METASYSTEMS
5.5 Planar metasurface retroreflector
In this section we show that cascaded metasurfaces, each performing a pre-defined mathematical transformation [343], provide a new optical design framework [139]
that enables new functionalities not previously demonstrated with single metasurfaces.
Specifically, we demonstrate that retroreflection can be achieved with two vertically stacked planar metasurfaces, the first performing a spatial Fourier transform and its inverse, and the second imparting a spatially varying momentum to the Fourier transform of the incident light. Using this concept, we fabricate and test a planar monolithic near-infrared retroreflector, made of two layers of silicon nano-posts, that reflects light along its incident direction with normal incidence efficiency of 78%, and a large half power FOV of 60◦. The metasurface retroreflector demonstrates the potential of cascaded metasurfaces for implementing novel high performance components and enables low-power and low-weight passive optical transmitters [344–
346].
The achievements in the field of metasurfaces open up a new paradigm in optical design, as we now can envision optical devices where light undergoes precise mathematical transformation as it propagates through multiple metasurface layers either planar of with arbitrary 2D shape. Compared to single-layer devices, multi-layer metasurfaces enable both increased performance [139] and new functionalities.
One functionality that has not previously been reported using single metasurfaces is retroreflection, defined as the ability to reflect light along its incident direction over a continuous range of incident angles. Optical retroreflectors are desirable in laser tracking [347] and for integration with planar modulators to realize mod- ulating retroreflectors. A modulating retroreflector uses power from the incident
beam to transmit data, thus enabling passive transmitters with very low power consumption. Such passive transmitters have applications in optical free space com- munication [344–346], dynamic optical tags [348], optical sensor networks [349], and remote sensing [350]. Low weight and cost, and a planar shape (which is required for integration with modulators) are desirable features in these applications, but neither conventional retroreflector designs (i.e., corner cubes and cat’s eye configurations) based on bulk optics nor novel designs [351,352] have been able to offer them. Here we present retroreflection as a spatial linear filtering that can be implemented using cascaded metasurfaces, and experimentally demonstrate an efficient and low-weight planar metasurface retroreflector which can be mass-produced using cost-effective conventional semiconductor manufacturing techniques.
a b
Metasurface I
Metasurface II Mirror 4GVTQTGƀGEVQT Gradient metasurface
pr=pi pr=−pi pr =pi+pm
Figure 5.20: Planar retroreflector concept. (a)Schematic illustration of reflec- tion by a mirror, a planar retroreflector, and a gradient metasurface. The mirror does not change the in-plane component of the momentum (pk) of incident light, while a retroreflector changes its sign, and the gradient metasurface adds a momentum (pm) to it. (b)Illustration of a planar retroreflector composed of two metasurfaces. Metasurface I performs a spatial Fourier transformation directing light with different incident angles to different spots on the metasurface II. The metasurface II operates as a gradient metasurface and adds a spatially varying momentum equal to twice that of the incident light but with the opposite sign.
Figure 5.20a illustrates reflection form a mirror, a retroreflector, and a reflective gradient metasurface. All three of these components flip the direction of the normal component of the momentum of incident light. However, the mirror does not change the in-plane component of the momentum of incident light (pi||), the retroreflector flips the direction ofpi||, and the gradient metasurface adds an in-plane momentum component (pm) to it. The in-plane momentum added by the gradient metasurface is proportional to the gradient of the local reflection phase [21], has negligible dependence on the incident angle [125], and might vary across the metasurface. The
gradient metasurface might be designed such that it reflects back light incident at a particular angle (i.e.,pm =−2pi||0), but it will reflect light incident at any other angle to a direction different from the incident one (as shown in Fig.5.20). This issue can be resolved if optical waves with different incident angles are directed to different locations on the gradient metasurface, and the gradient metasurface is designed to impart a spatially varying momentumpm(x)=−2pi||(x), wherepi||(x)is the in-plane momentum of optical waves directed to the locationxon the metasurface.
