Bridging the gap between optical fibers and silicon photonic integrated circuits

We present a rigorous approach for designing a highly efficient coupling between single mode optical fibers and silicon nanophotonic waveguides based on diffractive gratings. The structures are fabricated on standard SOI wafers in a cost-effective CMOS process flow. The measured coupling efficiency reaches −1.08 dB and a record value of −0.62 dB in the 1550 nm telecommunication window using a uniform and a nonuniform grating, respectively, with a 1dB-bandwidth larger than 40 nm. ©2014 Optical Society of America OCIS codes: (130.0130) Integrated optics; (050.1950) Diffraction gratings. References and links 1. F. A. Kish, D. Welch, R. Nagarajan, J. L. Pleumeekers, V. Lal, M. Ziari, A. Nilsson, M. Kato, S. Murthy, P. Evans, S. W. Corzine, M. Mitchell, P. Samra, M. Missey, S. DeMars, R. P. Schneider, M. S. Reffle, T. Butrie, J. T. Rahn, M. Van Leeuwen, J. W. Stewart, D. J. Lambert, R. C. Muthiah, H. Tsai, J. S. Bostak, A. Dentai, K. Wu, H. Sun, D. J. Pavinski, J. Zhang, J. Tang, J. McNicol, M. Kuntz, V. Dominic, B. D. Taylor, R. A. Salvatore, M. Fisher, A. Spannagel, E. Strzelecka, P. Studenkov, M. Raburn, W. Williams, D. Christini, K. J. Thomson, S. S. Agashe, R. Malendevich, G. Goldfarb, S. Melle, C. Joyner, M. Kaufman, and S. G. Grubb, “Current status of large-scale InP photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1470–1489 (2011). 2. A. Melloni, F. Morichetti, R. Costa, G. Cusmai, R. G. Heideman, R. Mateman, D. H. Geuzebroek, and A. Borreman, “TriPleX: a new concept in optical waveguiding,” presented at the 13th European Conference on Integrated Optics, Copenhagen, Denmark, ThA3 (2007). 3. J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Günter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. Fedeli, H. Yu, and W. Bogaerts, “Silicon-organic hybrid electro-optical devices,” IEEE J. Sel. Top. Quantum Electron. 19(6), 3401413 (2013). 4. M. J. Heck, H. Chen, A. W. Fang, B. R. Koch, D. Liang, H. Park, M. N. Sysak, and J. E. Bowers, “Hybrid silicon photonics for optical interconnects,” IEEE J. Sel. Top. Quantum Electron. 17(2), 333–346 (2011). 5. S. Klinger, M. Grözing, W. Sfar Zaoui, M. Berroth, M. Kaschel, M. Oehme, E. Kasper, and J. Schulze, “Ge on Si p-i-n photodiodes for a bit rate of up to 25 Gbit/s,” presented at the European Conference on Optical Communication, Vienna, Austria, 9.2.3 (2009). 6. J. Liu, L. C. Kimerling, and J. Michel, “Monolithic Ge-on-Si lasers for large-scale electronic-photonic integration,” Semicond. Sci. Technol. 27(9), 094006 (2012). 7. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004). 8. N. Fang, Z. Yang, A. Wu, J. Chen, M. Zhang, S. Zou, and X. Wang, “Three-dimensional tapered spot-size converter based on (111) silicon-on-insulator,” IEEE Photonics Technol. Lett. 21, 820–822 (2009). 9. M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010). 10. R. Takei, M. Suzuki, E. Omoda, S. Manako, T. Kamei, M. Mori, and Y. Sakakibara, “Silicon knife-edge taper waveguide for ultralow-loss spot-size converter fabricated by photolithography,” Appl. Phys. Lett. 102(10), 101108 (2013). 11. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002). 12. D. Taillaert, W. Bogaerts, and R. Baets, “Efficient coupling between submicron SOI-waveguides and singlemode fibers,” in Proceedings of Symposium IEEE/LEOS Benelux Chapter, Enschede, The Netherlands (2003), pp. 289–292. #201350 $15.00 USD Received 14 Nov 2013; revised 5 Jan 2014; accepted 5 Jan 2014; published 13 Jan 2014 (C) 2014 OSA 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001277 | OPTICS EXPRESS 1277 13. W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, “Basic structures for photonic integrated circuits in silicon-on-insulator,” Opt. Express 12(8), 1583–1591 (2004). 14. G. Z. Masanovic, G. T. Reed, W. Headley, B. Timotijevic, V. M. Passaro, R. Atta, G. Ensell, and A. G. Evans, “A high efficiency input/output coupler for small silicon photonic devices,” Opt. Express 13(19), 7374–7379 (2005). 