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Abstract
Metasurfaces, the promising artificial micro-nano structures with the ability to manipulate the wavefront of light, have been widely studied and reported in recent years. However, dynamic control of the wavefront using dielectric metasurfaces remains a great challenge. Here, unlike the previously reported reconfigurable metasurfaces that offer only binary functions or limited switchable states, we propose and numerically demonstrate an active dielectric metasurface with the metamolecule unit-cell design that enables full-range phase or amplitude tuning in the telecommunications band using the phase-change material Ge2Sb2Se4Te1 (GSST). Selective control of the phase transition of each GSST nanopillar in the metamolecule allows multi-level modulation of the phase and amplitude of the light to be achieved. The functionalities of the structure are validated through the generation of optical vortices, phase-only hologram, and pure amplitude modulation. Benefiting from its dynamic wavefront control capability, the proposed metasurface offers major potential for use in future applications including complex beam steering, optical communications, 3D holograms, and displays.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Manipulation of light fields using the compact devices is becoming increasingly important in modern photonic systems [1]. Optical metasurfaces [2], which are two-dimensional artificial metamaterials with sub-wavelength thicknesses and compact feature sizes, have attracted considerable attention for use in integrated photonic devices because they enable flexible manipulation of optical fields via various mechanisms. Numerous types of these metasurfaces have been demonstrated to manipulate the spatially varied phase, amplitude and polarization of optical fields, including optical antennas with symmetric and asymmetric resonances [3,4], Pancharatnam-Berry phase [5–7] or detour phase metasurfaces [8–10], dielectric Huygens metasurfaces [11,12] and high-efficiency dielectric metasurfaces with magnetic and electric dipole resonances [13,14]. Despite the availability of these manipulation mechanisms, most metasurfaces reported to date are not tunable because their physical properties are set when they are fabricated [15]. Traditionally, dynamic control of optical wavefronts is realized through use of liquid crystal devices [16]. However, the bulky sizes and low response rates of these devices will limit further applications in the development of next generation photonic devices [17]. Some programmable metasurfaces have been reported for operation in the terahertz band [18–20], but the approaches used cannot be adapted to other bands. Recently, reconfigurable metasurfaces [21] have been investigated in an attempt to achieve tunable functions by introducing either flexible or physically changeable materials in the meta-atoms design [22–24] or by combining dielectric metasurfaces with liquid crystals [25–27]. Switchable or dynamic functionalities have been realized with these active counterparts, which have optical properties that can be changed by external stimulation [15] while the basic modulation mechanisms are quite diverse and include thermo-optical [22,28] or magneto-optical control [23], mechanical stretching [24,29] and charge carrier excitation [30,31]. Nevertheless, the relatively weak modulation effects (e.g., thermo-optical, magneto-optical) and nonnegligible induced optical losses (e.g., charge carrier excitation) further restrict the performances and potential applications of these materials.
Another promising method for active metasurface design involves use of optical phase-change materials (PCMs) [32], which exhibit large refractive index differences between their amorphous state (A-state) and their crystalline state (C-state) [33] while also offering very high switching speeds of up to 109 Hz [32]. Tunable devices and functions including reconfigurable zone plates [34], beam steering [35] and metalens [36] have been demonstrated by modulating optical wavefronts using PCMs. However, because they are limited by the binary states of the PCMs, the tuning functions of these metasurfaces are also inevitably binary. As an alternative, multi-state control can be achieved through phase transition of the select meta-atoms in the PCMs based metasurface [37]. It is also possible to realize independent multi-state functions by selectively altering the crystalline fraction of the PCMs [38,39], but no related metasurface of this type has been reported to date. This ability to transform between two states arbitrarily enables potential applications in optical storage [32,39] and opens up possible ways to achieve multi-level phase/amplitude modulation. However, flexible switching between multiple states remains challenging and requires the external stimulation to be controlled selectively and independently.
