Coherent control of high efficiency metasurface beam deflectors with a back partial reflector

Boundaries between two different materials yield the reflection and diffraction of light according to Snell’s law. This relationship can be modified by introducing patterned dielectric/metal nanofilms at the boundary.¹ By properly designing these patterns as in a passive phased array antenna (namely, “metasurfaces (MSs)”), the nanofilms can be used to tailor the wavefront of the input light and obtain myriad functions such as beam-deflection/splitting depending on the polarization,^1–3 polarization conversion and generation,^4–6 holograms,^4,7,8 achromatic focusing lenses,^9–12 optical angular momentum beam conversion,^1,13 and pulse shaping.¹⁴ However, in the case of beam deflectors, the beam deflection efficiency was somewhat low for the initial proposed design; only a small part of the input light (⁠$∼$10%) can couple to the MS if there is only a single layer with a conventional MS structure on a dielectric substrate.^1,16 To overcome this, high efficiency MSs have recently been proposed including MSs with an optically-thick back reflector (BR),^2,3 multiple-layered MSs,¹⁷ high aspect ratio all-dielectric MSs,^4,8,12,13 Huygens’ MSs,¹⁸ and their combinations.¹⁹ Of these approaches, introducing a BR is the simplest way to obtain the highest beam deflection efficiency (80%–90%) in the broadband regime. For these reflection-type high-efficiency MSs, the interference between the input light and the reflected light plays an essential role in enhancing the beam conversion efficiency.^2,3 The thick BR also eliminates the unwanted diffractions to irrelevant ports.

On the other hand, many research groups have been also developing various active control schemes to modify MS characteristics and functionality based on phase change materials, micro microelectromechanical systems, or electro-optic effect.^20–23 In addition, an interesting application of nanofilm MSs, namely, the coherent control of absorption via MSs, has been proposed and demonstrated experimentally even in single photon regime.^15,24,25 When a nanofilm MS is illuminated by a pair of counter-propagating light beams, light-matter interactions in the MS can be controlled by light interference between two counter-propagating beams. The absorption can be enhanced or suppressed coherently according to the phase difference between the two beams.^15,24 Such phenomena can be used for fast linear all-optical switching, optical computation, and coherent spectroscopy applications.^26–28 In principle, such an idea can be extended to other types of interactions, and recently the coherent control of MS beam deflectors has been proposed theoretically.²⁹ However, the proposed structures have not been optimized for higher efficiency coherent control (the simulated deflection efficiency normalized by the total input intensity is ∼24%). And a structure consisting of air-suspended gold nanofilm is not suitable for an experimental demonstration and practical applications. Therefore, the coherent control of beam deflection has yet to be realized.

In this paper, we propose and demonstrate the highly efficient coherent control of MS beam deflectors. To realize coherent control with a pair of counter-propagating beams, we employ a back partial reflector (BPR) instead of an optically thick BR under the MS beam deflector^2,3 as shown in Fig. 1(a). We employed a trapezoid shaped antenna array as an MS beam deflector.³ It is much easier to reproduce than other designs since the structure is very simple without any tiny gaps (other discrete antenna design should be used for designing other complicated functions⁴). Additionally, a spacer layer and a BPR layer are introduced below the MS layer. Figure 1(b) shows the switching operations schematically. The MS with a BPR realizes optical deflection into Port C when illuminated from one side (Port A or B). However, when illuminated from both sides (Ports A and B), it shows a distinct response depending on the relative phase of electric field between the two beams. When $Δ ϕ$ (the relative phase difference between Port A and B) is in-phase (⁠$Δ ϕ = 0$⁠), the beam deflection into Port C is greatly enhanced. By contrast, when $Δ ϕ$ is out-of-phase (⁠$Δ ϕ$ = $π$⁠), the deflection is greatly suppressed, which is known as interference-induced transparency (IIT).¹⁵ Therefore, the deflection intensity can be controlled with $Δ ϕ$⁠. For coherent perfect absorption, the transmission and reflection normal to a MS absorber are canceled by destructive interference, and then the MS absorption is enhanced up to 100% (so the antinode of the standing wave is set around the center of MS). Here, the same thing also happens even with putting a MS deflector alternatively—enhanced beam deflection happens with canceling the normal transmission and reflection.²⁹ 

