1. Introduction

Metasurface, an ultrathin layer of judiciously designed artificial micro- and nano-structures, has shown extraordinary capabilities in manipulating electromagnetic waves [1]. These capabilities are widely explored in the form of wavefront shaping in free space, where a free-space optical mode (usually a single or multiple freely propagating plane waves) is converted to another free-space mode (e.g. an optical vortex [2], a hologram [3], a focus [4] or a deflected light beam [5]). Similarly, metasurfaces can also realize conversion between different confined optical modes, to facilitate functionalities such as asymmetric power flow [6], light focusing [7,8], mode conversion [9], signal routing [10] and fiber-to-chip coupling [11]. In these two categories of metasurfaces, the input and output can be considered as belonging to the same group of light: they are either both free-space light or both guided light. Whereas, this work targets a third category of metasurfaces, where they bridge these two groups and allow for the transition between various free-space modes and guided modes [12]. Metasurfaces in this category can leverage advantages of integrated devices (e.g. a small form factor and a high integration density) while providing optical access to free space. In particular, in the form of meta-structured waveguides, or meta-waveguides [12], they could lead to novelty solutions for emerging applications such as augmented reality projection [13,14], LiDAR (light detection and ranging) [15] and free-space optical communication [16].

Being a versatile tool for wavefront shaping, metasurfaces can transit an incident free-space light beam into a range of different guided modes, including surface plasmons on a metal film [17–19], driven surface waves on a dielectric meta-grating [20], whispering gallery modes in a microcavity [21], as well as waveguide modes in straight waveguides [22,23]. The transition can also be in the opposite direction: for example, for input as a waveguide mode on a photonic chip, the corresponding output is off chip in free space. Functionalities such as light focusing [24–27], beam deflection [28], optical vortex generation [29,30], holography [31–34] and Airy beam generation [35] have all be realized by decorating waveguides with metasurfaces.

Aiming at future applications utilizing the photonic integrated circuit platform, this work concentrates on using integrated metasurfaces to extract light from Si waveguides on an SOI (silicon-on-insulator) chip. To enable off-chip wavefront control in all the three dimensions above a waveguide, the metasurface has to be a 2D (two-dimensional) array of light scatterers, as opposed to a single line of light scatterers on top of a stand-alone waveguide [12]. To optically drive such 2D arrays, the existing solution is to use a wide waveguide [12]. However, a wide waveguide usually supports multiple eigen modes, and the integrity of the input mode is consequently vulnerable to perturbations to the driving field (see Section A of the Supplement 1 for a numerical demonstration). This solution thus requires all the light scatterers to be extremely weak in strength, which increases not only the complexity of the nanostructures but also the challenges in device design and nanofabrication. In this work, we show an alternative approach to integrate a 2D metasurface with waveguides: to use an array of single-mode waveguides. This integration has a relatively straightforward device layout and is suitable for off-chip light shaping applications that only require a limited aperture.

2. Generic device structure and the 2π phase coverage

Figure 1(a) shows schematically the generic layout of the proposed all-dielectric, waveguide-driven metasurfaces. The layout shares a key feature with the conventional metasurfaces that bridge two free-space modes: it contains a planar, subwavelength array of light scattering units. The major difference here is that, all the units now reside on top of light-feeding Si waveguides. For a conventional metasurface illuminated by a plane wave, all the light scatterers are assumed to be driven at the same strength and the same phase by the incident light, and this assumption has been a fundamental principle for metasurface design. For the layout shown in Fig. 1(a), the incident light inevitably changes its phase and strength as it propagates along the waveguides, clearly violating this design principle. Consequently, the traditional design strategies have to be modified for the integrated metasurfaces discussed here.

