Chiral phase-imaging meta-sensors

2.1 Metasurface design

The metasurfaces developed in this work consist of Au rectangular nanoparticles (NPs) of different dimensions and orientations, arranged in a square lattice on a SiO₂/Au/SiO₂ stack deposited on the illumination window of a Ge photodetector (Figure 1a). The metal film prevents incident light from being transmitted directly into the underlying device active layer. As a result, photodetection can only take place through a plasmon-assisted process (Figure 1c), where light incident at a desired angle θ _p and polarization (RCP or LCP) is first converted into SPPs on the Au surface. These guided waves are then efficiently scattered into the substrate by the nearby slits [41], [42], in a process analogous to extraordinary optical transmission through sub-wavelength apertures in metal films. A similar device structure, with a one-dimensional periodic diffraction grating instead of the NP metasurface array, has been developed in our prior work focused on lensless compound-eye vision [4] and linearly polarized phase contrast imaging [6]. For phase imaging, the target detection angle θ _p should be small enough so that the resulting peak in the angular response overlaps asymmetrically with normal incidence (as in Figure 1b), leading to large variations in responsivity with illumination angle around θ = 0. The resulting devices can therefore be used to measure any deflection in the local direction of light propagation away from normal incidence, which in turn is proportional to the local transverse phase gradient of the incident light.

For the angle- and circular-polarization-selective excitation of SPPs, we rely on the combined use of the resonance phase and Pancharatnam–Berry (PB) phase of the individual meta-units, which provides a particularly effective route for chiral wavefront manipulation [30], [43], [44], [45], [46], [47], [48], [49]. The resonance phase φ _res here is associated with the excitation of localized plasmonic oscillations in the Au NPs and thus depends on the NP lateral dimensions. Despite the dipolar nature of these resonances, φ _res can be tuned over a broad range of nearly 2π through the coupling of the NP plasmonic oscillations with their mirror image in the underlying metal film [50]. The PB or geometric phase φ _PB is associated with the anisotropic optical response of the rectangular NPs and thus depends on their orientation relative to the axes of the metasurface array [51]. The combined effect of both phase contributions can be evaluated from the Jones matrix that describes scattering of the incident light by each meta-unit in the RCP/LCP basis:

Here, r _ξ and r _ψ are the amplitude reflection coefficients for linearly polarized light along the two axes of the rectangular NP, and α is the NP orientation angle relative to the sides of the square unit cell (Figure 2a). If the NPs are designed so that r ξ + r ψ ≪ r ξ − r ψ , most of the incident RCP light experiences a reversal in the direction of field rotation accompanied by a total phase shift φ t o t = arg r ξ − r ψ + 2 α . Similarly, the LCP component is scattered with the same resonance phase φ r e s = arg r ξ − r ψ but equal and opposite PB phase φ _PB = −2α. The selective detection of either state of circular polarization in the proposed PIMSs is enabled by this sign difference for the PB phase contribution.

Figure 2:

Design simulations. (a) Schematic top-view image of a meta-unit. (b) Calculated scattering efficiency 1 4 r ξ − r ψ 2 versus resonance phase φ r e s = arg r ξ − r ψ for all simulated NPs. The red circles indicate the NPs used in the devices reported in this work. (c) Total scattering phase φ _tot = φ _res + φ _PB of all the NPs in the metasurface of device R versus NP number for RCP (red) and LCP (blue) incident light. Device L features the same scattering phase profiles with the two states of circular polarization interchanged.

Specifically, in these devices, each NP is rotated relative to its preceding unit along the x direction (in the system of coordinates of Figure 2a) by a fixed angle Δα. At the same time, its resonance phase (determined by its lateral dimensions L _ξ and L _ψ) differs from that of the preceding NP by a fixed amount Δφ _res. As a result, the overall metasurface scattering phase varies linearly with NP position along the x direction with slope Δ k t o t = Δ φ r e s ± 2 Δ α / Δ x , where the plus and minus signs correspond to RCP and LCP light, respectively. Here Δx is the array lattice constant, which we set at a reasonably small value of 600 nm, well below the PIMS design wavelength λ ₀ = 1,550 nm. Under these conditions, when incident light is scattered by the metasurface, its in-plane wavevector k _‖ is shifted by the fixed amount x ̂ Δ k t o t . If the resulting wavevector k ‖ + x ̂ Δ k t o t matches that of an SPP supported by the Au film, the same SPP can be efficiently excited by the incident light.

