Ultralow-loss optical interconnect enabled by topological unidirectional guided resonance

Grating couplers that interconnect photonic chips to off-chip components are crucial for various optoelectronics applications. Despite numerous efforts in past decades, the existing grating couplers are still far from optimal in energy efficiency and thus hinder photonic integration toward a larger scale. Here, we propose a strategy to achieve ultralow-loss grating couplers by using unidirectional guided resonances (UGRs), suppressing the useless downward radiation with no mirror on the bottom. By engineering the dispersion and apodizing the geometry of grating, we experimentally realize a grating coupler with a record-low loss of −0.34 dB and 1-dB bandwidth exceeding 30 nm at the telecom wavelength of 1550 nm and further demonstrate an optic via with a loss of only −0.94 dB. Given that UGRs ubiquitously exist in a variety of grating geometries, our work sheds light on a systematic method to achieve energy-efficient optical interconnect and paves the way to large-scale photonic integration.


Introduction
Optical I/Os are indispensable building blocks for silicon photonics since they are responsible for coupling the light into and out of the chip [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] .To tackle higher coupling efficiency, a variety of techniques such as micro-optics 18,19 , edge coupling [20][21][22] , grating coupling  ,and photonic wire bonding 47,48 are proposed and investigated. Amongthese techniques, the grating coupling is a particularly promising method owing to its small footprint, great flexibility in arrangement, and potential in mass production [2][3][4][5] .However, despite extensive efforts, existing grating couplers still suffer from poor energy efficiency that would significantly degrade the power budget of the optical links, and thus hinders its application in large-scale photonic integration for next-generation optoelectronic system-on-chip (SoC) that needs to drive tens of Tbps of bandwidth directly into or out of high-performance ICs through a massive of optical interconnects on a single chip. Becaus conventional gratings radiate both upwards and downwards, nearly half of the light wastes at the lower substrate, and consequently, causes an intrinsic loss of ∼3 dB unless a mirror is placed at the bottom [35][36][37][38] .Recently, unidirectional radiation without mirrors has been discovered from the view of topology.It is found that a class of unidirectional guided resonances (UGRs) [49][50][51][52] can be realized by merging a pair of half-integer topological charges upon one side of the grating while leaving them apart on the other side 49,50 .The UGRs are proved to be ubiquitous in periodic photonic structures since the half-charges can be either created from splitting an integer charge carried by a bound state in the continuum (BIC) [53][54][55][56][57][58][59][60][61] , or alternatively, spawned from a void point owing to the inter-band coupling effect 49,50 .UGRs shed light on the new possibilities of unidirectional emission, while how to utilize them to construct a complete, practical, and fabrication-friendly grating coupler to support ultra-low-loss optical interconnect remains an important but elusive problem.
Here, we theoretically propose and experimentally demonstrate a method to realize ultralow-loss grating couplers by utilizing the unidirectional emission nature of topological UGRs 49,50 .
We adopt an L-shaped structure that is simple and planar-process-compatible and show the integer topological charge carried by a symmetry-protected BIC splits into a pair of half-charges.By continuously tuning the grating geometry, the half-charges evolve in the momentum space and restore integer charge at the lower side of the grating to form a UGR.The design is optimized by engineering the dispersion and apodizing the geometry to best reduce back-scattering and promote the model overlap with the fiber 62 .We fabricate the grating coupler samples on a 340 nm thick SOI wafer and obtain a record-low insertion loss of 0.34 dB and 0.94 dB for the schemes of chip-tofiber and stacked-chip interconnects at telecom wavelength of 1550 nm, with their 1 dB bandwidth exceeding 30 nm and 20 nm, respectively.Our findings pave the path to ultra-high energy-efficient optical interconnects of silicon photonics and reveal the potential of photonic integration toward ultra-density and 3D-stacking applications.
