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Abstract
Varifocal mirrors, which have various applications in optical coherent tomography and three-dimensional displays, are traditionally based on the fluid pressure or mechanical pusher to deform the mirror. The limitations of conventional varifocal mirrors are obvious, such as the heavy size of the device and constraints of tunability, due to their mechanical pressure control elements. The reprogrammable metasurface, a new flat photonic device with multifunction in an ultrathin dimension, paves the way towards an ultrathin and lightweight mirror with precise phase profile. Here, an active reconfigurable metasurface is proposed to achieve the manipulation of the wavefront. The meta-atom in the metasurface is integrated with one varactor diode to manipulate the electromagnetic response. As the bias voltage increases from 0 to 20 V, the resonant frequency shifts from 5.5 to 6.0 GHz, which generates a broad tunable phase region, leading to 5 diopters (about 50%) change without any mechanical element and a broad tunable frequency band. In addition, the focus point can not only be steered in the axial line above the metasurface but also in the whole working plane. The proposed focus-tunable metasurface mirror may be a key in enabling future ultrathin reconfigurable optical devices with applications such as multiphoton microscopy, high speed imaging and confocal microscopy.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The focusing mirror is a ubiquitous optical device in the most imaging systems. Many applications, such as optical coherence tomography (OCT) and confocal microscope, use the compact mirror with tunable distance to improve the lateral resolution and depth [1,2]. Various methods are utilized to develop the varifocal mirror [3–5]. Mechanical and electromechanical tuning mechanisms are two prevalent approaches to adjust the mirror with deformable solid or liquid filled. Though some of these have a fast repose time and a precise control precision, they are still bulky (for the filled material) and with limited tunability. The liquid crystal switchable mirror [6] has higher tuning speed, while it suffers from weakness like polarization dependence as well as a limited tuning range. Some freeform optical elements are even based on mechanical movement [7], which is hardly to be fast due to the cumbersome element.
Metasurface, a planar two-dimensional (2D) version of metamaterial [8–15], has been proposed as an alternative way for the focusing mirror [16]. Dielectric metasurfaces are versatile for their precise wavefront control and subwavelength resolution [17–21]. Based on the generalized Snell’s laws proposed in 2011 [12], researchers have flexibly designed and distributed constituent meta-atoms to manipulate light–matter interactions, thereby leading to numerous interesting functions, e.g. the control of phase, polarization, or special component of light [22–24]. The advantages of low profile and easy manufacture promote it as a suitable candidate for design of optical mirror and lens [25–27].
However, conventional passive metasurfaces confine the applications of metasurface-based focusing mirror due to its fixed focus length. In other words, the passive meta-atoms are not able to modulate the phase profile due to their intrinsic dispersive behavior once the structures are determined. Recently, active elements like varactors and diodes are utilized to perform dynamic electromagnetic (EM) wave control [28–30]. Metasurface which is composed of those active elements has been proposed to realize various applications like reprogrammable hologram, reconfigurable reflector, beam forming, etc. [31–34]. Considering the phase-tunable characteristic, the reprogrammable metasurface provides an alternative solution for the varifocal mirror and has great application potentials in miniaturized and reconfigurable devices and systems.
Here, we present a one-dimension metasurface mirror with a tunable focus point. Furthermore, the focus point is not only movable in the axial line above the metasurface, but also can be steered in the whole working plane which is along the phase change direction. The dispersion response of the element can be tailored by incorporating varactor diode which is controlled by the direct current (DC) bias voltage, and the voltage is managed by the microcontroller unit (MCU), thus it is possible to achieve focus-tunable metasurface mirror (∼5 diopters, corresponding to about 50% change) without any movement or deformation of the mirror, and such a rapid phase control brings the fast focus switching or scanning. In this paper, theoretical analysis is performed first, which is further demonstrated by simulations. Finally, A prototype is fabricated and tested to verify its varifocal performance. To the best of our knowledge, this is the first focus-tunable mirror based on metasurface that provides center and off-center focusing performance. The concepts and techniques used in our metasurface can be combined with other devices like metasurface doublet and ultrathin optical devices to save space and enable lateral scanning of focus.
2. Concept and meta-atom design
Figure 1 shows the schematic of the focus-tunable mirror. The metasurface is composed of $\textrm{31} \times \textrm{10}$ unit cells and has an identical phase response along each column. Besides, each column acts as a bias line to provide the voltage for varactor diode, thus the phase response of each column can be elaborately independently tailed. The metasurface mirror works from 5.5 to 6.0 GHz, and the axial focus length can be tuned in the range from 100 to 200 mm, besides, the focus point can be steered off the center line.
