1.

Introduction

The remarkable multiple degrees of freedom (DOFs) possessed by light, including large bandwidth and high-speed transmission capabilities, make photonic technology an extremely promising platform for high-speed communication and high-performance computing in information science.^1–3 Over the last decade, metasurfaces have emerged as an unprecedented approach for manipulating light in various DOFs using compact, artificial two-dimensional nanostructures.^4,5 Metasurfaces have demonstrated significant promise for a wide range of applications in both fundamental science and industry, including wavefront shaping,^6,7 polarization control,^8–10 imaging,^11,12 spectrometry,^13,14 and computation.¹⁵ Recently, considerable research efforts have been devoted to developing metasurfaces to achieve tunable or reconfigurable functionalities.^3,16 A high-speed spatiotemporally controlled metasurface possesses the potential to facilitate novel physics and practical applications within the realm of photonic technology. Numerous materials and strategies have been proposed to empower tunable metasurfaces, including the utilization of phase-change materials, liquid crystal, thermo-optic effect, and electro-optic effect.^17–22 However, effectively exploring tunability in multiple DOFs with high speed and sufficient efficiency remains a significant challenge in metasurface research.

On the other hand, photonic integrated circuits (PICs) represent an alternative to traditional electronic technologies by utilizing light. Diverse applications have been demonstrated with PICs, including high-speed optical communication, signal processing, computing, and emerging technologies in quantum, biomedicine, and sensing.^23–28 Particularly, the advent of lithium niobate on insulator (LNOI) has propelled PICs as a promising platform for future high-speed electro-optic (EO) integrated devices,²⁹ such as high-performance modulators,^30,31 frequency combs,^32,33 polarization controllers,^34,35 and quantum optics circuits.^36,37 However, the full utilization of the DOFs of light in traditional two-dimensional PICs has not been realized, thereby limiting their application in optical information technologies. Recently, the integration of metasurfaces with waveguides has enabled PICs to manage multiple DOFs of light in both free space and waveguides with on-chip devices, providing a highly integrated platform for efficient photonics management.³⁸ A variety of applications have been reported with the guided-wave-driven metasurfaces, such as mode conversion,^39,40 on-chip lenses,^41,42 holography,^43,44 OAM generators,^3,45–48 as well as polarization control.^49,50 Nevertheless, achieving high-speed wavefront shaping and switching capabilities through the integration of metasurfaces, photonic waveguides, and electrical circuits remains a significant scientific and technological challenge for PICs and metasurfaces.

In this work, we propose and demonstrate a gigahertz-rate-switchable wavefront shaping by integrating metasurfaces with LNOI PICs. An arbitrarily polarized light could be generated by combining a waveguide with two orthogonally propagated modes and nanoscatterers at the specific positions.⁴⁵ Through the introduction of a Mach–Zehnder interferometer (MZI) and a phase shifter together with two pairs of electrodes, both the amplitude and the phase of the two orthogonal modes could be managed, enabling the generation of light with arbitrary polarizations spanning the entire surface of Poincaré sphere at high speed. Meanwhile, a well-designed polarization-dependent metasurface is introduced to achieve the desired functionality and facilitate high-speed modulation or switching. With this stratagem, switchable focusing with lateral focal positions and focal length, OAMs as well as Bessel beams are demonstrated. By effectively combining the propagation phase and geometric phase of birefringent nanostructures within this waveguide scheme, we demonstrate the switchability of these functionalities in arbitrary orthogonal polarizations. The switching speed reaches gigahertz rates, while the modulation speeds can be optimized to reach hundreds of gigahertz using tailored electrodes and LNOI PIC waveguides. This approach provides a versatile and efficient means of controlling light propagation in a compact and integrated system with simple electrical wiring and low power consumption, and promises important advantages in scenarios such as optical communication, computation, sensing, and imaging.

2.