 

Fig. 1. Schematic of a generic design of a Si waveguide-integrated metasurface. (a) The device utilizes the widely adopted SOI (silicon-on-insulator) platform. The waveguides in the xy plane feed energy to the light scatterers, which are z-oriented Si nanopillars arranged in a planar array. (b) The smallest unit of the device is a meta-waveguide building block (MBB). It consists of a section of waveguide that is 220 nm in height, 500 nm in width, and p in length. On top of the center of the waveguide is a Si nanopillar. Its height along the z axis is 1250 nm. It has an elliptical cross section, with the dimensions ${R_x}$ and ${R_y}$ as tunable parameters. The Si substrate visible in panel (a) is not depicted here, in order to improve visualization. (c) A target output wavefront, where the phase changes continuously with position, is approximated pixel by pixel in the integrated metasurface. To simplify the design process, the waveguide length p is set to be identical or very close to ${\lambda _{eff,w}}$, the effective wavelength in the waveguide.

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A new design method can be obtained by examining an individual metasurface element shown in Fig. 1(b). The element here, named as an MBB (Meta-waveguide Building Block), consists of a light emitting Si cylinder and a section of light-feeding Si waveguide of length p. Light emitted by an MBB thus has a phase of $\theta $ that contains two parts

The numerical simulation was conducted using FDTD (finite-difference time-domain) method-based commercial software (Lumerical). The SiO₂ BOX (buried oxide) layer of the SOI (silicon-on-insulator) wafer had a thickness of 2 µm, optically isolating the waveguide from the bottom Si substrate. The refractive indices [36] of the Si and SiO₂ were set as 3.48 and 1.44, respectively, at ${\lambda _0}$ of 1550 nm. The Si waveguide was 220 nm in height and 500 nm in width, and it supported only a single TE mode. For an isolated (i.e. far away from any adjacent waveguide), bare (i.e. having no nanopillar on top) waveguide, ${\lambda _{eff,w}}$ was found to be 650.2 nm, corresponding to an effective index ${n_{eff,w}}$ of 2.384. In a metasurface-decorated waveguide array, ${\lambda _{eff,w}}$ is affected by both the nano-scatterers and inter-waveguide coupling (see Section B in the Supplement 1 for details). As discussed in more details in Sections 3 and 4, ${\lambda _{eff,w}}$ is approximately 625 nm and 630 nm in the beam deflector and the metalens, respectively.

Figure 2 shows the dependence of ${\theta _c}$, the contribution to output phase from Si cylinders, on the cylinder’s cross section. The simulation is conducted on a single waveguide surrounded by perfectly matched layers, and input light is fed into the waveguide beneath the nanopillar. All the cylinders have a uniform height of 1250 nm and an elliptical, but tunable, cross section. One of the principal axes of the ellipse is always aligned along the waveguide (i.e. the x axis in Fig. 1), with the light experiencing a right-left mirror symmetry as it propagates forward in the waveguide. This right-left mirror symmetry forbids the y-polarized incident light from generating any x-polarized output, which eliminates polarization rotation in the output and simplifies analysis. Parametric sweep is conducted by tuning the principal semi-axis dimensions ${R_x}$ and ${R_y}$ from 70 nm to 250 nm at a step of 10 nm, with the upper boundary of 250 nm constrained by the width of the waveguide. This sweep creates a library of $19 \times 19 = 361$ nanopillar geometries that is analyzed in Fig. 2.

 

Fig. 2. Output phase of nanopillars, obtained from (a) numerical simulation and (b) a numerical-analytical hybrid approach. The principal semi-axis dimensions ${R_x}$ and ${R_y}$ range from 70 nm to 250 nm at a step of 10 nm. The values in both maps are normalized against the phase of the smallest nanopillar, which has ${R_x} = {R_y} = 70\; \textrm{nm}$.

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Figure 2(a) shows the numerically simulated output phase of these 361 nanopillars, all extracted from the same location that is 2 µm above the nanopillar top. The values shown here have been normalized against the value of the smallest nanopillar (i.e. ${R_x} = {R_y} = 70\; \textrm{nm}$), a process that eliminates the contribution of ${\theta _w}$ for any value of p. As this smallest, reference nanopillar well approximates a point scatterer, the phase shown in Fig. 2(a) can be interpreted as the output phase of nanopillars ${\theta _c}$, normalized against an infinitesimally small, point scatterer.

