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Abstract
We demonstrate all-metallic grating couplers that enable vertical, compact and broadband fiber-coupling. The grating couplers are based on a metal layer and directly convert a vertical fiber mode into surface plasmon polaritons (SPPs). In combination with a focusing arrangement, the grating couplers require only a small footprint of 13.5 × 12 µm2. We characterize the grating couplers with both periodic and apodized gratings and experimentally show a 1-dB bandwidth of 115 nm with a coupling efficiency of 2.9 dB.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber-to-chip coupling schemes are among the most essential building blocks of an integrated circuit. Such couplers should enable the transfer of signal from an optical fiber to the chip and vice versa with the least loss at the most compact footprint across the largest spectral range [1–5].
Prominent coupling schemes rely either on edge or surface coupling [4,6–9]. Edge coupling, also known as end-fire coupling, provides highest efficiency over a very broadband spectral range, and has been widely used in silicon photonics as well as III/V semiconductor photonics [1]. Unfortunately, they can be deployed only at an edge of a chip, limiting dense integration opportunities. Moreover, edge coupling requires implementation with lensed fibers and additional fabrication processes, such as polishing facets. Conversely, grating couplers can be arranged two-dimensionally on a chip with standard single mode fibers, and require relatively simple fabrication processes. However, grating couplers typically have narrow optical bandwidth due to the resonant nature of the gratings. To overcome this issue, several attempts to broaden the spectral range of grating couplers have been reported, for example, photonic subwavelength grating couplers, silicon nitride grating couplers and inverse designed grating couplers [10–15]. Such couplers have already demonstrated 1-dB optical bandwidths of 100 nm and beyond [13,16]. Yet, broadband characteristic have been obtained by decreasing the refractive index step within the gratings, and as a result of weak scattering [10,13]. Such photonic grating couplers end up with relatively large device footprints.
A compact fiber-to-chip coupling scheme offering lowest losses and broadband spectral coupling is not only desirable for photonic devices but is increasingly needed for the emerging class of plasmonic devices [17]. Plasmonic devices offer spectral bandwidths far beyond 100 nm on a most compact footprint [18–20]. For instance, plasmonic devices with a pitch below 36 and 12 µm have been introduced [21,22]. To access these devices at such densities, one would need most compact couplers that require a fraction of the space which is currently consumed by couplers. Antenna based couplers [23,24] or metallic grating [21,25] have already been introduced. However, there is no grating technology that can offer efficient broadband coupling at a compact space of e.g., ~10 × 10 µm2 with reasonably low losses.
In this paper, we propose and demonstrate that all-metallic grating couplers offer vertical, broadband fiber-coupling on a compact footprint with low loses, see Fig. 1. The grating couplers introduced here, comprise of only metal and a dielectric layer and directly convert a fiber mode into surface plasmon polaritons (SPPs). The all-metallic grating couplers are arranged as focusing gratings and each occupies a footprint of only 13.5 × 12 µm2. To characterize the grating couplers we used a multicore fiber (MCF) integrated with a dielectric-loaded surface plasmon polariton waveguide (DLSPPW) [26–28]. Experimentally a 1-dB bandwidth of 115 nm with a coupling efficiency of −2.9 dB (51%) has been demonstrated.
Fig. 1 (a) Schematic of the grating couplers integrated with a DLSPPW. (b) Electric field distribution in the xy plane at 50 nm above the metal surface. (c) Simulated electric field distribution at the wavelength of 1550 nm in the xz plane. The color scale between the figures is adapted to increase visibility. (d) Experimental and computational results of the coupling efficiency of the periodic and apodized grating.
2. Principle of operation
In this section, we first discuss the bandwidths of the metallic grating couplers. Second, we investigate the performance of our grating couplers using 2D-FDTD simulations by means of bandwidth, coupling efficiency and fabrication tolerance. Finally, we design the grating couplers with a focusing configuration by performing 3D-FDTD simulations.