To verify the feasibility of the metasurface-based focus-tunable mirror, we first designed the unit cell. Figure 2(a) shows that the designed unit with a varactor diode (Skyworks SMV1430), whose junction capacitance changes from 0.35 to 1.24 pF as the DC bias varies from 0 to 20 V. The copper patterns with a thickness of 35 µm are printed on the top of 2 mm thick F4B substrate with a dielectric constant of 2.3 and a loss tangent of 0.003. The interdigital structure, whose detailed dimensions are $e = la = 0.5\,mm$ and $ha = 1.4\,mm$, is used to enhance the coupling capacitance between two copper sheets [35]. The relationship between reflecting spectra of the unit cell and the bias voltages applied to the varactor diode are obtained with the commercial Maxwell equation solver, i.e. CST Microwave Studio. The simulation result is carried out with time domain solver, accompanies with electric boundary conditions (Et = 0) in y-direction and magnetic boundary (Ht = 0) in x-direction. And the varactor diode in the simulation is replaced by a lump element capacitance. Moreover, the spatial grid size is suitable with the default setting, i.e. 10 cells per wavelength. As displayed in Fig. 2(b), the simulation results illustrate that the bandwidth of the proposed unit is approximately 1 GHz and it is able to cover arbitrary phases of $2\pi $ from 5.5 to 6.0 GHz.
Fig. 2. (a) Schematic of the considered unit cell with fixed parameters p = 15.5 mm, t = 2 mm and m = 1.5 mm. The normal incident wave is x-polarized. The distance between two copper sheets is a = 1.7 mm. The land, to which the varactor welds, is with dout = 1 mm and am = 1.2 mm; (b) Simulated relationship between phases and the bias voltage of the designed unit cell using CST; (c) Measured relationship between phases and the bias voltage of the fabricated cell in experiment.
To measure the reflection responses, we apply different reversed bias DC voltages from 0 to 20 V on the varactor diode to tune the capacitance. Two horn antennas, connected with a network analyzer, are placed in front of the metasurface, each inclined with an angle of 5° relative to the normal direction of the metasurface. All the units are applied with the same bias voltage to reduce the impact of mutual coupling and edge diffraction; thus, the reflection responses are derived from the measured transmission coefficient S21. The experimental results are shown in Fig. 2(c). It can be seen that the resonant unit still covers a large frequency band from 5.5 to 6.0 GHz, and it is easy to expand the working band by using a more expensive varactor diode like MACOM MGV 125-08 which owns a wider range of capacitance values. The results are not perfect enough due to the fabrication and measure error and the deviation is mainly attributed to three reasons. First, the solders on the varactor diode and the feed lines link the voltage supplier with the metasurface will bring additional structure. Second, the uncertainties in dielectric properties. Third, the low frequency signals also bring the discrepancies. Exploiting the experimental results of the unit cell, the relationship between voltages and phases is able to be coded into MCU to control the whole metasurface.
3. Simulation & experiments
3.1 Metasurface design
In order to achieve a metasurface-based focus-tunable mirror operates on yoz plane, phase distribution of each column are designed according to the simple geometrical formula [36],
where f is the focal length of the mirror, ${y_0}$ means the y-axis coordinate of metasurface center, $\lambda$ is the wavelength in vacuum and $\phi (y )$ is the required phase of the unit located in the place $y = np$, n is an integer and p is the period of the metasurface unit.The reconstruction of focus effect is numerically examined by Rayleigh-Sommerfeld diffraction theory on the two-dimension plane [37], which can be applied to the calculation of the electronic field distribution of the one-dimension metasurface. The phase sequences for the further simulation and experiment with different positions, i.e. $f = 100\,mm$, $f = \textrm{2}00\,mm$ and $f = 1\textrm{5}0\,mm$ (off-center) at the two operating frequencies are calculated by Eq. (1) and illustrated using the form of color bar in Fig. 3. The focusing ability of the metasurface depends on the numerical aperture $NA = \sin [{\tan ^{ - 1}}(D/2f)]$, where D is the width of the mirror. Consequently, with different focus length f, the numerical aperture ranges from 0.77 to 0.92.
Fig. 3. 3D full wave simulation results of amplitude distribution on y-polarization with the field of incident wave subtracted, where metasurface is on the y-axis. The color bar on the y-axis illustrates the degree of each unit cell.