For the detection of light with k _‖ along the x direction and angle of incidence θ _p (e.g., point A in the reciprocal-space diagram of Figure 1c), this phase matching condition becomes Δ k t o t = k 0 n S P P − sin θ p , where k ₀ = 2π/λ ₀ and n _SPP is the SPP effective index. To enforce this condition for RCP light, we select the NP dimensions and orientations such that Δφ _res and Δα satisfy

With these prescriptions, the resonance and PB phase produce equal contributions to the RCP in-plane wavevector shift Δ k t o t = Δ φ r e s + 2 Δ α / Δ x , which add up to each other to bridge the k _‖ mismatch k 0 n S P P − sin θ p between the incident light and SPPs (black arrows in Figure 1c). In contrast, under LCP illumination the resonance and PB contributions of the same metasurface become equal and opposite (due to the sign change in the latter), and therefore cancel each other to yield Δk _tot = 0. As a result, scattering of LCP light by the metasurface simply results in specular reflection without SPP excitation. Similarly, if Δα in Eq. (2) is replaced by −Δα (i.e., the NPs are rotated by the same angle as in the previous design but in the opposite direction), the metasurface will selectively couple LCP light incident at θ _p to SPPs while at the same time reflecting the RCP component.

Geometrically, the two metasurfaces just described form an enantiomer pair, as their NP distributions are the mirror images of one another without being superimposable. The detailed metasurface design is based on a library constructed via finite difference time domain (FDTD) simulations of individual NPs of different dimensions (see Supplementary material, Section S1). The resulting data set is shown in Figure 2b, where we plot 1 4 r ξ − r ψ 2 versus φ r e s = arg r ξ − r ψ at λ ₀ = 1,550 nm for all simulated values of L_ξ and L_ψ (ranging from 0 to 600 nm in steps of 10 nm). Here 1 4 r ξ − r ψ 2 is the cross-polarized scattering efficiency according to Eq. (1), and thus provides a measure of how efficiently the NP can couple circularly polarized light into SPPs. The full NP arrays were constructed from this data set according to the prescriptions of Eq. (2), with Δφ _res and Δα set to 79° and 39.5°, respectively, to produce a suitably small angle of peak detection θ _p = −2°. Each metasurface consists of 25 different NPs along the x directions, repeated periodically along y. The 25 NPs [indicated by the red circles in Figure 2b and described in more detail in Supplementary material, Section S1] were selected to produce the required values of the resonance phase φ _res while at the same time maximizing the scattering efficiency 1 4 r ξ − r ψ 2 .

For the PIMS designed for angle-sensitive detection of RCP light (labeled device R in the following), the resulting RCP and LCP scattering phase profiles φ t o t x are plotted in Figure 2c. Figure 1b shows FDTD simulation results for the complete device including the slits. Identical traces with the two states of circular polarization interchanged are obtained for its chiral twin (device L). As expected, the RCP metasurface transmission in Figure 1b exhibits a sharp peak at the target detection angle θ _p = −2°, while the LCP transmission is weaker and relatively isotropic. The shaded region in the same figure indicates the range of possible angles of incidence on the sensor array for a representative microscope configuration. Within this range, the RCP transmission varies almost linearly with angle, so that any local wavefront distortion can be measured based on the resulting change in photocurrent compared to normal-incidence illumination. The other peak observed in this trace at about 22° is associated with first-order diffraction by the NP array, whereby the incident-light wavevector is shifted by x ̂ Δ k t o t − 2 π / Δ x as discussed in more detail below. Finally, the finite background transmission and small angular fluctuations in both traces of Figure 1b are ascribed to incomplete destructive interference of the light waves scattered by all the NPs in the array (due to their finite number and different scattering efficiencies), leading to partial SPP excitation even away from resonance.

2.2 Device fabrication and characterization

Our experimental samples consist of metal-semiconductor-metal photoconductors, with the metasurface fabricated on a Ge substrate and surrounded by two metal contacts for biasing and current collection. While this configuration is particularly convenient in terms of fabrication simplicity, the same metasurfaces could be similarly combined with any other type of planar photodetector. The target layer thicknesses are 60/100/60 nm for the SiO₂/Au/SiO₂ stack supporting the NP array, and 50 nm for the Au NPs. Each slit section contains 5 linear slits perforated through the entire stack with 200-nm width and 400-nm period (these parameter values were selected via multiple FDTD simulations to maximize the SPP coupling through the slits). The complete samples consist of a few (7) identical repetitions of the 15-μm-wide 25-NP structure described above, with each section surrounded symmetrically by two sets of slits, and with a large (300 μm) separation between the two electrodes. This arrangement (equivalent to multiple identical pixels binned together) is convenient for the angle-resolved photocurrent measurements. Figure 3a shows scanning electron microscopy (SEM) images of the NP arrays of the two devices. The symmetry relationship between the two metasurfaces, one being the mirror image of the other, is well evidenced in these pictures. A schematic diagram of a complete device can be found in Supplementary material, Section S2.