15. F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007). 16. S. K. Selvaraja, D. Vermeulen, M. Schaekers, E. Sleeckx, W. Bogaerts, G. Roelkens, P. Dumon, D. Van Thourhout, and R. Baets, “Highly efficient grating coupler between optical fiber and silicon photonic circuit,” presented at the Conference on Lasers and Electro-Optics, Baltimore, Maryland, CTuC6 (2009). 17. X. Chen, C. Li, C. K. Fung, S. M. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photonics Technol. Lett. 22(15), 1156–1158 (2010). 18. A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A gratingcoupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011). 19. A. Mekis, S. Abdalla, D. Foltz, S. Gloeckner, S. Hovey, S. Jackson, Y. Liang, M. Mack, G. Masini, M. Peterson, T. Pinguet, S. Sahni, M. Sharp, P. Sun, D. Tan, L. Verslegers, B. P. Welch, K. Yokoyama, S. Yu, and P. M. De Dobbelaere, “A CMOS photonics platform for high-speed optical interconnects,” in Proceedings of IEEE Photonics Conference (2012), pp. 356–357. 20. C. Zhang, J.-H. Sun, X. Xiao, W.-M. Sun, X.-J. Zhang, T. Chu, J.-Z. Yu, and Y.-D. Yu, “High efficiency grating coupler for coupling between single-mode fiber and SOI waveguides,” Chin. Phys. Lett. 30(1), 014207 (2013). 21. B. Schmid, A. Petrov, and M. Eich, “Optimized grating coupler with fully etched slots,” Opt. Express 17(13), 11066–11076 (2009). 22. 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). 23. 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). 24. F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photonics Technol. Lett. 19(23), 1919–1921 (2007).


Introduction
As the need for higher data rates is nowadays rising more and more, the demand for high bandwidth communication increases at all levels.This includes long, medium and short reach interconnects starting from data centers down to backplanes, chip-to-chip and on-chip communication links.The optical interconnection technology has been proved to be the best candidate to replace the electrical copper links at high data rates owing to the larger bandwidth, lower energy consumption and immunity to electromagnetic interference.Nevertheless, the high costs produced by the assembling of discrete optics represent a major obstacle for this emerging technology.Indeed, the integration of optical devices enabled a substantial progress in the realization of more cost-effective solutions to achieve a high-speed connectivity, but no universal approach has yet been adapted.The photonic integration needs to be compatible with conventional technology processes to maintain low-cost manufacturing and the integrated components have to exhibit the same or better performance than their stand-alone counterparts.Here, the question which semiconductor platform will be the most adequate choice is still controversial since each approach has its advantages and drawbacks.While silicon-on-insulator (SOI) is gaining more and more interest due to the maturity of the complementary metal-oxide-semiconductor (CMOS) fabrication process and the ability for high-density integration, other materials such as indium phosphide (InP) offer even more functionalities, e.g.optical amplifiers and lasers [1], whereas the silicon-nitride-silicondioxide (Si 3 N 4 -SiO 2 ) TriPleX platform provides lower waveguiding and coupling losses [2].Furthermore, several groups are investigating some mixed approaches, for example based on the silicon-organic hybrid (SOH) [3] integration or the combination of silicon photonics with III/V semiconductors [4], and have shown an enhanced performance in terms of speed and power consumption.It turns out that for short and middle term the hybrid integration may be the most meaningful solution for optical interconnects to benefit from the advantages of each material.In addition, the field of silicon photonics has to continue to be developed since it represents an excellent low-cost host platform and is compatible to the existing electronic system architectures.