First, we verify the qualitative coherent control of MS beam deflectors with BPR by using finite element method simulations. Figure 2 summarizes the theoretical model and the simulated results. Figure 2(a) illustrates the relative position of each port and the target MS.³ Here, we employ a measured gold film index (Section V). We set the structural parameters at an x-pitch P_x = 1.2 $μ$m, a y-pitch P_y = 0.2 $μ$m, a trapezoid length L = 0.8 $μ$m, a shorter trapezoid width W_S = 30 nm, a longer trapezoid width W_L = 160 nm, a MS thickness d_MS = 30 nm, a spacer thickness d_SP = 65 nm, and a BPR thickness d_BPR = 32 nm. The input wavelength $λ$ is fixed at 633 nm (He-Ne laser). The theoretical beam deflection angle is 32° with these settings. For the plane wave input, we put Port A (top air side) and Port B (bottom SiO₂ side) above and below the MS with a spacing of 0.5 $μ$m. The inputs from both Ports A and B are assumed to have a transverse magnetic polarization (the E_y component is perpendicular to the paper). We also positioned Port C to detect the deflection intensity. Figures 2(b)–2(g) summarize the steady-state responses of the E_y distribution under different input conditions. Figures 2(b) and 2(c) show the single input from Port A and Port B, respectively. The beam deflection from Port A to Port C is not perfectly induced because of the partial reflection from the BPR. This means we still have a fraction of beam deflection even with the input from Port B, which is the intrinsic difference from MSs with optically thick BR.^2,3 Figures 2(d) and 2(e) show the simultaneous inputs from both ports with $Δ ϕ$ = 0 and $π$⁠. In (d), P_C is coherently enhanced. On the other hand, in (e), P_C is coherently attenuated. Therefore, we verified that this asymmetric configuration can be used for coherent control. If we use a symmetric MS without a BPR, the transmittances from Port A to Port C (T_CA) and from Port B to Port C (T_CB) become the same. In this situation, the ON/OFF extinction ratio is simply maximized under the symmetric input (P_A = P_B).²⁹ Actually, the proposed structure has asymmetric transmittances (⁠$T C A ≠ 𝑇 C B$⁠). Even in this case, the extinction ratio can be maximized by employing a proper input ratio $α$ (=P_B/P_A). Figures 2(f) and 2(g) show the results obtained using a proper asymmetric input with $Δ ϕ = 0$ and $π$⁠. When $α$ = T_CA/T_CB, both the transmitted powers to Port C P_AT_CA and P_BT_CB are same. Therefore, coherent enhancement and attenuation are induced perfectly in this case. In fact, we confirmed that the clear IIT can be induced from (g).

To clarify the advantage of our proposed device, we define a figure of merits (FOM) for all-optical switching as follows:

where P_{w/o ctrl} and P_w/ctrl are the output intensities without and with control light from Port B, respectively. P_sig and P_ctrl are the intensities of the signal and control light. Therefore, FOM expresses a hybrid barometer for coherent control indicating how high an efficiency and how deep a modulation can be obtained with how small a loss. For example, with a loss-less linear coherent controllable beam deflector (T_CA = T_CB = 0.5), FOM reaches a maximum value of unity. In our configuration, the parameters are given as P_{w/o ctrl} = P_{C_max}, P_w/ctrl = P_{C_min}, P_sig = P_A, and P_ctrl = P_B.