Results and Discussions

Figure 1(a) schematically shows the PIC-driven metasurface device. Two fundamental transverse-electric (${\mathrm{TE}}_0$) modes from LN ridge waveguides are transformed into two orthogonally propagated ${\mathrm{TE}}_0$ modes in the slab waveguide. This transformation is achieved through the use of adiabatic tapers, as illustrated within the dashed square in Fig. 1(a). The zoomed-in view of the region is provided in Fig. 1(b). The electromagnetic wave in the slab waveguide can be expressed as

Fig. 1

(a) Schematic diagram of PIC-driven metasurface device with LNOI; the red arrow is the direction of optical axis. (b) The zoomed-in scheme of the integrated metasurface is depicted with the fictitious wavefront of the waveguide modes. (c) The simulated static electric field when 1 V is applied between the electrodes, superimposed with the simulated optical field profile of the ${\mathrm{TE}}_0$ mode in the LN ridge waveguide. The black dashed lines indicate the electrodes. They have a height of 300 nm and are spaced apart by $6.5\mu \mathrm{m}$. The top width of the LN ridge waveguide is $1\mu \mathrm{m}$, and the etch depth is 210 nm.

The device is designed and fabricated on an $x$-cut LNOI platform to provide the best electro-optical performance. Considering the anisotropy of $x$-cut LN, both ${\mathrm{TE}}_0$ modes are specifically designed to propagate at a 45 deg angle to the short optical axis of LN. This arrangement ensures that the wave vectors ${\beta }_x={\beta }_y$ and maintains a symmetric polarization distribution, as shown in Fig. 1(a). To precisely get the polarization distribution on the waveguide, we perform a finite-difference time-domain (FDTD) simulation to get the amplitude and phase evolution over the slab waveguide at the experiment wavelength of 1550 nm, as shown in Fig. S1 in the Supplementary Material. Directional couplers (DCs) are employed to achieve the tunable splitting function of the MZI, having a center-to-center spacing of $4.5\mu \mathrm{m}$ and a length of $300\mu \mathrm{m}$. Meanwhile, ground–signal–ground (G–S–G) electrodes are used in the inner and outer phase shifters of the MZI to induce phase shifts in a single-drive push–pull configuration, so that the electric field induces phase shifts in both arms with equal magnitude but opposite signs. The simulated optical field profile of the ${\mathrm{TE}}_0$ mode in the LN ridge waveguide together with the static electric field between the electrodes is shown in Fig. 1(c), exhibiting a good overlap of the two fields.

The PIC-driven metasurface is initially investigated to showcase a functionality with arbitrary reconfigurable polarization. In order to demonstrate the feasibility of this approach, a focusing beam achieved with a silicon nanocylinder metasurface is investigated. The Jones matrix of isotropic silicon nanocylinders is given by $e^{i\alpha }\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, where $\alpha$ is the propagation phase of the nanocylinders. The electromagnetic wave extracted to free space by silicon cylinders can be expressed as

Thus, the phase profile of the free-space electromagnetic wave depends on the location of the silicon cylinders. On the other hand, to generate a focused beam in free space, the phase of light scattered from the metasurface has a distribution described as

Fig. 2

(a) The microscope image of the fabricated device. The length of the two sets of electrodes is 0.5 mm. (b) SEM image of the fabricated metasurface on the waveguide. (c) The measured intensity profile at the $x-z$ plane. (d) The measured polarization states on the Poincaré sphere of the focal spot. The blue dots on the Poincaré sphere represent the polarization states of the focal spot obtained from experimental testing. (e) Stokes parameters of one of the generated polarization state (45 deg linear polarization as shown in the inset) as a function of time. (f) Stokes parameters by switching between two generated polarization states.

