Two Polarizations,” IEEE Photonics J. 11(4), 1–9 (2019). [CrossRef]  

13. X. Chen and H. K. Tsang, “Polarization-independent grating couplers for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 36(6), 796–798 (2011). [CrossRef]  

14. W. S. Zaoui, A. Kunze, W. Vogel, and M. Berroth, “CMOS-compatible polarization splitting grating couplers with a backside metal mirror,” IEEE Photonics Technol. Lett. 25(14), 1395–1397 (2013). [CrossRef]  

15. Z. Cheng and H. Tsang, “Experimental demonstration of polarization-insensitive air-cladding grating couplers for silicon-on-insulator waveguides,” Opt. Lett. 39(7), 2206–2209 (2014). [CrossRef]  

16. D. Gostimirovic and W. N. Ye, “An Open-Source Artificial Neural Network Model for Polarization-Insensitive Silicon-on-Insulator Subwavelength Grating Couplers,” IEEE J. Sel. Top. Quant. Electron. 25(3), 1–5 (2019). [CrossRef]  

17. N. Purwaha, A. Atieh, and W. N. Ye, “Broadband and polarization flexible SOI grating coupler based on sub-wavelength gratings with low back reflections,” OSA Continuum 2(4), 1350–1357 (2019). [CrossRef]  

18. R. Halir, D. Vermeulen, and G. Roelkens, “Reducing polarization-dependent loss of silicon-on-insulator fiber to chip grating couplers,” IEEE Photonics Technol. Lett. 22(6), 389–391 (2010). [CrossRef]  

19. A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A Grating-Coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quant. Electron. 17(3), 597–608 (2011). [CrossRef]  

20. J. Zou, Y. Yu, and X. Zhang, “Two-dimensional grating coupler with a low polarization dependent loss of 0.25 dB covering the C-band,” Opt. Lett. 41(18), 4206–4209 (2016). [CrossRef]  

21. Y. Sobu, S.-H. Jeong, and Y. Tanaka, “Si-wire two-dimensional grating coupler with polarization-dependent loss of lower than 0.3 dB over a 60-nm-wide spectral range,” Jpn. J. Appl. Phys. 57(11), 112501 (2018). [CrossRef]  

22. Y. Xue, H. Chen, Y. Bao, J. Dong, and X. Zhang, “Two-dimensional silicon photonic grating coupler with low polarization-dependent loss and high tolerance,” Opt. Express 27(16), 22268–22274 (2019). [CrossRef]  

23. L. Carroll, D. Gerace, I. Cristiani, and L. Andreani, “Optimizing polarization-diversity couplers for Si-photonics: reaching the −1 dB coupling efficiency threshold,” Opt. Express 22(12), 14769–14781 (2014). [CrossRef]  

24. Y. Luo, Z. Nong, S. Gao, H. Huang, Y. Zhu, L. Liu, L. Zhou, J. Xu, L. Liu, S. Yu, and X. Cai, “Low-loss two-dimensional silicon photonic grating coupler with a backside metal mirror,” Opt. Lett. 43(3), 474–477 (2018). [CrossRef]  