The goal of this work is to develop an ultra-low-loss grating coupler with a sufficiently broad bandwidth by utilizing a resonance with unidirectional radiation, namely a UGR.To make the device practically useful, the design has to be applied on a standard SOI wafer and the geometry should be compatible with the planar CMOS process.To fulfill these requirements, we start with a schematic design illustrated in Fig. 1a, in which a "L-shaped" grating is patterned on a 340 nm thick SOI wafer with a periodicity of a = 528 nm and then buried by a standard silicon dioxide cladding layer for protection.The unit-cell design of the grating (inset, Fig. 1a) has two different widths and depths with vertical sidewalls, denoted as w 1 , h 1 and w 2 , h 2 , respectively.Such a structure can be fabricated by simple overlay lithography and dry etch steps, to avoid sophisticated tiled etching 49 or dual-layer deposition processes 23,24 .As reported, the key to generating the UGRs is to create a pair of half-integer topological charges (q = ±1/2) carried by circularly polarized (CP) states, which can be accomplished by splitting an integer-charge q = ±1 of tunable BIC 49 , or zero-charge q = 0 of a void point through inter-band coupling 50 .However, such mechanisms usually require a relatively thick wafer and thus are not easy to be compatible with standard SOI thickness [49][50][51][52] .
Alternatively, we turn to work on a symmetry-protected BIC which robustly resides at the Brillouin zone (BZ) center for any slab thickness.As shown in Fig. 1c, the grating operates at the lowest, anti-symmetric transverse electric (TE) band that we denote it as TE-A band.We treat the L-shaped hole as a combination of two rectangular blocks B1 and B2 with different widths and depths.When the small block B1 is absent, the grating restores C 2 symmetry and raises a symmetry-protected BIC at the Γ point 55 , carrying a topological charge of q = −1 and exhibiting as a diverged quality factor (Q) (black line, Fig. 1c).The presence of the small block B1 breaks the C 2 symmetry and splits the integer charge into a pair of half-charges q = −1/2.Accordingly, the Qs of resonances in the vicinity of the Γ point degrade to ∼ 134 (red line, Fig. 2c) which is sufficiently low to support broadband operation.A UGR is found at k x = −0.1192with an asymmetry ratio (defined as the ratio between upward and downward radiation intensity) reaching η ∼ 65 dB.As confirmed by the field pattern (Fig. 1b), the UGRs unidirectionally radiate toward the upper direction while nearly no energy leaks into the lower substrate.
The trajectories of topological charge upon the downward radiation are shown in Fig. 1d: red for right-handed circularly polarized (RCP) and blue for left-handed circularly polarized (LCP) which are opposite in helicity.By gradually increasing the depth of the small block h 1 from 0 nm to 100 nm, a pair of half-charges q = −1/2 split from the BIC, and evolve in a y-mirror symmetric manner in the momentum space.The RCP and LCP trajectories meet on the k x axis at k x = −0.1192at which h 1 = 100 nm.At this point, any downward radiation needs to be both LCP and RCP at the same time, which can never be satisfied.As a result, the grating resonance cannot have any downward radiation, even without a mirror on the bottom.
Next, we design the complete structure of the grating coupler to incorporate the UGR with waveguide and fiber modes.Fig. 2a shows the top view of the unidirectional grating coupler, which consists of a tapered-waveguide region, an apodization region, and a uniform region.The dispersion of the UGR and waveguide modes are plotted in Fig. 2b, showing that the group velocities v g = dω/dk of the waveguide modes are almost constant when the waveguide width shrinks from 20 µm to 2 µm.By fine-tuning the unit-cell geometry of the grating, we also make the group velocity of the uniform region (red curve, Fig. 2b) almost identical to the tapered waveguides (black and gray lines, Fig. 2b).Therefore, the group-velocity-matching has been fulfilled that allows the energy to efficiently transit between the grating and waveguide modes.