To gain an insight of how to design the parameters of a broadband grating coupler, we start with a discussion of the grating equation and study the tolerance of the coupling efficiency in terms of the diffraction angle. Then, we derive an expression for the sensitivity of the coupling efficiency with respect to the wavelength, as introduced in [10]. The angle of diffracted light can be obtained from the phase-matching condition for horizontal gratings
where k0 = 2π/λ is the wavenumber in vacuum, neff is the effective mode index of the waveguide, m is the order of the diffraction, Λ is the pitch of the gratings, nc is the refractive index of the cladding and θ is the angle of the diffracted light against the normal. In many cases, grating couplers are designed with the −1 order of diffraction [13] and thus the equation can be written as follows.By taking the derivative of this equation with the angle θ, we can investigate the dependence of the wavelength on the diffraction angle where the derivative dneff/dλ describes the dispersion of the waveguide. Since the coupling efficiency is related to the angle difference between the diffracted light and the fiber mode (dθ), the bandwidth of the grating coupler can be described by using the wavelength sensitivity on the diffraction angle dλ/dθ [10]where C1dB is a coefficient related to other factors of the grating coupler (e.g., amplitude decay rate of the gratings, length of the gratings and input fiber mode size). Previous works reported that the coefficient varies around ~0.1 with photonic grating couplers. This coefficient can be calculated by exploring more detailed analysis, given in [29].It can be seen from the Eq. (5) that the grating pitch Λ is the most critical parameter that goes into the bandwidth of a grating coupler. Therefore, a large grating pitch is desirable to achieve a broad coupling bandwidth. Yet, the grating pitch depends on the effective mode index of the waveguide. By inserting Λ = λ0/neff (see Eq. (2) where λ0 is the center wavelength for θ = 0) into Eq. (5), we obtain
Now, if we introduce the group index, ng = neff – λ0·dneff/dλ, into Eq. (6), the equation becomes even simplerThus, a practical approach to increase the bandwidth is to keep the effective group index low. This can be achieved by reducing the effective mode index of the grating coupler waveguide [10,13]. Also dispersion engineering might be applied. To reduce the effective refractive index, researchers are resorting often to low-refractive index materials such as silicon nitride (n ~2.0, Λ ~1400 nm) [16,30] or sub-wavelength structures to lower the effective mode index (Λ ~1100 nm) [11–13]. However, reducing the refractive index of a photonic grating coupler also causes weak scattering because of the small index contrasts, resulting in a small coupling efficiency and a large device length [13].In contrast to photonic grating couplers, the key scattering mechanism in plasmonic grating couplers do not stem from refractive index contrasts in the waveguide. This can be seen by the fact that the effective mode indices are almost identical along the metallic grating coupler (e.g., neff = 1.38 at x = 1 µm and and neff = 1.42 at x = 0 in Fig. 2(a)). With a plasmonic grating coupler, strong resonant scattering occurs at the metallic grooves which results in a high diffraction efficiency allowing for a compact footprint. Additionally, a large grating period pitch Λ is obtained if metal-insulator SPPs rather than highly confined metal-insulator-metal gap-plasmons are used [31].
Fig. 2 (a) Cross-sectional schematic of the vertical all-metallic grating coupler. The input fiber mode is a Gaussian beam with a 6-µm mode diameter vertically aligned to the gratings. (b) Coupling efficiencies of the grating couplers with periodic and apodized gratings obtained from 2D-FDTD simulations. (c) Intensity decay profile (blue) in the dielectric layer 200 nm above metal, fitted by an exponential decay function (red). The SPP mode is launched at x = 1 µm and propagates backwards in this case. (d) Effective mode index of the SPP waveguide over the wavelength. The result is obtained by examining the eigenmode of the waveguide at x = 1 µm. The slope gives the waveguide dispersion, dneff/dλ = −0.186 µm−1.
