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High positional freedom SOI subwavelength grating coupler (SWG) for 300 mm foundry fabrication

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Abstract

We present an apodized, single etch-step, subwavelength grating (SWG) high positional freedom (HPF) grating coupler based on the 220 nm silicon-on-insulator (SOI) with 2μm BOX substrate. The grating coupler was designed for 1550 nm light with transverse electric (TE) polarization. It has a measured maximum coupling efficiency of −7.49 dB (17.8%) and a −1 dB/-3 dB bandwidth of ~14 nm/29.5 nm respectively. It was fabricated in a 300mm state of the art CMOS foundry. This work presents an SOI-based grating coupler with the highest—to the best of our knowledge— −1 dB single mode fiber lateral alignment of 21.4 μm × 10.1 μm.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

220 nm-thick silicon-on-insulator (SOI) has been a platform for silicon photonics integrated circuits since before 2003 [1]. Although other thicknesses were originally offered, for economic and historical reasons [2], 220 nm SOI has become a standard platform in multi-project wafer (MPW) foundries (e.g. imec, LETI, IME) [3] despite larger thicknesses (250 nm – > 400 nm) being the optimal thickness for photonic MPWs [2].

To ensure high chip yield, optical testing of a wafer at its various process steps is required. This usually involves coupling light from an external laser source via a single mode fiber into the on-chip waveguide. However, there is a large modal mismatch between the mode size of an SMF28 fiber (from Corning, 1550 nm mode field diameter (MFD) of 10.4 μm) and a 450 × 220 nm SOI single mode strip waveguide.

There are two common methods of mode-size conversion: butt-coupling via tapers / inverse tapers and vertical coupling via grating couplers. (Inverse) taper solutions typically require dicing of the wafer and polishing of the chip edge. This prevents their use in wafer scale testing. Furthermore, their alignment accuracy is about −3 dB for ± 1–2.3 µm of misalignment [4–7]. Additionally, in the case of inverse tapers, the tip must be very narrow, e.g. 30 nm [8], resulting in a low-yield of inverse taper devices or in some cases, designs being incompatible with standard CMOS processes. Lastly, some tapers’ resulting mode size is still smaller than a cleaved SMF28, requiring a lensed SMF28 to improve modal matching [9,10]. However, there are other designs which match to a cleaved SMF28 [11–13].

In contrast, grating couplers are not limited to chip-edge real estate, do not require wafer dicing (easily facilitating non-destructive wafer-scale testing) and are compatible with cleaved SMF28 optical fibers. In this sense, optical grating couplers are the equivalent of electrical test pads in the electronics world.

Most of the literature regarding subwavelength grating (SWG) couplers (see Table 1) have been designs to maximize the chip-fiber directionality [14]; mode-matching to an SMF28 [15]; polarization diversity [16–18]; bandwidth [19,20]; and 3D integration [21], and have achieved measured coupling efficiencies of ~-2 – −6 dB.

Tables Icon

Table 1. A comparison of recent SWG Grating Couplers

Although grating couplers have greater lateral misalignment tolerances than tapers, to ensure consistent results, optical wafer-scale testers should still have lateral alignment accuracies of < 1 µm, height control of < 5 µm, and fiber angle control < 0.2° [40]. The lateral misalignment tolerances of 220 nm SOI SWG grating couplers are not generally published, but they should be on a similar scale to that of a 220 nm SOI non-SWG grating coupler with a 1 µm BOX, as shown in Fig. 1(a) [42], i.e. a −1 dB misalignment tolerance of ± 2.5 µm. As another point of comparison, Fig. 1(b) [43] is the misalignment tolerance of a 250 nm SOI non-SWG grating coupler with a 3 µm BOX.

 figure: Fig. 1

Fig. 1 (a) Comparison of simulation and measurement results of the lateral alignment tolerances of a grating coupler with an SOI thickness of 220 nm and a BOX thickness of 1 µm. The normalized coupling efficiency is shown as function of the lateral position of the fiber. The smooth curves are simulation results. The vertical distance between fiber and grating is approximately 10 µm. −0.5 and −1 dB contours are indicated on the figure. From [42] © 2006 The Japan Society of Applied Physics. (b) The absolute coupling efficiency as a function of the lateral position of the fiber for a grating coupler with an SOI thickness of 250 nm and a BOX thickness of 3 µm. From [43] © 2011 IEEE. The wavelength is 1550 nm and is TE-polarized in both references.

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By increasing the misalignment tolerance, we can reduce the complexity of the machinery (for automated probers) as well as the skill of the technician (for manual probers) in aligning the optical fiber probes needed for wafer scale testing. An SWG single through-etch design also requires only one mask level and the buried oxide (BOX) of the SOI wafer acts as a natural etch-stop, thus simplifying fabrication and eliminating effects from misaligning multiple masks.

A non-SWG grating coupler has been designed to have high positional freedom in z-, the vertical axis, achieving ~-6 – −8 dB between + 50 µm – + 300 µm for 1550 nm [44,45]. However, earlier research has shown that for z < 15 µm, the additional coupling loss is negligible, and only −0.5 dB for z = 55 µm [42].

Separately, another non-SWG grating coupler achieved a horizontal misalignment tolerance of ~-3 dB for ± 4 µm along the direction of the waveguide (x-axis) (y-axis misalignment tolerance not stated) [46].

Lastly, it has been shown that a Si3N4-on-SOI grating coupler with a uniform flat-top E-field output as long as a millimeter is possible for applications in optical phased arrays [47]. If used as a grating coupler, it would theoretically have an x-axis misalignment tolerance on the order of a millimetre, though its coupling efficiency would likely be very low.

Thus, this work presents an SWG grating coupler to maximize the lateral positional freedom of the SMF28 while maintaining a reasonable coupling efficiency. This is the first attempt (to our knowledge) of maximising lateral positional freedom using an SWG. The grating coupler has a peak coupling efficiency of −7.49 dB, −1 dB misalignment tolerance of 21.4 µm × 10.1 µm, and a measured coupling efficiency of −1 dB / −3 dB bandwidth of ~14 nm / 29.5 nm respectively.

2. Design methodology—2D

The simulation software used for optimizing this design was Lumerical FDTD, a commercial-grade simulator based on the finite-difference time-domain method [48]. Lumerical FDTD utilizes ‘Particle Swarm Optimization’, a population-based stochastic optimization technique to optimize nanophotonic designs. For the remainder of this paper, unless otherwise stated, ‘optimization’ will refer to Lumerical’s ‘Particle Swarm Optimization’.

The grating coupler was first designed 2-Dimensionally in the x-z plane with a 24 µm-long, TE-polarized, 1550 nm planewave input with a 10° tilt from the surface normal, as shown in Fig. 2. 2D placeholders occupied the etched low-index sections of the SWG with an equivalent refractive index, neq, i, which would later determine the dimensions of ly, Si and ly, SiO2 via a combination of Effective Medium Theory (EMT) and 3D FDTD. Preliminary research indicated that the optimal apodization method for such a long input source was to maximize coupling efficiency into the waveguide by apodizing the periods, i, in batches with a nearest-to-waveguide order.

 figure: Fig. 2

Fig. 2 Schematic drawing of the SWG high positional freedom grating coupler. The input source is a 24 µm-long, 1550 nm, TE-polarized planewave tilted 10° from vertical (E-field profile shown as black line). The grating coupler was first apodized 2-Dimensionally in the x-z plane, with neq, i as 2D placeholders for the lower index etched sections of the SWG. Λy, ly, Si and ly, SiO2 were later determined by full 3D FDTD that did not use a periodic boundary condition simulation box [15,21,23,26,30]. Adapted from [49]

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Thus, optimization occurred in 4 stages in a nearest-to-waveguide fashion, through increasingly finer iterations based on powers of 2:

Stage 1: the SWG was apodized as a single set of 40 periods. 24 µm spans about 36 periods for most grating couplers based on the 220 nm SOI platform (24 µm / 0.66 µm ≈36). 40 periods for this grating coupler was chosen as it is slightly larger than 36 and divisible by powers of 2.

Stage 2: periods were apodized as batches of 24: periods 1–16 were optimized, then 17–40.

Stage 3: periods were apodized as batches of 23: periods 1–8 were optimized, followed by 9–16, 17–24, 25–40.

Stage 4: periods were apodized as batches of 22: the grating was optimized as 10 batches of periods of 4.

Theoretically, a fifth and sixth stage are possible where periods would be apodized as batches of 21 and finally 2°, but these were skipped due to exponentially increasing computational demands and diminishing returns in coupling efficiency.

The variables for each optimization stage were: the center position of the planewave source from the grating start (12 ± 2 µm), a given batch’s period, Λx, (0.64 ± 0.2 µm), a given batch’s duty cycle=lx, SiΛx, (0.3–0.7) and the equivalent index of the etched section, neq, i, (1.444–3.476).

The completion of the fourth stage of 2D FDTD optimization yielded the results in Table 2.

Tables Icon

Table 2. 24 µm Planewave High Positional Freedom Grating Coupler dimensions

There is a general decrease in SWG neq, i as the period number increases, which corresponds with a stronger grating strength at higher periods. This gradual ‘ramping up’ of grating strength allows the grating coupler to have a large, uniform radiated mode in the z-direction.