In this paper, we propose a metamolecule-based metasurface design to achieve multi-level phase/amplitude modulation. Using both the metamolecule-based design and the localized phase transitions of PCMs in a single metasurface, a metamolecule that consists of four nanopillars forming eight-level states is capable of achieving eight-level amplitude or phase modulations that cover the full 2π range. In addition to the multiple states obtained through selective control of the crystalline fraction of the PCMs [39], this method aims to enable local modulation of the bi-states of PCMs and thus further reduces the difficulty of multi-level-state control while also easing the mask design requirements for the fabrication process. We verify the proposed method numerically using a tunable metasurface that is capable of realizing a variety of reconfigurable functions, including optical vortex generation, phase-only 3D holography and amplitude-only display. This metasurface can further extend multi-functional applications of integrated meta-devices and can be used as a spatial light modulator that offers very compact device size and high modulation speeds.
2. Reconfigurable metamolecule design
When compared with typical phase-change materials (e.g., Ge2Sb2Te5), the Ge2Sb2Se4Te1 (GSST) alloy used here has lower losses over a broadband range in the infrared regime for both the A- and C-states [40,41], which enables binary phase/amplitude modulations of the light field. Therefore, we select the GSST alloy for use as the basic material for the designed reconfigurable metasurface at the operating wavelength of 1550 nm. Figure 1(a) shows a schematic that illustrates the reconfigurable multi-function applications that are possible with a single metasurface that consists only of the same type of metamolecule. Here we use optical vortex (OV) generation and holographic display as the functions for the proof-of-concept demonstrations. Using the phase-information encoding method, it is possible to achieve different functions by controlling the switching of the bi-states (A- and C-states) of meta-atoms locally. An OV beam is generated when encoding the vortex phase pattern into the metasurface, while switching to the holographic phase pattern leads to the generation of holographic images.
Fig. 1. Schematic and design of the metamolecule. (a) Schematic illustration of the reconfigurable metasurface. The single metasurface can perform different functions (e.g., OV generation, holographic display) by simply encoding it with different phase information. (b) Metamolecule structure consisting of four meta-atoms with a period P2=1600 nm. (c) Designed meta-atom that consists of a GSST nanopillar located on a silica substrate. The meta-atom period is P1=800 nm, the GSST nanopillar height is H=800 nm and the diameter D can be varied. (d, e) Numerically calculated results for the (d) modulated phase and (e) transmittance for periodical meta-atoms array in the A- and C-states at a wavelength of 1550 nm produced by varying the diameter D.
The basic meta-atom consists of a GSST nanopillar sitting upon a silica substrate. Each GSST nanopillar acts as a dielectric resonator that supports the electric or magnetic response (e.g., dipole, quadrupole) and thus enables phase/amplitude modulation in response to the incident light for both the A- and C-states [42]. We calculated the modulated complex electric field of the periodical meta-atoms array numerically by sweeping the geometric diameter D of the GSST nanopillar using finite-difference time-domain (FDTD) simulations, within which the period P1 of the meta-atom and the nanopillar height H are both fixed at 800 nm [Fig. 1(c)], and using horizontally polarized plane-wave excitation at a wavelength of 1550 nm. The complex refractive indices for both the A- and C-states of the GSST used in the simulations are presented in the Supplement 1 (Fig. S1). We first calculate the modulated phases and transmittances of the periodically distributed bi-states meta-atoms array with varying diameter D [Figs. 1(d) and 1(e)], where the modulated phases cover nearly the entire 2π range for the A-state within the complete sweep range, while the phase range for the C-state is inaccessible. To break through the restriction of the small tuning phase range [Fig. 1(d)] and the limitation of the bi-states, we also propose a metamolecule configuration that consists of four GSST nanopillars with an extended period P2=1600 nm to achieve multi-level phase/amplitude modulation by changing the phase states of the nanopillars selectively [Fig. 1(b)]. Typical metamolecule design methods activated by the independent effects of meta-atoms have previously achieved an abundant range of functions in multiplex metasurfaces [43–45]. However, these methods were based on the finite multiplexing information of the optical field, e.g., the polarization [43] and the wavelength [44,45]. Another meta-molecule design that involves an equivalent effect of superimposed modulation results for all the meta-atoms inside the metamolecule was also demonstrated [46,47], this method enables multiplexing for arbitrary polarization, wavelengths and even angles of light incidence [46]. Despite the use of multiplexing methods, all functions mentioned above became constant when the devices were fabricated, thus limiting the quantity of the realized functions using a single metasurface. The meta-molecule design proposed here, combined with a phase-change active metasurface, can provide a further breakthrough in terms of the quantity of the achieved functions, which is approximately unlimited in the design in this work. The effect of the designed metamolecule is equivalent to the superimposed results of the light field for all the four meta-atoms. Similar to the conversion of number systems, the four GSST nanopillars with their freely-varying diameters theoretically have a total of 16 states produced by the combinations of the bi-states for each nanopillar. For example, one of the four nanopillars that is changing phase from the A- to the C-state will be considered to be a state of the metamolecule, while the phase changes of the other nanopillars correspond to other states. This method, which uses only four fixed-diameter GSST nanopillars, eases mask-pattern design during the fabrication process and further relaxes the modulation phase range beyond that of the single GSST nanopillar. By considering the strict limiting conditions, we eventually select eight states of the metamolecule to modulate both the light amplitude and the full-range phase.