Indeed, a significant progress has been achieved in silicon photonics to enhance the performance of the key devices for optical interconnects starting from the coupling elements to passive waveguides, high-speed photodetectors [5], modulators, and recently monolithic germanium-on-silicon lasers [6], but many obstacles are still encountering this technology.One of the primary problems is how to couple light efficiently from the optical fiber backbone to the photonic integrated circuits (PICs).As the SOI platform offers a high refractive index difference between core and cladding, the cross section of single mode waveguides is a factor of ~10 −3 smaller than that of standard single mode fibers (SMF), and hence the large dimension mismatch induces large coupling losses.To bridge the gap between silicon PICs and the outside world, highly efficient coupling structures have to be developed with the stringent conditions to be compact in size, broadband and cost-effective in fabrication.In fact, an elegant solution based on diffractive gratings has been shown around ten years ago to have a theoretical efficiency better than −0.5 dB with a large bandwidth [7], but this value has not been realized in the reality up to now.In this paper we review the last progress on grating couplers and demonstrate a highly efficient structure with a record measured value of −0.62 dB, a 1dB-bandwidth of 40 nm, and compact dimensions as small as 15 µm x 15.2 µm.

Latest developments on coupling structures
Due to the importance of the coupling issue between optical fibers and PICs, several groups have proposed different solutions to enhance the efficiency, for example using threedimensional spot-size converters [8] or inverted tapers [9].These structures exhibit a high efficiency in the order of −0.5 dB in addition to a low polarization and wavelength dependence.Recently, a knife-edge inverted taper has been reported with a coupling efficiency of −0.35 dB and −0.21 dB for transversal electric (TE) and transversal magnetic (TM) polarizations, respectively [10].However, such kinds of couplers have large dimensions with a length of several hundreds of µm and work in general only for lensed fibers.In addition, the chips have to be diced and edge polished to ensure horizontal butt-coupling for measurement and testing purposes.
The other approach is based on diffractive gratings [11], which couple light vertically or under a small tilt angle from a standard fiber to any integrated waveguide on the chip or vice versa, as it can be seen in Fig. 1(a).Thus, this allows a wafer-scale testing with easy fiber adjustments and good alignment tolerances of nearly ± 2 µm for 1 dB loss penalty in lateral and longitudinal directions [12].Moreover, with compact dimensions smaller than 20 µm x 20 µm, a large 1dB-bandwidth of around 40 nm, and ability to work as polarization beam splitters, these coupling elements provide almost all advantages needed in optical links.The only missing feature is the high efficiency, which can make grating couplers compete with the inverted tapers.Indeed, there has been an important development along the last years with the target to achieve a better efficiency than −1 dB using different approaches, however, with a limited success.Figure 1(b) shows the most important experimental results reported in literature over the last ten years.Starting from the first structures with an efficiency of only around −7 dB [11][12][13], the performance has been quickly ameliorated using different methods, such as dual grating-assisted directional coupling [14], gold mirrors [15], distributed Bragg reflectors (DBR) [16], and apodized gratings [17][18][19][20], to reach a record value of −0.62 dB as it is demonstrated in this work.Here, we will show how the benchmark of −1 dB can be exceeded to achieve efficiencies even better than −0.5 dB in the near future.

Design of highly efficient grating couplers
The overall efficiency η = P out /P in can be expressed as the product of following factors [21] 1 2 3 , where η 1 represents the scattering efficiency η 2 describes the directionality, i.e. the ratio of the diffracted optical power from the integrated waveguide to the fiber, or vice versa, to the total diffracted power and η 3 represents the overlap integral between the upward diffracted field and the fiber fundamental mode in longitudinal and lateral directions, where E up and E out correspond to the electric field distributions of the scattered wave and fiber mode, respectively.Here we assume that the grating is passivated by a SiO 2 layer and a matching index material is introduced between the cladding and the fiber to prevent Fresnel reflections.This can be done using for example light-curing resins or matching index liquids.
To achieve a high scattering efficiency η 1 ~1, it is enough to design a sufficiently long periodic grating that fulfills the Bragg condition at the target wavelength.Hence, the main factors to realize a large overall efficiency are the directionality and matching the upward diffracted field to the Gaussian mode of the SMF.The former quantity can be enhanced using a DBR [16] or a metal layer as a perfect mirror [15,22], which reflect back the downward optical power, and thus prevent substrate losses.The distance between the grating and the backside mirror is of main importance since the light has to be redirected constructively to achieve an optimal directionality.Simulation and measurement results have shown that the efficiency can be improved by around 1.5 dB in comparison to standard grating couplers when designing the reflector adequately [22].Nevertheless, the overall efficiency of a uniform grating can theoretically attain only a maximum value of nearly −0.8 dB due to the mismatch between the diffracted field profile and the fiber beam profile of the optical fiber, which can be seen in Fig. 2(a) for a grating period Λ = 600 nm and a fill factor FF = 0.5.
