Focusing-curved subwavelength grating couplers for ultra-broadband silicon photonics optical interfaces

We report on the design and characterization of focusing-curved subwavelength grating couplers for ultra-broadband silicon photonics optical interfaces. With implementation of waveguide dispersion engineered subwavelength structures, an ultra-wide 1-dB bandwidth of over 100 nm (largest reported to date) near 1550 nm is experimentally achieved for transverse-electric polarized light. By tapering the subwavelength structures, back reflection is effectively suppressed and grating coupling efficiency is increased to −4.7 dB. A compact device footprint of 40 μm × 20 μm is realized by curving the gratings in a focusing scheme. ©2014 Optical Society of America OCIS codes: (050.2770) Gratings; (050.6624) Subwavelength structures. References and links 1. M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photon. 4(8), 492–494 (2010). 2. M. Asghari and A. V. Krishnamoorthy, “Silicon photonics: Energy-efficient communication,” Nat. Photon. 5(5), 268–270 (2011). 3. M. 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Introduction
Complementary metal-oxide-semiconductor (CMOS) compatible silicon photonics offers an attractive platform for future chip-level optical interconnects [1,2].The large refractive index (RI) contrast between silicon core and its cladding enables high degree of photonic integration.However, the large RI contrast becomes a problem for optical interfaces because it induces significant coupling loss due to mode mismatch between a conventional single mode optical fiber (core diameter of ~9 µm) and a silicon waveguide (cross-section dimensions of ~0.5 µm × 0.22 µm).Since getting optical amplification in silicon is challenging, highly efficient fiber-to-chip coupling interfaces are essential for silicon photonics.There are two major solutions for the fiber-to-chip coupling: edge coupling and surface coupling.Edge coupling is usually realized by implementing lensed fibers, polished facets and inverted tapers [3,4] to adiabatically convert the optical mode from fiber to waveguide.Surface coupling, utilizing diffraction grating couplers to collect light, has advantages over edge coupling in terms of simplicity of fabrication, compactness of footprint, flexibility of optical input/output (I/O) positions, capability of wafer-scale test, ease of alignment and potentially low cost of packaging [5].However, compared to the broadband operation of edge coupling, the bandwidth of grating couplers is rather narrow, which is intrinsically limited by waveguide dispersion [6].For many optical interconnects applications such as wavelength-division multiplexing (WDM) and frequency-comb generation, a flat spectrum offered by wideband optical interface is highly desired.While most previous studies have focused on increasing the efficiency of silicon grating couplers, only a few attempts to improve their bandwidth have been reported so far [6][7][8][9][10].
In this paper, we present the design of broadband subwavelength grating couplers (SWGCs) in a focusing-curved scheme.The SWGCs are fabricated by electron-beam lithography (EBL) on a standard silicon-on-insulator (SOI) platform with a single-step fulletching.A 1-dB bandwidth of over 100 nm around 1550 nm is measured for transverseelectric (TE) polarized light.To the best of our knowledge, this is the largest bandwidth reported in silicon grating couplers to date.The improvement of bandwidth is achieved by applying subwavelength grating structures to suppress the waveguide dispersion.By designing small anti-reflection tapers, the back reflection of gratings is effectively suppressed and the coupling efficiency is improved to −4.7 dB.In addition, the SWGCs are designed in a focusing-curved geometry, which significantly shrinks the length of the adiabatic taper from several hundred microns required by straight-line grating designs [7,9] to only 20 µm, and yields a compact device footprint of 40 µm × 20 µm without introducing performance penalties.