Figure 3:

Measurement results. (a) Top-view SEM images of the metasurfaces in the two devices reported in this work, illustrating their chiral relationship. (b), (c) Responsivity of device R versus polar θ and azimuthal ϕ angles of incidence for RCP (b) and LCP (c) light. (d) Horizontal line cuts of the color maps of (b) and (c) (red and blue traces, respectively). (e), (f), (g) Same as (b), (c), (d) for device L. All the data presented in these plots were measured at 1,550-nm wavelength and were normalized to the responsivity of a similar device without any metasurface.

The measurement results are in good agreement with expectations. The color maps of Figure 3b and c shows, respectively, the RCP and LCP responsivity ℛ of device R measured as a function of polar θ and azimuthal ϕ angles of incidence at λ ₀ = 1,550 nm. The curved region of high responsivity near the origin of the RCP map is a direct consequence of the phase-matched SPP excitation process described above (see Figure 1c). The additional peak originating from first-order diffraction is also observed in the same map. Incidentally, this peak could be entirely removed from the angular response by replacing the slits on the left-hand side of the NP array with a suitably designed metasurface reflector, at the expense of a somewhat larger pixel area (responsivity data measured with such a device are presented in Supplementary material, Section S3). In any case, for RCP-selective phase imaging, the key feature of these data is the finite versus near-zero responsivity slope |dℛ/dθ| around normal incidence (θ = 0) for RCP and LCP light, respectively (see horizontal line cuts in Figure 3d). Similar results with the two states of circular polarization interchanged were obtained with device L (Figure 3e–g).

All the data presented in these figures are normalized to the measured normal-incidence responsivity of a similar device without any metasurface (29 mA/W/V). The resulting peak values observed in Figure 3d and g [about 29 % and 27 % for the RCP and LCP responsivity of devices R and L, respectively] are reasonably consistent with expectations. Specifically, from the ratio between the peak metasurface transmission computed in Figure 1b (28 %) and the Fresnel transmission of the uncoated Ge surface in the reference sample (62 %), the expected normalized peak responsivity is 45 %. The difference between the measured and calculated values can be primarily ascribed to SPP scattering by surface roughness in the experimental samples, which is also responsible for the observed decrease in peak-to-background ratio in Figure 3d and g compared to Figure 1b.

Another distinctive feature of the experimental maps of Figure 3b and f is the observed asymmetry of the curved regions of high responsivity with respect to the horizontal axis. This behavior is not accounted for by the phase-matching considerations presented above and can instead be explained in terms of spin conservation. It is now well established that SPPs possess a transverse spin angular momentum σ _SSP proportional to the cross product of their real and imaginary wavevectors, which can be interpreted as a manifestation of the quantum spin Hall effect for light [22], [52], [53]. As an illustration, in Figure 1c we show the direction of σ _SSP for SPPs excited in our devices by light incident with two mirror-symmetric wavevectors (at points B and B′ in the k _x  − k _y plane). Circularly polarized light instead features a longitudinal spin determined by its handedness, i.e., parallel and antiparallel to the wavevector for LCP and RCP, respectively. Therefore, if LCP light is incident at point B′, its in-plane spin component σ _|| is nearly parallel to the spin σ _SSP of the resulting excited SPP, as can be seen in Figure 1c. Due to spin conservation, such spin alignment maximizes the photon/SPP coupling efficiency upon scattering by each NP [54], [55]. For the same optical wave incident at B, σ _|| and σ _SSP are nearly antiparallel and the SPP excitation is correspondingly decreased. This argument explains the asymmetry observed in Figure 3f, and similar considerations in reverse can be applied to Figure 3b for RCP light. The metasurface configuration reported in this work therefore also provides an interesting platform to study the role of spin conservation in photon/plasmon interactions towards novel optoelectronic device applications. In fact, this effect could be exploited in similar metasurface photodetectors to further tailor their angular response maps into more complex patterns.