The output beam of the uniform grating has an exponentially decaying function along the propagation direction, and so the spatial distribution of the scattered power, which induces a limited overlap integral with the Gaussian function of the SMF.Hence, the diffracted field has to be reshaped to adapt the fiber mode profile by adjusting the coupling strength of the grating.Here, the radiated field needs to be reduced at the interface to the input waveguide and maximized around the middle of the grating to exhibit a Gaussian-like shape.For this purpose we have implemented an algorithm that adapts the length and fill factor of each period to achieve the best overlap with the fiber mode, and therefore the highest coupling efficiency, taking into account the minimal size of the ribs r and grooves g that can be technologically realized.The fill factor is defined here as the ratio of the rib to the period length, i.e.FF = r/(r + g) = r/Λ.
The algorithm is implemented in MATLAB and the two-dimensional (2D) simulations are carried out using the open source software CAMFR, which is based on an eigenmode expansion method.The starting structure is a standard uniform grating with a backside metal mirror, 26 periods, Λ = 600 nm, and FF = 0.5 for TE polarized light at a wavelength of 1550 nm.The silicon (Si) waveguide and the buried oxide (BOX) have a thickness of d Si = 250 nm and d BOX = 3 µm, respectively, the etch depth of the grating is 70 nm, and the fiber off-vertical tilt angle is 9°.In a first step the algorithm sweeps the fill factor from 0.01 to 0.99 for a set of period values around 600 nm starting from the first rib-groove pair and saves the dimensions that deliver the highest coupling efficiency.This procedure is applied subsequently for all rib-groove pairs and is defined as a generation.The routine is repeated again for the whole structure, until the obtained result converges, i.e. the efficiency improvement is smaller than 0.1%.The number of iterations is defined then as the product of the rib-groove pairs and the number of generations.In a second step each rib or groove, a socalled element, is optimized separately starting from a variation of ± 10 nm down to ± 1 nm.A generation is defined here when all ribs and grooves are investigated during a single optimization cycle.The routine is repeated again for the whole structure, until no higher efficiency can be obtained.In this step the number of iterations corresponds to the product of the number of elements and generations.This procedure serves solely as a refinement step since only a predefined set of periods and fill factors are taken into consideration in the first step in order to ensure a relatively short simulation time.The whole optimization takes nearly 26 h on an 8-core processor.The used algorithm can be adapted for TM polarized light, for gratings working as 3dB-splitters, or also for 2D polarization splitting grating couplers [23].
Figure 2(b) shows the typical progression of the efficiency as a function of the overall iteration steps.The first iterations are determining and indicate an enhancement of ~0.4 dB, whereas the second step of the algorithm increases the efficiency by solely 0.1 dB.The reason for this behavior is that the first few periods at the interface to the input waveguide are responsible for the high power radiation, and it is sufficient to adapt the fill factor in this small section to decrease the coupling strength and get a Gaussian-like shape of the diffracted field.Figure 2(c) illustrates both fiber and field profile of the obtained nonuniform grating.It is clear that the similarity of the radiated beam form to the SMF Gaussian function is much better than for the periodic case, which explains the large efficiency > −0.5 dB driven by the higher overlap.Moreover, the alignment tolerance along the z-direction is improved to better than ± 2.5 µm for 1 dB loss penalty, as it can be seen in Fig. 2(d).Since the Gaussian shape requires very small grating parameters < 100 nm at the interface to the input waveguide, which can be technologically challenging, different optimizations with variable critical dimensions have been carried out.While the first grating should have no stringent conditions, the second structure should have a minimum rib and groove length of 100 nm and 60 nm, respectively, to be able to be realized by our electron beam lithography system.The third structure has to be limited to at least 100 nm for both parameters, so that it may also be fabricated by means of UV lithography.The final results are verified by the commercial software RSoft using a 2D finite-difference-time-domain (FDTD) method.Figure 2(e) represents the simulated FDTD-spectrum of the three obtained gratings.The first structure (GC1) has a minimum rib and groove length of r min = 87 nm and g min = 42 nm, respectively, and exhibits a coupling efficiency of −0.26 dB at 1550 nm.The second structure (GC2) with r min = 115 nm and g min = 60 nm shows an efficiency of −0.33 dB, whereas the third grating (GC3) with r min = 115 nm and g min = 110 nm still exhibits a high value of −0.41 dB.That means even with relaxed parameters the coupling efficiency can theoretically exceed −0.5 dB.All three structures show a high 1dB-bandwidth of nearly 43 nm.