The phase distribution shown in Fig. 2(a) consists of multiple curved bands that are roughly symmetric with respect to the diagonal line that connects the smallest (${R_x} = {R_y} = 70\; \textrm{nm}$) to the largest nanopillar (${R_x} = {R_y} = 250\; \textrm{nm}$). This symmetry suggests that ${R_x}$ and ${R_y}$ have roughly equal influence on the output phase. This conclusion, combined with the shape of the bands, further indicates that ${\theta _c}$ mostly depends on the cross-sectional area of these nanopillars. Nevertheless, ${\theta _c}$ still shows a different sensitivity to ${R_x}$ and ${R_y}$ in Fig. 2(a). This is because the input electric field beneath the nanopillar is dominantly y-polarized.

A critical feature of Fig. 2(a) is the full 2π phase coverage, which suggests the possibility of full wavefront control in such waveguide-driven metasurfaces. Regarding the origin of this phase coverage, the tall (height at 1250 m) and thin (${R_x}$ and ${R_y}$ equal 250 nm at maximum) shape of the nanopillars suggests that it comes from light propagation. To verify this assumption, a propagation phase is calculated for each nanopillar and shown in Fig. 2(b). This propagation phase is expressed as $2\; \pi \; h{/\lambda_{eff,c}}$, where h is the height of the cylinder and equals 1250 nm. Meanwhile, $\lambda _{eff,c}$ is the effective wavelength of light inside each type of cylinder, obtained in numerical simulation by assuming an infinite cylinder height. The value of $\lambda _{eff,c}$ depends on the cross-sectional size and shape of the cylinder, and reaches the smallest value of 563.8 nm in the largest nanopillar (i.e. ${R_x} = {R_y} = 250\; \textrm{nm}$). For small nanopillars (with ${R_x} \times {R_y}$ roughly below 150 × 150 nm²), no guided mode exists, and the value of $\lambda _{eff,c}$ thus takes 1550 nm in the calculation. This method is a numerical-analytical hybrid method [37], as it contains both a numerical element (in the calculation of $\lambda _{eff,c}$) and an analytical element (in the assumption of the dominance of the propagation phase). Although different in the absolute values for many nanopillars, the phase map computed using this method [Fig. 2(b)] possesses a high degree of similarity to the purely numerical results [Fig. 2(a)], in both the overall phase coverage and the dependence on planar dimensions. This similarity confirms that the 2π phase coverage in Fig. 2(a) mainly comes from the phase accumulation in light propagation, which is either mostly in free space (for small pillars) or as a guided mode (for larger pillars).

To demonstrate the light manipulation capability promised by the 2π phase coverage, we have designed and evaluated two types of functional metasurfaces, one as a beam deflector and the other a light-focusing lens. They are discussed in the following two sections separately.

3. Metasurface beam deflector as the first example device

The metasurface beam deflector discussed in this section (Fig. 3) possesses a unique light-manipulation capability: it emits light into the same direction, even if the input light reverses its direction. In other words, it has a constant absolute light deflection angle. This is in sharp contrast to a conventional grating, where it is the relative light deflection angle that stays invariant with changing the input direction. To be more specific, the absolute deflection angle is the angle between the light emission direction and a fixed coordinate, and it is defined here as the deviation from the + z direction (i.e. the vertical direction) towards the + x direction. By comparison, the relative deflection angle is with respect to the variable incident light direction.

 

Fig. 3. The first example design: a metasurface beam deflector. (a) Schematic of the meta-deflector. The simulated device contains 12 identical waveguides, with 24 nanopillars on top of each waveguide. The input light is along either the + x direction (the solid arrows) or the -x direction (the dashed arrows). (b) Output phase profile ${\theta _c}$ along a section of a waveguide, with the theoretical target (the black line) compared against the numerical output (the red dots). (c) Output electric field in an area of 20 µm × 7.5 µm at the central xz plane of the metasurface. The bottom of the area is 1.5 µm above the top of the nanopillars. The field is normalized against its peak amplitude in the map. The input light propagates in the + x direction. The direction of the main output is indicated using the black arrow. (d) The corresponding electric field in the same area, with the input light reversed in its direction. (e, f) Electromagnetic intensity distribution in the far field. The input light propagates along (e) the + x direction and (f) the -x direction.

