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Abstract
Simultaneous control of phase and polarization offers a large degree of freedom to tailor the beam properties, for instance, enabling generation of structured beams such as vector beams and vector vortex beams. Here, we propose an ultrathin freestanding metasurface operating at the terahertz frequency for efficient generation of vector vortex beam with an arbitrarily defined topological charge from linearly polarized excitation. The metasurface is composed of bilayer metallic patterns separated by a thin quartz slab, with one layer determining the transmission polarization and the other controlling the transmission phase. The tightly cascaded two layers form a Fabry-Perot cavity to maximize the efficiency of the polarization and phase control. Two metasurfaces for generation of radially polarized vector beam with uniform phase and vortex phase are fabricated and tested at 0.14 THz. The experimental results successfully demonstrate the generation of high-quality vector beams with the desired phase. In the experiment, the ultrathin and freestanding properties allow the metasurface to be easily combined with other components, which shows great potential for the development of various compact terahertz systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Polarization is a basic property of electromagnetic waves. Linearly polarized light and circularly polarized light are widely used in optical systems, whose polarization states are spatially homogeneous in the propagation cross section. Recently, a growing number of studies are focused to cylindrical vector beams (VBs) [1], of which the polarization is spatially inhomogeneous in the propagation cross section. Radial and azimuthal polarization are two typical states. The polarization symmetry endows the VBs with a series of unique features. When radially polarized light is focused through a high-numerical-aperture lens, a strong longitudinal field component is generated at the focus. The focal spot size is much smaller than that of linear polarized beam. These properties promise profound applications in optical microscopy [2], optical trapping [3,4], electron acceleration [5], and multiplexing communication [6].
Vector vortex beams (VVBs) are vector beams carrying a vortex phase profile eilφ in the cross section, where l is the topological charge and φ is the azimuthal angle. In other words, VBs are a special case of VVBs with l = 0. VVBs carry orbital angular momentum (OAM) of lħ per photon, which provide additional degrees of freedom for optical manipulation [7]. VVBs can be widely used in high resolution imaging [8], optical communication [9,10], optical manipulation [11–13], quantum technologies [14] and so on.
The generation methods of VBs and VVBs have been extensively studied. Bulky birefringence crystal [15] and conical Brewster window [16] inside the laser cavity help to select the proper VBs mode after precise alignment. VBs with high polarization purity can be obtained via interferometric summation of orthogonally polarized beams through complicated light path [17–19]. Spatially variant metasurfaces with π phase retardation [20,21] are compact linear-to-vectorial polarization generators. In contrast, spatially variant metasurfaces with π/2 phase retardation [22] will convert circular polarized beam into VVB with l = ±1 due to the spin-orbital coupling and the geometric phase. Reflective metasurfaces are shown to achieve circular-to-vectorial polarization conversion with l = 1 based on proper superposition of left-handed circular polarization and right-handed circular polarization waves [23].
In the above studies, some can generate VBs and some generate VVBs with fixed topological charge. In order to achieve VVBs with other topological charges, spiral phase elements [21,24], spatial light modulators [25] or cascaded structures [26] should be used for additional phase compensation, which complicate the system. Hence, it is still challenging to achieve VVBs with arbitrary topological charge in a compact way, where independent control of the polarization and phase is urgently needed. Recently, metasurfaces capable of complete control of phase and polarization have been reported, where different types of VBs and VVBs have been demonstrated using a circular polarized excitation [27–29]. This can be achieved by simultaneous change of the orientation and the dimension of the inclusions [27,28], or by implementing the phase profile with a hologram and the polarization profile with subwavelength apertures embedded in the hologram [29].
In this article, we propose and experimentally prove ultrathin metasurfaces that generate VB and VVBs of arbitrary topological charges at the terahertz (THz) frequency from the more widely used linear polarization. The freestanding metasurface with total thickness of λ/14 is attached to a plano-convex lens for collimation and generation of structured beam in a very compact way. The metasurface is composed of tightly cascaded metallic structured layers on the opposite side of an ultrathin quartz wafer, one of which is used for rotation of the linear polarization by a desired angle and the other for phase control. The tightly cascaded two layers form a Fabry-Perot cavity to maximize the rotation efficiency and to tune the transmission phase. Our findings potentially open up new avenues for realizing high-purity structured beams with large flexibility in practical and compact terahertz systems.