References

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  1. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luysseart, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005).
    [Crossref]
  2. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
    [Crossref]
  3. R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photonics Res. 7(2), 201–239 (2019).
    [Crossref]
  4. A. Michaels and E. Yablonovitch, “Inverse design of near unity efficiency perfectly vertical grating couplers,” Opt. Express 26(4), 4766–4779 (2018).
    [Crossref]
  5. D. Benedikovic, C. Alonso-Ramos, S. Guerber, X. Le Roux, P. Cheben, C. Dupré, B. Szelag, D. Fowler, É Cassan, D. Marris-Morini, C. Baudot, F. Boeuf, and L. Vivien, “Sub-decibel silicon grating couplers based on L-shaped waveguides and engineered subwavelength metamaterials,” Opt. Express 27(18), 26239–26250 (2019).
    [Crossref]
  6. W. S. Zaoui, M. F. Rosa, W. Vogel, M. Berroth, J. Butschke, and F. Letzkus, “Cost-effective CMOS-compatible grating couplers with backside metal mirror and 69% coupling efficiency,” Opt. Express 20(26), B238–B243 (2012).
    [Crossref]
  7. Y. Ding, C. Peucheret, H. Ou, and K. Yvind, “Fully etched apodized grating coupler on the SOI platform with −0.58 dB coupling efficiency,” Opt. Lett. 39(18), 5348–5350 (2014).
    [Crossref]
  8. D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
    [Crossref]
  9. W. Bogaerts, D. Taillaert, P. Dumon, D. Van Thourhout, R. Baets, and E. Pluk, “A polarization-diversity wavelength duplexer circuit in silicon-on-insulator photonic wires,” Opt. Express 15(4), 1567–1578 (2007).
    [Crossref]
  10. D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. DeLa Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photonics Technol. Lett. 15(9), 1249–1251 (2003).
    [Crossref]
  11. J. Zou, Y. Yu, and X. Zhang, “Single step etched two dimensional grating coupler based on the SOI platform,” Opt. Express 23(25), 32490–32495 (2015).
    [Crossref]
  12. T. Watanabe, Y. Fedoryshyn, and J. Leuthold, “2-D Grating Couplers for Vertical Fiber Coupling in Two Polarizations,” IEEE Photonics J. 11(4), 1–9 (2019).
    [Crossref]
  13. X. Chen and H. K. Tsang, “Polarization-independent grating couplers for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 36(6), 796–798 (2011).
    [Crossref]
  14. W. S. Zaoui, A. Kunze, W. Vogel, and M. Berroth, “CMOS-compatible polarization splitting grating couplers with a backside metal mirror,” IEEE Photonics Technol. Lett. 25(14), 1395–1397 (2013).
    [Crossref]
  15. Z. Cheng and H. Tsang, “Experimental demonstration of polarization-insensitive air-cladding grating couplers for silicon-on-insulator waveguides,” Opt. Lett. 39(7), 2206–2209 (2014).
    [Crossref]
  16. D. Gostimirovic and W. N. Ye, “An Open-Source Artificial Neural Network Model for Polarization-Insensitive Silicon-on-Insulator Subwavelength Grating Couplers,” IEEE J. Sel. Top. Quant. Electron. 25(3), 1–5 (2019).
    [Crossref]
  17. N. Purwaha, A. Atieh, and W. N. Ye, “Broadband and polarization flexible SOI grating coupler based on sub-wavelength gratings with low back reflections,” OSA Continuum 2(4), 1350–1357 (2019).
    [Crossref]
  18. R. Halir, D. Vermeulen, and G. Roelkens, “Reducing polarization-dependent loss of silicon-on-insulator fiber to chip grating couplers,” IEEE Photonics Technol. Lett. 22(6), 389–391 (2010).
    [Crossref]
  19. A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A Grating-Coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quant. Electron. 17(3), 597–608 (2011).
    [Crossref]
  20. J. Zou, Y. Yu, and X. Zhang, “Two-dimensional grating coupler with a low polarization dependent loss of 0.25 dB covering the C-band,” Opt. Lett. 41(18), 4206–4209 (2016).
    [Crossref]
  21. Y. Sobu, S.-H. Jeong, and Y. Tanaka, “Si-wire two-dimensional grating coupler with polarization-dependent loss of lower than 0.3 dB over a 60-nm-wide spectral range,” Jpn. J. Appl. Phys. 57(11), 112501 (2018).
    [Crossref]
  22. Y. Xue, H. Chen, Y. Bao, J. Dong, and X. Zhang, “Two-dimensional silicon photonic grating coupler with low polarization-dependent loss and high tolerance,” Opt. Express 27(16), 22268–22274 (2019).
    [Crossref]
  23. L. Carroll, D. Gerace, I. Cristiani, and L. Andreani, “Optimizing polarization-diversity couplers for Si-photonics: reaching the −1 dB coupling efficiency threshold,” Opt. Express 22(12), 14769–14781 (2014).
    [Crossref]
  24. Y. Luo, Z. Nong, S. Gao, H. Huang, Y. Zhu, L. Liu, L. Zhou, J. Xu, L. Liu, S. Yu, and X. Cai, “Low-loss two-dimensional silicon photonic grating coupler with a backside metal mirror,” Opt. Lett. 43(3), 474–477 (2018).
    [Crossref]

2019 (6)