By adjusting the voltages applied to the electrodes of the MZI and the phase shifter, the polarization state of the focal spot can be dynamically manipulated. To evaluate the performance of the reconfiguration polarizations of our device, two triangle wave signals with frequencies of 1 and 100 kHz are applied to the electrodes of the MZI and phase shifter, respectively. The peak-to-peak drive voltages ($V_{\text{pp}}$) are set to 9.2 V, corresponding to a phase shift of $\sim 2\pi$. The blue dots in Fig. 2(d) depict the measured sampling points on the Poincaré sphere (the schematic diagram of the experimental setup is presented in section 6 in the Supplementary Material and the corresponding measured Stokes parameters are presented in section 7 in the Supplementary Material), representing the polarization states of the focal spot. The polarization extinction ratio (PER) was measured to be $\sim 20\mathrm{dB}$ (section 3 in the Supplementary Material). The majority of the Poincaré sphere’s surface is covered, with the exception of two areas near the north and south poles. This deviation is mainly due to imperfections in the fabrication process, resulting in a splitting ratio of the DC in the MZI that deviates from the ideal 50:50 ratio. This issue can be addressed by employing an additional electrically controlled interferometer to improve the splitting ratio.³⁴ Figure 2(e) depicts the good stability of the generated polarization state, indicating its robustness. Figure 2(f) showcases the switching performance between two polarizations, highlighting the high repeatability of polarization generation. By adjusting the voltages applied to the electrodes, transitions between any polarized states within the blue region of Fig. 2(d) can be achieved with the same level of stability and repeatability. These results exhibit the promising capability of our device for wavefront shaping with good control over reconfigurable arbitrary polarization states.

In addition to enabling the generation of a single wavefront with reconfigurable polarizations, this scheme has the capability to achieve high-speed switchable multifunctionalities through the incorporation of polarization-dependent metasurfaces, which holds tremendous potential for a wide range of applications. To exhibit this capability, we first introduce a geometric metasurface to the PIC device, enabling the realization of two focal points with orthogonal polarizations at different lateral positions. The metasurface is composed of two sets of silicon nanobars as shown in Fig. 3(a), which are designed to realize two foci based on left circular polarization (LCP) and right circular polarization (RCP) states, respectively. The two sets of nanostructures are spatially multiplexed with a near face centered square unit with the period of the effective wavelength of the ${\mathrm{TE}}_0$ mode in the slab waveguide (section 2 in the Supplementary Material). In this arrangement, the two sets of nanostructures are positioned in locations with the same local polarization $\psi$. By adjusting the voltages applied to the electrodes, the local polarization $\psi$ can be dynamically switched between LCP and RCP states. Through this control mechanism, the scattered light can be switched between the two designed focal spots, respectively. Meanwhile, the unwanted co-polarization noise will be greatly suppressed due to the phase mismatch.⁴⁵

Fig. 3

(a) The schematic of the switchable metasurface design. (b) SEM image of the fabricated metasurface structure. (c)–(e) Calculated results of foci under different local polarization states ψ depicted in the figures. (f)–(h) The corresponding experimental results. The polarization states are realized by applying different voltages shown in the figures to the electrodes, respectively. (i) The intensity of the right focus in (f) as a function of applied voltage. (j) Peak electro-optic amplitude for modulation frequencies up to 2 GHz (Video 1, MP4, 120 KB [URL: https://doi.org/10.1117/1.AP.6.1.016005.s1]).

In the experiment, the silicon nanobars have a uniform length ($L$) of 300 nm, width ($W$) of 100 nm, and height ($H$) of 1000 nm. The corresponding SEM image of fabricated metasurface on the slab waveguide is shown in Fig. 3(b). The two foci are designed at $x=5\mu \mathrm{m}$ and $x=-5\mu \mathrm{m}$, with the center of the metasurface array serving as the origin of coordinates. The focal length is set to $f=50\mu \mathrm{m}$ for both spots. Figures 3(f)–3(h) show the recorded images of the foci at different voltages for the phase control. The voltage of the MZI is offset to ensure equal amplitudes in the two arms. By adjusting the voltages applied to the phase shifter, the scattered energy gradually transitions between the two focal spots. The experimental results align well with the calculated images based on the corresponding designed local polarizations, as shown in Figs. 3(c)–3(e). This result demonstrates the effectiveness of the adopted strategy. A video illustrating the dynamic modulation process is provided in the Supplementary Material.