We also define other 2 characteristic parameters, which are more intuitive as regards comparison with other previous reports such as in Ref. 21. Where the net deflection efficiency (NE) is defined as follows:

NE represents the fraction of the total input that is deflected. Therefore, NE corresponds to the beam deflection efficiency under coherent control with $Δ ϕ = 0$⁠. In the following, we optimized our device to maximize the FOM or NE. The other one is ON/OFF extinction ratio (ER) as follows:

As we show in Fig. 2, an asymmetric input leads to a significant improvement in ER. FOM, NE, and ER are derived in Section S1 of the supplementary material. Figure 3 summarizes the calculated performance based on Eqs. (S3) and (S4) (Section S1) and simulated T_CA and T_CB (Section S2). Figure 3(a) shows the contour plot of the FOM with different d_SP and d_BPR values. The FOM can be maximized to 0.44 with (d_SP, d_BPR) = (70 nm, 23 nm) (indicated by the blue stars in Figs. 3(a)–3(c)). Since there is a clear tradeoff between T_CA and T_CB against d_BPR, an appropriate d_BPR gives the optimum FOM. Adjusting d_SP is also important if we are to obtain the coherent enhancement of T_CA as well as a smaller absorption loss.² Figure 3(b) shows NE, and it is maximized to 52% when (d_SP, d_BPR) = (65 nm, 34 nm) (indicated as red stars in Figs. 3(a)–3(c)). Figure 3(c) shows ER. When the total thickness decreases, the MS becomes closer to a symmetric design (T_CA ∼ T_CB). Therefore, ER is increased with decreasing d_SP and d_BPR except for d_BPR ∼ 18 nm. We have significant plasmonic absorption when d_BPR ∼ 18 nm (Section S3).

Figure 4 shows the FOM with the maximized ER when employing a non-unity $α$ (please note that $α$ is different at each point). Under this constraint, the distribution of FOM and NE become identical, so we have provided two color bars for a single contour plot. The plot has two local maxima: one (yellow star) gives the best FOM and NE and the other one ((d_SP, d_BPR) = (75 nm, 22 nm)) gives almost the same FOM and NE with a more practical d_BPR for actual fabrications. We should also note that FOM and NE are always degraded when we try to maximize ER by adjusting the asymmetric input (Section S1 of the supplementary material).

The performances of four proposed combinations (d_SP, d_BPR) as indicated in Figs. 3 and 4 are compared in Table I, which includes Ref. 29. By introducing appropriate d_SP and d_BPR values, the transmittances can be engineered flexibly. The blue star structure gives the best FOM with better NE and ER. With $α$ = T_CA/T_CB (yellow and green stars), all the performances are better than Ref. 29. The simulated result presented above clearly shows that high deflection efficiency into Port C is achievable by our proposed design.

We have also confirmed the broadband response of our designed MS deflectors in whole visible regime (⁠$λ$ = 400 – 800 nm) as summarized in Fig. 5. Please note that we did not assume the material dispersion of n_Au. (n_Au is fixed as the measured value at $λ$ = 633 nm). We simulated three optimized structures corresponding to the structures in Table I or Figs. 3 and 4 (blue, red, and yellow stars). Basically all the structures show no degradations in terms of FOM (Fig. 5(a)), NE (Fig. 5(a)), and ER (Fig. 5(a)) with $α$ = 1 at least within 500 – 800 nm. Therefore, our designed MSs maintain their capability in broadband width since their thicknesses are still in the range of sub-wavelength. In general, FOM and NE are degraded a lot at much shorter wavelength regime around 400 – 450 nm. ER can be improved at longer $λ$ because of the thinner effective thickness. For the yellow star structure which is optimized for the case of $α$ = T_CA/T_CB, it shows smaller degradation than the other two structures at the shorter wavelength.

For the actual fabrication, we chose (d_SP, d_BPR) = (70 nm, 23 nm), which correspond to the blue star in Fig. 3. In terms of the trapezoid antenna, we employed the same parameters as for the above-simulated models. Figure 6(a) is a schematic showing the flow of the device fabrication. The three layers were formed through Au BPR deposition, SiO₂ spacer deposition and a lift-off process on a quartz substrate (Section V). We also fabricated a sample without BPR for the control experiment (Section S7 of the supplementary material). Figure 6(b) shows the electron microscope images of the completed sample. We formed a sufficiently large MS region of 1.6 × 1.6 mm² to illuminate the input lights without focusing or collimation. The average measured structural parameters of the fabricated trapezoid antenna were L ∼ 0.794 $μ$m, W_S ∼ 32 nm, and W_L ∼ 158 nm, which were close enough to the original design.