Principle, simulation and layout design
The first-order diffraction of a grating coupler is governed by the well-known phase matching condition: 2 sin , where k o = 2π/λ o is the wavenumber in vacuum, n eff is the grating effective RI, n c is the cladding RI, θ is the incident angle (the angle between the fiber axis and the grating surface normal, as shown in Fig. 1(a)), and Λ G is the grating period.From Eq. ( 1), the bandwidth of a grating coupler can be derived as [7]: cos , ( ) sin ( ) where η is a coefficient related to fiber beam waist [10] and λ o is the operating wavelength in vacuum.The dispersion term dn eff (λ)/dλ in Eq. ( 2) is negative for silicon waveguides.At a fixed wavelength, the absolute value of the dispersion decreases with decreasing grating effective RI, as the light confinement becomes weaker.According to Eq. ( 2), reducing dispersion (approaching zero from negative values) can lead to a larger bandwidth.Hence, for grating couplers fabricated in a specific material system, operating at a fixed central wavelength and angle of incidence, the most feasible approach to increase the bandwidth is to reduce the grating effective RI.The grating effective RI can be dramatically reduced by applying subwavelength structures [7][8][9].According to effective medium theory [7,11], a periodic subwavelength region can be treated as a uniform material with an effective index equal to the weighted average of the material indices of silicon and the cladding.Then the subwavelength structures can be designed as periodically interleaved regions with high and low indices, as shown in Fig. 1(a).Reducing the grating effective RI can both improve the bandwidth and reduce the coupling efficiency, because the index contrast between cladding and grating is also reduced [9].In order to achieve a good compromise between bandwidth and efficiency, we optimized the grating design by tuning critical parameters such as grating period, filling factor, and effective indices.Different from the design approaches presented in [7][8][9], the simulation and optimization in this work were conducted using two-dimensional finite difference time domain (2-D FDTD) method coupled with particle swarm optimization (PSO) algorithm.In PSO, the potential solutions (called particles) are randomly initialized in the parameter space.A figure of merit (FOM) function is defined to evaluate the particle position.While moving the particle position in the swarm, the best achieved FOM is recorded.The optimization process terminates when a large number of iterations is reached [12].We used the built-in PSO simulation tool in Lumerical FDTD Solutions [13].First we set the grating parameters and their ranges for sweeping based on previous studies [7][8][9].Then we chose the product of 1-dB bandwidth and coupling efficiency at 1550 nm as the FOM, and calculated up to 8 generations for optimization.For TE polarized light with an incident angle of 20°, the optimized 1-dB bandwidth reaches 122 nm with an efficiency of −2.72 dB at 1550 nm, as shown in Fig. 2.This result was obtained with a grating period of 1.16 µm, a filling factor of 0.5, and effective indices of 2.79 and 1.71 at 1550 nm for the high and low index regions, respectively.Considering the subwavelength condition [14] and the feasible minimum feature size of EBL, we chose a subwavelength grating period of 0.3 µm (with a direction perpendicular to the light propagation direction), subwavelength filling factors of 0.67 and 0.13 for the high and low index regions, respectively.All these grating parameters are illustrated in Fig. 1(b).The performance of the SWGC was optimized with the material system (220-nm silicon on 3-µm buried oxide with 1.975-µm oxide cladding) shown in Fig. 1(c), which is given by the fabrication process.If customized thicknesses of buried oxide and oxide cladding are available, the coupling efficiency can be further improved [15].By adding thicknesses of buried oxide and oxide cladding as variables into the PSO algorithm model, the coupling efficiency can reach −1.91 dB with 2.84-µm buried oxide and 1.837-µm oxide cladding.The conventional straight-line grating design shown in Fig. 1(a) requires a 500-µm-long adiabatic taper to convert the optical mode from the gratings to the waveguide with low loss [7,9].In order to reduce the length of the adiabatic taper, the gratings can be designed in a curved geometry to produce a circular wavefront and focus the optical mode into the waveguide.According to [16,17], the phase matching condition given in Eq. ( 1) can be expressed as where x and y are Cartesian coordinates with the grating-waveguide connection point defined as the origin and x-y axes defined in Fig. 1 Equation ( 4) indicates that the curved grating lines are a series of confocal ellipses with the focus located at the grating-waveguide connection point (origin).Thus, the optical mode can be directly focused from the grating to the waveguide, obviating the long adiabatic taper for mode conversion.Thereby the focusing-curved grating coupler has a much smaller footprint and yields a higher degree of integration than the straight-line grating coupler.By applying the simulation-optimized grating parameters into Eq.( 4), the layout of the focusing-curved SWGCs can be captured.In theory, rigorous 3-D FDTD simulation should be conducted to verify the performance of the focusing-curved SWGCs.However, 3-D simulation with accurate mesh level is very time consuming in practice.Therefore, we rely on the results obtained from the 2-D simulation, which proves to have sufficient accuracy with acceptable calculation time [17,18].