3. Design methodology—3D

The dimensions for ly, SiO2 and Λy were initially determined by 2nd order Effective Medium Theory (EMT), as proposed by Rytov [50]. For the sake of completeness, the formulae for the equivalent effective index for both TE- and TM-polarized light are given.

Below are the equations for zeroth order EMT:

1nLTE(0)=[fynhole2+1fynSi2]12
nLTM(0)=[nhole2fy+nSi2(1fy)]12

where nLTE(0) and nLTM(0) are the refractive indices of the etched portions for TE and TM polarization respectively; fy is the fill factor in the y-direction; nSi is the refractive index of Si; nhole is the refractive index of the in-filled material (SiO2). Zeroth order EMT is considered applicable when Λy ≪ λ/2πneff [9,15], where λ is the free-space wavelength (here, λ = 1.55 µm) and neff is the maximum effective index of the slab waveguide fundamental TE-polarized mode (here, neff = 2.8265), so when Λy ≪ 87 nm.

However, the solutions to zeroth order EMT can then be used in 2nd order EMT, also formulated by Rytov, but re-expressed in [36]:

nLTE(2)=nLTE(0)[1+π23R2fy2(1fy)2(nhole2nSi2)2×(nLTM(0)neff,TE)2(nLTE(0)nholenSi)4]12
nLTM(2)=nLTM(0)[1+π23R2fy2(1fy)2(nhole2nSi2neff,TMnLTM(0))2]12

where R = neffΛy/λ, neff is the mode effective index in the slab waveguide with 220 nm thickness (neff, TE = 2.8265 and neff, TM = 2.1024, calculated in 2D FDTD).

2nd order EMT is generally considered more accurate than zeroth order EMT [9,33,36,51], but is only considered applicable when Λy is sufficiently small to frustrate all but the zeroth diffraction order, i.e., Λy < ΛBragg = λ/neff [15,26,33]. In this case, when Λy < 548 nm.

An expression for 4th order EMT is available in [52].

By rearranging Eq. (2a), we can find an expression for fy and therefore ly, SiO2. The range of artificial equivalent indices, neq, i, required by the period batches of the HPF design (1.821 < neq, i < 2.998) and the minimum feature size achievable (100 nm) by reactive ion etch (RIE) on a 220 nm-thick SOI substrate mandated that Λy ≥ 450 nm, according to 2nd order EMT. However, 3D FDTD optimizations of the resulting designs for Λy = 450 nm, 500 nm, 550 nm showed that the necessary minimum feature sizes for neq, i = 2.968, 2.998 would be < 100 nm. As a compromise between the minimum fabricable dimensions by the RIE process, and preventing higher order diffraction effects, we chose Λy = 600 nm.

Our hypothesis as to 2nd order EMT’s inaccuracy—aside from the large Λy—is that the 1550 nm Bloch guided mode, as it transitions from the SOI to the SWG, has a significant portion of its field in the top oxide and BOX, and so encounters an neq significantly weighted towards SiO2. Consequently, to achieve the higher neq, i required by the design, the corresponding ly, SiO2 should be much smaller than the values predicted by EMT.

As Λy = 600 nm > 548 nm—beyond which 2nd order EMT is no longer valid—full 3D FDTD simulations were undertaken to maximize the transmission into the waveguide. Period-batch-by-period-batch, the homogenous neq placeholders were replaced with discrete etched structures whose ly, SiO2 lengths were swept in two stages: in 10 nm steps around the values calculated by 2nd order EMT, and then in 1 nm steps. A similar method was used by [22]. Though computationally-intensive, this method was pursued as the numerical method of 3D simulation of only one Λy period with periodic y-boundary conditions used in [15,21,23,26,30] did not approach the same values as full 3D FDTD.

After all homogenous placeholders were replaced (Round 1), the method was repeated (Round 2), with significant changes in the etch width dimensions. It was repeated once more to confirm that the optimal etch width values had indeed converged.

The final ly, SiO2 dimensions (to the nearest nm) are shown in Table 2, and are indeed much smaller than otherwise predicted by 2nd order EMT. The numerically calculated ly, SiO2 dimensions are plotted with their corresponding neq, i for Λy = 600 nm in Fig. 3, along with those calculated by 0th and 2nd order EMT. It should be stressed that the ly, SiO2 dimensions thus obtained do not actually correspond to EMT neq values: at Λy = 600 nm, this HPF design is not strictly within the subwavelength regime, and indeed there are Bragg reflection effects and radiation effects competing with the synthesized subwavelength neq [49] while simultaneously generating ± 1st order modes [30]. The numerically calculated 3D FDTD ly, SiO2 dimensions should be interpreted as a compromise between the synthesized neq and these other effects which best optimizes the HPF GC design. Indeed, neq, 21—24 = 2.567 for ly, SiO2, 21—24 = 270 nm, while a similarly valued neq, 25—28 = 2.562 has a significantly different ly, SiO2, 25—28 = 239 nm.

 figure: Fig. 3

Fig. 3 neq, Equivalent Refractive Index for Λy = 600 nm for 1550 nm, TE-polarized light on a 220 nm SOI substrate, according to 0th order EMT (red dotted), 2nd order EMT (red line) and full 3D FDTD (black crosses).

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Nevertheless, the numerically calculated ly, SiO2 dimensions and the fitted fifth order polynomial Eq. (3a) serve as a heuristic for future TE-polarized, 1550 nm, Λy = 600 nm subwavelength devices.

neq=1×1013ly,SiO25+2×1010ly,SiO242×107ly,SiO23+4×105ly,SiO220.0076ly,SiO2+3.4713
or re-expressed in a more useful form:

ly,SiO2(µm)=0.083neq5+1.1837neq46.5508neq3+17.566neq223.057neq+12.351.

The SiO2 diffracting elements had 3 different y-lateral layouts: Rectangular, where WGr = 15 µm, linear taper length = 500 µm; Circular, where the SWG diffracting elements were curved around 50° concentric arcs; and Elliptical, where the SWG diffracting elements were curved around ellipses as determined by the method in [53] with a minimum grating order of 19. For both curved designs, the elements were ‘rotated & not translated’, similar to [26], as shown in Fig. 4(c). Rotation would be unnecessary if the elements were circles of equivalent area [24], although research on the ideal element shape is still ongoing [30,33,51].

 figure: Fig. 4

Fig. 4 Comparison of different adjustments of the diffracting elements in a curved SWG grating coupler. (a) The whole circular HPF design with a highlight of the relevant section (b) Diffraction elements neither rotated nor translated. Note Λy = 656 nm. (c) Diffraction elements rotated but not translated, as in . Note Λy = 653 nm. (d) Diffraction elements rotated and translated. Note Λy ≈600 nm. (e) Diffraction elements translated but not rotated. (f) Diffraction elements skewed but not translated, similar to [37,38]. (g) Diffraction elements skewed and translated. (h) Diffraction elements radially aligned with different Λy’s, similar to [54].

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On arguments of geometry alone, the elements should be rotated and translated, as in Fig. 4(d). The farther the diffracting elements deviate from the centerline of the grating coupler, the greater Λy deviates from 600 nm. At the extreme of ± 25°, a lateral step of 600 nm in y produces a Λy of 656 nm. These curved lateral layout designs performed significantly poorer (c.f. Figs. 8(c), 8(d)). Further experiments among ‘not rotated & not translated’ (Fig. 4(b)), ‘rotated & not translated’ (Fig. 4(c)), and ‘rotated & translated’ (Fig. 4(d)) orientations were undertaken to measure their effects on grating coupler performance.

For the sake of completion, Fig. 4 also covers other ways rectangular scattering elements can be manipulated in curved SWG GCs: ‘not rotated & translated’ (Fig. 4(e)); ‘skewed & not translated’, as in [37,38], (Fig. 4(f)); ‘skewed & translated’ (Fig. 4(g)); ‘radially aligned but with varying Λy’s’, as in [54].

4. Fabrication

The devices were fabricated in a state-of-the-art 300mm CMOS foundry using 220 nm-thick SOI wafers. The HPF gratings and waveguides were patterned using an industry-standard ASML 193 nm immersion lithography scanner and then formed using a single reactive ion etch (RIE) step. Approximately 5.14 µm of SiO2 top cladding was deposited via plasma enhanced chemical vapor deposition (PECVD) tetraethyl orthosilicate (TEOS).

Representative scanning electron microscopy (SEM) images of the rectangular, circular and elliptical layouts of the design are shown in Fig. 5 below, after the full silicon etch step and before silicon dioxide deposition.

 figure: Fig. 5

Fig. 5 Scanning Electron Micrograph (SEM) images of the Planewave High Positional Freedom (HPF) grating coupler just after full silicon etch for (a) Rectangular, (b) Rectangular (close up), (c) Circular, (d) Elliptical (close up) lateral layouts.

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SEM measurements of Device 2 from Fig. 7 are given in the last two columns of Table 2. Most fabricated dimensions were greater than 90% of the designed values, with the exception of periods 1–8. This is expected as those scattering elements were the smallest and so would experience the most significant RIE lag. However, they were all greater than 85% of the designed values.