3. Pure phase modulation
Using the metamolecule design described above, the proposed method can be used to realize full-range phase modulation. The eight-level phases with π/4 intervals are selected to be −3π/4, −π/2, −π/4, 0, π/4, π/2, 3π/4 and π. To obtain this accurate eight-level phase modulation, which corresponds to eight states of the metamolecule, we calculated the modulated superimposed complex electric field of the four GSST nanopillars numerically as:
According to the calculated results, the diameters selected for the four nanopillars are D1=470 nm, D2=435 nm, D3=410 nm and D4=365 nm, and the eight-level states and the corresponding combinations of the nanopillars with the different phase states are illustrated in Fig. 2(a). All the selected GSST nanopillars maintain their relatively high modulated efficiencies in the A-state [Fig. 2(b)]. However, the corresponding efficiencies for the C-state are relatively lower because of the strong optical absorption [Fig. 2(c)]. The metamolecule forms eight-level phases that cover the 2π range by modulating the states of the four GSST nanopillars selectively while maintaining relatively high efficiency for most phase states [Figs. 2(d), 2(e)]. For example, the combination of three C-state nanopillars (D2, D3, D4) with one A-state nanopillar (D1) forms a metamolecule that corresponds to the modulated −3π/4 phase [first level in Fig. 2(a)].
Fig. 2. Metamolecule design for independent eight-level phase modulation. (a) Localized phase states in metamolecule forming the eight-level phases operating at the wavelength of 1550 nm. The diameters of the four nanopillars are D1=470 nm, D2=435 nm, D3=410 nm, D4=365 nm and are the same for all eight-level phases. (b, c) Transmittance spectra of the periodically distributed meta-atoms array of fixed-parameters as in Fig. 1(c) for (b) the A-state and (c) the C-state with the different nano-pillar diameters used in eight-level phase modulation. (d, e) Modulated eight levels of the (d) phase and (e) amplitude in (a) at the wavelength of 1550 nm.
As a proof of concept, first-order OV generation is achieved by appropriate arrangement of the metamolecules. The encoded 2π-range phase is discretized into eight levels and is then arrayed in the azimuthal orientation of the metasurface; the entire dimension is limited to within a circle with a diameter of 128 µm (80 metapixels) in the simulation. By simply exciting the arranged metamolecules using a Gaussian wave, first-order OV is generated and the simulated far-field results obtained via the Fresnel diffraction formula (see the Supplement 1) show the OV distributions with modulated efficiency of approximately 37% at 1550 nm [Figs. 3(a)–3(d)]. Furthermore, the vortex phase pattern is even maintained at the wavelength of 1500 nm (see Fig. S2 in the Supplement 1). The inhomogeneous intensity distributions are caused by the differences in the modulation efficiencies between the modulated levels, in which the modulated amplitude is approximately zero at the seventh level [Fig. 2(e)] due to the destructive interference among the modulated light fields of those four meta-atoms in a single metamolecule. Furthermore, higher-order OVs can be generated by changing the states of the nanopillars selectively inside the arranged metamolecules. As an example, a fourth-order OV is produced and the patterns are as shown in Figs. 3(e)–3(g).