The schematic cross-section of the metallic grating coupler is shown in Fig. 2(a). We use a 450-nm-thick poly(methyl methacrylate) (PMMA) layer and a 200-nm-thick gold layer for the plasmonic waveguide. The metallic grating coupler has staircase gratings and features vertical coupling [21,32]. The staircase grating has two diffraction points and couples the light only into one direction, whereas a simple binary grating coupler splits the incident light to the left and the right and would therefore come with an extra 3 dB loss. The performance of the grating coupler is confirmed by conducting two-dimensional finite difference time domain (2D-FDTD) simulations [33]. A Gaussian beam with a 6-µm mode diameter (where intensity drops to 1/e2) is launched on the top of the gratings. We monitored the power of the SPPs coupled to the surface of the gold at x = 1 µm, where the first grating starts at x = 0. The grating depths and widths are optimized using the particle swarm optimization method built in the simulation software (Lumerical FDTD Solutions) [33]. A coupling efficiency of −1.9 dB (65%) is obtained with a 1-dB bandwidth of 147 nm. We find that the optimized grating widths and depths are = 500 nm, = 150 nm, = 140 nm and = 70 nm with a grating pitch of Λ = 1040 nm. The optimized position of the fiber mode is x = −2 µm and seven gratings are sufficient to couple all the power from the input fiber more. Furthermore, we apply apodization to the metallic grating coupler using the evolutional strategy with sampling points [2,34]. We apodize the grating widths and pitches rather than the etching depths because a variation of the etching depths is not compatible with the conventional dry-etching fabrication processes. The apodized geometry is optimized for the optimum coupling at wavelength 1550 nm. The spectrum of the coupling efficiency of the apodized grating coupler is plotted in Fig. 2(b). A coupling efficiency of −1.1 dB (78%) with a 1-dB bandwidth of 104 nm is predicted from the simulations.
Our metallic grating coupler is integrated on a dielectric-loaded plasmonic layer with PMMA, and the refractive index of PMMA is low (n ~1.48). Despite of the low refractive index of the waveguide the plasmonic grating provides strong scattering and small footprint due to the plasmonic resonances. In order to find the directionality of the grating we study how the amplitude changes from left to right along the grating. The intensity of the electric field is plotted in Fig. 2(c), and we find an amplitude gain of α = 0.18 µm−1 by fitting with an exponential curve (). This value is comparatively larger over those from photonic gratings [29], showing that the metallic gratings yield strong scattering. Thus, the metallic grating coupler only needs a small number of gratings and thus offers a short device length that can be coupled to a small fiber mode (e.g., seven gratings and 7 µm device length with a 6 µm fiber mode diameter). By applying the analytical expression in [29] to calculate the coefficient C1dB, we obtain C1dB = 0.16. Finally, with the waveguide dispersion of 0.186 (see Fig. 2 (d)), the calculated bandwidth from Eq. (5) becomes as large as 141 nm. This is in good agreement with the 147 nm bandwidth predicted from the 2D-FDTD simulations.
In reality, fabrication errors in grating widths ( and ) and etch-depths ( and ) will likely degrade the performance of the grating coupler. Figure 3 shows the anticipated fabrication tolerances of the grating coupler when sweeping the critical fabrication parameters with 2D-FDTD simulations. It can be seen that the coupling efficiency remains within a 1 dB excess loss for fabrication errors of < ± 70 nm, < ± 60 nm, < ± 30 nm and < ± 40 nm around the center wavelength of 1550 nm.
Fig. 3 Fabrication tolerance of the coupling efficiency on grating parameters. Coupling efficiencies are plotted in dB together with the wavelength dependence.