5. Manual measurements

Each lateral layout design was paired with a well-characterized, standard ‘Process of Record’ (POR) grating coupler with a 2 cm-long, 220 nm-thick × 550 nm-wide strip waveguide connecting them. A cleaved SMF28 was placed over the input HPF grating coupler and tilted at a nominal 14.5° to the surface normal to account for refraction at the air-SiO2 interface in the absence of index matching fluid (IMF). A lensed multimode fiber (MMF) (50 µm minimum illumination diameter) was centerd over the output POR grating coupler and tilted at a nominal 9° to the surface normal.

The HPF grating coupler was measured topologically with TE-polarized 1550 nm light while stepping the entire wafer stage in 1.125μm steps in the x-direction with a Cascade Microtech (Beaverton, OR) PBR04 Poseidon optics bench (c.f. Figure 6(c)). As the lensed MMF has a much larger numerical aperture compared to the cleaved SMF (estimated 0.47 vs 0.13), it has a much larger cone of acceptance and is therefore significantly more tolerant to misalignments in x and y. Every 3 steps, the x-position of the lensed MMF output was re-adjusted to obtain maximum throughput, thereby ensuring that any changes in the power throughput was solely a function of the x-misalignment of the cleaved SMF over the input HPF grating coupler. This method was chosen as the fiber micropositioners are analog devices (Cascade Microtech (Beaverton OR) DPP210 micropositioners), which would make consistent incremental movements in x- difficult to reproduce. 6 rectangular HPF grating couplers were measured from separate die radially outwards from the center of the wafer.

 figure: Fig. 6

Fig. 6 Manual measurement steps. a) POR GC pair characterised with cleaved SMF-28 for both input (right) and output (left). b) POR GC pair characterised with cleaved SMF-28 for input and an MMF for output. c) HPF GC characterised with a cleaved SMF-28 for input and an MMF for output; the optical bench is rastered in x.

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To characterize the absolute insertion loss into the HPF, we subtracted 1) the waveguide loss (characterized on another structure), 2) the ouput loss from the POR grating couper to the lensed MMF.

To obtain 2), we measured the insertion loss of a pair of POR grating couplers with cleaved SMF28s at both input and output (Fig. 6(a)), subtracted the waveguide loss and divided by 2 to obtain 3) the insertion loss of a cleaved SMF28 to one POR grating coupler.

We then measured the same pair of POR grating couplers, but with a lensed MMF over the output (Fig. 6(b)). Subtracting waveguide loss and 3) from this yields 2), the output loss from a POR grating coupler to a lensed MMF.

The absolute insertion losses of the 6 devices are shown in Fig. 7. While the measured values exceed those of the simulation, this is within experimental variances as the coupling efficiency at a specific wavelength is angle-dependent and the fiber tilt is adjusted manually on a Cascade Microtech (Beaverton, OR) Lightwave Probe (LWP).

 figure: Fig. 7

Fig. 7 Insertion loss of the HPF grating coupler as a function of the x-position of the SMF28 for 1550 nm TE-polarized light. The negative x-direction is towards the waveguide. The SMF28 was tilted to a nominal 14.5° and, as coupling efficiency is angle-dependent, is the likely cause of measured values exceeding the simulation. Device 4 was topologically scanned and the data is presented in Fig. 8(b).

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Using a similar method mentioned above, Device 4 was rastered topologically in x- and y-, and the data presented in Fig. 8(b). As a point of comparison with Fig. (1), a half-etched (i.e. requiring 2 masks) POR grating coupler was also rastered topologically and presented in Fig. 8(a). Insertion losses are in dB. The origins (0, 0) are the points with highest throughputs. The listed loss in dB refers to those peaks. Contour lines are spaced 1 dB apart. Where possible, the x- and y- dimensions have been limited to show the topologies over roughly equal areas, i.e. 40 μm × 40 μm. In all graphs, the waveguide is to the left.

 figure: Fig. 8

Fig. 8 Topological scans of absolute insertion loss of grating couplers with 1550 nm, TE-polarized light. The negative x-direction is towards the waveguide. Peak coupling efficiencies are located at the origins (0, 0) and are stated in the respective graphs. Contours are −1 dB apart. (a) Process of Record (POR) grating coupler, (b) Rectangular high positional freedom (HPF) grating coupler, (c) Circular HPF grating coupler with rotated, but not translated diffracting elements, (d) Elliptical HPF grating coupler with rotated, but not translated diffracting elements.

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Figures 8(c) and 8(d) show topological scans of the circular and elliptical HPF grating couplers from the same die as Device 4 respectively. Further experiments were undertaken in Section 6. Semi-automated measurements to determine if the lack of translation was a significant contributor to the decrease in performance compared to Fig. 8(b).

Bandwidth measurements were taken with a Keysight Technologies (Santa Rosa, CA) 81980A Compact Tunable Laser Source external cavity InGaAsP laser with a wavelength range of 1465 nm – 1575 nm. Similar to the x-scan in Fig. 7, Device 4 was stepped in x in 1.125 µm increments and the laser swept across its wavelength at each position. Bandwidth losses were measured for the waveguide and the output POR grating coupler to MMF on separate structures and subtracted to obtain Fig. 9(b), the absolute bandwidth insertion loss for the rectangular HPF grating coupler as a function of the SMF28’s x-position. Figure 9(a) shows the full 3D FDTD simulation result of the same structure. Black lines on both graphs indicate the −1 dB, −2 dB and −3 dB contours. Figure 9(c) shows a subset of 9(b) with the contours marked in clear bands: −1 dB (red), −2 dB (yellow), −3 dB (green).

 figure: Fig. 9

Fig. 9 Rectangular HPF grating coupler bandwidth as a function of SMF28 x-position. Black lines indicate −1 dB, −2 dB and −3 dB contours. (a) Full 3D FDTD simulated bandwidth, (b) measured bandwidth, (c) subset of (b) with −1 dB (red), −2 dB (yellow) and −3 dB (green) bandwidth contours. The −1 dB and −3 dB bandwidths are ~14 nm and 29.5 nm respectively.

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Bandwidth is a function of several variables, including fiber tilt and position. Generally, for a non-HPF grating coupler, the larger the SMF x-position, the larger the ‘effective interaction area’ (the effective grating area covered by the fiber beam) and consequently, the narrower the bandwidth [55]. However, for an HPF grating coupler, the ‘effective interaction area’ is constant for most of the SMF’s x-travel, and so the −1 dB bandwidth should be generally unchanged, as shown in Fig. 9(a). The measured structure’s fin-shaped deviation from the ‘rectangular’ bandwidth pattern is hypothesized to be due to RIE lag, as scattering elements closer to the waveguide are smaller and according to SEM measurements (c.f. Table 2) are slightly underetched (85%) compared to bigger element (90–98%).

Nevertheless, within the range of SMF28 x-position values measured, the −1 dB and −3 dB bandwidths are ~14 nm and ~29.5 nm respectively, which is slightly less than half of other SWG grating couplers built on similar platforms (see Table 1).

6. Semi-automated measurements

As manual measurements were labor-intensive, a semi-automated method was used to map the lateral misalignment tolerance of the various curved HPF SWG GC sub-types (i.e. circular vs elliptical; ‘not rotated & not translated’ vs ‘rotated & not translated’ vs ‘rotated & translated’). HPF SWG GCs of the same sub-type were laid out as pairs on a macro compatible with a 20 individual single mode fibre V-Groove assembly by OZ Optics (Ottawa, Ontario). The grating couplers were 127µm apart and connected by 100 µm-long straight waveguides (Fig. 10). POR grating couplers were used as the outermost pair for the V-Groove assembly optical alignment. As the assembly was polished to 8° and the tilt relatively fixed (~8°), the laser wavelength used to characterise the topologies was adjusted to 1603 nm (determined empirically) to compensate.

 figure: Fig. 10

Fig. 10 Example macro of 8 HPF SWG GC pairs used for semi-automated measurements. Grating couplers are spaced 127 µm apart and are connected by 0.22 µm-thick × 0.55 µm-wide strip waveguides with 100 µm straight waveguides. All HPF pairs were measured with the same fiber pair (channel 2) on the V-Groove assembly.

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All fibre pairs in the V-Groove assembly were used to measure the same HPF SWG GC sub-type pair to determine which channel (2) had the lowest loss. Channel 2 of the V-Groove assembly was then used to measure all HPF SWG GC sub-type pairs in order to avoid zero-ing issues in loss.

Topological measurements were collected with a Keysight Technologies (Santa Rosa, CA) 81606A Tunable Laser Source and a N7745A Optical Multiport Power Meter. The V-Groove assembly was spiral-rastered in x-y by Physik Instrumente (Karlsruhe,Germany) P-611.3 NanoCube XYZ Piezo System fibre positioners in 0.4µm steps. Total insertion loss was divided by 2 to obtain fibre insertion loss per HPF GC. Waveguide and bend loss are ignored as the straight waveguides were short (100 µm each) and the bend radii were large (63.5 µm). To show across-wafer repeatability, the HPF SWG GC sub-type pairs were measured over 5 dice.