Additional measurements (shown in Supplementary material, Section S4) reveal a steady shift in the angle of peak detection as the illumination wavelength is detuned from its design value of 1,550 nm, consistent with the phase-matching condition discussed above. Figure 4a shows the resulting wavelength dependence of the RCP and LCP normal-incidence responsivity slopes (i.e., d R R C P / d θ and d R L C P / d θ at θ = 0) of device R. For chiral phase imaging with this device, d R R C P / d θ should be as large as possible to maximize the photocurrent sensitivity to small RCP wavefront distortions; at the same time, d R L C P / d θ should be as small as possible to minimize any crosstalk from the LCP wavefronts. The plot of Figure 4a therefore suggests that this sample can provide comparable phase imaging performance to the 1,550-nm results presented below over a spectral range of about 70 nm (the full width at half maximum of the red trace, denoted by the double arrow). In the same spectral range, the ratio d R R C P / d θ / d R L C P / d θ is 37× on average, which can be taken as a measure of the polarization selectivity with respect to phase gradient of this device. Similar considerations apply to device L (Figure 4b), with somewhat smaller bandwidth (60 nm) but larger average selectivity (71×). It should also be noted that the operation bandwidth of these chiral PIMSs could be further expanded using more complex meta-unit geometries, e.g., similar to extensive prior work on achromatic metalenses [56].

Figure 4:

Wavelength dependence. (a) Absolute value of the normal-incidence responsivity slope under RCP (red squares) and LCP (blue circles) illumination measured as a function of wavelength with device R. (b) Same as (a) for device L. All responsivity values are normalized as in Figure 3. The double arrows indicate the full width at half maximum of their respective traces.

2.3 Computational imaging results

A possible pixel configuration for the simultaneous independent measurement of the incident RCP and LCP wavefronts is shown schematically in Figure 5. Here the sensor array is partitioned into blocks of four adjacent pixels coated with the metasurfaces of devices R, L, and their replicas rotated by 180° (labeled R ̄ and L ̄ in the following). The experimental RCP and LCP responsivity maps of all four devices in each superpixel are also shown in the figure (same as in Figure 3 but zoomed in on a narrower region of the k _x  − k _y plane). The black circles in these maps indicate the pupil-function cutoff spatial frequency of the imaging system (corresponding to a maximum angle θ _c = 2.3°), assuming 20× magnification and 0.8 objective numerical aperture. Within these circles, one responsivity map of each device exhibits a nearly linear dependence on k _x , whereas the other is essentially constant with k. As a result, any deflection in the local direction of propagation of the RCP component away from normal incidence produces equal and opposite changes in I _R and I R ̄ (the photocurrent signals measured by the R and R ̄ PIMSs in each superpixel), and no significant change in I _L and I L ̄ (and vice versa for any LCP wavefront distortion).

Figure 5:

Chiral phase imaging system. The sensor array is partitioned into blocks of four adjacent pixels coated with the metasurfaces of devices R, L, and their replicas rotated by 180° (labeled R ̄ and L ̄ ). In this example, the incident light consists of a superposition of RCP and LCP components with equal magnitudes and different phase profiles. The RCP (LCP) phase profile can be reconstructed from the readout signals of pixels R and R ̄ (L and L ̄ ). The experimental RCP and LCP angular response maps of all four pixels in each block are also shown for θ ≤ 6°. The black circle in each color map indicates the pupil-function cutoff frequency of the imaging optics, corresponding to a maximum angle of incidence θ _c = 2.3°.

The imaging system of Figure 5 can therefore be used to record, in a single shot, two independent differential-phase-contrast images of the RCP and LCP incident wavefronts, i.e., S R = I R ̄ − I R / I R ̄ + I R and S L = I L ̄ − I L / I L ̄ + I L . Specifically, the readout signal S _R computed from the photocurrents I _R and I R ̄ of each superpixel is zero, positive, or negative if the local angle of incidence θ of the RCP component is zero, positive, or negative, respectively, regardless of the total incident intensity and of the direction of propagation of the LCP component (and similarly for S _L with the two states of circular polarization interchanged). Since local angle of incidence is proportional to transverse phase gradient, the resulting edge-enhanced images can then be numerically inverted to reconstruct the underlying RCP and LCP phase distributions.