In order to confine wide Gaussian beam into narrow plasmonic waveguide mode, one may introduce a focusing arrangement for the grating. Conventional photonic grating couplers with straight-line gratings, for instance, have more than 200 µm-long adiabatic taper to confine and couple the light into a waveguide with a negligible loss. Such a long taper cannot be accepted especially for a metallic grating coupler because of the plasmonic propagation losses [35]. Therefore, we introduce a focusing structure to avoid a long taper. The pattern of a focusing grating coupler follows an elliptic equation [36–38]
where x and y are the coordinates from the focal point of the grating coupler and N is the number of grating lines. Since the equation becomes the formula of a circle with the vertical incident condition (θ = 0), our metallic gratings are arranged as concentric circles. The geometrical parameters of the focusing grating coupler are given in Fig. 4(a). We choose a radius of 6 µm to maximize the total coupling efficiency of the grating coupler. The focusing grating coupler has a total footprint of 13.5 µm × 12 µm. 3D-FDTD simulations have been performed and a coupling efficiency of −2.7 dB (54%) at a wavelength of 1569 nm is obtained with a bandwidth of 144 nm. The focusing grating coupler with apodized gratings provides a coupling efficiency of −1.9 dB (65%) and a bandwidth of 100 nm in the 3D-FDTD simulations.Fig. 4 (a) Top view of the focusing all-metallic grating coupler. A Gaussian mode is launched at (x,y) = (−8,0) with the height of 2 µm in the 3D-FDTD simulations. The mode overlap to the waveguide is obtained as the coupling efficiency at x = 0. (b) Coupling efficiencies of the focusing grating coupler. The maximum coupling efficiency of −2.7 dB is found at the wavelength of 1569 nm (e.g., −2.8 dB at the wavelength of 1550 nm) with the periodic structure. Also, the maximum coupling efficiency of −1.9 dB at the wavelength of 1565 nm (e.g., −2.0 dB at the wavelength of 1550 nm) is found with the apodized structure.
3. Experimental results
Vertical metallic grating couplers were fabricated on a 200-nm-thick gold layer, which was deposited using electron-beam evaporation. A positive-tone electron-beam resist was used as a mask during the etching process. The stair-case gratings were made through two-step dry-etching processes with Ar-ions. We applied PMMA resist with a thickness of 450 nm by spin-coating, and the waveguide structure was formed by developing the PMMA layer after exposure.
The schematic of the measurement setup is shown in Fig. 5. Two metallic grating couplers are placed within a distance of 36 µm and connected by a dielectric loaded plasmonic waveguide. An optical signal with a spectral range of 1460-1640 nm from a tunable laser diode (TLD) was fed into the device through one core of the MCF (two-dimensionally arrayed 19 cores with a mode diameter of 6 µm) after its polarization was controlled. The transmitted signal was coupled out into a neighboring core and detected by a photodiode (PD).
Fig. 5 Schematic of the experimental setup. The insertion loss of the device was measured using a MCF. An optical signal in the wavelength range of 1460-1640 nm was fed from a tunable laser diode after a polarization controller (PC). The optical signal was fed into the device through a core of the MCF. The input optical signal is converted into the SPP and propagated along the dielectric-loaded plasmonic waveguide for 36 µm. The transmitted signal was coupled out by the output grating coupler to another core of the MCF, and detected by a photodiode (PD). The subset shows a microscopic image of the device.
The propagation loss of the dielectric-loaded plasmonic waveguide was measured with different waveguide lengths. The measured propagation loss was 0.07 dB/µm, leading to a 1.4 dB loss for the 20 µm waveguide section (see the subset in Fig. 5). We subtracted this propagation loss and the setup loss from the total insertion loss of the device, and we plot the coupling efficiency of the focusing metallic grating coupler in Fig. 6(b). A coupling efficiency of −3.6 dB (44%) was obtained for the periodic grating coupler and −2.9 dB (51%) for the apodized grating coupler. The bandwidths of the grating couplers were 116 nm and 115 nm for the periodic and apodized grating couplers, respectively.
Fig. 6 (a) Effective mode index (blue) and propagation length (red) of the DLSPPW. (b) Measured coupling efficiencies of the grating couplers. The periodic grating coupler has a coupling efficiency of up to −3.5 dB around a wavelength of 1510 nm (−3.6 dB at 1550 nm) with a bandwidth of 116 nm. With the apodized grating coupler a coupling efficiency of −2.9 dB was measured at a wavelength of 1550 nm and a 1 dB bandwidth of 115 nm was found.
We also examined the fiber-positioning tolerance of the grating coupler as shown in Fig. 7. Since we use a multicore fiber we will detune both the input and output coupler simultaneously when moving the positioning stage. It should therefore be noted that a 2-dB additional loss in the fiber-to-fiber insertion loss (as reported here) corresponds to a 1-dB loss for a single grating coupler, since the device consists of two grating couplers. The measured 1-dB positioning tolerances of the grating coupler were ± 1.4 µm in the x direction, and ± 1.6 µm in the y direction, respectively.