To miniaturize the back-scattering between the grating and waveguide, we perform an adiabatic transformation of grating geometry to handle the momentum mismatch between the UGR and waveguide mode.A detailed side view of the apodization region is illustrated in Fig. 2c, in which the grating periodicity a and the width of blocks B1 and B2 (w 1 , w 2 ) are continuously adjusted, marked as gradient colors.We pick up three grating geometries at different positions from A to C, and calculate their bulk dispersion, respectively (Fig. 2b).As expected, the apodization smoothly transits the UGRs to the targeted waveguide mode that fulfills the requirement of momentum-matching.
Further, we design the grating coupler to best match its radiation distribution with a standard single-mode fiber (Corning SMF-28e+) with core and cladding diameters of 8.2 µm and 125 µm.
As light propagates down the fiber, the beam maintains a nearly Gaussian cross-sectional profile with a mode field diameter (MFD) of 10.4 µm (Fig. 2d).To promote the overlap coefficient with the fiber mode, the spatial and angular distributions of the radiation field need to be tuned simultaneously.By carefully arranging the apodization region, we obtain the optimized design of the unidirectional grating coupler.Numerical simulation (Fig. 2d, Lumerical FDTD) confirms that the waveguide mode propagates through grating with minor back-scatterings, and the light only radiates upwards in an oblique direction of θ = 13.72 • .The detailed spatial and angular distributions of the radiation field are presented in Fig. 2e, showing nearly Gaussian shapes that match well with the targeted standard single-mode fiber.
To show the bandwidth and angular tolerance performances of the unidirectional grating coupler, we calculate the map of fiber-to-coupler coupling efficiency (CE) over the wavelength and alignment angle (Fig. 2f).The red and blue contours represent the CE thresholds of 3 dB and 1 dB, showing that the unidirectional grating coupler works in a spectrum width of 57.6 nm and 28.9 nm with angular tolerance of 6 • and 3 • , respectively.The calculation confirms that the designed grating coupler has excellent robustness owing to the topological nature of the UGR, and it is capable of broadband operation and easy assembly.

Sample fabrication and experimental characterization
To verify the design and principles, we fabricate the unidirectional grating coupler samples on a standard 340-nm-thick SOI wafer by using overlaid electron-beam lithography and inductively coupled plasma etching (See Methods for more details).Our design doesn't require sophisticated silicon deposition 23,24 or tilted etching steps 49 , and thus significantly simplifies the fabrication process.A top-view of the grating coupler sample is observed by using an optical microscope, showing a total grating footprint of 20 × 20 µm (Fig. 3a).The scanning electron microscope images of the apodization and uniform regions are presented in Fig. 3c,d, and the detailed side and top views of the "L-shaped" grating patterns are shown in Fig. 3b,e, which gives a = 528 nm, w 1 = 158 nm, w 2 = 200 nm, h 1 = 100 nm, h 2 = 262 nm in the fabricated samples.The underlying SiO 2 layer is maintained, while for the simplicity of testing, the grating coupler is immersed into a refractive index liquid of n = 1.46 to simulate the deposited upper cladding of SiO 2 in the foundry process.
To evaluate the performance of the unidirectional grating coupler, we construct a fiber-todetector optical interconnect in which the light transmits through two identical grating couplers and the waveguide connected them, as schematically shown in Fig. 4a.A tunable telecommunication laser with light in the C + L band is first sent through a polarization controller to match with the grating and then transmits into the fiber.We use a free-space photodiode with an active area of 10 × 10 mm to receive the light (See Methods for more details.)By sweeping the wavelength from 1510 to 1590 nm, we measure the insertion losses of the fiber-to-detector link as illustrated in Fig. 4b, showing a minimal loss of 1.24 dB at 1550 nm.
Since the fiber and photodiode have different receiving areas and apertures, their overlap factors with respect to the coupler are also different.We calculate the overlap ratio between the coupler-to-detector and coupler-to-fiber interfaces from the devices' parameters (inset, Fig. 4b).In this test, the chip contains a waveguide in the length of 7 mm to connect the two unidirectional grating couplers, and we calibrate the waveguide losses from some reference samples (see Supplementary Section for details).As a result, we decompose the total link loss to the coupler-to-detector CE and coupler-to-fiber CE, respectively (Fig. 4b).The measured results show good agreement with the design.The peak CE at the coupler-to-fiber interface reaches a record-high value of 0.34 dB at 1550 nm, namely 92.47% of light energy successfully couples into the fiber.Accordingly, the 1 dB bandwidth of the unidirectional grating coupler exceeds 30 nm, guaranteeing its capability of broadband operation.