2. Design
2.1 Basic principle and metaatom design
As shown in Fig. 1(a), the bilayer metallic metasurface, located in the x-y plane, transforms the x-polarized THz excitation into the beam of radial polarization with arbitrary phase profile. For clarify, the patterns in the top layer (incident side) and the bottom layer (transmission side) are separately shown in Fig. 1(b) and 1(c) for generation of radially polarized VB with uniform phase profile. The bottom layer (BL) is a metallic wire grating with the functionality of polarization selection. The top layer (TL) is anisotropic resonators with proper orientation in order to scatter the linearly polarized beam into a generally elliptically polarized one with a specific phase tuned by the dimensions of the resonators. For the cases where the polarization rotation is not needed, the BL grating is replaced by a resonator to enhance the transmission efficiency and to control the phase. In order to simplify the design, the metasurface is discretized laterally into eight sectors (S1-S8) as shown in Fig. 1(c), with each sector composed of one type of bilayer elements. The symmetry axis of each sector is marked sequentially as x, u, y, v, x, u, y, v axes, where u-v axes are 45° relative to the x-y axes as marked in Fig. 1(b).
Fig. 1. (a) Schematic of the bilayer metasurface for VBs’ generation. (b) and (c) show the structure in the top and bottom layers, respectively, where the discretized sectors and their symmetry axes are marked. (d) Schematic of the polarization conversion in each sector and the orientation of the metaatoms.
A metallic wire grating with deep subwavelength lattice constant A shows high transmittance (reflectivity) to light polarized perpendicular (parallel) to the wires. In each sector of the metasurface, the transmission axis ψ of the BL grating is always oriented to the target polarization direction to selectively pass the desired polarization component. As shown in Fig. 1(d), in order to achieve a radially polarized vector beam, ψ is along u, y and v axes for sectors 2-4, respectively, and repeats for sectors 6-8. The top layer (TL) of the metaatom is a double-C-shaped metallic resonator. The axis of symmetry of the outer and inner C shapes are usually different. It scatters the x-polarized incident beam into a general elliptical polarization, and the target polarization component will go through the BL. So the TL is used to change the polarization, and the BL is to select the desired one. The polarization direction does not need to be changed in S1 and S5. If the BL is still the grating, it would be transparent to the incident beam. As will be shown next, tuning the TL resonator is not enough to ensure high transmission amplitude. Therefore, the metaatom in S1 and S5 is changed into a two-resonator design in Fig. 1(d).
As shown in Fig. 2(a), the double-C resonator has 7 geometric parameters, the inner and outer radius of the large C (Rin and Rout), the inner and outer radius of the small C (rin and rout), the direction of axis of symmetry of the large C and the small C (θ and θ), and the half opening angle (α). α is the same for inner and outer C shapes in this study. For metaatoms in S1 and S5, the top layer is a double-T resonator and the bottom layer is a rectangular C-shape resonator. Detailed parameters in the TL and BL are marked in Fig. 2(b)–2(c), respectively. Desired phase control is achieved by changing the geometric parameters of the resonators. Therefore, the transmission polarization and phase can be independently manipulated by controlling the orientation of the grating and by choosing the dimensions of the resonators, respectively.
Fig. 2. (a) Schematic diagram of the metaatom structure with the period P = 805 µm. The bottom layer contains 5 evenly distributed metal grating, with the grating period A = 161 µm and the grating width W = 80.5 µm. The angle between the transmission axis of the grating and the x axis is ψ. The top layer is a double-C resonator, with 7 geometric parameters: the inner and outer radius of the large C (Rin and Rout), the inner and outer radius of the small C (rin and rout), the direction of axis of symmetry of the large C and the small C (θ and θ), and the same half opening angle (α) of the double Cs. The top layer (b) is a double-T resonator and the bottom layer (c) is a rectangular C-shape resonator with geometric parameters marked.