Fig. 7 (a) Measured fiber-positioning tolerance on misalignment from the optimal fiber position. The device has two grating couplers, indicating that a 2-dB excess loss corresponds to a 1-dB excess loss for one grating coupler. (b) Measured and simulated positioning tolerances in the x direction and, (c) in the y direction. The two plots have been taken by detuning the position along the dash-dotted line shown in plot (a).
4. Conclusion
In conclusion, we have demonstrated that all-metallic grating couplers offer extreme broadband coupling. We have shown experimentally that apodized grating couplers provide a 1-dB bandwidth beyond 115 nm with a coupling efficiency of −2.9 dB. Further, it is shown that such grating couplers are also compact (13.5 µm × 12 µm) and are ideal matches to all-plasmonic circuits. Simulations indicate that metallic grating couplers might even offer broader spectral bandwidths if fabricated properly.
Funding
European Union (688166 PLASMOfab); European Research Council (670478 PLASILOR).
Acknowledgments
This work was partially carried out at the Binnig and Rohrer Nanotechnology Center (BRNC).
References
1. A. E. J. Lim, J. F. Song, Q. Fang, C. Li, X. G. Tu, N. Duan, K. K. Chen, R. P. C. Tern, and T. Y. Liow, “Review of Silicon Photonics Foundry Efforts,” IEEE J. Sel. Top. Quantum Electron. 20(4), 405–416 (2014). [CrossRef]
2. T. Watanabe, M. Ayata, U. Koch, Y. Fedoryshyn, and J. Leuthold, “Perpendicular Grating Coupler Based on a Blazed Antiback-Reflection Structure,” J. Lightwave Technol. 35(21), 4663–4669 (2017). [CrossRef]
3. C. Scarcella, K. Gradkowski, L. Carroll, J. S. Lee, M. Duperron, D. Fowler, and P. O’Brien, “Pluggable Single-Mode Fiber-Array-to-PIC Coupling Using Micro-Lenses,” IEEE Photonics Technol. Lett. 29(22), 1943–1946 (2017). [CrossRef]
4. P. I. Dietrich, M. Blaicher, I. Reuter, M. Billah, T. Hoose, A. Hofmann, C. Caer, R. Dangel, B. Offrein, U. Troppenz, M. Moehrle, W. Freude, and C. Koos, “In situ 3D nanoprinting of free-form coupling elements for hybrid photonic integration,” Nat. Photonics 12(4), 241–247 (2018). [CrossRef]
5. R. Marchetti, C. Lacava, L. Carroll, K. Gradkowski, and P. Minzioni, “Coupling strategies for silicon photonics integrated chips [Invited],” Photon. Res. 7(2), 201–239 (2019). [CrossRef]
6. T. A. Birks, I. Gris-Sanchez, S. Yerolatsitis, S. G. Leon-Saval, and R. R. Thomson, “The photonic lantern,” Adv. Opt. Photonics 7(2), 107–167 (2015). [CrossRef]
7. T. Yoshida, E. Omoda, Y. Atsumi, M. Mori, and Y. Sakakibara, “Elephant Coupler: Vertically Curved Si Waveguide with Wide and Flat Wavelength Window Insensitive to Coupling Angle,” ECOC 2015 41st European Conference on Optical Communication (2015). [CrossRef]
8. P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, “Broadband polarization independent nanophotonic coupler for silicon waveguides with ultra-high efficiency,” Opt. Express 23(17), 22553–22563 (2015). [CrossRef] [PubMed]
9. N. Lindenmann, G. Balthasar, D. Hillerkuss, R. Schmogrow, M. Jordan, J. Leuthold, W. Freude, and C. Koos, “Photonic wire bonding: a novel concept for chip-scale interconnects,” Opt. Express 20(16), 17667–17677 (2012). [CrossRef] [PubMed]