These results are achieved using 2D simulations to reduce computing time and expense, and hence no information on the third dimension is delivered.That means that the simulated curves correspond to the overall efficiency η only under the condition that η 3,y = 1.To maintain the obtained high coupling efficiency, the overlap integral in the lateral direction has therefore to be maximized, i.e. the width of the grating has to be designed so that no considerable loss penalty is introduced.Assuming a Gaussian distribution of the waveguide fundamental mode and no conversion losses between the waveguide and the grating, the overlap integral with the SMF mode in the y-direction can be approximated for different widths.Figure 2(f) shows that for maximal lateral matching with an overlap higher than 90% the grating width has to be between 11 µm and 16 µm.Smaller and larger values may produce a mismatch and derogate the overall efficiency.

Experimental results
The structures are fabricated on a SOI wafer with a 3 µm BOX and a 250 nm Si-layer thickness using a standard CMOS technology process [22].The gratings and waveguides are defined by electron beam lithography and realized by a two-step dry etching.Afterwards, a 1 µm passivation layer is deposited on top of the wafer and membrane windows are etched on the backside of the wafer underneath the gratings.Finally, an aluminum (Al) layer is deposited in these mirror windows.To measure the efficiency of the designed couplers, two identical gratings serving as input and output optical power interfaces, linked by a 1 mm long and 15 µm wide waveguide, are fabricated.The efficiency in dB is then determined as half the difference between the output and input optical power in dBm since the waveguide losses can be neglected [22].When designing integrated circuits based on single mode waveguides with a width in the order of 400 nm, a taper with a length of around 200 μm at least has to be introduced to prevent mode conversion losses to the wide gratings.Alternatively, some focusing schemes can be adopted to decrease the taper length to less than 15 μm [24].It should be noted that a fused silica matching liquid (Cargille 50350) is used in the measurements in order to prevent Fresnel reflections between the fibers and the top passivation layer.
First, two standard uniform gratings with a period of 600 nm and 850 nm for TE and TM polarizations, respectively, are investigated.The TE-grating exhibits a coupling efficiency of −1.08 dB at 1551 nm and 9° with a 1dB-bandwidth larger than 42 nm, whereas the TMgrating shows a similar behavior and an efficiency of −1.14 dB at 1550 nm and 8° with a 1dBbandwidth larger than 43 nm, as it can be seen in Figs.3(a) and 3(b).The difference to the simulation results is only ~0.2 dB, which shows the high quality of the fabrication process.It should be noted that the efficiency is enhanced by 0.5 dB in comparison to the value reported in [22] since the grating width is increased from 10 µm to 15 µm, and hence a better lateral matching to the fiber mode is guaranteed.The fabricated nonuniform coupler GC2 is illustrated in Fig. 4(a) and the dimensions of the grating are 15 µm x 15.2 µm.At the designed fiber tilt angle of 9° the efficiency reaches its maximum −0.74 dB at the target wavelength 1550 nm, which shows the good agreement between simulation and experiment except the slightly lower value.The best measured coupling efficiency is −0.62 dB at a wavelength of 1531 nm and 11° with Δλ 1dB = 40 nm and Δλ 3dB = 67 nm, as it can be seen in Fig. 4(b).To the best of our knowledge, this is the highest measured efficiency on a grating coupler reported to date.Here, we can also introduce the definition of the efficiency-bandwidth-product EBP = η • Δλ 3dB to describe the tradeoff between both quantities and get a value of 58 nm.The 19 nm blue shift of the highest efficiency from the target wavelength 1550 nm and the 0.29 dB lower value than in theory can be attributed to the accumulated parameter deviations, such as the Si layer thickness and the critical dimensions of the small ribs and grooves.In addition, the BOX thickness has been determined to be smaller than assumed, which also shifts the transmission maximum to smaller wavelengths and larger tilt angles.Figure 4(c) illustrates a typical distribution of d BOX on a SOITEC wafer with a nominal thickness of 3 µm measured using a spectroscopic ellipsometer and shows a mean value of ~2.96 µm.Finally, the grating width may need to be adjusted to achieve a better overlap in the lateral direction.