First, we input non-polarized white light into the sample from Port A to quickly verify the deflection angle and the potential of the broadband operation. Figure 6(c) shows the observed anomalous reflection to Port C. The array of samples (3 × 3) was illuminated by the halogen lamp. Then a horizontally extended rainbow appeared on the screen with a reflection angle ranging from 18.3 to 42.0° in the visible regime. This reflection angle range provides a good fit with the simulated range of 19.0°–42.4°. In terms of $λ$ = 633 nm, the measured reflection angle is 32.7°, which also corresponds to the designed value of 32.0°.

Next, we launched a dual facing input to demonstrate our proposed concept. Figure 7 is a schematic of the free-space optics. First, the laser light from a He-Ne laser is polarized through a half wave plate and a polarization filter (PF). This polarized light is split at a beam splitter (BS) and normally input into the sample from the top and bottom simultaneously. The mirror angles are aligned so that the two beams are aligned in the same propagation direction and position. $Δ ϕ$ is continuously modulated by using a mirror with a piezo-actuator and a function generator. $α$ is changed with the attenuators on each arm. P_C is detected and monitored with a photodetector and an oscilloscope (Section V).

Figure 8(a) (Multimedia view) shows the relative output intensity modulation to Port C when we employ a dual facial input with different $Δ ϕ$ values. This result clearly shows that the deflection intensity into Port C is sinusoidally modulated as changing $Δ ϕ$ as a result of the coherent interference. As far as we know, this is the first demonstration of coherent control of deflection by a sub-wavelength-thick MS. The FOM is around 0.31 which is not far from the simulated value of 0.44. Figure 8(c) (Multimedia view) shows that the FOM is maximized at $α$ = 1, as expected from the calculation. In addition, Figure 8(d) (Multimedia view) shows that the NE is also very high (44.7%) at $α$ = 1. These characteristics should be hardly achievable when employing conventional MSs. As predicted from the simulation in Section II, ER can be improved up to >25 dB for the asymmetric input (when $α$ > 1). Figure 8(b) (Multimedia view) shows the result for $α$ = 9.6. The ER as a function of $α$ is shown in Fig. 8(e) (Multimedia view). The overlapping gray lines in Fig. 8 (Multimedia view) represent the theoretical values estimated from the experimental T_CA (46.5%) and T_CB (4.8%) (Eqs. (S3) and (S4) in Section S1 of the supplementary material). These results show an excellent agreement with the measured values. This agreement unambiguously proves that we have experimentally demonstrated the coherent control of deflection, and it also shows that our simple modeling can accurately predict the device performance.

To confirm the results in Fig. 8 (Multimedia view), we also compared a series of simulated and measured transmittances against a single input from Port A (top MS side) or Port B (BPR side) to each port as shown in Fig. 9. For the series of transmittances from Port A to the other 5 ports (B, C, D, E, and F), all the measured transmittances agreed very well with the simulated value. T_CA/T_CB becomes ∼9.6, which corresponds to the value of $α$ at the maximum ER as shown in Figs. 8(b) and 8(e) (Multimedia view). On the other hand, the result for Port B appears to show a good agreement in terms of the distribution ratio. However, all the absolute experimental values are about half the values of the simulated results. This is due to the wavelength dependence of the transmittances caused by Fabry-Perot resonance between the bottom quartz boundary (reflectance ∼3.6%) and the BPR (reflectance ∼69%). This means that the transmittance from Port B to the MS fluctuated in the 22%–42% range with a free spectral range of ∼0.9 nm. We can avoid this by employing an antireflection coating on the bottom of the quartz substrate.

We have experimentally demonstrated the coherent control of MS beam deflectors with a counter-propagating symmetric or asymmetric input for the first time. We defined FOM and other performance characteristics of the device and optimized them. We found that transmittances can be engineered flexibly by tuning d_SP and d_BPR. All the performance characteristics can be better than those in Ref. 29 by employing an asymmetric design with a thin bottom mirror.