Experiment and discussion
The focusing-curved SWGCs were fabricated on a standard silicon-on-insulator (SOI) platform (220-nm silicon on 3-µm buried oxide) with oxide cladding using EBL.In order to achieve the optimized effective RI (~1.71) in the low RI region, only one step of full-etch is conducted in the fabrication process.The material system detail is shown in Fig. 1(c).Multiple SWGCs with parameter variations around the optimal values were fabricated.The scanning electron microscopy (SEM) image of a focusing-curved SWGC is shown in Fig. 3(a), and Fig. 3(b) gives a magnified view of the interleaved subwavelength structures.Thanks to the focusing-curved design, the total size of this device is only 40 µm × 20 µm, which is only ~10% of the footprint of the straight-line SWGCs reported in [7,9].A pair of input and output focusing-curved SWGCs with 127 µm pitch was connected by a short strip waveguide with negligible loss for testing.A fiber array is used to test these SWGCs on a setup similar to the setup describe in [19].Light is launched from a tunable laser with a spectral range of 1480-1620 nm and a resolution of 0.02 nm.A polarization controller is located after the tunable laser to adjust the polarization of the input light.The measured transmission spectrum of a focusing-curved SWGC is shown in Fig. 4. The 1-dB bandwidth of this SWGC is over 100 nm with a peak coupling efficiency of −6.4 dB near 1550 nm.Straight-line SWGCs with similar grating parameters were also fabricated and the measurement results have shown that the focusing-curved design introduces no performance penalties [20].Compared to the simulation result shown in Fig. 2, the bandwidth meets the expectation, while the efficiency is much lower.This can be explained as follows.The fiber array used in this work has a cleaved angle of ~20°.According to Snell's Law, when the fiber end is parallel to the grating surface, the light incident angle becomes ~30° in the air.Hence, to reach the designed incident angle (20°) as well as high coupling efficiency for operating wavelength centered near 1550 nm, the fiber array needs to be rotated, inducing an air gap between the fiber end and the chip.Extra distance is also kept to ensure the fiber array would not scratch the chip.When light propagates in this air gap, the optical mode profile becomes larger, which adds extra loss.The result shown in Fig. 2 was obtained assuming no such an air gap.If an air gap is introduced in the FDTD model, the simulated coupling efficiency would decrease and match better with the experimental result [19].As shown in Fig. 5, the simulated peak coupling efficiency matches with the measured value (~-6.4 dB) when the air gap is ~70 μm.According to [9,21], this kind of extra loss can be reduced by applying index matching fluid to fill in the air gap.It should also be noted that compared to partial-etched gratings, the full-etched gratings suffer higher loss due to larger back reflection, which is evidenced by the small ripples observed in Fig. 4.These ripples originate from the Fabry-Perot (F-P) interferometric cavity formed by a pair of input and output SWGCs, where Fresnel reflection occurs at the gratingwaveguide boundaries due to the RI contrast.It can be measured from the inset of Fig. 4 that the small ripples have a free spectral range (FSR) of ~1.1 nm.This FSR value corresponds to an F-P cavity length of ~295 µm, which matches well with the total length of the waveguide connecting the pair of input and output SWGCs.Another interesting observation from Fig. 4 is that there exists a second set of F-P ripples with larger FSR, which is similar to the phenomenon reported in [8].The FSR of the second set of ripples is measured to be ~18 nm, which corresponds to an F-P cavity length of ~18 µm.This value is very close to the distance between the front and rear curves of the SWGCs, hence it can be concluded that the second set of ripples is caused by the F-P interference between the front and rear curves of the SWGCs.
It has been demonstrated that gradient-index anti-reflective subwavelength structures can effectively reduce the planar waveguide facet reflectivity [22].In order to reduce the back reflection and increase the coupling efficiency, we applied similar anti-reflective structures in the focusing-curved SWGCs.As shown in Fig. 6, the modified gratings have tapered connection between high and low RI regions, instead of the sharp boundaries present in Fig. 3.The measured transmission spectrum of a focusing-curved SWGC with tapered grating design is shown in Fig. 7. Compared with the measured spectrum of the non-tapered grating design (Fig. 4), the peak coupling efficiency of the tapered grating design improves from −6.4 dB to −4.7 dB, while the 1-dB bandwidth maintains over 100 nm.From the insets of Fig. 4 and Fig. 7, it can be measured that the extinction ratios of both sets of F-P interference ripples in the tapered grating design are reduced by ~50% compared with the non-tapered grating design.These results validate the implementation of tapered subwavelength grating design can mitigate the RI contrast, thus reducing the back reflection and increasing the coupling efficiency of the focusing-curved SWGCs.Table 1 gives a summary of the previously realized broadband SWGCs and the tapered focusing-curved SWGCs demonstrated in this work.All the SWGCs are operating near 1550 nm.The devices were fabricated with full-etching on different SOI platforms (i.e., the thicknesses of top silicon and buried oxide are different).Devices in [7] and [9] are straightline grating designs which require a 500-µm adiabatic taper.The device footprint is significantly reduced in [8] and this work, where the gratings are designed in a focusingcurved geometry.The focusing-curved SWGCs demonstrated in this work show an ultra-wide 1-dB bandwidth of over 100 nm, which is the highest reported to date.However, the coupling efficiency is still not high enough to compete with the shallow-etched grating couplers [5].Further design optimization, such as apodizing the grating [23,24] and adopting a correction term of the effective RI in Eq. (3) [16,25], is required to increase the coupling efficiency of the focusing-curved SWGCs.