To accurately assess the modulation performance, we integrated the recorded focal intensities in Fig. 3 and observed an extinction ratio of $\sim 10.2\mathrm{dB}$. The electro-optical tunability of the device was evaluated by directing the light from one focus to a high-speed photon detector [FINISAR XPDV21x0(RA)] for analysis (section 6 in the Supplementary Material). The measured $V_{\pi }$ of the device is $\sim 4.6\mathrm{V}$ as shown in Fig. 3(i) (corresponding to a $V_{\pi }·L$ of 2.3 V·cm). Figure 3(j) presents the peak electro-optic modulation amplitude for frequencies up to 2 GHz. The result indicates the electro-optic bandwidth of the sample is around 1.4 GHz, providing clear evidence of its gigahertz tunability. Furthermore, the switching speed could be further improved to hundreds of gigahertz by carefully optimized the electrodes and waveguide design.

Apart from the ability to vary the lateral positions of the focal points, this scheme also enables dynamic switching of the focal length, which holds great significance and has garnered plenty of attention.^51,52 To demonstrate this concept, two different sets of nanostructures are designed, resulting in two focal points with focal lengths of $f=35\mu \mathrm{m}$ and $f=50\mu \mathrm{m}$, respectively. Figures 4(d)–4(f) show the recorded images of the foci by varying the voltage applied to the phase shifter, which agrees well with the calculated results [Figs. 4(a)–4(c)]. The focal points can be dynamically adjusted between these two states or any intermediate states. These integrated lenses with high-speed switchable focal positions and lengths hold promise for future high-speed portable imaging applications, opening up new possibilities in the field.

Fig. 4

(a)–(c) Calculated results of switchable focal length under different local polarization states depicted in the figures. (d)–(f) The corresponding experimental results were realized by applying different voltages to the electrodes as shown in the figures, respectively. (g)–(i) Calculated results of switchable OAM beams with switchable topological charges under different local polarization states depicted in the figures. (j)–(l) The corresponding experimental results were realized by applying different voltages to the electrodes as shown in the figures, respectively.

The high-speed switchable wavefront-shaping technique holds immense potential for various applications such as optical communications, imaging, optical computation, sensing, and more. Particularly, the generation of optical orbital angular momentum (OAM) with a large modulation bandwidth is of significant importance in the realm of optical communication.⁵³ We replace the focus beams with two OAMs with different topological numbers and locations by mapping the required phase distributions to the two sets of metasurfaces. Figures 4(j)–4(l) show the typical recorded OAM images by varying the voltages applied to the electrode of the phase shifter, which agree well with the calculated results under certain corresponding polarizations, shown in Figs. 4(g)–4(i). The left OAM beam is designed with $l=+1$ in LCP state and the right one is designed with $l=-1$ in RCP state. The results exhibit that the integrated device has the capability to dynamically manipulate OAM beams with various topological numbers, offering promising applications in optical communications and manipulations. These findings indicate the feasibility of utilizing a geometric phase-based spatial multiplexing multichannel device within our platform.

The aforementioned multifunction switchable devices are designed with a geometric phase constraint limited to circular polarizations. Indeed, it is important to note that this constraint can be extended to encompass any arbitrary orthogonal polarization states by considering the geometric phase and propagation phase of birefringent nanostructures for free-space light.⁵⁴ It holds significant importance in applications involving polarization optics, offering enhanced versatility and adaptability. However, this scheme is still awaiting clarification in the guided-wave-driven metasurfaces due to the overlapping of the in-plane waveguide mode and the nanostructures. Meanwhile, the scattering efficiency of the nanostructures on the waveguide exhibits a strong dependence on their size, and this behavior differs significantly from the transmission characteristics of metasurfaces in the free-space configuration. Here, we present the successful engineering and dynamic switching of a wavefront in arbitrary polarization states with the metasurface on a PIC device. When a birefringent nanostructure scatters the waveguide mode with an arbitrary local polarization of ${\mathrm{\Psi }}_1$, the scattered light can be decomposed into a pair of orthogonal polarization states, ${\mathrm{\Psi }}_2^{+}$ and ${\mathrm{\Psi }}_2^{-}$, respectively. The two decomposed components can be expressed as