Figure 11(a)-11(f) shows sample topological measurements of the Planewave Λy = 600nm HPF GC designs from die: (−1,0). Peak coupling efficiencies and the −1 dB areas are listed in the center of each figure. Contour lines are 1 dB apart.

 figure: Fig. 11

Fig. 11 Sample semi-automated in-circuit testing (ICT) topological measurements of rectangular and curved grating couplers with different scattering element arrangements. (a) Rectangular. (b) Circular with ‘not rotated & not translated’ scattering elements. (c) Circular with ‘rotated & not translated’ scattering elements. (d) Circular with ‘rotated & translated’ scattering elements. (e) Elliptical with ‘not rotated & not translated’ scattering elements. (f) Elliptical with ‘rotated & translated’ scattering elements. Peak coupling efficiencies and the −1 dB areas are listed in the center of each figure. Contour lines are 1 dB apart. All measurements were done at λ = 1603 nm.

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The maximum coupling efficiencies, −1dB areas and −3dB areas of the scattering element orientation sub-type designs were averaged across 5 dice and their results shown in Table 3.

Tables Icon

Table 3. Effects of Scattering Element Orientation on HPF SWG Grating Coupler Performance (λ = 1603 nm)

There is a peak coupling efficiency and −1 dB Area improvement of 9.9% and 12.8% respectively for Elliptical: Rotated & translated. However, Circular: Rotated & translated suffered a peak coupling efficiency deprovement of −15.9%.

The same experiment was conducted on a slightly modified design: periods 29–36 were based on Λy = 300 nm instead of 600 nm, ostensibly to compare if this modification was more resistant to RIE lag, but also offers another perspective on the effects of scattering element orientation. The averaged results across the same 5 dice are shown in Table 4.

Tables Icon

Table 4. Effects of Scattering Element Orientation on HPF SWG Grating Coupler Performance where Periods 29–36 Utilise Λy = 300 nm (λ = 1603 nm)

Again, we see consistent—albeit modest—improvement in efficiency and area for the Elliptical: Rotated & translated orientation. Circular: Rotated & translated again suffered an efficiency deprovement of −15.1%. In both tables, ‘Rotated & not translated’ orientations consistently suffered peak coupling efficiency deprovements and generally suffered −1 dB Area deprovements as well. This could be caused by increased, undesirable, higher order scattering effects as the rotated scattering elements present a greater y-z cross-sectional area to an oncoming wave. The improvements of ‘Rotated & translated’ and the deprovements of ‘Rotated & not translated’ orientations suggest that the ‘Translated & not rotated’ orientation (c.f. Figure 4(e)) would have the best performance among the three, though further experiments would be needed to confirm this.

7. Conclusion

We have designed an SWG grating coupler with a −1 dB misalignment tolerance of 21.4μm × 10.1μm for 1550 nm TE-polarized light. It has a maximum coupling efficiency of −7.49 dB and a −1 dB / −3 dB bandwidth of ~14 nm / 29.5 nm respectively. To be fabricable by RIE on a 220 nm-thick SOI substrate, Λy was chosen to be 600 nm, which is one of only 2 designs from Table 1 for TE-polarized light using such large Λy values.

The increase in misalignment tolerance was traded for a narrower bandwidth. It was also likely traded for a more stringent tilt misalignment tolerance, as the two are inversely related: a grating coupler with a larger radiated mode has a narrower distribution of power in wave-vector space and so tighter tilt tolerances [56]. Figure 12(a) shows 2D FDTD simulation of the HPF GC’s coupling efficiency as a function of position and tilt. Figure 12(b) shows the coupling efficiency specifically as a function of tilt when x = 15.0 µm. From Fig. 12(b), we can see an expected fiber tilt tolerance of ~-0.4 dB for ± 1°, and ~-2.0 dB for ± 3°.

 figure: Fig. 12

Fig. 12 (a) 2D FDTD simulation of coupling efficiency at λ = 1550 nm for various fiber tilts as a function of SMF-28 x-position. (b) 2D FDTD simulation of fiber tilt angle tolerance at SMF x-Position = 15 µm.

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However, this grating coupler could potentially be used for inline testing of waveguide loss, where fiber tilts are not often adjusted, as a rapid, single etch design with high reproducibility. Understandably, Fig. 7 shows a variation of ~1 dB, but within the context of in-line testing, these grating couplers would be used to show that waveguide losses are within reasonable specifications at a particular process step. Hence, the variation of ~1 dB is considered having high reproducibility. Alternatively, it could also be used in narrow bandwidth, wafer-to-wafer bonding applications, which require higher misalignment tolerances for high yield.

Additionally, curved SWG designs were experimentally confirmed to perform better when their scattering elements were ‘Rotated & translated’ compared to ‘Not rotated & not translated’. However, the data suggests that ‘Translated & not rotated’ orientations should have even greater improvement.

Funding

Air Force Research Laboratory (FA8650-15-2-5220).

Acknowledgments

This material is based on work by the Integrated Photonics Institute for Manufacturing Innovation operating under the name of the American Institute for Manufacturing Integrated Photonics (“AIM Photonics”). The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of Air Force Research Laboratory, the U.S. Government or AIM Photonics.

References and links

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References

  • View by:

  1. D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. de La Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photonics Technol. Lett. 15(9), 1249–1251 (2003).
    [Crossref]
  2. D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
    [Crossref]
  3. L. Chrostowski and M. Hochberg, Silicon photonics design: from devices to systems (Cambridge University, 2015).
  4. K. Yoo and J.-H. Lee, “Design of a high-efficiency fiber-to-chip coupler with reflectors,” IEIE SPC 5(2), 123–128 (2016).
    [Crossref]
  5. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
    [Crossref] [PubMed]
  6. S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III–V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 369–379 (2014).
    [Crossref]
  7. J. Wang, Y. Xuan, C. Lee, B. Niu, L. Liu, G. N. Liu, and M. Qi, “Low-loss and misalignment-tolerant fiber-to-chip edge coupler based on double-tip inverse tapers,” in Optical Fiber Communications Conference and Exhibition (OFC), 2016 (2016), pp. 1–3.
  8. S. McNab, N. Moll, and Y. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11(22), 2927–2939 (2003).
    [Crossref] [PubMed]
  9. X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
    [Crossref]
  10. Y. Ding, H. Ou, and C. Peucheret, “Ultrahigh-efficiency apodized grating coupler using fully etched photonic crystals,” Opt. Lett. 38(15), 2732–2734 (2013).
    [Crossref] [PubMed]
  11. M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016).
    [Crossref] [PubMed]
  12. B. Snyder, G. Lepage, S. Balakrishnan, P. de Heyn, P. Verheyen, P. Absil, and J. van Campenhout, “Ultra-broadband, polarization-insensitive SMF-28 fiber edge couplers for silicon photonics,” in CPMT Symposium Japan (ICSJ),2017IEEE (2017), pp. 55–58.
    [Crossref]
  13. M. Tokushima, A. Kamei, and T. Horikawa, “Dual-tapered 10-µm-spot-size converter with double core for coupling polarization-independent silicon Rib waveguides to single-mode optical fibers,” Appl. Phys. Express 5(2), 022202 (2012).
    [Crossref]
  14. D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
    [Crossref] [PubMed]
  15. R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J. G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
    [Crossref] [PubMed]
  16. J. Zou, Y. Yu, and X. Zhang, “Two-dimensional grating coupler with a low polarization dependent loss of 0.25 dB covering the C-band,” Opt. Lett. 41(18), 4206–4209 (2016).
    [Crossref] [PubMed]
  17. Y. Sobu, S.-H. Jeong, Y. Tanaka, and K. Morito, “300-mm ArF-immersion lithographytechnology based Si-wire grating couplers with high coupling efficiency and low crosstalk,” in OptoElectronics and Communications Conference (OECC) held jointly with 2016 International Conference on Photonics in Switching (PS), 2016 21st (2016), pp. 1–3.
  18. J. Zou, Y. Yu, and X. Zhang, “Single step etched two dimensional grating coupler based on the SOI platform,” Opt. Express 23(25), 32490–32495 (2015).
    [Crossref] [PubMed]
  19. Y. Wang, W. Shi, X. Wang, Z. Lu, M. Caverley, R. Bojko, L. Chrostowski, and N. A. F. Jaeger, “Design of broadband subwavelength grating couplers with low back reflection,” Opt. Lett. 40(20), 4647–4650 (2015).
    [Crossref] [PubMed]
  20. Y. Wang, H. Yun, Z. Lu, N. A. F. Jaeger, and L. Chrostowski, “State-of-the-art sub-wavelength grating couplers for silicon-on-insulator platform,” in 2016 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE) (2016), pp. 1–4.
    [Crossref]
  21. H. Li, B. Cui, Y. Liu, H. Liu, Z. Zhang, C. Zhang, C. Tang, and E. Li, “Investigation of the chip to photodetector coupler with subwavelength grating on SOI,” Opt. Laser Technol. 76, 79–84 (2016).
    [Crossref]
  22. F. Qi, Q. Ma, Y. Wang, and W. Zheng, “Large-aperture subwavelength grating couplers,” Appl. Opt. 55(11), 2960–2966 (2016).
    [Crossref] [PubMed]
  23. D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, J. Lapointe, S. Wang, S. Janz, R. Halir, A. Ortega-Moñux, and M. Dado, “High-efficiency fully etched fiber-chip grating couplers with subwavelength structures for datacom and telecom applications,” in Proc. SPIE 9516. Integrated Optics: Physics and Simulations II, SPIE Proceedings (SPIE, 2015), 95160I.
  24. X. Chen and H. K. Tsang, “Nanoholes grating couplers for coupling between silicon-on-insulator waveguides and optical fibers,” IEEE Photonics J. 1(3), 184–190 (2009).
    [Crossref]
  25. Y. Wang, L. Xu, A. Kumar, D. Patel, Z. Xing, R. Li, M. G. Saber, Y. D’Mello, E. El-Fiky, and D. V. Plant, “Broadband sub-wavelength grating coupler for O-band application,” in Group IV Photonics (GFP), 2017 IEEE 14th International Conference on (2017), pp. 129–130.
    [Crossref]
  26. D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
    [Crossref] [PubMed]
  27. 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]
  28. L. Liu, M. Pu, K. Yvind, and J. M. Hvam, “High-efficiency, large-bandwidth silicon-on-insulator grating coupler based on a fully-etched photonic crystal structure,” Appl. Phys. Lett. 96(5), 051126 (2010).
    [Crossref]
  29. Y. Ding, C. Peucheret, H. Ou, and K. Yvind, “Fully etched apodized grating coupler on the SOI platform with -0.58 dB coupling efficiency,” Opt. Lett. 39(18), 5348–5350 (2014).
    [Crossref] [PubMed]
  30. A. Mizutani, Y. Eto, and H. Kikuta, “A grating coupler with a trapezoidal hole array for perfectly vertical light coupling between optical fibers and waveguides,” Appl. Phys. Express 10(12), 122501 (2017).
    [Crossref]
  31. R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
    [Crossref] [PubMed]
  32. K. Debnath, H. Arimoto, M. K. Husain, A. Prasmusinto, A. Al-Attili, R. Petra, H. M. H. Chong, G. T. Reed, and S. Saito, “Low-loss silicon waveguides and grating couplers fabricated using anisotropic wet etching technique,” Front. Mater. 3, 10 (2016).
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2017 (1)