Despite these small deviations, the efficiency still exceeds −0.75 dB at the target angle and wavelength.The designed grating coupler GC3 with the relaxed dimensions has also been fabricated and characterized and exhibits a highest efficiency of −0.73 dB at 12° and 1522 nm with a 1dB-bandwidth of 38 nm.
To verify the reproducibility of the high efficiency results, the same structure including two grating couplers GC2 linked by a 1 mm long waveguide is placed on different positions on the whole wafer.The measured efficiency of the 19 structures is depicted in Fig. 5(a).It can be seen that only 5 structures have an inferior performance, whereas the rest exhibits an efficiency better than −0.7 dB, giving a yield of nearly 75%.The gratings with an inferior behavior originate from the very edges and the derogated efficiency is caused by the poor quality of the metal mirrors underneath, as it can be observed in Fig. 5(b).
In fact, as the Si substrate thickness varies in the range of 625 µm ± 15 µm, some residuals can persist in the membrane windows after the backside etching step.Hence, the metal deposition cannot occur properly on the BOX and the remaining Si clusters may prevent the constructive interference of the reflected part with the upward diffracted field due to the additional thickness.This problem can be solved for example by trying to overetch the substrate without affecting the BOX layer.Regardless of the few structures with a lower performance, the technological process can be considered as highly reliable and the fabricated nonuniform gratings with the backside Al mirror exhibit unprecedented results.

Conclusion
We have given in this work a short summary on the last developments on coupling structures between single mode fibers and photonic integrated waveguides in silicon.Furthermore, we have presented a method how to design outperforming grating couplers with efficiencies higher than −0.5 dB and demonstrated a structure with a record measured efficiency of −0.62 dB at a wavelength of 1531 nm and a 1dB-bandwidth of 40 nm.The performance is improved through a backside metal mirror to enhance the directionality and an aperiodic grating that diffracts the field in a Gaussian-like form, and hence improves the overlap with the fiber mode.In addition, the grating width is increased to 15 µm in comparison to previous works, and thus allows a better overlap in the lateral direction.The repeatability of the results is determined to be around 75%.We believe that efficiencies −0.5 dB can be experimentally achieved with even a better yield when the structures are designed more properly using the exact wafer parameters and the technological process is better controlled.The obtained results can be considered as a milestone in the silicon photonics since the coupling gap between optical fibers and nanophotonic integrated waveguides is bridged using the presented highly efficient designs.

#Fig. 1 .
Fig. 1.(a) Schematic design of a grating coupler with an optical fiber core on top.(b) Summary of published experimental results of grating couplers with respect to their coupling efficiency over the last ten years.

Fig. 2 .
Fig. 2. (a) Fiber mode profile versus diffracted field profile of a periodic grating with 26 periods, Λ = 600 nm, FF = 0.5, and 5 µm long input and output waveguides at 1550 nm.The mode field diameter of the SMF is 10.4 µm.(b) Typical overall coupling efficiency progression using the optimization algorithm.The first iteration corresponds to the periodic grating.(c) Fiber mode profile versus diffracted field profile of the obtained nonuniform grating.(d) Alignment tolerance along the z-direction of both grating couplers.The origin corresponds to the z-position of the fiber at highest transmission.(e) Coupling efficiency spectrum of the three designed structures with variable critical dimensions.(f) Overlap integral in lateral direction η 3,y versus grating width.

Fig. 5 .
Fig. 5. (a) Measured coupling efficiency of the 19 fabricated gratings GC2 on the whole wafer.(b) Microscopic pictures of two backside metal mirrors at different positions on the wafer.Top: perfect membrane window, bottom: window with silicon residuals.