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Abstract
We present a new, to the best of our knowledge, formalism in the design of metasurface beamsplitters with arbitrarily chosen split beam directions. This technique is based on the well-established array theory; in particular the Fourier transform method of array synthesis, to cast an obliquely incident plane wave to multiple designer-selected scattering directions. To show the efficacy of this approach, a beamsplitting metasurface reflector is designed and verified experimentally and numerically. The metasurface is fabricated by screen-printing patterns of metallic rectangular-shaped resonators of conductive ink onto a ground plane-backed substrate. The beamsplitting characteristics are quantified using a simple free-space transmit/receive horn system operating at 10.525 GHz. It is shown that the presented design technique accurately predicts the scattering properties of the fabricated metasurface and is a useful method for electromagnetic wave manipulation.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years metasurfaces, the planar equivalent of metamaterials [1], have been applied to numerous topics in electromagnetics such as anomalous reflection and refraction [2] and holography [3,4], and are now finding applications in enhancing 5G and millimeter-wave antennas [5,6], healthcare and biomedical imaging and sensing [7,8], and radar cross-section (RCS) reduction and stealth technologies [9–11]. More recently beam-splitting from gradient metasurfaces has been demonstrated [12–15]. A beamsplitter is an important optical component that splits incident light into two or more directions with applications in interferometry, spectroscopy, and multiplexing. Traditionally, beamsplitters fall into two forms: cubes made from two glass prisms adhered together, or dielectric plate beamsplitters [16]. These types of beamsplitters tend to be large and bulky, meaning they cannot be used in miniaturized systems and photonic devices. Metasurfaces are a potential solution allowing for beamsplitter integration into miniaturized instrumentation due to their small size and wide-ranging ability to manipulate light. This could lead to the miniaturization of laboratory quality instrumentation, such as an interferometer, to be cast into a small and more portable footprint.
Previous work on metasurface beamsplitters [12–15] has been confined to the scheme of gradient metasurfaces. In a gradient metasurface, an arrangement of subwavelength diffractive elements are arranged in a supercell in such a way that a full $2\pi $ phase cycle occurs over the supercell period. This periodic nature confines the wave scattering from the metasurface to diffraction orders defined by the grating period of the super cell. In this work we do not confine ourselves to the gradient metasurface paradigm and as such are not restricted to beamsplitting into diffraction orders.
In this paper we present an approach to generate metasurface beamsplitters with arbitrary split beam directionality based on the Fourier transform method of array synthesis. This method is used to calculate the required reflection magnitude and phase distribution across the metasurface to generate two reflected beams scattering at arbitrarily chosen directions. The metasurface beamsplitter reflector design realized in this work directs a normally incident, horizontally polarized wave into two desired reflected waves, one beam at 25 degrees, and the other at 45 degrees with an operating frequency of 10.525 GHz. Unit cell simulations of various sized rectangular-shaped resonators are performed, the results of which are used to develop the metasurface design. The metasurface beamsplitter is then fabricated using a low-cost screen-printing technique and conductive ink, with printing tolerances informing the unit cell size. The scattering properties of the metasurface beamsplitter are characterized using a low voltage, linearly polarized Gunn diode transmitter and receiver operating at 10.525 GHz. The resulting experimental data is then compared to the theoretical predictions and full-wave simulations.
2. Theory
This presented technique is based on array theory; in particular the Fourier transform method of array synthesis, for the design of an arbitrarily directed metasurface beamsplitter. According to array theory [17], when illuminated by a plane wave, the total scattered wave from a metasurface can be expressed as the superposition of the scattered waves from each individual unit cell on the metasurface. For an M-by-N planar metasurface, the total scattered wave is given by
To design a beamsplitting metasurface, an array factor $F({u,v} )$, describing a far-field pattern with two or more main peaks is chosen, and Eq. (3) is solved for the complex amplitudes. The split beam peaks are defined by two-dimensional delta functions in $({u,v} )$-space, with the array factor given as
3. Design
Unit cell simulations of various sized conductive rectangular patches on a ground plane-backed acrylic substrate were performed in ANSYS HFSS. A normally incident 10.525 GHz, x-polarized plane-wave illuminates the unit cell and periodic boundaries are applied. The unit cell is a square with periodicity $p = 9.3\; \textrm{mm}$ and is composed of a 50-micron thick rectangular patch with a conductivity of $12500\; \textrm{S}/\textrm{m}$ on a 0.7938 mm-thick acrylic substrate with aluminum backing. The x and y side lengths, ${l_x}$ and ${l_y}$, of the conductive rectangular patch are varied from 50 microns to 9.3 mm and the reflection magnitude and phase are modeled. The unit cell layout is shown in Fig. 1(a), and the simulated reflection properties of the metasurface unit cell with varying size conductive rectangular patches are shown in Fig. 1(b,c). The unit cell period is chosen such that the various sizes of conductive rectangular patches adhere to the fabrication tolerances and capabilities of screen-printing while providing the necessary reflection properties. The thickness of the conductive rectangular patches is chosen based on typical ink deposition layer thicknesses of screen-printing.