In the practical design, the TL and BL are separated by a quartz slab with the thickness of 155 µm and refractive index of 1.96. The metallic resonators are made of gold with the thickness of 200 nm. With the target working frequency of 0.14 THz, the period of the metaatom is selected as P = 805 µm. Five grating wires with period of A = 161 µm are included in a metaatom with the duty cycle of 50% (W = A/2) to ensure near perfect polarization selectivity.
Next, we will show that the two layers not only serve for change-selection of the polarization with desired phase, but also serve for enhancing the conversion efficiency through a Fabry-Perot cavity effect. We select one metaatom for each sector (S1-S4) and study the transmission amplitude with and without the BL in Fig. 3 through the finite-difference time-domain (FDTD) simulation in Lumerical FDTD. tij is the transmission amplitude with the incident beam polarized along i and the transmitted beam polarized along j direction. A metaatom is simulated with periodic boundary conditions in the metaatom plane, and perfectly matched layers along z. The incident light is x-polarized plane wave at the frequency of 0.14 THz. The source is located half-wavelength before the TL of the metaatom. The metal patterns in the TL and BL layers are modelled as two-dimensional perfect electric conductor patterns, which is a good approximation at the studied frequency. The minimum mesh size within the metasurface plane is 20 µm to resolve the grating wires. A monitor is placed 0.8λ away after the metasurface to detect the transmitted field, with the transmission coefficient generally written as ${t_{xx}}\tilde{x} + {t_{xy}}\tilde{y}$. txu and txv in S2, S4, S6 and S8 are calculated as ${t_{xu}} = {t_{xx}}\tilde{x} + {t_{xy}}\tilde{y}$ and ${t_{xv}} = {t_{xy}}\tilde{y} - {t_{xx}}\tilde{x}$.
Fig. 3. Transmission amplitude of the metaatoms in S1-S4 with and without the BL. (a) txx in S1 without and with the bottom layer. (b) txu in S2 without and with the grating oriented along u (ψ = 45°). (c) txy in S3 without and with the grating oriented along y (ψ = 90°). (d) txv in S4 without and with the grating oriented along v (ψ = 135°).
For metaatoms of S2-S4 in Fig. 3(b)–3(d), the existence of the grating dramatically increases the transmission efficiency over a wide bandwidth, and at the same time improves the polarization purity of the transmitted beam. This can be explained by considering the BL and TL as a Fabry-Perot cavity for the undesired polarization component, since the desired component will directly go through the BL and the rest will be reflected back to the resonator for iterative scattering. In order to verify that the enhanced transmission is due to the multiple beam interference from the Fabry-Perot cavity, we plot the transmission amplitude of the metaatom in S3 with different spacer thickness D at the frequency of 0.14 THz. It can be clearly seen from Fig. 4 that txy periodically vibrates with D as a result of Fabry-Perot interference. Here we choose a minimum D = 155 µm (λ/14) corresponding to the first transmission peak to ensure an ultrathin design. For the metaatom in S1 and S5, the bilayer resonator also enhances the transmission as compared to a monolayer resonator, as shown in Fig. 3(a).
Fig. 4. Variation of the transmission amplitude txy in S3 with the thickness D of the quartz spacer layer at the frequency of 0.14 THz.
There are totally 9 and 7 geometric parameters for metaatoms in S1 and S2-S4, respectively. The reason why so many parameters are involved is to increase the flexibility of phase control. However, the relation between the phase response with all the parameters cannot be intuitively shown by figures. For clarity, Fig. 5 summarizes the transmission phase of metaatoms in S1 to S4, by sweeping two geometric parameters of the resonator. The phase can be tuned within 0.8π in S1 and S3 from Fig. 5(a) and 5(c), and 0.65π in S2 and S4 from Fig. 5(b) and 5(d). In fact, by changing more geometric parameters, the phase range can be larger than that shown in Fig. 5. By limiting the transmission amplitude above 0.6 and sweeping all the parameters, the phase range covers 1.4π for polarization-maintained metaatoms in S1 and S5, 2π for 90°-polarization-rotating metaatoms in S3 and S7, and π for 45°-polarization-rotating metaatoms in S2, S4, S6 and S8. The metaatoms in S2 and S4 with symmetric geometry relative to the y axis show the same transmission phase. For radially polarized beam, the electric fields in the opposite sectors are out of phase. So it is desired that the overlapped phase tuning range among all the sectors covers π. By properly selection of the metaatoms, such phase requirement can be satisfied.