Conclusion
In summary, we have demonstrated the ultra-broadband grating couplers with focusingcurved subwavelength structures for silicon photonics optical interfaces.By applying waveguide dispersion engineered subwavelength tapered grating structures, we have experimentally achieved a 1-dB bandwidth of over 100 nm (largest reported to date) with −4.7 dB coupling efficiency near 1550 nm.With focusing-curved grating design, we have minimized the device footprint to be only 40 µm × 20 µm.

Fig. 1 .
Fig. 1.(a) 3-D schematic illustration of the periodic subwavelength gratings with interleaved high and low RI regions.(b) Top-view of the periodic subwavelength gratings.G Λ and G ff are the grating period and filling factor, S Λ is the subwavelength grating period, SH ff and SL ff are the subwavelength filling factors of the high and low RI regions, respectively.(c) Cross-section showing the material system of the subwavelength gratings.The drawings are not to scale.

Fig. 3 .
Fig. 3. SEM images of a fabricated focusing-curved SWGC.The lower-right grating region of (a) is zoomed and shown in (b).

Fig. 4 .
Fig. 4. Measured transmission spectrum of the focusing-curved SWGC.Inset shows the Fabry-Perot ripples near the spectrum peak.

Fig. 5 .
Fig. 5. Simulated peak coupling efficiency versus the air gap between the fiber and the grating surface.

Fig. 6 .
Fig. 6.SEM images of a fabricated focusing-curved SWGC with tapered grating design.The lower-right grating region of (a) is magnified and shown in (b).

Fig. 7 .
Fig. 7. Measured transmission spectrum of the focusing-curved SWGC tapered grating design.Inset shows the Fabry-Perot ripples near the spectrum peak.

Table 1 . Comparison of the broadband SWGCs realized to date
Designed for TM polarized light.The rest are for TE polarized light.% NA means the result is not reported.$ Including the length of an adiabatic taper.