R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photonics Res. 7(2), 201–239 (2019).
[Crossref]

D. Benedikovic, C. Alonso-Ramos, S. Guerber, X. Le Roux, P. Cheben, C. Dupré, B. Szelag, D. Fowler, É Cassan, D. Marris-Morini, C. Baudot, F. Boeuf, and L. Vivien, “Sub-decibel silicon grating couplers based on L-shaped waveguides and engineered subwavelength metamaterials,” Opt. Express 27(18), 26239–26250 (2019).
[Crossref]

T. Watanabe, Y. Fedoryshyn, and J. Leuthold, “2-D Grating Couplers for Vertical Fiber Coupling in Two Polarizations,” IEEE Photonics J. 11(4), 1–9 (2019).
[Crossref]

D. Gostimirovic and W. N. Ye, “An Open-Source Artificial Neural Network Model for Polarization-Insensitive Silicon-on-Insulator Subwavelength Grating Couplers,” IEEE J. Sel. Top. Quant. Electron. 25(3), 1–5 (2019).
[Crossref]

N. Purwaha, A. Atieh, and W. N. Ye, “Broadband and polarization flexible SOI grating coupler based on sub-wavelength gratings with low back reflections,” OSA Continuum 2(4), 1350–1357 (2019).
[Crossref]

Y. Xue, H. Chen, Y. Bao, J. Dong, and X. Zhang, “Two-dimensional silicon photonic grating coupler with low polarization-dependent loss and high tolerance,” Opt. Express 27(16), 22268–22274 (2019).
[Crossref]

2018 (3)

2016 (1)

2015 (2)

2014 (3)

2013 (1)

W. S. Zaoui, A. Kunze, W. Vogel, and M. Berroth, “CMOS-compatible polarization splitting grating couplers with a backside metal mirror,” IEEE Photonics Technol. Lett. 25(14), 1395–1397 (2013).
[Crossref]

2012 (1)

2011 (2)

X. Chen and H. K. Tsang, “Polarization-independent grating couplers for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 36(6), 796–798 (2011).
[Crossref]

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A Grating-Coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quant. Electron. 17(3), 597–608 (2011).
[Crossref]

2010 (1)

R. Halir, D. Vermeulen, and G. Roelkens, “Reducing polarization-dependent loss of silicon-on-insulator fiber to chip grating couplers,” IEEE Photonics Technol. Lett. 22(6), 389–391 (2010).
[Crossref]

2007 (1)

2006 (1)

2005 (1)

2003 (1)

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. DeLa Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photonics Technol. Lett. 15(9), 1249–1251 (2003).
[Crossref]

Alonso-Ramos, C.

Andreani, L.

Atieh, A.

Baets, R.

Bao, Y.

Baudot, C.

Beckx, S.

Benedikovic, D.

Berroth, M.

W. S. Zaoui, A. Kunze, W. Vogel, and M. Berroth, “CMOS-compatible polarization splitting grating couplers with a backside metal mirror,” IEEE Photonics Technol. Lett. 25(14), 1395–1397 (2013).
[Crossref]

W. S. Zaoui, M. F. Rosa, W. Vogel, M. Berroth, J. Butschke, and F. Letzkus, “Cost-effective CMOS-compatible grating couplers with backside metal mirror and 69% coupling efficiency,” Opt. Express 20(26), B238–B243 (2012).
[Crossref]

Bienstman, P.

Boeuf, F.

Bogaerts, W.

Borel, P. I.

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. DeLa Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photonics Technol. Lett. 15(9), 1249–1251 (2003).
[Crossref]

Butschke, J.

Cai, X.

Carroll, L.

R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photonics Res. 7(2), 201–239 (2019).
[Crossref]

L. Carroll, D. Gerace, I. Cristiani, and L. Andreani, “Optimizing polarization-diversity couplers for Si-photonics: reaching the −1 dB coupling efficiency threshold,” Opt. Express 22(12), 14769–14781 (2014).
[Crossref]

Cassan, É

Cheben, P.

Chen, H.

Chen, X.

Cheng, Z.

Chong, H.

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. DeLa Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photonics Technol. Lett. 15(9), 1249–1251 (2003).
[Crossref]

Cristiani, I.

Dado, M.