Fig. 5. (a) Transmission phase of txx in S1 and S5 with the variation of M3 and M7. (b) Transmission phase of txu in S2 and S6 with the variation of Rin and rin. (c) Transmission phase of txy in S3 and S7 with the variation of rin and rout. (d) Transmission phase of txv in S4 and S8 with the variation of Rin and rin. All the results are obtained at 0.14 THz.
2.2 Design and simulation of metasurfaces for VB and VVB generation
In order to show the independent control of phase and polarization, we design two metasurfaces for generation of radially polarized vector beam with uniform phase (VB) and vortex phase (VVB with the topological charge of 1), respectively. This process can be expressed as
Fig. 6. (a) The electric field vector distribution in the cross section of the radially polarized VB (top row) and VVB (bottom row) with l = 1 at different time instants. f is the frequency 0.14 THz. (b) Amplitude and phase responses of the 8 metaatoms for generation of radially polarized VB at 0.14 THz. (c) Amplitude and phase responses of the 8 metaatoms for generation of radially polarized VVB with l = 1 at 0.14 THz. The black circles represent the amplitude, and the blue dots represent the phase.
Two metasurfaces for VB or VVB generation are designed by filling each sector with the metaatoms in Fig. 6(b)–6(c), respectively. To match the spot size of the source, the size of the metasurface is 2 inches (around 5 cm) with 60 metaatoms along the diameter. FDTD simulation of the whole metasurface is very challenging. The minimum feature size determined by the metallic grating is only 80 µm, while the total simulation domain is more than 5 cm. Therefore, the numerical simulation of the whole metasurface would require very fine mesh and considerable computer resources. As the metaatoms in a single sector are the same, the local response of the metasurface will be very close to that of the metaatoms in a periodic pattern. This assumption holds except for a few metaatoms at the sector boundaries, which only take 6.7% of the total number of metaatoms and do not affect the accuracy of far field calculation significantly. To a good approximation, one can directly find the electric and magnetic field profile at the output BL based on the metaatom responses. Then the metasurface can be considered as an artificial source with equivalent electric and magnetic current determined by the local response of periodic metaatoms from FDTD. The field at the observation point can be solved with the help of the dyadic Green’s function (DGF) [30–32]. (More detailed information about the FDTD-DGF calculation is included in Supplement 1, Section II.
3. Results and discussion
We used the standard optical lithography and lift-off process to fabricate the metasurfaces. The 155 µm-thick and 2-inch quartz wafer was ultrasonically cleaned with acetone, isopropanol, and deionized water in sequence for 10 minutes. The photonresist (AZ 5214) was spin-coated at 4000 rpm on the quartz wafer and baked at 95°C for 90 s. After 7s of exposure to ultraviolet light, the pattern was transferred from the mask to the photoresist. Next, the sample was developed for 40 s using a developer solution (TMAH). A 200 nm-thick gold film was deposited by sputtering. Then the sample was immersed into acetone ultrasonically for the peeling process. After the fabrication of the metallic pattern in the top layer, it was coated by photoresist for protection. And the metallic pattern in the bottom layer was prepared following the same procedure. Once the two patterns are prepared, the protecting photoresist is removed, leading to a freestanding bi-layer metasurface. Figure 7(a) shows the optical images of the fabricated VB metasurface and VVB metasurface. The zoom-in views of the top and bottom patterns are included. In Fig. 7(b), the side view of the VB metasurface is compared with a coin to show its thickness.
Fig. 7. (a) Optical images of the fabricated VB and VVB metasurfaces and enlarged top and bottom views. (b) Comparison the ultrathin freestanding metasurface with a coin.