Fig. 1. (a) Metasurface unit cell consisting of a conductive rectangular-patch resonator of dimensions ${l_x}$ and ${l_y}$ atop an aluminum-backed Acrylic substrate. $p = 9.3\; mm$ and $h = 0.7983\; mm$. Simulated reflection (b) and phase (c) of the metasurface unit cell as a function of the normalized side lengths $({{{l_x}}/ p}, {{l_y}}/ p)$ of the conductive patches.
To demonstrate the effectiveness of this approach a metasurface beamsplitter reflector was designed, simulated, and tested. The metasurface reflector is intended to split a normally incident (${\theta _i} = 0,\; {\phi _i} = 0$), horizontally polarized wave into two reflected waves; one beam is directed at 25 degrees (${\theta _{r1}} = 25,\; {\phi _{r1}} = 0$), and the other beam is directed to 45 degrees (${\theta _{r2}} = 45,\; {\phi _{r2}} = 0$). The complex reflection coefficients distributed across the surface of a 241.8 mm by 241.8 mm metasurface beamsplitter were determined from Eqs. (3) and (4) and the chosen reflection angles above. A nearest-neighbor search is performed on the simulated data to determine the ${l_x}$ and ${l_y}$ patch lengths to yield the desired reflection properties across the surface using a Euclidean distance metric. The Euclidean distance metric is applied on a two-dimensional space composed of the reflection magnitude on one axis and reflection phase (normalized) on the other axis, and is the distance between the calculated reflection properties and the simulated reflection properties. A full UV-space plot of the beamsplitting properties are shown in Fig. 2(a), and the surface reflection and phase properties are shown in Fig. 2(c,d). The metasurface was specifically designed to operate at 10.525 GHz to accommodate the fixed frequency used by our low voltage, linearly polarized Gunn diode transmitter and receiver. It can be seen in Fig. 2(b), using numerical simulations performed in CST Microwave Studio, that there is a rapid fall off in efficacy as we move away from the intended frequency of operation.
Fig. 2. (a) Full UV-space beamsplitting patterns for the designed metasurface. (b) Simulated reflection coefficient for the designed metasurface at varying frequencies. (c) Calculated reflection magnitude and (d) reflection phase surface distribution for the metasurface beamsplitter.
The demonstrated metasurface beamsplitter scatters all beams into the horizontal plane, thus the calculated reflection properties of the metasurface are constant in the vertical direction. Although the metasurface beamsplitter presented casts the two reflected beams into the horizontal plane, the framework described above also applies to the case where the reflected beams are no longer in the same plane. That is, one beam could be in the plane of incidence while the other is being scattered out of plane. This would result in a metasurface with structures varying in both spatial directions.
4. Fabrication and experimental setup
The beamsplitter was fabricated using the screen-printing process to deposit the metasurface pattern onto a 304.8 mm by 304.8 mm by 0.7938 mm acrylic substrate (Fig. 3(a)). The total printed pattern area is 241.8 mm by 241.8 mm allowing for a 21 mm margin surrounding the illuminated metasuface which is later used to secure the aluminum reflector. Screen-printing has been previously applied to the fabrication of frequency selective surfaces in the microwave [19,20] and millimeter-wave [21] regimes. The beamsplitter pattern was developed in MATLAB (Fig. 3(b)) using the presented theory and finalized in Adobe Illustrator to be laser printed onto a clear transparency. The transparency was then used as a stencil and transferred to an RXP Dual Cure emulsion coated 350-micron 584.2 mm by 787.4 mm aluminum framed mesh screen through UV curing for 180 s. The uncured emulsion was then washed away leaving only the beamsplitter pattern in the screen [22].
Fig. 3. (a) Screen-printing process used to create metasurface beamsplitter. (b) Screen template for the investigated splitting configuration used to make the screen. (c) Final printed metasurface beam-splitter sample. This image shows the print quality achieved with this process.
Super shield nickel conductive ink was used to create the conductive rectangular patches. The conductive ink was evenly bled through the screen, directly onto the acrylic substrate, using a 70-durometer wood squeegee, as shown in Fig. 3(a). The nickel ink was chosen due to the relatively low cost, low resistivity of $0.004\; \mathrm{\Omega }\cdot \textrm{cm}$, and a suspended particle size of approximately 30 nm. Although the conductive ink used had a stated resistivity of $0.004\; \mathrm{\Omega }\cdot \textrm{cm}$, printing trials showed a consistent conductivity of 12500 S/m after curing. With this screen-printing setup, the conductive ink was deposited in an approximately 50-micron thick layer. The print quality achieved is shown in Fig. 3(c) where evidence of ink bleeding as well as some areas of poor deposition are shown. The aluminum reflector was later secured to the non-printed side of the acrylic substrate using adhesive strips attached to the perimeter.
Experimental characterization of the beamsplitter metasurface was performed with a PASCO microwave optics system (WA-9314C). The essential components of this system include a Gunn diode transmitter, receiver, a goniometer with fixed and rotatable arms and degree scale, and necessary mounting stands and component holders (Fig. 4(a)). The transmitter uses a low voltage source to produce linearly polarized microwaves with a fixed frequency of 10.525 GHz at 15 mW. The receiver has a built-in amplifier, as well as a variable sensitivity scale that was externally connected to a 3½ digit precision digital multimeter.