A. Mizutani, Y. Eto, and H. Kikuta, “A grating coupler with a trapezoidal hole array for perfectly vertical light coupling between optical fibers and waveguides,” Appl. Phys. Express 10(12), 122501 (2017).
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2016 (8)

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

K. Debnath, H. Arimoto, M. K. Husain, A. Prasmusinto, A. Al-Attili, R. Petra, H. M. H. Chong, G. T. Reed, and S. Saito, “Low-loss silicon waveguides and grating couplers fabricated using anisotropic wet etching technique,” Front. Mater. 3, 10 (2016).

C. J. Oton, “Long-working-distance grating coupler for integrated optical devices,” IEEE Photonics J. 8(1), 1–8 (2016).
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K. Yoo and J.-H. Lee, “Design of a high-efficiency fiber-to-chip coupler with reflectors,” IEIE SPC 5(2), 123–128 (2016).
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M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016).
[Crossref] [PubMed]

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

H. Li, B. Cui, Y. Liu, H. Liu, Z. Zhang, C. Zhang, C. Tang, and E. Li, “Investigation of the chip to photodetector coupler with subwavelength grating on SOI,” Opt. Laser Technol. 76, 79–84 (2016).
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F. Qi, Q. Ma, Y. Wang, and W. Zheng, “Large-aperture subwavelength grating couplers,” Appl. Opt. 55(11), 2960–2966 (2016).
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2015 (4)

2014 (4)

R. Halir, A. Ortega-Moñux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Sel. Top. Quantum Electron. 20(4), 279–291 (2014).
[Crossref]

D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III–V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 369–379 (2014).
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Y. Ding, C. Peucheret, H. Ou, and K. Yvind, “Fully etched apodized grating coupler on the SOI platform with -0.58 dB coupling efficiency,” Opt. Lett. 39(18), 5348–5350 (2014).
[Crossref] [PubMed]

2013 (4)

2012 (6)

K. Qin, D. Gao, C. Bao, Z. Zhao, X. Zhou, T. Lu, and L. Chen, “High efficiency and broadband two-dimensional blazed grating coupler with fully etched triangular holes,” J. Lightwave Technol. 30(14), 2363–2366 (2012).
[Crossref]

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]

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]

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, “Apodized focusing subwavelength grating couplers for suspended membrane waveguides,” Appl. Phys. Lett. 101(10), 101104 (2012).
[Crossref]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

M. Tokushima, A. Kamei, and T. Horikawa, “Dual-tapered 10-µm-spot-size converter with double core for coupling polarization-independent silicon Rib waveguides to single-mode optical fibers,” Appl. Phys. Express 5(2), 022202 (2012).
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2011 (2)

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. de Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

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

2010 (2)

L. Liu, M. Pu, K. Yvind, and J. M. Hvam, “High-efficiency, large-bandwidth silicon-on-insulator grating coupler based on a fully-etched photonic crystal structure,” Appl. Phys. Lett. 96(5), 051126 (2010).
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R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

2009 (2)

R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J. G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
[Crossref] [PubMed]

X. Chen and H. K. Tsang, “Nanoholes grating couplers for coupling between silicon-on-insulator waveguides and optical fibers,” IEEE Photonics J. 1(3), 184–190 (2009).
[Crossref]

2007 (1)

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]

2006 (1)

D. Taillaert, F. van Laere, M. Ayre, W. Bogaerts, D. van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

2003 (3)

1998 (1)

1956 (1)

S. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Absil, P.

B. Snyder, G. Lepage, S. Balakrishnan, P. de Heyn, P. Verheyen, P. Absil, and J. van Campenhout, “Ultra-broadband, polarization-insensitive SMF-28 fiber edge couplers for silicon photonics,” in CPMT Symposium Japan (ICSJ),2017IEEE (2017), pp. 55–58.
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Al-Attili, A.

K. Debnath, H. Arimoto, M. K. Husain, A. Prasmusinto, A. Al-Attili, R. Petra, H. M. H. Chong, G. T. Reed, and S. Saito, “Low-loss silicon waveguides and grating couplers fabricated using anisotropic wet etching technique,” Front. Mater. 3, 10 (2016).

Almeida, V. R.

Alonso-Ramos, C.

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

R. Halir, A. Ortega-Moñux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Sel. Top. Quantum Electron. 20(4), 279–291 (2014).
[Crossref]

Arimoto, H.

K. Debnath, H. Arimoto, M. K. Husain, A. Prasmusinto, A. Al-Attili, R. Petra, H. M. H. Chong, G. T. Reed, and S. Saito, “Low-loss silicon waveguides and grating couplers fabricated using anisotropic wet etching technique,” Front. Mater. 3, 10 (2016).

Ayre, M.

D. Taillaert, F. van Laere, M. Ayre, W. Bogaerts, D. van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Baets, R.

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]

D. Taillaert, F. van Laere, M. Ayre, W. Bogaerts, D. van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

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

Balakrishnan, S.

B. Snyder, G. Lepage, S. Balakrishnan, P. de Heyn, P. Verheyen, P. Absil, and J. van Campenhout, “Ultra-broadband, polarization-insensitive SMF-28 fiber edge couplers for silicon photonics,” in CPMT Symposium Japan (ICSJ),2017IEEE (2017), pp. 55–58.
[Crossref]

Bao, C.

Bedard, D.

Benedikovic, D.

Bienstman, P.

D. Taillaert, F. van Laere, M. Ayre, W. Bogaerts, D. van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Bock, P. J.

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Bogaerts, W.

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]

D. Taillaert, F. van Laere, M. Ayre, W. Bogaerts, D. van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Bojko, R.

Borel, P. I.

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

Caverley, M.

Cheben, P.

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016).
[Crossref] [PubMed]

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

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J. G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
[Crossref] [PubMed]

Chen, L.

Chen, R. T.

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]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Chen, X.

D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

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]

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]

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, “Apodized focusing subwavelength grating couplers for suspended membrane waveguides,” Appl. Phys. Lett. 101(10), 101104 (2012).
[Crossref]

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

X. Chen and H. K. Tsang, “Nanoholes grating couplers for coupling between silicon-on-insulator waveguides and optical fibers,” IEEE Photonics J. 1(3), 184–190 (2009).
[Crossref]

Cheng, Z.

Chong, H.

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

Chong, H. M. H.

K. Debnath, H. Arimoto, M. K. Husain, A. Prasmusinto, A. Al-Attili, R. Petra, H. M. H. Chong, G. T. Reed, and S. Saito, “Low-loss silicon waveguides and grating couplers fabricated using anisotropic wet etching technique,” Front. Mater. 3, 10 (2016).

Chrostowski, L.

Y. Wang, W. Shi, X. Wang, Z. Lu, M. Caverley, R. Bojko, L. Chrostowski, and N. A. F. Jaeger, “Design of broadband subwavelength grating couplers with low back reflection,” Opt. Lett. 40(20), 4647–4650 (2015).
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Y. Wang, H. Yun, Z. Lu, N. A. F. Jaeger, and L. Chrostowski, “State-of-the-art sub-wavelength grating couplers for silicon-on-insulator platform,” in 2016 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE) (2016), pp. 1–4.
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Claes, T.

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]

Covey, J.

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]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Cui, B.