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To reveal the contrast between the meta-deflector and a conventional grating in light emission, we first derive a generic light deflection equation that encompasses both types of devices. Here we consider an array of Si waveguides in the xy plane on top of a BOX layer, which has the same layout as shown in Fig. 3(a). All the waveguides are along the x axis, and they are evenly spaced along the y axis at a subwavelength interval. On each waveguide, a line of light scatterers is evenly spaced at a periodicity of p (it can take any subwavelength value at this stage of general analysis), which may possess a phase gradient of ${k_p}$ along the + x direction in light scattering. For light deflection in the xz plane, the deflection angle can be obtained by matching the in-plane momentum between the guided mode and the output light. The absolute deflection angle $\alpha $ is derived to be

A clear difference exists between the two terms of $1{/\lambda _{eff,w}}$ and ${k_p}/2\pi $ in Eq. (3): the former depends on the input direction while the latter does not. If all the light scatterers are identical, as in a conventional waveguide-integrated grating, we have ${k_p} = 0$. If this grating only has a single deflection order, with $n = 1$ or $n ={-} 1$, the angle $\alpha $ then switches between $\textrm{arcsin}(\lambda {_0{/_{\lambda eff,w}}{ -\lambda _0}/p} )$ and $- \textrm{arcsin}({\lambda _0{/\lambda _{eff,w}}{ -\lambda _0}/p} )$ with reversing the direction of input light. In comparison, for the beam deflector in Fig. 3, as $p{ = _\lambda{eff,w}}$ and ${k_p} \ne 0$, we can reduce Eq. (3) to

In the example metasurface shown in Fig. 3, four different MBBs are selected from the library in Fig. 2 to form a metasurface super unit cell (see Section C of the Supplement 1 for the dimensions of each nanopillar), and the super unit cell is repeated by six times along a waveguide. As mentioned in Section 2, the value of p follows that of $_\lambda{eff,w}$, and it is set as 625 nm here. Figure 3(b) shows that these 24 MBBs produce a linear phase ramp that changes by $\pi /2$ over every 625 nm along a waveguide. The whole metasurface contains 12 identical waveguides placed at a periodicity of $2p = 1250\; \textrm{nm}$ along the y axis. A value of 1250 nm rather than 625 nm is chosen here, as it can reduce inter-waveguide coupling and side leakage [38–40] and the nanopillar array still remains in the subwavelength regime. For all the 12 waveguides, the input is assumed to be uniform in phase and intensity, which can be realized in experiment by using a multi-stage binary splitter tree [41,42].

The phase ramp seen in Fig. 3(b) is intrinsic to the nanostructure design and does not change with the direction of the incident light. This feature is clearly observed in the near-field light scattering from the nanopillars [Figs. 3(c) and 3(d)], where the majority of the output propagates towards the top-right corner in both maps. Differences in the details between the two maps are mainly attributed to the shadowing effect, for which nanopillars closer to the light source experience stronger excitation. The influence of this effect appears to be more pronounced in Fig. 3(c) than in Fig. 3(d), in the form of stray output towards the top-left corner of the map. This phenomenon is further discussed at the end of Section 4.