Fig. 4. Experimental setup (a) shows the location of the TX and RX horns with ray beams drawn to illustrate hypothetical locations of the reflected beams. (b) Top down view to show rotation of the metasurface beam-splitter to achieve changes in the angle of incidence. The RX arm was then manually rotated from $- {90}$° to $+ {90}$° in increments of ${1}$° relative to the beam-splitter, fixed at a constant distance. (c) Top down view to illustrate procedure to capture reflection data at the location of the TX using a partial reflector at normal incidence.
The metasurface was affixed to a rotational component holder central to the goniometer and the receiver horn (WA-9800) positioned at 40 cm relative to this center on the free-moving rotation arm. The transmitter horn (WA-9801) is fixed at a single location pointing normally towards the metasurface at a distance of 40 cm as shown in Fig. 4(b). The receiver is manually rotated about the metasurface from -90 degrees to +90 degrees in 1-degree increments. The incident angle between the transmitter and the metasurface surface normal is controlled by rotating the component holder. Measurement sweeps for oblique incident angles were performed for every 5-degree increments between -60 degrees to +60 degrees to fully characterize the scattering properties of the metasurface. Pyramidal foam absorbers were positioned about the measurement area to reduce stray scattering from the surroundings.
There were a total of three trials performed for each angle sweep at each incident angle. Before each trial a full reflector was positioned in place of the metasurface to measure the incident electric field intensity, ${E_i}$. This was done to properly determine the relative intensities produced by the metasurface beamsplitter reflector for appropriate comparisons with theoretical and numerical calculations. Due to the fixed physical position of the transmitter a small fraction of data was initially not able to be collected. This was remedied by positioning a partial reflector at the central position with the metasurface setback on a rotational component holder allowing the partially reflected field from the metasurface to be reflected back to the receiver, see Fig. 4(c). This allowed for the split beam peak reflection location data to be acquired for regions where the transmitter is physically in the way of the path of the rotation arm and receiver.
5. Results
Numerical simulations of the designed metasurface beamsplitter were performed in CST Microwave Studio using the time domain solver with a steady-state accuracy of -30 dB and far-field Electric field monitors. A 10.525 GHz, horizontally polarized plane wave is used as the excitation and is swept through incident angles from -60 degrees to +60 degrees in 5-degree increments. A direct comparison between the experimental, theoretical, and numerical reflections is shown in Fig. 5. As can be seen, the experimental design presented produces excellent and clearly distinct peak beam splitting characteristics at the intended splitting angles that agree with both theoretical and numerical calculations. Oblique incidence is measured and a direct comparison between theory, numerical, and experiment of the split beam peak locations is shown in Fig. 5(b). A full reflection profile is presented for the theoretical and numerical simulations Fig. 5(c,d). The numerical simulation data in Fig. 5(d) shows the prevalence of the specular reflection above incident angles of 20 degrees but the split beams are still clearly pronounced throughout.
Fig. 5. (a) Normal incident comparison for experimental, theoretical, and numerical reflections. (b) Split beam peak location comparison for experimental, theoretical, and numerical reflections as a function of incident angle. Surface plot of field intensities for oblique incident angles for (c) theoretical and (d) numerical calculations.
The experimental data was collected over a total of three trials. Between each trial the screen had to be removed and replaced with a full reflector to measure the incident electric field, ${E_i}$. The metasurface screen was then placed back and carefully centered and leveled before data acquisition. The reflection data collected for that trial was then divided by ${E_i}$ and later all three trials were averaged together. Figure 5(a) shows the average experimental data from these measured trials along with error bars illustrating the maximum deviation from the average for all collected trials. The deviations observed in the experimental measurements potentially arise from the small variations in the metasurface alignment process between each trial.
A comparison between the theoretical performance, numerical simulations, and experimental measurements of the metasurface beamsplitter, shown in Fig. 5(b), exemplifies the accuracy of the presented technique. Over all incident angles, the measured split beam peak locations vary from the theoretical predictions by less than 4 degrees. Over incident angles ranging from -20 degrees to +60 degrees, the split beam peak locations from the numerical simulations varied from the theoretical predictions by less than 2 degrees. Outside of this range, the numerical simulations showed a variation in split beam location of up to approximately 12 degrees as the incident angle approached -60 degrees.
6. Conclusion
In this paper, we proposed an inverse design technique for generating arbitrarily directed split beams from a reflective metasurface. The efficacy of our technique was evaluated through numerical and experimental verification by designing a metasurface beamsplitter that reflected a normally incident, horizontally polarized 10.525 GHz wave to 25 degrees and 45 degrees. The resulting metasurface beamsplitter is unlike previously reported metasurface beamsplitters in that ours is not confined to the scheme of a gradient metasurface. Therefore, the directions of the split beams are not dependent on a grating period. Furthermore, the technique presented can be applied to beamsplitters with more than two split beams, as well as beamsplitters with simultaneous split beams in and out of the plane of incidence. The design technique shown in this paper is a highly useful method of electromagnetic wave manipulation and has a broad array of potential applications.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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