H. Li, B. Cui, Y. Liu, H. Liu, Z. Zhang, C. Zhang, C. Tang, and E. Li, “Investigation of the chip to photodetector coupler with subwavelength grating on SOI,” Opt. Laser Technol. 76, 79–84 (2016).
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de Dobbelaere, P.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. de Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
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B. Snyder, G. Lepage, S. Balakrishnan, P. de Heyn, P. Verheyen, P. Absil, and J. van Campenhout, “Ultra-broadband, polarization-insensitive SMF-28 fiber edge couplers for silicon photonics,” in CPMT Symposium Japan (ICSJ),2017IEEE (2017), pp. 55–58.
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Densmore, A.

Ding, Y.

Eto, Y.

A. Mizutani, Y. Eto, and H. Kikuta, “A grating coupler with a trapezoidal hole array for perfectly vertical light coupling between optical fibers and waveguides,” Appl. Phys. Express 10(12), 122501 (2017).
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Frandsen, L. H.

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

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A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. de Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
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M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016).
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D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
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D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref] [PubMed]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

R. Halir, A. Ortega-Moñux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Sel. Top. Quantum Electron. 20(4), 279–291 (2014).
[Crossref]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J. G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
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W. Zhang, W. Zhang, F. Yang, and Z. He, “Polarization independent fiber-to-waveguide coupling by hexagon dots/holes grating,” in Asia Communications and Photonics Conference (2017), Su1D‐6.
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M. Tokushima, A. Kamei, and T. Horikawa, “Dual-tapered 10-µm-spot-size converter with double core for coupling polarization-independent silicon Rib waveguides to single-mode optical fibers,” Appl. Phys. Express 5(2), 022202 (2012).
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Hosseini, A.

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).
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X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
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Hugonin, J.-P.

Husain, M. K.

K. Debnath, H. Arimoto, M. K. Husain, A. Prasmusinto, A. Al-Attili, R. Petra, H. M. H. Chong, G. T. Reed, and S. Saito, “Low-loss silicon waveguides and grating couplers fabricated using anisotropic wet etching technique,” Front. Mater. 3, 10 (2016).

Hvam, J. M.

L. Liu, M. Pu, K. Yvind, and J. M. Hvam, “High-efficiency, large-bandwidth silicon-on-insulator grating coupler based on a fully-etched photonic crystal structure,” Appl. Phys. Lett. 96(5), 051126 (2010).
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Jaeger, N. A. F.

Y. Wang, W. Shi, X. Wang, Z. Lu, M. Caverley, R. Bojko, L. Chrostowski, and N. A. F. Jaeger, “Design of broadband subwavelength grating couplers with low back reflection,” Opt. Lett. 40(20), 4647–4650 (2015).
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Y. Wang, H. Yun, Z. Lu, N. A. F. Jaeger, and L. Chrostowski, “State-of-the-art sub-wavelength grating couplers for silicon-on-insulator platform,” in 2016 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE) (2016), pp. 1–4.
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D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016).
[Crossref] [PubMed]

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

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

R. Halir, A. Ortega-Moñux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Sel. Top. Quantum Electron. 20(4), 279–291 (2014).
[Crossref]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J. G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
[Crossref] [PubMed]

Kamei, A.

M. Tokushima, A. Kamei, and T. Horikawa, “Dual-tapered 10-µm-spot-size converter with double core for coupling polarization-independent silicon Rib waveguides to single-mode optical fibers,” Appl. Phys. Express 5(2), 022202 (2012).
[Crossref]

Keyvaninia, S.

D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

Kikuta, H.

A. Mizutani, Y. Eto, and H. Kikuta, “A grating coupler with a trapezoidal hole array for perfectly vertical light coupling between optical fibers and waveguides,” Appl. Phys. Express 10(12), 122501 (2017).
[Crossref]

Kwong, D.

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]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Lalanne, P.

Lamontagne, B.

Lapointe, J.

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
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D. Benedikovic, P. Cheben, J. H. Schmid, D.-X. Xu, B. Lamontagne, S. Wang, J. Lapointe, R. Halir, A. Ortega-Moñux, S. Janz, and M. Dado, “Subwavelength index engineered surface grating coupler with sub-decibel efficiency for 220-nm silicon-on-insulator waveguides,” Opt. Express 23(17), 22628–22635 (2015).
[Crossref] [PubMed]

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

R. Halir, A. Ortega-Moñux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Sel. Top. Quantum Electron. 20(4), 279–291 (2014).
[Crossref]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
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K. Yoo and J.-H. Lee, “Design of a high-efficiency fiber-to-chip coupler with reflectors,” IEIE SPC 5(2), 123–128 (2016).
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B. Snyder, G. Lepage, S. Balakrishnan, P. de Heyn, P. Verheyen, P. Absil, and J. van Campenhout, “Ultra-broadband, polarization-insensitive SMF-28 fiber edge couplers for silicon photonics,” in CPMT Symposium Japan (ICSJ),2017IEEE (2017), pp. 55–58.
[Crossref]

Li, E.

H. Li, B. Cui, Y. Liu, H. Liu, Z. Zhang, C. Zhang, C. Tang, and E. Li, “Investigation of the chip to photodetector coupler with subwavelength grating on SOI,” Opt. Laser Technol. 76, 79–84 (2016).
[Crossref]

Li, H.

H. Li, B. Cui, Y. Liu, H. Liu, Z. Zhang, C. Zhang, C. Tang, and E. Li, “Investigation of the chip to photodetector coupler with subwavelength grating on SOI,” Opt. Laser Technol. 76, 79–84 (2016).
[Crossref]

Liow, T.-Y.

Lipson, M.

Liu, H.

H. Li, B. Cui, Y. Liu, H. Liu, Z. Zhang, C. Zhang, C. Tang, and E. Li, “Investigation of the chip to photodetector coupler with subwavelength grating on SOI,” Opt. Laser Technol. 76, 79–84 (2016).
[Crossref]

Liu, L.

L. Liu, M. Pu, K. Yvind, and J. M. Hvam, “High-efficiency, large-bandwidth silicon-on-insulator grating coupler based on a fully-etched photonic crystal structure,” Appl. Phys. Lett. 96(5), 051126 (2010).
[Crossref]

Liu, Y.

H. Li, B. Cui, Y. Liu, H. Liu, Z. Zhang, C. Zhang, C. Tang, and E. Li, “Investigation of the chip to photodetector coupler with subwavelength grating on SOI,” Opt. Laser Technol. 76, 79–84 (2016).
[Crossref]

Lu, T.

Lu, Z.

Y. Wang, W. Shi, X. Wang, Z. Lu, M. Caverley, R. Bojko, L. Chrostowski, and N. A. F. Jaeger, “Design of broadband subwavelength grating couplers with low back reflection,” Opt. Lett. 40(20), 4647–4650 (2015).
[Crossref] [PubMed]

Y. Wang, H. Yun, Z. Lu, N. A. F. Jaeger, and L. Chrostowski, “State-of-the-art sub-wavelength grating couplers for silicon-on-insulator platform,” in 2016 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE) (2016), pp. 1–4.
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Ma, Q.

Ma, R.

Marzban, B.

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III–V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 369–379 (2014).
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Mashanovich, G. Z.

D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
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A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. de Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
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Mekis, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. de Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
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S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III–V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 369–379 (2014).
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S. Romero-García, F. Merget, F. Zhong, H. Finkelstein, and J. Witzens, “Silicon nitride CMOS-compatible platform for integrated photonics applications at visible wavelengths,” Opt. Express 21(12), 14036–14046 (2013).
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Mizutani, A.

A. Mizutani, Y. Eto, and H. Kikuta, “A grating coupler with a trapezoidal hole array for perfectly vertical light coupling between optical fibers and waveguides,” Appl. Phys. Express 10(12), 122501 (2017).
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Molina-Fernández, I.

Molina-Fernández, Í.

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
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R. Halir, A. Ortega-Moñux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Sel. Top. Quantum Electron. 20(4), 279–291 (2014).
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Narasimha, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. de Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
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D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
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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).
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M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016).
[Crossref] [PubMed]

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

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

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

R. Halir, A. Ortega-Moñux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Sel. Top. Quantum Electron. 20(4), 279–291 (2014).
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Peucheret, C.

Pinguet, T.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. de Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
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Prasmusinto, A.

K. Debnath, H. Arimoto, M. K. Husain, A. Prasmusinto, A. Al-Attili, R. Petra, H. M. H. Chong, G. T. Reed, and S. Saito, “Low-loss silicon waveguides and grating couplers fabricated using anisotropic wet etching technique,” Front. Mater. 3, 10 (2016).

Pu, M.

L. Liu, M. Pu, K. Yvind, and J. M. Hvam, “High-efficiency, large-bandwidth silicon-on-insulator grating coupler based on a fully-etched photonic crystal structure,” Appl. Phys. Lett. 96(5), 051126 (2010).
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Qin, K.

Reed, G. T.

K. Debnath, H. Arimoto, M. K. Husain, A. Prasmusinto, A. Al-Attili, R. Petra, H. M. H. Chong, G. T. Reed, and S. Saito, “Low-loss silicon waveguides and grating couplers fabricated using anisotropic wet etching technique,” Front. Mater. 3, 10 (2016).

D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
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Romero-García, S.