Owing to the protection of topology, the unidirectional grating coupler is expected to maintain fairly good performance under geometry deviation 49,50 .To evaluate and verify the fabrication tolerance, we fabricate a group of samples with the rectangular blocks B1 and B2 slightly shifting in the transverse direction which is a common type of imperfection in the overlaid lithography process (inset, Fig. 4d).Specifically, we sweep the shift from -50 nm to 50 nm in a step of 10 nm and obtain the coupler-to-fiber CE by using the approach elaborated above.As shown in Fig. 4d, the peak CEs keep higher than 1 dB across all samples and can remain better than 0.6 dB if the shift error is below ± 30 nm.We also plot the map of CE on the wavelength and shift in Fig. 4c, confirming that the ultra-low and broadband feature of the unidirectional coupler is robust under fabrication deviation.
To reveal the robustness and repeatability of the unidirectional grating coupler again random disorders, we further fabricate 36 identical devices by applying the ideal design to the same fabrication process, in which the standard deviations of the pattern locations and widths are estimated to be about 5 nm.The measured CEs statistically show an average value of -0.426 dB with a variance of 0.005 dB (Fig. 4e).The averaged 1dB bandwidth is 32.83 nm across the samples, with a variance of 0.55 nm.

Discussions
Above theory and experiments demonstrate a new method of realizing ultra-low-loss grating coupler from the perspective of topological charge manipulation.We achieve a record-low peak CE of 0.34 dB in a standard 340 nm SOI wafer with grating shapes that are compatible with the foundry process.Our finding provides a vivid example of improving the photonic devices from the view of topology and reveals the feasibility of ultra-high energy-efficient optical interconnects of silicon photonic for dense integration and 3D stacked integration.Given that topological UGRs ubiquitously exist in many symmetry-broken photonic structures, the proposed technique can be applied to other material systems (such as lithium niobate on insulator platform) to improve chip-to-fiber coupling efficiencies, in which the vertical sidewalls are usually hard to achieve.

Conclusion
To summarize, we present a new method of ultra-low-loss interconnect by using a unidirectional radiating grating coupler.By splitting and then restoring an integer topological charge and apodizing the grating geometry to adiabatically match the waveguide with the fiber mode, we achieve a record-low fiber-to-chip coupling efficiency of 0.34 dB with its bandwidth exceeding 30 nm.The unidirectional grating coupler also enables an energy-efficient interconnect between two stack photonic chips, with an interlay insertion loss of only 0.94 dB.Our work highlights the great potential of silicon photonics for the next-generation ultra-dense data transmission, and paves the way to large-volume on-chip photonic signal processing and computing.defined by the first round of exposure and etching.Next, the waveguide and tapered-waveguided regions are fabricated by overlaying another round of exposure and etching described above to etch through the silicon layer.The ICP etch times are carefully controlled for different shapes and depths.
Measurement system.A Santec TSL-550 tunable laser generates the source from 1510 nm to 1590 nm.A Thorlabs FDG10X10 photodiode with a 10 mm×10 mm large receiver area is used to fully collect the radiation energy.To measure the interlay coupling efficiency between two chips, two samples with grating arrays are stacked.A Thorlabs PT3-Z8 three-dimensional motorized translation stage is used to sweep the upper grating to the optimal position.The sweep region is reduced to the region given by the spacing of the grating array.During the measurement, the chips are immersed in a refractive index liquid of n = 1.46 (Cargille, Series A) to simulate the SiO 2 cladding in the foundry process.

Figure 3 :
Figure 3: Sample fabrication.(a) Optical microscope image of the grating coupler composed