As compared to the near-field maps of Figs. 3(c) and 3(d), the far-field distributions show even weaker dependence on incident direction [Figs. 3(e) and 3(f)]. For input towards the + x direction, the output peaks at 39.7°, with an FWHM (full width at half maximum) along the x axis at 8.5° [Fig. 3(e)]. For the -x input, the output peaks at a very similar angle of 38.0°, and the x-axis FWHM is 8.9° [Fig. 3(f)]. These two deflection angles, 39.7°and 38.0°, are very close to the theoretical value derived from Eq. (3), which is 38.3°. The very small difference in the deflection angle between the two input directions can be eliminated by slightly tuning the input wavelength (see Section D in the Supplement 1 for details). The effective aperture along the x axis, which can be derived from the FWHM, is about 12 µm, or 80% of the physical aperture. It indicates that light has decayed significantly as it reaches the end of the metasurface. The output efficiency, defined as the power ratio of the main output beam [extracted from the far fields shown in Figs. 3(e) and 3(f)] and the total input, is 11.7% and 28.7% for the + x and the -x input direction, respectively. The lower efficiency in Fig. 3(e) can be associated with the stronger stray light seen in Fig. 3(c), which in turn is attributed to a stronger shadowing effect. To make the diffraction efficiency less sensitive to input direction, a potential solution is to include the scattering efficiency of each nanopillar into element selection.

4. Metalens as the second example device

In this section, we use a metalens as the second example device (Fig. 4). Unlike the beam deflector shown in Section 3, where the phase gradient is only uniaxial, here the phase gradient is radial from the center of the nanopillar array, meaning that the nanopillars are no longer identical across waveguides. Here we consider a metalens that produces a spherical wavefront in free space, which requires a hyperbolic phase profile in the metasurface output [43]:

 

Fig. 4. The second example design: a light-focusing metalens. (a) Schematic of the device. The simulated device contains 45 × 45 nanopillars, and the input light reverses its direction (the black arrows) between adjacent waveguides. (b) The output phase profile ${\theta _c}$ of all the 2025 nanopillars. After all the nanopillars are selected and assembled here, their phases are adjusted by a constant to set the phase at the center of the map to -π. This adjustment is purely for visualization and does not affect the overall phase coverage of the map. (c) The simulated output phase of the nanopillars along the central waveguide (the red dots), compared against the analytical target phase profile (the black line). (d-f) Electromagnetic field intensity of the focus, shown in (d) the xz plane, (e) the yz plane, and (f) the xy plane. (g, h) Field intensity along (g) the x axis and (h) the y axis across the center of the focal spot, with the numerically simulated results (the solid lines) compared against the analytical results (the dashed lines).

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Figure 4(a) shows the schematic of the device. Different from the previous device of beam deflector where all the waveguides have the same input, here the input light reverses its direction between adjacent waveguides. This change provides two benefits: it improves the symmetry of the output focus, and it increases the effective aperture of the device. The second feature will be discussed in more details at the end of this section. The whole device contains 45 (the number of waveguides) × 45 (the number of nanopillars on top of each waveguide) nanopillars, distributed in a square array with a lattice constant of 630 nm along both the x and the y axes. The dimensions of 23 representative nanopillars are listed in Section C of the Supplement 1. Figure 4(b) shows the output phase of all the 2025 nanopillars in this device. The maximal phase coverage, which is from a corner to the center of the map, is $2.6\; \times \; 2\pi $. The derivation from the target phase averages at 1.9°, which is a very small value. This excellent phase match can be visualized in Fig. 4(c), which compares the simulated output of 45 nanopillars [taken along the line of $y = 0$ in Fig. 4(b)] against the analytical target of Eq. (5).

Figures 4(d), 4(e) and 4(f) show the output focus at the xz, yz and xy plane, respectively. A clear and well-defined focus is observed. The focal length, defined as the distance between the nanopillar top plane and the location with the highest field intensity, is 46.5 µm, slightly shorter than the target value of 50 µm. The FWHM of the focus is 2.41 µm, approximately $1.55\; {\lambda _0}$, along the central x axis. Meanwhile, it is 2.59 µm, approximately $1.67\; {\lambda _0}$, along the central y axis. The output efficiency, with the output power computed in a square of 7.77 µm × 7.77 µm (three times of the FWHM along the y axis) at the focal plane, is 18.2%. Several weak, isolated sidebands are observed along the x and y axis across the center of the focus, which originate from the square shape of the lens. Here, we took the side length of the lens as $l = 27.72\; \mu m$ (i.e. the distance between the centers of the outmost nanopillars along the x and y axis), and calculated the Fraunhofer diffraction pattern at the focus. The theoretical results, obtained from $sin{c^2}[{\pi \; l\; x/({f\; {\lambda_0}} )} ]$ and $sin{c^2}[{\pi \; l\; y/({f\; {\lambda_0}} )} ]$, match well with the simulated intensity in Figs. 4(g) and 4(h). This close match confirms the high quality of the light focusing; it also confirms that the effective aperture reaches the value of the physical aperture.