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III–V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 369–379 (2014).
[Crossref]

S. Romero-García, F. Merget, F. Zhong, H. Finkelstein, and J. Witzens, “Silicon nitride CMOS-compatible platform for integrated photonics applications at visible wavelengths,” Opt. Express 21(12), 14036–14046 (2013).
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Sahni, S.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. de Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
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Saito, S.

K. Debnath, H. Arimoto, M. K. Husain, A. Prasmusinto, A. Al-Attili, R. Petra, H. M. H. Chong, G. T. Reed, and S. Saito, “Low-loss silicon waveguides and grating couplers fabricated using anisotropic wet etching technique,” Front. Mater. 3, 10 (2016).

Scheerlinck, S.

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]

Schmid, J. H.

M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016).
[Crossref] [PubMed]

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

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

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

R. Halir, A. Ortega-Moñux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Sel. Top. Quantum Electron. 20(4), 279–291 (2014).
[Crossref]

D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

Schrauwen, J.

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]

Selvaraja, S. K.

D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

Shen, B.

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III–V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 369–379 (2014).
[Crossref]

Shi, W.

Shum, P.

Snyder, B.

B. Snyder, G. Lepage, S. Balakrishnan, P. de Heyn, P. Verheyen, P. Absil, and J. van Campenhout, “Ultra-broadband, polarization-insensitive SMF-28 fiber edge couplers for silicon photonics,” in CPMT Symposium Japan (ICSJ),2017IEEE (2017), pp. 55–58.
[Crossref]

Subbaraman, H.

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]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Taillaert, D.

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]

D. Taillaert, F. van Laere, M. Ayre, W. Bogaerts, D. van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

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

Tang, C.

H. Li, B. Cui, Y. Liu, H. Liu, Z. Zhang, C. Zhang, C. Tang, and E. Li, “Investigation of the chip to photodetector coupler with subwavelength grating on SOI,” Opt. Laser Technol. 76, 79–84 (2016).
[Crossref]

Thomson, D. J.

D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

Tokushima, M.

M. Tokushima, A. Kamei, and T. Horikawa, “Dual-tapered 10-µm-spot-size converter with double core for coupling polarization-independent silicon Rib waveguides to single-mode optical fibers,” Appl. Phys. Express 5(2), 022202 (2012).
[Crossref]

Tsang, H. K.

van Campenhout, J.

B. Snyder, G. Lepage, S. Balakrishnan, P. de Heyn, P. Verheyen, P. Absil, and J. van Campenhout, “Ultra-broadband, polarization-insensitive SMF-28 fiber edge couplers for silicon photonics,” in CPMT Symposium Japan (ICSJ),2017IEEE (2017), pp. 55–58.
[Crossref]

van Laere, F.

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]

D. Taillaert, F. van Laere, M. Ayre, W. Bogaerts, D. van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

van Thourhout, D.

D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

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]

D. Taillaert, F. van Laere, M. Ayre, W. Bogaerts, D. van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Vašinek, V.

Verheyen, P.

B. Snyder, G. Lepage, S. Balakrishnan, P. de Heyn, P. Verheyen, P. Absil, and J. van Campenhout, “Ultra-broadband, polarization-insensitive SMF-28 fiber edge couplers for silicon photonics,” in CPMT Symposium Japan (ICSJ),2017IEEE (2017), pp. 55–58.
[Crossref]

Vivien, L.

Vlasov, Y.

Wang, S.

Wang, X.

Wang, Y.

Wangüemert-Pérez, G.

Wangüemert-Pérez, J. G.

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

R. Halir, A. Ortega-Moñux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Sel. Top. Quantum Electron. 20(4), 279–291 (2014).
[Crossref]

R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J. G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
[Crossref] [PubMed]

Witzens, J.

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III–V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 369–379 (2014).
[Crossref]

S. Romero-García, F. Merget, F. Zhong, H. Finkelstein, and J. Witzens, “Silicon nitride CMOS-compatible platform for integrated photonics applications at visible wavelengths,” Opt. Express 21(12), 14036–14046 (2013).
[Crossref] [PubMed]

Wong, C. Y.

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, “Apodized focusing subwavelength grating couplers for suspended membrane waveguides,” Appl. Phys. Lett. 101(10), 101104 (2012).
[Crossref]

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]

Xiao, Z.

Xu, D.-X.

M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016).
[Crossref] [PubMed]

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

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

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

R. Halir, A. Ortega-Moñux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Sel. Top. Quantum Electron. 20(4), 279–291 (2014).
[Crossref]

D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J. G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
[Crossref] [PubMed]

Xu, K.

Xu, X.

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]

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Yang, F.

W. Zhang, W. Zhang, F. Yang, and Z. He, “Polarization independent fiber-to-waveguide coupling by hexagon dots/holes grating,” in Asia Communications and Photonics Conference (2017), Su1D‐6.
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Ye, W. N.

Yoo, K.

K. Yoo and J.-H. Lee, “Design of a high-efficiency fiber-to-chip coupler with reflectors,” IEIE SPC 5(2), 123–128 (2016).
[Crossref]

Yu, Y.

Yun, H.

Y. Wang, H. Yun, Z. Lu, N. A. F. Jaeger, and L. Chrostowski, “State-of-the-art sub-wavelength grating couplers for silicon-on-insulator platform,” in 2016 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE) (2016), pp. 1–4.
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Yvind, K.

Y. Ding, C. Peucheret, H. Ou, and K. Yvind, “Fully etched apodized grating coupler on the SOI platform with -0.58 dB coupling efficiency,” Opt. Lett. 39(18), 5348–5350 (2014).
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L. Liu, M. Pu, K. Yvind, and J. M. Hvam, “High-efficiency, large-bandwidth silicon-on-insulator grating coupler based on a fully-etched photonic crystal structure,” Appl. Phys. Lett. 96(5), 051126 (2010).
[Crossref]

Zhang, C.

H. Li, B. Cui, Y. Liu, H. Liu, Z. Zhang, C. Zhang, C. Tang, and E. Li, “Investigation of the chip to photodetector coupler with subwavelength grating on SOI,” Opt. Laser Technol. 76, 79–84 (2016).
[Crossref]

Zhang, J.

Zhang, W.

W. Zhang, W. Zhang, F. Yang, and Z. He, “Polarization independent fiber-to-waveguide coupling by hexagon dots/holes grating,” in Asia Communications and Photonics Conference (2017), Su1D‐6.
[Crossref]

W. Zhang, W. Zhang, F. Yang, and Z. He, “Polarization independent fiber-to-waveguide coupling by hexagon dots/holes grating,” in Asia Communications and Photonics Conference (2017), Su1D‐6.
[Crossref]

Zhang, X.

Zhang, Z.

H. Li, B. Cui, Y. Liu, H. Liu, Z. Zhang, C. Zhang, C. Tang, and E. Li, “Investigation of the chip to photodetector coupler with subwavelength grating on SOI,” Opt. Laser Technol. 76, 79–84 (2016).
[Crossref]

Zhao, Z.

Zheng, W.

Zhong, F.

Zhou, X.

Zou, J.

Appl. Opt. (1)

Appl. Phys. Express (2)

A. Mizutani, Y. Eto, and H. Kikuta, “A grating coupler with a trapezoidal hole array for perfectly vertical light coupling between optical fibers and waveguides,” Appl. Phys. Express 10(12), 122501 (2017).
[Crossref]

M. Tokushima, A. Kamei, and T. Horikawa, “Dual-tapered 10-µm-spot-size converter with double core for coupling polarization-independent silicon Rib waveguides to single-mode optical fibers,” Appl. Phys. Express 5(2), 022202 (2012).
[Crossref]

Appl. Phys. Lett. (3)

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

L. Liu, M. Pu, K. Yvind, and J. M. Hvam, “High-efficiency, large-bandwidth silicon-on-insulator grating coupler based on a fully-etched photonic crystal structure,” Appl. Phys. Lett. 96(5), 051126 (2010).
[Crossref]

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, “Apodized focusing subwavelength grating couplers for suspended membrane waveguides,” Appl. Phys. Lett. 101(10), 101104 (2012).
[Crossref]

Front. Mater. (1)

K. Debnath, H. Arimoto, M. K. Husain, A. Prasmusinto, A. Al-Attili, R. Petra, H. M. H. Chong, G. T. Reed, and S. Saito, “Low-loss silicon waveguides and grating couplers fabricated using anisotropic wet etching technique,” Front. Mater. 3, 10 (2016).