To substantiate the phase imaging capabilities of our experimental samples in the configuration of Figure 5, we use a computational imaging model based on the measured angular response maps, following our prior work with plasmonic diffractive photodetectors [4], [6]. This model involves a Fourier decomposition of the light incident on the sensor array into plane waves propagating along different directions, which are detected by each pixel according to its angular response [57]. In the PIMSs of the present work, the RCP and LCP components of each plane wave are captured (i.e., converted into SPPs which eventually contribute to the photocurrent) with different transfer functions t _RCP(k) and t L C P k because of the chiral nature of these devices. The magnitudes of these polarization-dependent transfer functions can be obtained from the experimental results of Figure 3, where the input light is a plane wave of either circular polarization X = RCP or LCP and variable in-plane wavevector k, and the measured responsivity map R X ( k ) is therefore proportional to t X ( k ) 2 . In a sensor array illuminated with arbitrary polarization and field distribution, the photocurrent of each pixel can then be evaluated as

Here F − 1 denotes the inverse spatial Fourier transform evaluated at the pixel location, Δ k is the phase difference between the two transfer functions t R C P k and t L C P k , and E R C P k and E L C P k are the Fourier transforms of the incident RCP and LCP optical fields on the sensor array. Physically, the two terms in the curly brackets of eq. (3) correspond to the SPPs excited by the Fourier components of in-plane wavevector k of the RCP and LCP incident waves, which add up coherently to one another before being collected at the slits. To estimate Δ k , we have measured the angle-resolved photocurrent of our experimental samples under s and p linearly polarized illumination, and then we have used eq. (3) [with the data of Figure 3 for R R C P k and R L C P k ] to fit the resulting responsivity curves. This procedure (described in more detail in Supplementary material, Section S5) yields accurate fits with Δ ≈ 43° across the pupil-function passband of the envisioned microscope.

Representative computational imaging results based on this model are shown in Figure 6, where we consider the PIMS array of Figure 5 combined with a telecentric imaging system with 20× magnification and 0.8 numerical aperture. The simulated array comprises 90 × 90 square pixels, each with lateral dimension of 17 μm (the combined size of the 25-NP metasurface and adjacent 5-slit section in our experimental samples). The incident light used in these calculations consists of a superposition of RCP and LCP components with equal magnitudes and different phase profiles φ R C P r and φ L C P r shown on the left-hand side of Figure 5. Specifically, both φ _RCP and φ _LCP oscillate as a function of x with the same period (14 μm) but different amplitudes (0.3 and 0.2 rad, respectively) and opposite polarity. These field distributions allow for a simple illustration of our devices’ phase imaging capabilities. At the same time, similar oscillatory patterns of opposite polarity are measured in samples consisting of alternating domains of opposite circular birefringence, such as banded spherulites of various molecular crystals including aspirin [18].

Figure 6:

Chiral phase imaging simulation results. (a) Horizontal line cut through the middle of the differential-phase-contrast image S R r recorded by devices R and R ̄ for the phase object of Figure 5. (b) Horizontal line cut of the differential-phase-contrast image S L r simultaneously recorded from the readout signals of devices L and L ̄ . (c) Phase profile φ R C P r of the RCP component of the incident light (grey trace) and computationally reconstructed image (red trace). (d) Phase profile φ L C P r of the LCP component of the incident light (grey trace) and computationally reconstructed image (blue trace).

Figure 6a and b displays horizontal line cuts of the differential-phase-contrast images S R r and S L r computed with the model of eq. (3). The line cuts of the corresponding phase profiles φ R C P r and φ L C P r are shown by the grey lines in Figure 6c and d. Consistent with expectations, at any location where φ R C P x increases (decreases) with x [i.e., where the incoming RCP component is deflected in the positive (negative) x direction], a peak (dip) is introduced in S R x in Figure 6a. Similar considerations apply to φ L C P x and S L x in Figure 6b. Finally, to reconstruct the two phase objects φ R C P r and φ L C P r from S R r and S L r we have adapted a numerical inversion algorithm that is commonly used with phase imaging systems based on sequential oblique illumination [58] (see Supplementary material, Section S6). The horizontal line cuts of the reconstructed phase profiles are plotted in Figure 6c and d, showing good agreement with the original patterns (the full reconstructed images are also displayed on the right-hand side of Figure 5). These results indicate that the measured angular response characteristics of our devices provide the required sensitivity to phase contrast and polarization selectivity for circular-polarization-resolved wavefront sensing. Further improvements could be obtained with PIMSs featuring taller responsivity peaks, e.g., by minimizing the surface roughness in the Au layer or by using additional NP geometries that can provide more uniform scattering efficiency across the metasurface. Another important design parameter is the number of meta-units, which determines the peak angular width, and thus controls the tradeoff between the phase-contrast measurement sensitivity (proportional to the normal-incidence responsivity slope) and dynamic range (limited by the range of angles over which the responsivity varies strongly with incident angle).