Before concluding this work, it is worth discussing more on the novelty of the waveguide array proposed in this work, after two example devices have been analyzed. The nanopillar selection used in both devices [Figs. 3(b) and 4(b)] is based on the assumption that the output phase of any individual nanopillar [Fig. 2(a)] is independent from its position in a metasurface. As shown in Fig. S1(b) in the Supplement 1, this assumption becomes invalid in a wide, multi-mode waveguide, because the phase of input light beneath a nanopillar is noticeably affected by the presence of other nanopillars. In this case, each nanopillar will respond not only to the input light but also to light scattered by other nanopillars, similar to the meta-atoms in some light-emitting metasurfaces [44]. Moreover, as shown in the second device, the waveguide array brings another benefit, which is the separation of input light that propagates in oppose directions. If the metalens discussed in this section is integrated with a single wide waveguide instead, sending light into the waveguide in opposite directions would create a standing wave. Although a metalens can be driven by a standing wave of freely propagating light and show interest coherent tuning [45], it remains an open question whether the integrated version of such coherently controlled metalenses also exists.

It is also worth discussing some key differences between these meta-waveguides and the most investigated, free-space metasurfaces. Although for the latter, it is a common practice to assume that all the meta-atoms are driven at the same phase and the same strength by an input, this assumption has to be treated with more caution in the meta-waveguides discussed here. By setting the length of an MBB to a single effective wavelength, we have shown that, it is possible to drive all the meta-atoms at the same phase. Nevertheless, a shadowing effect still exists, where the Si nanopillars further down a waveguide are driven at weaker strength, as seen in Section A in the Supplement 1. A clear sign of this shadowing effect is a smaller effective aperture as compared to the physical aperture, as seen in the first example device. Suppressing the scattering strength of individual meta-atoms could weaken this effect, but this approach necessitates designing more complicated meta-atoms and is beyond the scope of this proof-of-principle demonstration. As an alternative approach to partly circumvent this problem, the second example device alternates the input direction between adjacent waveguides. The effective aperture along the waveguide has doubled to ∼28 µm, as compared to the first example device, and it equals the physical aperture.

5. Conclusion

To conclude, we have proposed and numerically tested a new design approach for SOI chip-integrated metasurfaces. In this new approach, the metasurface is integrated with an array of single-mode waveguides. As these waveguides only support the fundamental TE modes, the input mode is relatively robust against perturbation induced by nano-scatterers. As a result, Si nanopillars can be placed directly on top of these waveguides to produce the 2π phase coverage required for full wavefront shaping. Two example devices have been designed and numerically characterized. The first device, a metasurface beam deflector, can deflect light at the same absolute angle (approximately 38°) at both input directions. The second device, a metalens, can focus light at 46.5 µm above the metasurface, into a focal spot approximately the same size as the ideal Fraunhofer diffraction.

The off-chip light shaping capabilities demonstrated here could be useful for devices where a relatively small planar size (e.g. below 100 µm as side length) is desirable (e.g. in neuro probes [46–48]). The waveguides and the nanostructures of these devices are all made of Si only, suggesting that they can be mass produced at low cost using standard CMOS fabrication technology [49]. Factors such as tolerance to potential pillar-waveguide misalignment and phase/power fluctuation across the input channels need be tested in future experiments. As each waveguide in the array could be addressed individually, this device configuration could be explored in the future to realize more advanced wavefront shaping and wavelength multiplexing [50] functionalities.