10. X. Chen, K. Xu, Z. Cheng, C. K. Y. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett. 37(17), 3483–3485 (2012). [CrossRef] [PubMed]
11. Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, “Broadband focusing grating couplers for suspended-membrane waveguides,” Opt. Lett. 37(24), 5181–5183 (2012). [CrossRef] [PubMed]
12. X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Colorless grating couplers realized by interleaving dispersion engineered subwavelength structures,” Opt. Lett. 38(18), 3588–3591 (2013). [CrossRef] [PubMed]
13. Q. Zhong, V. Veerasubramanian, Y. Wang, W. Shi, D. Patel, S. Ghosh, A. Samani, L. Chrostowski, R. Bojko, and D. V. Plant, “Focusing-curved subwavelength grating couplers for ultra-broadband silicon photonics optical interfaces,” Opt. Express 22(15), 18224–18231 (2014). [CrossRef] [PubMed]
14. L. Su, R. Trivedi, N. V. Sapra, A. Y. Piggott, D. Vercruysse, and J. Vučković, “Fully-automated optimization of grating couplers,” Opt. Express 26(4), 4023–4034 (2018). [CrossRef] [PubMed]
15. N. V. Sapra, D. Vercruysse, L. Su, K. Y. Yang, J. Skarda, A. Y. Piggott, and J. Vuckovic, “Inverse Design and Demonstration of Broadband Grating Couplers,” IEEE J. Sel. Top. Quantum Electron. 25(3), 1–7 (2019). [CrossRef]
16. W. D. Sacher, Y. Huang, L. Ding, B. J. F. Taylor, H. Jayatilleka, G. Q. Lo, and J. K. S. Poon, “Wide bandwidth and high coupling efficiency Si3N4-on-SOI dual-level grating coupler,” Opt. Express 22(9), 10938–10947 (2014). [CrossRef] [PubMed]
17. W. Heni, Y. Fedoryshyn, B. Baeuerle, A. Josten, C. B. Hoessbacher, A. Messner, C. Haffner, T. Watanabe, Y. Salamin, U. Koch, D. L. Elder, L. R. Dalton, and J. Leuthold, “Plasmonic IQ modulators with attojoule per bit electrical energy consumption,” Nat. Commun. 10(1), 1694 (2019). [CrossRef] [PubMed]
18. C. Haffner, W. Heni, D. L. Elder, Y. Fedoryshyn, N. Dordevic, D. Chelladurai, U. Koch, K. Portner, M. Burla, B. Robinson, L. R. Dalton, and J. Leuthold, “Harnessing nonlinearities near material absorption resonances for reducing losses in plasmonic modulators,” Opt. Mater. Express 7(7), 2168–2181 (2017). [CrossRef]
19. A. Dorodnyy, Y. Salamin, P. Ma, J. V. Plestina, N. Lassaline, D. Mikulik, P. Romero-Gomez, A. F. I. Morral, and J. Leuthold, “Plasmonic Photodetectors,” IEEE J. Sel. Top. Quantum Electron. 24(6), 1–13 (2018). [CrossRef]
20. C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018). [CrossRef] [PubMed]
21. M. Ayata, Y. Fedoryshyn, W. Heni, B. Baeuerle, A. Josten, M. Zahner, U. Koch, Y. Salamin, C. Hoessbacher, C. Haffner, D. L. Elder, L. R. Dalton, and J. Leuthold, “High-speed plasmonic modulator in a single metal layer,” Science 358(6363), 630–632 (2017). [CrossRef] [PubMed]
22. U. Koch, A. Messner, C. Hoessbacher, W. Heni, A. Josten, B. Baeuerle, M. Ayata, Y. Fedoryshyn, D. L. Elder, L. R. Dalton, and J. Leuthold, “Ultra-Compact Terabit Plasmonic Modulator Array,” J. Lightwave Technol. 37(5), 1484–1491 (2019). [CrossRef]
23. A. Andryieuski, R. Malureanu, G. Biagi, T. Holmgaard, and A. Lavrinenko, “Compact dipole nanoantenna coupler to plasmonic slot waveguide,” Opt. Lett. 37(6), 1124–1126 (2012). [CrossRef] [PubMed]
24. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011). [CrossRef]
25. S. B. Raghunathan, C. H. Gan, T. van Dijk, B. Ea Kim, H. F. Schouten, W. Ubachs, P. Lalanne, and T. D. Visser, “Plasmon switching: observation of dynamic surface plasmon steering by selective mode excitation in a sub-wavelength slit,” Opt. Express 20(14), 15326–15335 (2012). [CrossRef] [PubMed]
26. C. Garcia, V. Coello, Z. Han, I. P. Radko, and S. I. Bozhevolnyi, “Partial loss compensation in dielectric-loaded plasmonic waveguides at near infra-red wavelengths,” Opt. Express 20(7), 7771–7776 (2012). [CrossRef] [PubMed]
27. J. C. Weeber, K. Hassan, L. Saviot, A. Dereux, C. Boissière, O. Durupthy, C. Chaneac, E. Burov, and A. Pastouret, “Efficient photo-thermal activation of gold nanoparticle-doped polymer plasmonic switches,” Opt. Express 20(25), 27636–27649 (2012). [CrossRef] [PubMed]
28. J. C. Weeber, J. Arocas, O. Heintz, L. Markey, S. Viarbitskaya, G. Colas-des-Francs, K. Hammani, A. Dereux, C. Hoessbacher, U. Koch, J. Leuthold, K. Rohracher, A. L. Giesecke, C. Porschatis, T. Wahlbrink, B. Chmielak, N. Pleros, and D. Tsiokos, “Characterization of CMOS metal based dielectric loaded surface plasmon waveguides at telecom wavelengths,” Opt. Express 25(1), 394–408 (2017). [CrossRef] [PubMed]
29. Z. Xiao, T. Y. Liow, J. Zhang, P. Shum, and F. Luan, “Bandwidth analysis of waveguide grating coupler,” Opt. Express 21(5), 5688–5700 (2013). [CrossRef] [PubMed]
30. E. W. Ong, N. M. Fahrenkopf, and D. D. Coolbaugh, “SiNx bilayer grating coupler for photonic systems,” OSA Continuum 1(1), 13–25 (2018). [CrossRef]
31. J. Leuthold, C. Hoessbacher, S. Muehlbrandt, A. Melikyan, M. Kohl, C. Koos, W. Freude, V. Dolores-Calzadilla, M. Smit, I. Suarez, J. Martínez-Pastor, E. P. Fitrakis, and I. Tomkos, “Plasmonic Communications: Light on a Wire,” Opt. Photonics News 24(5), 28–35 (2013). [CrossRef]
32. W. Yao, S. Liu, H. Liao, Z. Li, C. Sun, J. Chen, and Q. Gong, “Efficient Directional Excitation of Surface Plasmons by a Single-Element Nanoantenna,” Nano Lett. 15(5), 3115–3121 (2015). [CrossRef] [PubMed]
33. Lumerical FDTD Solutions. Available: https://www.lumerical.com/products/fdtd/.
34. A. Dorodnyy, V. Shklover, L. Braginsky, C. Hafner, and J. Leuthold, “High-efficiency spectrum splitting for solar photovoltaics,” Sol. Energy Mater. Sol. Cells 136, 120–126 (2015). [CrossRef]
35. V. A. Zenin, A. Andryieuski, R. Malureanu, I. P. Radko, V. S. Volkov, D. K. Gramotnev, A. V. Lavrinenko, and S. I. Bozhevolnyi, “Boosting Local Field Enhancement by on-Chip Nanofocusing and Impedance-Matched Plasmonic Antennas,” Nano Lett. 15(12), 8148–8154 (2015). [CrossRef] [PubMed]
36. 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). [CrossRef]
37. Y. Wang, H. Yun, Z. Q. Lu, R. Bojko, W. Shi, X. Wang, J. Flueckiger, F. Zhang, M. Caverley, N. A. F. Jaeger, and L. Chrostowski, “Apodized Focusing Fully Etched Subwavelength Grating Couplers,” IEEE Photonics J. 7(3), 1–10 (2015). [CrossRef]
38. J. Hoffmann, K. M. Schulz, G. Pitruzzello, L. S. Fohrmann, A. Y. Petrov, and M. Eich, “Backscattering design for a focusing grating coupler with fully etched slots for transverse magnetic modes,” Sci. Rep. 8(1), 17746 (2018). [CrossRef] [PubMed]