De Dobbelaere, P.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A Grating-Coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quant. Electron. 17(3), 597–608 (2011).
[Crossref]

DeLa Rue, R.

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. DeLa Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photonics Technol. Lett. 15(9), 1249–1251 (2003).
[Crossref]

Ding, Y.

Dong, J.

Dumon, P.

Dupré, C.

Fathpour, S.

Fedoryshyn, Y.

T. Watanabe, Y. Fedoryshyn, and J. Leuthold, “2-D Grating Couplers for Vertical Fiber Coupling in Two Polarizations,” IEEE Photonics J. 11(4), 1–9 (2019).
[Crossref]

Fowler, D.

Frandsen, L. H.

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. DeLa Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photonics Technol. Lett. 15(9), 1249–1251 (2003).
[Crossref]

Gao, S.

Gerace, D.

Gloeckner, S.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A Grating-Coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quant. Electron. 17(3), 597–608 (2011).
[Crossref]

Gostimirovic, D.

D. Gostimirovic and W. N. Ye, “An Open-Source Artificial Neural Network Model for Polarization-Insensitive Silicon-on-Insulator Subwavelength Grating Couplers,” IEEE J. Sel. Top. Quant. Electron. 25(3), 1–5 (2019).
[Crossref]

Gradkowski, K.

R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photonics Res. 7(2), 201–239 (2019).
[Crossref]

Guerber, S.

Halir, R.

Huang, H.

Jalali, B.

Janz, S.

Jeong, S.-H.

Y. Sobu, S.-H. Jeong, and Y. Tanaka, “Si-wire two-dimensional grating coupler with polarization-dependent loss of lower than 0.3 dB over a 60-nm-wide spectral range,” Jpn. J. Appl. Phys. 57(11), 112501 (2018).
[Crossref]

Kunze, A.

W. S. Zaoui, A. Kunze, W. Vogel, and M. Berroth, “CMOS-compatible polarization splitting grating couplers with a backside metal mirror,” IEEE Photonics Technol. Lett. 25(14), 1395–1397 (2013).
[Crossref]

Lacava, C.

R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photonics Res. 7(2), 201–239 (2019).
[Crossref]

Lamontagne, B.

Lapointe, J.

Le Roux, X.

Letzkus, F.

Leuthold, J.

T. Watanabe, Y. Fedoryshyn, and J. Leuthold, “2-D Grating Couplers for Vertical Fiber Coupling in Two Polarizations,” IEEE Photonics J. 11(4), 1–9 (2019).
[Crossref]

Liu, L.

Luo, Y.

Luysseart, B.

Marchetti, R.

R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photonics Res. 7(2), 201–239 (2019).
[Crossref]

Marris-Morini, D.

Masini, G.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A Grating-Coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quant. Electron. 17(3), 597–608 (2011).
[Crossref]

Mekis, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A Grating-Coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quant. Electron. 17(3), 597–608 (2011).
[Crossref]

Michaels, A.

Minzioni, P.

R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photonics Res. 7(2), 201–239 (2019).
[Crossref]

Narasimha, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A Grating-Coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quant. Electron. 17(3), 597–608 (2011).
[Crossref]

Nong, Z.

Ortega-Moñux, A.

Ou, H.

Peucheret, C.

Pinguet, T.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A Grating-Coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quant. Electron. 17(3), 597–608 (2011).
[Crossref]

Pluk, E.

Purwaha, N.

Roelkens, G.

R. Halir, D. Vermeulen, and G. Roelkens, “Reducing polarization-dependent loss of silicon-on-insulator fiber to chip grating couplers,” IEEE Photonics Technol. Lett. 22(6), 389–391 (2010).
[Crossref]

Rosa, M. F.

Sahni, S.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A Grating-Coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quant. Electron. 17(3), 597–608 (2011).
[Crossref]

Schmid, J. H.

Sobu, Y.

Y. Sobu, S.-H. Jeong, and Y. Tanaka, “Si-wire two-dimensional grating coupler with polarization-dependent loss of lower than 0.3 dB over a 60-nm-wide spectral range,” Jpn. J. Appl. Phys. 57(11), 112501 (2018).
[Crossref]

Szelag, B.

Taillaert, D.

Tanaka, Y.