The photograph and the schematic plot of the experiment system is exhibited in Fig. 8(a) and 8(b), which is mainly composed of a THz source, a plano-convex lens, a metasurface, a polarizer, a detector and a 2-D translation stage. A continuous wave source (IMPATT diodes) operating at 0.14 THz radiates vertically polarized (y-polarized) beam with the output power of 30 mW. The beam is collimated by a TPX plano-convex lens (Tydex) with the focal length of 75 mm. The collimated beam has a beam waist of 4.26 cm. Thanks to the ultrathin and freestanding features, the metasurface like a film is tightly attached to planar interface of the lens by an optical mount, as shown in Fig. 8(c) and 8(d). A polarizer after the sample is rotated to select different polarization directions when necessary. A Schottky diode detector mounted on a two-dimensional translation stage is used to detect the intensity of the beam 8 cm away from the sample. The intensity distribution is collected over a scanning area of 60 mm × 60 mm with a resolution of 1 mm. A lock-in amplifier (Stanford Research System SR-830) with 500 Hz modulation rate is connected to the source and the detector to extract the signal.
Fig. 8. (a) The photograph of the experimental system. (b) Schematic plot of the light path. The laser beam at 0.14 THz is collimated by a plano-convex lens, and the metasurface is directly attached to the planar side of the lens via an optical mount. A polarizer after the metasurface is used to select proper polarization. The detector is mounted on a 2D translation stage to measure the intensity distribution. (c) A front view of the combined convex lens and meatsurface. (d) A back view of the combined convex lens and meatsurface.
For each metasurface, we measure the beam intensity profile 8 cm away from the metasurface without the polarizer, and with the polarizer under different polarization angles of 0°°, 45°, 90° and -45°. We also calculate the field distribution at the same distance for comparison. As shown in Fig. 9(a) and 9(f), the hollow-core donut shape intensity after the VB metasurface is observed in both simulation and experiment, which is a signature of vector beam. The segmentation of the metasurface has negligible effect on the beam quality. When the polarizer is added with the polarization direction along 0°, 45°, 90° and -45°, the theoretical and measured spots are shown in Fig. 9(b)–9(e) and 9(g)–9(j), further validating the polarization is along the radial direction.
Fig. 9. Simulated and experimentally measured intensity distributions after the metasurfaces without the polarizer (a, f, k, p) and with the polarizer oriented along 0° (b, g, l, q), 45° (c, h, m, r), 90° (d, i, n, s) and -45° (e, j, o, t). The first two rows are the simulation and experiment results of the VB metasurface, and the last two rows are the results of the VVB metasurface.
Similarly, the simulation and experimental results of the VVB metasurface with topological charge l = 1 are shown in Fig. 9(k)–9(t). The phase singularity disappears, and a bright center is observed. This is because the beam can be decomposed into a circularly polarized light (with bright center) and a circular polarized vortex light (with dark center) as
When the polarizer is added, the spot becomes a “S” shape of different directions with the rotation of the polarizer [23]. The experimental and simulation results are highly consistent for the two metasurfaces. The phase distribution of the VB and VVB cannot be directly measured in the current system. The simulated phase profiles with non-vortex and vortex features after the two metasurfaces are shown in Supplement 1, Section III. VVBs with other topological charges can be achieved similarly. Design and simulation of a VVB metasurface with l = -2 can be found in Supplement 1, Section IV.
4. Conclusions
In summary, we have studied a type of ultrathin and freestanding bilayer metallic metasurfaces capable of independent control of the polarization and phase profiles of the terahertz beam. The metasurface is composed of two layers of metallic patterns separated by a thin quartz wafer, with one layer determining the polarization and the other tuning the phase. The bilayer configuration forms a Fabry-Perot cavity to enhance the conversion efficiency of this process. As examples in actual application, metasurfaces converting a linearly polarized beam into a radially polarized one with uniform phase and vortex phase are designed, fabricated and experimentally tested. The metasurface is attached to a plano-convex lens for simultaneous collimation and structured beam generation during experiments. Such ultrathin metasurface can be attached to any other planar terahertz element conveniently for beam transformation in a very compact way. The measured results are in good agreement with the theoretical ones. The proposed design may find applications in various terahertz imaging and communication systems.
Funding
National Key Research and Development Program of China (No. 2017YFA0701000); National Natural Science Foundation of China (61805123, 61831012); Natural Science Foundation of Tianjin City (18JCQNJC02200).
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
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