Directing optical waves with different incident angles to different locations is equivalent to taking the spatial Fourier transform of incident waves, and can be conducted using a transmissive gradient metasurface. This is schematically shown in Fig.5.20b, where metasurface I functions as a lens and focuses optical waves with different incident angles to different points on metasurface II. The combination of metasurfaces I and II operates as a retroreflector provided that the metasurface II imparts a spatially varying momentum given bypm(x)=−2pi||(x). In the paraxial regime (i.e., incident angles within a few degrees from normal) the two metasurfaces can be considered as approximations of the two curved surfaces of a cat’s eye retroreflector [121]. However, as we show here, the metasurface retroreflector can operate over a much larger range of incident angles by selecting aspheric phase profiles for the metasurfaces. As proof of principle, we considered two metasurfaces as shown in Fig.5.20b, and assumed they were patterned on two sides of a 500-µm- thick glass substrate. We optimized the phase profiles of the metasurfaces using the ray tracing technique by minimizing the wavefront error of the retroreflected light over±50◦incident angles. The retroreflector was designed for operation at the wavelength of 850 nm. The details of the optimization process and the optimized phase profiles are presented in Appendix 5.7 and in Figs. 5.A21 and 5.A22, and Table5.A8.
We used the HCTA platform [67] to realize the metasurfaces. Metasurface I was implemented using the transmissive metasurface shown schematically in Fig.5.21a.
The transmissive metasurface is composed of an array ofα-Si nano-posts resting on a fused silica substrate, arranged on a hexagonal lattice with the lattice constant of 450 nm, and covered with a layer of SU-8 polymer. The array is non-diffractive in the substrate for incident angles up to∼47◦(see Appendix 5.7). The transmittance and transmission phase of the nano-posts as a function of their diameters are shown in Fig.5.21c, showing that the phase of the transmitted light can be varied from 0 to 2πby changing the nano-post diameters while keeping the transmittance close to one.
100 150 200 250 0
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Figure 5.21: Transmissive and reflective metasurfaces composing the retrore- flector. (a)Schematic illustration of the transmissive metasurface design used to implement metasurface I. The metasurface is composed of an array ofα-Si nano-posts with different diameters that are arranged in a hexagonal lattice and covered with a layer of SU-8 polymer. (b) Similar toa, but for the reflective metasurface design used to realize metasurface II. The reflective metasurface is similar to the transmissive one except for an additional gold layer deposited over the SU-8 cladding.(c), Simulated transmittance and transmission phase as a function of the nano-post diameter for the transmissive metasurface shown in a. (d)Simulated reflectance and reflection phase as a function of the nano-post diameter for the metasurface shown inb. The nano-post diameters correspond- ing to low transmittance (inc) or reflectance (in d), which are highlighted by grey rectangles, are excluded from the designs. The nano-posts are 600 nm tall, the lattice constant is 450 nm, and the simulation wavelength is 850 nm. See Appendix 5.7 for simulation details.
Intuitively, the nano-posts can be considered as short waveguides with circular cross section that support multiple resonances with relatively low quality factors [14,67, 125]. These localized resonances lead to the high transmission of the metasurface for a wide range of nano-post diameters, and enable high fidelity implementation of metasurfaces with rapidly varying phase profiles. We note that each of these resonances has several significant terms in their multipole expansions. This is in contrast to short silicon posts (nano-disks) that typically only support two main resonances; one with a significant electric and the other with a significant magnetic dipole term. The large number of significant terms in the multipole expansion of longer nano-posts prevents a simple explanation of their operation using multipoles.
Due to the high refractive index ofα-Si, the nano-posts are weakly coupled, thus allowing the realization of any desired phase profile by spatially varying the nano-post diameters (as shown in Fig.5.21a) [67]. The metasurface II was implemented using the reflective metasurface design shown in Fig.5.21b. The reflective metasurface design is the same as the transmissive one shown in Fig.5.21aexcept for the addition of a reflective gold layer deposited on the SU-8 layer. Light incident from the substrate side passes through the nano-post layer, reflects from the gold layer, and passes through the nano-post layer again; therefore, it experiences twice the phase shift imparted by the nano-post layer. The reflectance and the reflection phase of the reflective metasurface as a function of the nano-post diameter are depicted in Fig.5.21d, showing that 4πphase shift and high reflectance are achieved by varying the nano-post diameter from 68 to 288 nm.