Y. Sobu, S.-H. Jeong, and Y. Tanaka, “Si-wire two-dimensional grating coupler with polarization-dependent loss of lower than 0.3 dB over a 60-nm-wide spectral range,” Jpn. J. Appl. Phys. 57(11), 112501 (2018).
[Crossref]

Tsang, H.

Tsang, H. K.

Van Campenhout, J.

Van Thourhout, D.

Vermeulen, D.

R. Halir, D. Vermeulen, and G. Roelkens, “Reducing polarization-dependent loss of silicon-on-insulator fiber to chip grating couplers,” IEEE Photonics Technol. Lett. 22(6), 389–391 (2010).
[Crossref]

Vivien, L.

Vogel, W.

W. S. Zaoui, A. Kunze, W. Vogel, and M. Berroth, “CMOS-compatible polarization splitting grating couplers with a backside metal mirror,” IEEE Photonics Technol. Lett. 25(14), 1395–1397 (2013).
[Crossref]

W. S. Zaoui, M. F. Rosa, W. Vogel, M. Berroth, J. Butschke, and F. Letzkus, “Cost-effective CMOS-compatible grating couplers with backside metal mirror and 69% coupling efficiency,” Opt. Express 20(26), B238–B243 (2012).
[Crossref]

Wang, S.

Watanabe, T.

T. Watanabe, Y. Fedoryshyn, and J. Leuthold, “2-D Grating Couplers for Vertical Fiber Coupling in Two Polarizations,” IEEE Photonics J. 11(4), 1–9 (2019).
[Crossref]

Wiaux, V.

Xu, D.-X.

Xu, J.

Xue, Y.

Yablonovitch, E.

Ye, W. N.

N. Purwaha, A. Atieh, and W. N. Ye, “Broadband and polarization flexible SOI grating coupler based on sub-wavelength gratings with low back reflections,” OSA Continuum 2(4), 1350–1357 (2019).
[Crossref]

D. Gostimirovic and W. N. Ye, “An Open-Source Artificial Neural Network Model for Polarization-Insensitive Silicon-on-Insulator Subwavelength Grating Couplers,” IEEE J. Sel. Top. Quant. Electron. 25(3), 1–5 (2019).
[Crossref]

Yu, S.

Yu, Y.

Yvind, K.

Zaoui, W. S.

W. S. Zaoui, A. Kunze, W. Vogel, and M. Berroth, “CMOS-compatible polarization splitting grating couplers with a backside metal mirror,” IEEE Photonics Technol. Lett. 25(14), 1395–1397 (2013).
[Crossref]

W. S. Zaoui, M. F. Rosa, W. Vogel, M. Berroth, J. Butschke, and F. Letzkus, “Cost-effective CMOS-compatible grating couplers with backside metal mirror and 69% coupling efficiency,” Opt. Express 20(26), B238–B243 (2012).
[Crossref]

Zhang, X.

Zhou, L.

Zhu, Y.

Zou, J.

IEEE J. Sel. Top. Quant. Electron. (2)

D. Gostimirovic and W. N. Ye, “An Open-Source Artificial Neural Network Model for Polarization-Insensitive Silicon-on-Insulator Subwavelength Grating Couplers,” IEEE J. Sel. Top. Quant. Electron. 25(3), 1–5 (2019).
[Crossref]

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A Grating-Coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quant. Electron. 17(3), 597–608 (2011).
[Crossref]

IEEE Photonics J. (1)

T. Watanabe, Y. Fedoryshyn, and J. Leuthold, “2-D Grating Couplers for Vertical Fiber Coupling in Two Polarizations,” IEEE Photonics J. 11(4), 1–9 (2019).
[Crossref]

IEEE Photonics Technol. Lett. (3)

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. DeLa Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photonics Technol. Lett. 15(9), 1249–1251 (2003).
[Crossref]

W. S. Zaoui, A. Kunze, W. Vogel, and M. Berroth, “CMOS-compatible polarization splitting grating couplers with a backside metal mirror,” IEEE Photonics Technol. Lett. 25(14), 1395–1397 (2013).
[Crossref]

R. Halir, D. Vermeulen, and G. Roelkens, “Reducing polarization-dependent loss of silicon-on-insulator fiber to chip grating couplers,” IEEE Photonics Technol. Lett. 22(6), 389–391 (2010).
[Crossref]