IEEE J. Sel. Top. Quantum Electron. (4)

D.-X. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. van Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform—have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III–V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 369–379 (2014).
[Crossref]

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. de Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

R. Halir, A. Ortega-Moñux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Sel. Top. Quantum Electron. 20(4), 279–291 (2014).
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IEEE Photonics J. (2)

C. J. Oton, “Long-working-distance grating coupler for integrated optical devices,” IEEE Photonics J. 8(1), 1–8 (2016).
[Crossref]

X. Chen and H. K. Tsang, “Nanoholes grating couplers for coupling between silicon-on-insulator waveguides and optical fibers,” IEEE Photonics J. 1(3), 184–190 (2009).
[Crossref]

IEEE Photonics Technol. Lett. (2)

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

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]

IEIE SPC (1)

K. Yoo and J.-H. Lee, “Design of a high-efficiency fiber-to-chip coupler with reflectors,” IEIE SPC 5(2), 123–128 (2016).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

D. Taillaert, F. van Laere, M. Ayre, W. Bogaerts, D. van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Laser Photonics Rev. (1)

R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, Í. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures. A review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Opt. Express (7)

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]

S. Romero-García, F. Merget, F. Zhong, H. Finkelstein, and J. Witzens, “Silicon nitride CMOS-compatible platform for integrated photonics applications at visible wavelengths,” Opt. Express 21(12), 14036–14046 (2013).
[Crossref] [PubMed]

D. Benedikovic, C. Alonso-Ramos, P. Cheben, J. H. Schmid, S. Wang, R. Halir, A. Ortega-Moñux, D.-X. Xu, L. Vivien, J. Lapointe, S. Janz, and M. Dado, “Single-etch subwavelength engineered fiber-chip grating couplers for 1.3 µm datacom wavelength band,” Opt. Express 24(12), 12893–12904 (2016).
[Crossref] [PubMed]

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

S. McNab, N. Moll, and Y. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11(22), 2927–2939 (2003).
[Crossref] [PubMed]

M. Papes, P. Cheben, D. Benedikovic, J. H. Schmid, J. Pond, R. Halir, A. Ortega-Moñux, G. Wangüemert-Pérez, W. N. Ye, D.-X. Xu, S. Janz, M. Dado, and V. Vašinek, “Fiber-chip edge coupler with large mode size for silicon photonic wire waveguides,” Opt. Express 24(5), 5026–5038 (2016).
[Crossref] [PubMed]

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

Opt. Laser Technol. (1)

H. Li, B. Cui, Y. Liu, H. Liu, Z. Zhang, C. Zhang, C. Tang, and E. Li, “Investigation of the chip to photodetector coupler with subwavelength grating on SOI,” Opt. Laser Technol. 76, 79–84 (2016).
[Crossref]

Opt. Lett. (11)

R. Halir, P. Cheben, S. Janz, D.-X. Xu, I. Molina-Fernández, and J. G. Wangüemert-Pérez, “Waveguide grating coupler with subwavelength microstructures,” Opt. Lett. 34(9), 1408–1410 (2009).
[Crossref] [PubMed]

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Figures (12)

Fig. 1
Fig. 1 (a) Comparison of simulation and measurement results of the lateral alignment tolerances of a grating coupler with an SOI thickness of 220 nm and a BOX thickness of 1 µm. The normalized coupling efficiency is shown as function of the lateral position of the fiber. The smooth curves are simulation results. The vertical distance between fiber and grating is approximately 10 µm. −0.5 and −1 dB contours are indicated on the figure. From [42] © 2006 The Japan Society of Applied Physics. (b) The absolute coupling efficiency as a function of the lateral position of the fiber for a grating coupler with an SOI thickness of 250 nm and a BOX thickness of 3 µm. From [43] © 2011 IEEE. The wavelength is 1550 nm and is TE-polarized in both references.
Fig. 2
Fig. 2 Schematic drawing of the SWG high positional freedom grating coupler. The input source is a 24 µm-long, 1550 nm, TE-polarized planewave tilted 10° from vertical (E-field profile shown as black line). The grating coupler was first apodized 2-Dimensionally in the x-z plane, with neq, i as 2D placeholders for the lower index etched sections of the SWG. Λy, ly, Si and ly, SiO2 were later determined by full 3D FDTD that did not use a periodic boundary condition simulation box [15,21,23,26,30]. Adapted from [49]
Fig. 3
Fig. 3 neq, Equivalent Refractive Index for Λy = 600 nm for 1550 nm, TE-polarized light on a 220 nm SOI substrate, according to 0th order EMT (red dotted), 2nd order EMT (red line) and full 3D FDTD (black crosses).
Fig. 4
Fig. 4 Comparison of different adjustments of the diffracting elements in a curved SWG grating coupler. (a) The whole circular HPF design with a highlight of the relevant section (b) Diffraction elements neither rotated nor translated. Note Λy = 656 nm. (c) Diffraction elements rotated but not translated, as in . Note Λy = 653 nm. (d) Diffraction elements rotated and translated. Note Λy ≈600 nm. (e) Diffraction elements translated but not rotated. (f) Diffraction elements skewed but not translated, similar to [37,38]. (g) Diffraction elements skewed and translated. (h) Diffraction elements radially aligned with different Λy’s, similar to [54].
Fig. 5
Fig. 5 Scanning Electron Micrograph (SEM) images of the Planewave High Positional Freedom (HPF) grating coupler just after full silicon etch for (a) Rectangular, (b) Rectangular (close up), (c) Circular, (d) Elliptical (close up) lateral layouts.
Fig. 6
Fig. 6 Manual measurement steps. a) POR GC pair characterised with cleaved SMF-28 for both input (right) and output (left). b) POR GC pair characterised with cleaved SMF-28 for input and an MMF for output. c) HPF GC characterised with a cleaved SMF-28 for input and an MMF for output; the optical bench is rastered in x.
Fig. 7
Fig. 7 Insertion loss of the HPF grating coupler as a function of the x-position of the SMF28 for 1550 nm TE-polarized light. The negative x-direction is towards the waveguide. The SMF28 was tilted to a nominal 14.5° and, as coupling efficiency is angle-dependent, is the likely cause of measured values exceeding the simulation. Device 4 was topologically scanned and the data is presented in Fig. 8(b).
Fig. 8
Fig. 8 Topological scans of absolute insertion loss of grating couplers with 1550 nm, TE-polarized light. The negative x-direction is towards the waveguide. Peak coupling efficiencies are located at the origins (0, 0) and are stated in the respective graphs. Contours are −1 dB apart. (a) Process of Record (POR) grating coupler, (b) Rectangular high positional freedom (HPF) grating coupler, (c) Circular HPF grating coupler with rotated, but not translated diffracting elements, (d) Elliptical HPF grating coupler with rotated, but not translated diffracting elements.
Fig. 9
Fig. 9 Rectangular HPF grating coupler bandwidth as a function of SMF28 x-position. Black lines indicate −1 dB, −2 dB and −3 dB contours. (a) Full 3D FDTD simulated bandwidth, (b) measured bandwidth, (c) subset of (b) with −1 dB (red), −2 dB (yellow) and −3 dB (green) bandwidth contours. The −1 dB and −3 dB bandwidths are ~14 nm and 29.5 nm respectively.
Fig. 10
Fig. 10 Example macro of 8 HPF SWG GC pairs used for semi-automated measurements. Grating couplers are spaced 127 µm apart and are connected by 0.22 µm-thick × 0.55 µm-wide strip waveguides with 100 µm straight waveguides. All HPF pairs were measured with the same fiber pair (channel 2) on the V-Groove assembly.
Fig. 11
Fig. 11 Sample semi-automated in-circuit testing (ICT) topological measurements of rectangular and curved grating couplers with different scattering element arrangements. (a) Rectangular. (b) Circular with ‘not rotated & not translated’ scattering elements. (c) Circular with ‘rotated & not translated’ scattering elements. (d) Circular with ‘rotated & translated’ scattering elements. (e) Elliptical with ‘not rotated & not translated’ scattering elements. (f) Elliptical with ‘rotated & translated’ scattering elements. Peak coupling efficiencies and the −1 dB areas are listed in the center of each figure. Contour lines are 1 dB apart. All measurements were done at λ = 1603 nm.
Fig. 12
Fig. 12 (a) 2D FDTD simulation of coupling efficiency at λ = 1550 nm for various fiber tilts as a function of SMF-28 x-position. (b) 2D FDTD simulation of fiber tilt angle tolerance at SMF x-Position = 15 µm.

Tables (4)

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Table 1 A comparison of recent SWG Grating Couplers

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Table 2 24 µm Planewave High Positional Freedom Grating Coupler dimensions

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Table 3 Effects of Scattering Element Orientation on HPF SWG Grating Coupler Performance (λ = 1603 nm)

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Table 4 Effects of Scattering Element Orientation on HPF SWG Grating Coupler Performance where Periods 29–36 Utilise Λy = 300 nm (λ = 1603 nm)

Equations (6)

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1 n LTE (0) = [ f y n hole 2 + 1 f y n Si 2 ] 1 2
n LTM (0) = [ n hole 2 f y + n Si 2 ( 1 f y ) ] 1 2
n LTE (2) = n LTE (0) [ 1+ π 2 3 R 2 f y 2 ( 1 f y ) 2 ( n hole 2 n Si 2 ) 2 × ( n LTM (0) n eff,TE ) 2 ( n LTE (0) n hole n Si ) 4 ] 1 2
n LTM (2) = n LTM (0) [ 1+ π 2 3 R 2 f y 2 ( 1 f y ) 2 ( n hole 2 n Si 2 n eff,TM n LTM (0) ) 2 ] 1 2
n eq =1× 10 13 l y,SiO2 5 +2× 10 10 l y,SiO2 4 2× 10 7 l y,SiO2 3 +4× 10 5 l y,SiO2 2 0.0076 l y,SiO2 +3.4713
l y,SiO2 (µm)=0.083 n eq 5 +1.1837 n eq 4 6.5508 n eq 3 +17.566 n eq 2 23.057 n eq +12.351.

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