Fig. 3. OV generation in the simulations. (a) Simulated transmittance spectrum of OV generation with different values of the topological charge l over wavelengths from 1400 nm to 1600 nm. Blue-square line: l = 1; red-circle line: l = 4. The insets show the two-dimensional meta-molecules distributions with different phase states for vortex generation with topological charges l = 1 and l = 4. (b−d) Simulated results for (b) amplitude, (c) phase and (d) the interference pattern of the OV and the coaxial Gaussian beam generation for l = 1 at the wavelength of 1550 nm. (e–g) The same distributions of (e) amplitude, (f) phase and (g) the interference pattern for m=4 corresponding to (b)–(d), respectively.
In addition, the basic metamolecule with the same parameters can also be used to produce a phase-only hologram. To reconstruct a three-dimensional (3D) object that includes three capitalized letters (N, R and C) displayed at distances of z1=120 µm, z2=220 µm and z3=320 µm from the metasurface plane [plane z=0 in Fig. 4(a)], a method that combines the traditional Gerchberg-Saxton (GS) algorithm with angular spectrum theory is used to extract the phase information from the target object (see the Supplement 1). The phase distributions are also discretized to eight levels and then mapped to the corresponding states of the metamolecule. The simulated size is 128 µm×128 µm, which corresponds to 80×80 metapixels, and the excitation source in the simulation is a horizontally polarized plane wave with an operating wavelength of 1550 nm. The complex electric field distributions at the metasurface plane are shown in Figs. 4(b) and 4(c). The holographic images at the different positions along the + z direction [z1, z2 and z3 in Fig. 4(a)] are obtained by calculating the far-fields using angular spectrum theory [Figs. 4(d)–4(f)]. The total optical efficiency, which is defined as the ratio between the optical power projected to the three image planes and the input power, is 33% at the wavelength of 1550 nm when other optical losses are ignored.
Fig. 4. Simulation results of the hologram for a 3D object. (a) 3D object that consists of the capitalized letters “N”, “R” and “C” located at the different planes of z1=120 µm, z2=220 µm, and z3=320 µm, respectively. (b, c) Simulated distributions for the (b) phase and (c) amplitude as recorded near the metasurface. (d–f) Reconstructed images in the planes (d) z1, (e) z2 and (f) z3 at the wavelength of 1550 nm in the simulations.
4. Amplitude modulation
The proposed metamolecule also enables amplitude modulation in addition to the phase modulation counterpart. However, to form eight levels of amplitude modulation, the diameters of the four nanopillars should be redefined using Eq. (1). The diameters selected for amplitude modulation are d1=425 nm, d2=220 nm, d3=205 nm and d4=230 nm, as shown together with the corresponding combinations of the nanopillars for the different phase states in Fig. 5(a). The simulated conditions, including the complete dimensions and the light source, are the same as those in the case of phase-only holography. Figures 5(b) and 5(c) also show the modulated efficiencies of the selected periodical meta-atoms array in both the A- and C-states. The corresponding eight-level states of the metamolecules form the fine eight-level modulated amplitudes with one-eighth amplitude intervals [Fig. 5(d)], while the modulated phases maintain near accordance for all states [Fig. 5(e)].
Fig. 5. Metamolecule design for independent eight-level amplitude modulation. (a) Localized phase states in the metamolecules that form the eight amplitude levels operating at the wavelength of 1550 nm. The diameters of the four nanopillars are d1=425 nm, d2=220 nm, d3=205 nm and d4=230 nm and are the same for all eight-level phases. (b, c) Transmittance spectra of the periodically distributed meta-atoms array of fixed-parameters for (b) the A-state and (c) the C-state with the different nanopillar diameters used in the eight-level amplitude modulation. (d, e) Modulated eight levels of the (d) amplitude and (e) phase in (a) at the wavelength of 1550 nm.