J. Lightwave Technol. (2)

Jpn. J. Appl. Phys. (1)

Y. Sobu, S.-H. Jeong, and Y. Tanaka, “Si-wire two-dimensional grating coupler with polarization-dependent loss of lower than 0.3 dB over a 60-nm-wide spectral range,” Jpn. J. Appl. Phys. 57(11), 112501 (2018).
[Crossref]

Opt. Express (8)

Y. Xue, H. Chen, Y. Bao, J. Dong, and X. Zhang, “Two-dimensional silicon photonic grating coupler with low polarization-dependent loss and high tolerance,” Opt. Express 27(16), 22268–22274 (2019).
[Crossref]

L. Carroll, D. Gerace, I. Cristiani, and L. Andreani, “Optimizing polarization-diversity couplers for Si-photonics: reaching the −1 dB coupling efficiency threshold,” Opt. Express 22(12), 14769–14781 (2014).
[Crossref]

D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref]

W. Bogaerts, D. Taillaert, P. Dumon, D. Van Thourhout, R. Baets, and E. Pluk, “A polarization-diversity wavelength duplexer circuit in silicon-on-insulator photonic wires,” Opt. Express 15(4), 1567–1578 (2007).
[Crossref]

A. Michaels and E. Yablonovitch, “Inverse design of near unity efficiency perfectly vertical grating couplers,” Opt. Express 26(4), 4766–4779 (2018).
[Crossref]

D. Benedikovic, C. Alonso-Ramos, S. Guerber, X. Le Roux, P. Cheben, C. Dupré, B. Szelag, D. Fowler, É Cassan, D. Marris-Morini, C. Baudot, F. Boeuf, and L. Vivien, “Sub-decibel silicon grating couplers based on L-shaped waveguides and engineered subwavelength metamaterials,” Opt. Express 27(18), 26239–26250 (2019).
[Crossref]

W. S. Zaoui, M. F. Rosa, W. Vogel, M. Berroth, J. Butschke, and F. Letzkus, “Cost-effective CMOS-compatible grating couplers with backside metal mirror and 69% coupling efficiency,” Opt. Express 20(26), B238–B243 (2012).
[Crossref]

J. Zou, Y. Yu, and X. Zhang, “Single step etched two dimensional grating coupler based on the SOI platform,” Opt. Express 23(25), 32490–32495 (2015).
[Crossref]

Opt. Lett. (5)

OSA Continuum (1)

Photonics Res. (1)

R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photonics Res. 7(2), 201–239 (2019).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. (a) Schematic structure of the proposed 2D GC. (b) Cross-sectional view of the 2D GC and the access fiber.
Fig. 2.
Fig. 2. Coupling loss spectra of the P-polarized and S-polarized light at different RS while the area of each scatter is unchanged. The right most figure is with circular scatters when θ  = 3.3°.
Fig. 3.
Fig. 3. (a) Simulated coupling losses of P-polarized and S-polarized light as a function of over-cladding thickness h at 1310 nm wavelength, and (b) the corresponding PDLs.
Fig. 4.
Fig. 4. (a) Simulated spectra of the coupling losses for the proposed 2D GC and a conventional 2D GC, and (b) the corresponding PDLs.
Fig. 5.
Fig. 5. Fabrication tolerance analyses of the scatter pattern. (a) Coupling spectra and (b) PDL when the etching depth E deviates from 70nm. The two curves for each ΔE are for two polarizations. Contour maps of the peak coupling wavelength (c) and the worst PDL (d) within the 1 dB coupling bandwidth when RS and RL deviate from the optimal values.
Fig. 6.
Fig. 6. (a) Optical micrograph of back-to-back cascaded 2D GCs, the inset shows a scan-electron microscope image of the fabricated grating cells. (b) Measurement setup for back-side fiber access. (c) Optical micrograph of the GC and the coupling fiber during testing.
Fig. 7.
Fig. 7. (a) Measured coupling losses and (b) derived PDLs at different wavelengths for the proposed 2D GC with and without a metal mirror.

Tables (1)

Tables Icon

Table 1. Performances of 2D GCs on silicon.

Metrics