An array of retroreflectors was fabricated by patterning the metasurfaces I and II on opposite sides of a 500-µm-thick fused silica substrate. The schematic illustration of a single retroreflector is shown in Fig.5.22a. The diameters of the metasurface I and II are 500µm and 600µm, respectively. The metasurface I was first fabricated on one side of the substrate and was covered with a layer of SU-8. The SU-8 layer was then cured to form a rigid layer over the metasurface I and protect it during the fabrication of the metasurface II on the other side of the substrate (see Appendix 5.7 for fabrication details). An optical image of the fabricated array of retroreflectors is presented in Fig.5.22bthat shows the two metasurface layers patterned on the two sides of the substrate. A scanning electron micrograph of the nano-posts composing the metasurfaces (taken before the SU-8 cladding step) is shown as an inset in Fig.5.22b.
The retroreflectance of the fabricated planar retroreflector for unpolarized light was
1 Pm
a
800 Pm Metasurface I
Metasurface II
b
500 Pm Metasurface I
Metasurface II Glass substrate
600 Pm
Figure 5.22: Monolithic planar retroreflector made of two metasurfaces. (a) Schematic drawing of the planar retroreflector. Two metasurfaces are patterned on opposite sides of a glass substrate. (b)Optical image of an array of retrore- flectors. Each retroreflector is composed of metasurface I on the front side and metasurface II on the backside. The third metasurface seen in the photo behind metasurface II is the image of the metasurface I in the reflective gold coating of metasurface II. An SEM image of the nano-posts composing the metasurfaces is also shown. The image is taken before covering nano-posts with SU-8. See Appendix 5.7 for fabrication details.
characterized using the setup schematically shown in Fig.5.23a. The retroreflector was illuminated by unpolarized light emitted from an LED (center wavelength:
850 nm, FWHM bandwidth: ∼40 nm), and the reflected light was imaged using a camera for different rotation angles of the retroreflector (θ). We note that the retroreflector is circularly symmetric and all the rotation axes are equivalent. The measured retroreflectance profiles for θ from 0◦to 50◦ in 10◦steps are shown in Fig.5.23a(for the profiles measured at smaller steps see Fig.5.A23). The reflectance profile at normal incidence (θ = 0◦) shows the retroreflector and also areas of the sample without the metasurfaces (i.e., reflection from the backside gold layer). At largerθvalues, the two metasurfaces retroreflect while the light impinging on the areas without the metasurfaces is not reflected back along its incident direction and is not captured by the camera. The clear aperture of the retroreflector decreases asθ increases, which is partly due to the geometrical projection of the physical aperture (reduction proportional to cos(θ)) and partly due to the reduction of the overlap between the metasurface I and II (see Fig.5.A21).
The retroreflection efficiency, defined as the ratio of the power of the retroreflected beam to the power of the incident beam, was measured using the setup schematically shown in Fig.5.23b(see Appendix 5.7 for the measurement details). A polarized laser beam (center wavelength: 850 nm, FWHM bandwidth: ∼0.9 nm) was retroreflected
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Figure 5.23: Retroreflection profile and efficiency. (a)Schematic of the mea- surement setup (left), and measured reflectance of the retroreflector as a function of the illumination incident angle (right). An LED was used as the illumination (center wavelength: 850 nm, FWHM bandwidth: ∼40 nm), and the reflectance profile of the retroreflector was captured by the camera as the incident angle was varied by rotating the retroreflector.(b)Schematic of the measurement setup used for measuring retroreflection efficiency of the planar retroreflector (left), and measured efficiency as a function of incident angle (right). The efficiency values are measured for the TE and TM polarizations of the incident light. The measured data are shown by symbols and the solid lines are eye guides. See Appendix 5.7 for measurement details. BS: beamsplitter, L: lens, PC: polarization controller, FC: fiber collimator, P: polarizer, PD: photodetector. The focal lengths of lenses L1and L2are f1=5 cm and f2=20 cm, respectively.