The amplitude modulation pattern is chosen to demonstrate the concept. By encoding the amplitude information into the phase states of the metamolecules in the metasurface, an expected image of flower that is monitored at the near-field with the same size of 80×80 metapixels (128 µm×128 µm) and decoded using the proposed method is obtained (Fig. 6). The modulated amplitude pattern, with efficiency exceeding 32% at 1550 nm [Fig. 6(a)], is effective over a broadband range from 1400 nm to 1600 nm when compared with the original image [Figs. 6(b), 6(c)], while the modulated phase distributions fluctuate within a small range at the designed wavelength of 1550 nm [Fig. 6(d)].
Fig. 6. Simulation results for amplitude modulation pattern. (a) Simulated transmittance spectrum of amplitude modulation over wavelength range from 1400 nm to 1600 nm. (b) Original image of the flower with size of 80×80 pixels. (c, d) Numerically retrieved amplitude modulation patterns for the (c) intensity and (d) phase distributions at several wavelengths in the range from 1400 nm to 1600 nm.
5. Discussion and conclusions
The above numerical demonstration of the proposed metasurface design shows the abilities for active optical wavefront tuning. It is still not clear what the maximal thickness of the GSST nanopillars can be to achieve the reversible switch [41]. However, recent research about 1-µm-thick GSST metasurface design has been demonstrated with the phase transition from A- to C-state [36], and it has also achieved reversible switch with 200+ nm thickness of GSST metasurface through electrical method [48]. Even if the 800-nm thickness of GSST nanopillars is unavailable for now, the proposed metamolecules design is general and can be expanded to other wavelengths and with other phase-change materials.
Some possible experimental methods can be adopted to realize the independent modulation of GSST nanopillars. One possible method is using femtosecond laser pulses to achieve the phase transitions of A- to C-state or C- to A-state for GSST nanopillars with different pulse number and pulse energy [34]. Here, one can move the fabricated sample step by step using a high-accuracy displacement platform, and the sample move can be controlled by the encoded distributions of A- and C-states GSST nanopillars. However, this optical modulation requires the phase change of GSST nanopillars one by one and cannot switch rapidly. Another potential method is using the electrically independent modulation as is reported in phase-change memory [49,50]. In a similar way, the GSST nanopillars are placed on the electrodes (used for heating the nanopillars) and two sets of conducting lines are crosswise placed on the GSST nano-pillars top and bottom of the electrodes respectively. The phase transition of these GSST nanopillars can be achieved by separately applying external electrical pulse on different conducting lines. However, the fabrications of such devices will be of great challenge.
In conclusion, we propose a new method to achieve independent phase/amplitude modulation using a combination of optical phase-change materials and metamolecule design in a metasurface. Using only four GSST nanopillars with appropriately tailored diameters to form the metamolecule, we achieve eight different metamolecule states, corresponding to eight levels of modulated amplitudes or phases covering a 2π range by controlling the bi-states of the GSST nanopillars locally inside the metamolecule. As proof of the proposed methods, we have designed a metasurface that is capable of achieving a series of functions, including OV beam generation and holographic display, in simulations. This metasurface design presents flexible performance over traditional metasurfaces that take on untunable or finitely tunable properties and expands the number of modulated functions immensely. The designed metasurface can be used as an optical spatial light modulator with pixel size comparable to the wavelength scale. In addition, the purpose of this work is to pave the way toward the use of optical phase-change materials in active metasurface design. The experimental demonstration of these designs remains challenging at present.
Funding
National Key Research and Development Program of China (2018YFB1801801); National Natural Science Foundation of China (61935013, U1701661, 61975133, 11774240, 61622504, 11604218, 61705135); Leading Talents Program of Guangdong Province (00201505); Natural Science Foundation of Guangdong Province (2016A030312010, 2020A1515011185); Science and Technology Innovation Commission of Shenzhen (KQTD2017033011044403, KQJSCX20170727100838364, ZDSYS201703031605029, JCYJ20180507182035270, JCYJ20200109114018750); Shenzhen University (2019075).
Disclosures
The authors declare no competing financial interest.
See Supplement 1 for supporting content.
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