3.2 Simulation results and experimental validation
The focus phenomenon of the proposed metasurface mirror is first simulated using CST Microwave Studio through time domain solver with open boundary conditions, and the mesh setting is the same as the unit cell simulation. To simplify the simulation process, one phase sequence is discretized to eight phases, from -135° to 180° with 45° interval, which is illustrated on the y-axis in Fig. 3. The y-polarized plane wave is incident on the metasurface, the amplitude of Ex and Ez are too small to be ignored thus we only need to record the dominating copolarized y-component Ey. The relationship between the reflection phases and voltages are derived from Fig. 2(b), as well as the required phases deduced by the formula (1), and corresponding voltages are obtained by looking up the matchup. It should be noted that since CST can only give the total field Etotal, the incident field Eincident without metasurface is also simulated, hence, the reflected field ${E_{reflected}} = {E_{total}} - {E_{incident}}$. The simulated near-field distributions are shown in Fig. 3, where the normalized electric field intensity on the yoz plane at 5.5 GHz and 6 GHz are given. The energy patterns with same positional focused point at different frequencies are similar, the phase profile and energy focus at 100 mm, 200 mm, and 150 mm (off-center) for 5.5 GHz are presented in Fig. 3(a)–3(c), the similar results for 6 GHz are depicted in Fig. 3(d)–3(f). It corroborates that the proposed focusing mirror is able to work under a considerable bandwidth. In case of the metasurface mirror’s efficiency, calculated by the division of focus spot power and input power, the radius of the spot power is determined by formula, $R = 4\lambda {M^2}f/(\pi D)$, where M = 1 and D is the diameter of metasurface lens. f is the focal length and ${\lambda}$ is the wavelength. The spot size power, added up all the power of points falling in it, is calculated using MATLAB. The average calculated simulation focus efficiency is 39.6%. Although the efficiency is not as high as the metasurface which is composed of passive elements, the key point of our work is exploratory on varifocal effect, the promotion of efficiency is remained for future work.
In order to validate the simulated results, the focus-tunable metasurface mirror is fabricated by the standard printed circuit board process on F4B substrate ($\varepsilon \textrm{ = 2}\textrm{.65}$). The dispersion responses rely on the capacitance of the varactor diode which can be tuned through supplying different voltages. As observed from Fig. 2(c), arbitrary phase in the range of $\textrm{0 - }\pi $ can be obtained to produce the focus at predefined place. A feeding antenna with working bandwidth from 5 to 12 GHz, shown in Fig. 4, is employed to generate the y-polarized quasi plane waves, it is placed in front of the metasurface at an approximate distance of 300 cm, and a standard waveguide probe is used to scan the yoz plane ($\textrm{480 }mm\, \times \,480\,mm$) with a resolution of $5 \times 5\,m{m^2}$. The reflected field is calculated with the same principle as the simulation, the total field is measured first, then the incident plane wave is recorded, reflected field is concluded by subtracting the incident field from the total field. The focus scanning performance on the yoz plane is illustrated in Fig. 5. As expected, the good focusing phenomena at $f = 100\,mm$ and $f = \textrm{2}00\,mm$ along the central line for two frequencies is observed, In addition, we can also realize the off-center focusing phenomenon at $f = 1\textrm{5}0\,mm$ by design for 5.5 GHz and 6.0 GHz, as shown in Figs. 5(c) and 5(f). The average focusing efficiency, using the same method in simulation part, is 20.7%. The differences between the experiment and simulation are caused by the following factors. First, the phase has a drastic change near the resonant frequency, thus it is difficult to give a precise voltage to modulate the phase. Second, the phase range in the experiment is narrower than simulation, which means there is less freedom to satisfy the phase compensation. Third, the error is unavoidable in fabrication and measure processes. We experimentally verified the varifocal performance which shows a reasonable agreement with the simulation at 5.5 and 6.0 GHz, and moreover, any frequency point in the operating band can have the similar property.
Fig. 5. Performance of the fabricated varifocal focusing metasurface mirror evaluated at different frequencies. The metasurface is on the y-axis where the field of incident wave is subtracted. Other conditions in each case are similar to Fig. 3.
4. Conclusion
In summary, a varifocal metasurface mirror is proposed with a tunable focal length in broad operating band. Compared with previous work on metasurface focusing mirror [25,38,39], our work can dynamically steer the energy focus from 100 mm to 200 mm within the phase range from 5.5 to 6.0 GHz. The dynamical switching of focus point is realized by feeding required voltage to tune the reflection phase through MCU, and the approach of electric scanning leads to a rapid response, which is more suitable for real-time applications. The proposed focus-tunable metasurface which can concentrate the incident power into a size-limited area has extensive applications, such as wireless power transfer, imaging, and radio frequency identification.
Funding
National Natural Science Foundation of China (61601408, 61801423, 61805213); Fundamental Research Funds for the Central Universities; Natural Science Foundation of Zhejiang Province (LY19F010015).
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