The demonstrated device provides one way to realize ultrathin linear all-optical switches and logic gate arrays.^26,27 We do not use any nonlinear optical effects, thus the device can be operated even with ultralow input power, and the switching speed is not limited by the device itself but an optical phase shifter for control light. In the future, more and more sophisticated optical computation will become possible by integrating different functions in a multiple layered MS. The propagation length could become much shorter, which may be useful in terms of lower-latency optical computing. And the deflection angle, polarization dependence, and the function itself are totally controlled by the MS design. Therefore, the scope of the applications is expected to become broader and broader.

For the simulations, first we prepared a sample by depositing 1-nm and 30-nm thick Ti and Au, respectively, on a quartz substrate with an e-beam (EB) evaporator, and then we measured the deposited gold film index n_Au by using an ellipsometer. We obtained n_Au = 0.12051 + 3.0016i for $λ$ = 630 nm. We performed frequency domain simulations based on this result. We applied the periodic boundary condition in the y direction and the scattering boundary condition in the x and z directions. The number of periods in the x direction was fixed at 8. The transmittances were calculated from the square of the absolute S parameters. We also confirmed that the reported trapezoid type beam-deflecting MS³ has sufficient fabrication tolerance (Section S5 of the supplementary material).

For the fabrication, we employed a 2 in. quartz substrate (VIOSIL-SQ S-Grade, Shin-Etsu Chemical) with the arithmetic average of absolute roughness of <0.2 nm. After removing particles from the surface, we deposited an Au BPR with the same EB evaporator. We also deposited 1 nm-thick Ti immediately below and above the Au to realize better adhesion. Next, we measured the flatness of the Ti/Au/Ti surface by measuring the root-mean-square (RMS) value with an atomic force microscope. The measured RMS was 0.4–0.5 nm. Then we deposited a SiO₂ spacer with an electron cyclotron resonance sputter. After this, the RMS improved (∼0.3 nm) due to the smoothing effect (Section S8 of the supplementary material). For the lift-off process, we employed a bilayer positive EB resist (ZEP-520A, Zeon, and $Φ$-MAC, Daikin)³⁰ and a point-beam EB lithographic machine with an acceleration voltage of 125 kV. After the EB writing, we developed a pattern with o-xylene for ZEP-520A, and ZED-N50 (Zeon) for $Φ$-MAC. After descumming the resist using O₂ reactive ion etching, we again deposited 1 nm-thick Ti and 30 nm-thick Au. Finally, we removed the EB resist by using gentle sonication in a remover.

As regards the measurement, the relative phase difference $Δ ϕ$ was modulated periodically by using a movable mirror with a piezo actuator, a piezo controller, and a wave function generator. Attenuators were inserted into both the arms to vary $α$⁠. The absolute powers of the inputs and outputs to all ports were measured with a power meter. The output signal was monitored and detected with a photodetector and an oscilloscope. With the oscilloscope, we obtained the peak value (V_max) and the modulation amplitude (V_amp) from the sinusoidally modulated output signal. For our experimental NE evaluation, we utilized the relationship given below

where V_onlyA or V_onlyB, respectively, is the detected voltage with a single input from Port A or B. Here, we substituted the measured T_CA (46.5%) and T_CB (4.8%). We sampled V_max and V_amp > 100 times to obtain the standard deviation $σ$⁠, which gave the error bars seen in Figs. 8(c) and 8(d) (Multimedia view). Here, we observed a very short-term modulated output intensity fluctuation of ±5%–6% induced by the phase noise (Section S6 of the supplementary material). The dark current noise was subtracted from all the measured voltages.

See supplementary material for supporting content.

We thank Dr. A. Shinya, Dr. H. Sumikura, and Dr. D. Smith for helpful discussions. We thank Dr. H. Taniyama for help with the simulations. We also thank Dr. T. Tamamura and Mr. O. Moriwaki for supporting the fabrication work. We also thank Dr. A. Yokoo and Mr. S. Fujiura for AFM observations. This work was supported by Core Research for Evolutional Science and Technology, Japan Science and Technology Agency (CREST-JST).