Fig. 5

(a) The simulated intensity and (b) phase of the scattered light when the rectangular nanostructure’s length and width vary from 100 to 500 nm. (c) SEM image of the fabricated metasurface for Bessel beams. (d)–(f) Calculated results of switchable Bessel beams under different local polarization states depicted in the figures. (g)–(i) The corresponding experimental results by adjusting voltages applied to the electrodes, respectively. (j)–(l) The corresponding cross-sectional images along the white dashed lines in (g)–(i), respectively.

Similar to the geometric phase-based metasurfaces demonstrated above, by varying the polarization distribution within the planar waveguide region, we can switch the wavefronts designed upon the arbitrary independent polarization channels. As an example, here we demonstrate an integrated generation of switchable Bessel beams with arbitrary polarizations, which have garnered significant interest across a wide range of research fields. The polarization states of the two Bessel beams are designed with $1/\sqrt{5}[\begin{array}{cc}2& e^{i\pi /4}\end{array}{]}^T$ and $1/\sqrt{5}[\begin{array}{cc}1& 2e^{5i\pi /4}\end{array}{]}^T$, respectively. Figure 5(c) depicts the SEM images of fabricated sample. Figures 5(g)–5(i) illustrate the featured images through the adjustment of voltages applied to the MZI and the phase shifter. The formation of Bessel beams in different directions ($\pm 5\mathrm{deg}$) of the scattered light is clearly shown, and these adjustments align with the calculation results displayed in Figs. 5(d)–5(f), considering the corresponding polarizations. Figures 5(j)–5(l) show the recorded lateral images along the white dashed lines in Figs. 5(g)–5(i), respectively. The integrated generation of switchable nondiffracting Bessel beams with arbitrary polarization states demonstrates the feasibility of our method for achieving switchable functionalities in any arbitrary polarization state. Moreover, it introduces exciting new prospects for applications involving special beam characteristics.

We have demonstrated the capability of wavefront shaping and switching upon any orthogonal polarization states. Indeed, this high-speed switchable scheme could also be extended to nonorthogonal polarization states as well. By incorporating complex unit cell, interleave design, as well as artificial intelligence, the traditional limitation of two independent orthogonal channels could be broken, enabling the realization of more polarization-determined and switchable channels.⁹ This strategy not only enables the generation of specialized optical beams but also facilitates the implementation of various switchable and complex functionalities. In addition to generate switchable wavefronts in uniform polarization states, the PIC-driven metasurface exhibits the potential to produce complex vector wavefronts. Furthermore, this approach can also utilize alternative high-speed modulation PIC platforms and mechanisms, in addition to LNOI, such as carrier depletion, enabling increased levels of integration and compatibility with CMOS technology. The out-of-plane extraction efficiency of the integrated metasurface in our device can reach 11% with numerical simulation, which can be further improved by optimizing the geometric parameters of the metasurfaces and the waveguide^50,55 (section 8 in the Supplementary Material). These factors expand the applicability across a wide range of fields and applications.

3.

Conclusion

We have proposed and demonstrated an integrated electro-optical platform with PIC-driven metasurface on LNOI. By integrating an electrically controlled MZI and a phase shifter, we constructed a focusing beam with high-speed adjustable polarizations across almost the entire surface of the Poincaré sphere. Based on the reconfigurable polarizations across the waveguide, switchable focusing beams with lateral focal positions and focal lengths, OAM beams and Bessel beams were demonstrated. Our approach opens up possibilities for achieving more switchable functionalities with complex polarizations. The modulation bandwidth is measured to be 1.4 GHz and it has the potential to be improved to hundreds of gigahertz based on the electro-optical effect of LN. The demonstrated high-speed switchable PIC-driven metasurface provides a promising platform for a variety of applications in high-capacity optical communication, fast optical computation, imaging, and sensing. This integrated platform offers significant opportunities for advancing these fields and enabling a wide range of practical applications.