Time-Modulated Transmissive Programmable Metasurface for Low Sidelobe Beam Scanning

Programmable metasurfaces have great potential for the implementation of low-complexity and low-cost phased arrays. Due to the difficulty of multiple-bit phase control, conventional programmable metasurfaces suffer a relatively high sidelobe level (SLL). In this manuscript, a time modulation strategy is introduced in the 1-bit transmissive programmable metasurface for reducing the SLLs of the generated patterns. After the periodic time modulation, harmonics are generated in each reconfigurable unit and the phase of the first-order harmonic can be dynamically controlled by applying different modulation sequences onto the corresponding unit. Through the high-speed modulation of the real-time periodic coding sequences on the metasurface by the programmable bias circuit, the equivalent phase shift accuracy to each metasurface unit can be improved to 6-bit and thus the SLLs of the metasurface could be reduced remarkably. The proposed time-modulated strategy is verified both numerically and experimentally with a transmissive programmable metasurface, which obtains an aperture efficiency over 34% and reduced SLLs of about −20 dB. The proposed design could offer a novel approach of a programmable metasurface framework for radar detection and secure communication applications.

Programmable metamaterials were firstly proposed in 2014 to expand the concept of metamaterials through using dynamic sequences of "0" and "1" bits [18]. Thereafter, reflective or folded reflective programmable metasurfaces have been widely developed and exploited in many applications, through integrating lumped components for the dynamic alteration in metasurface unit resonant property [19][20][21][22][23]. Since there were serious feed blockages exhibited by the programmable reflective metasurfaces, transmissive programmable metasurfaces were proposed to improve the total radiation efficiency [24][25][26][27][28]. However, for all these programmable metasurfaces, only 1-bit or 2-bit phase resolutions are realized for the units, resulting in severe quantization losses of approximately 3 dB and 0.6 dB, respectively [29]. As for programmable metasurfaces with multiple-bit phase resolutions, the reconfigurable unit configurations and the corresponding control circuits would be extremely complicated for practical applications, especially in a large-scale metasurfaces. To achieve a more sophisticated EM manipulation, the time-modulated array technologies [30][31][32] were introduced and combined with programmable metasurfaces, and the space-time coding digital metasurfaces were thus proposed and verified to provide flexible beam steering, beam shaping, and scattering-signature control over optimized space-time coding sequences [33][34][35]. Many other promising applications are also conducted creatively through space-time coding digital metasurfaces, for example, implementing efficient harmonic control for far-field radiation or near-field distribution [36,37], manipulating the nonreciprocal effects dynamically for frequency conversion [38][39][40], realizing smart Doppler cloaks in the microwave domain for selfadaptive anti-Doppler shift [41,42], executing dynamic and arbitrary polarization syntheses [43,44], extracting the accurate electromagnetic parameters of complex lossy dispersive materials [45], and more importantly, constructing the minimalist or secure wireless communication architectures through space-and frequency-division multiplexing [46][47][48].
For applications in radar detection, high-resolution imaging, and secure communication, low sidelobe level (SLL) is an indispensable factor for the designed radiation beams, in order to reduce the coupling interference with other components in the integrated system and minimize the possibility of being detected by the potential adversaries [49]. Due to the difficulty in implementation of multiple-bit phase control, conventional programmable metasurfaces suffer a relatively high SLL. In this manuscript, we design and fabricate a 1-bit transmissive programmable metasurface and overcome its drawback in high SLL through employing a time modulation strategy. After the periodic time modulation, the harmonics are generated in each metasurface unit, and the phase of the first-order harmonic can then be dynamically manipulated by modulation sequences applied to corresponding unit. Through the high-speed modulation of the real-time periodic coding sequences on the metasurface by the programmable bias circuit along with the high-accuracy fieldprogrammable gate array (FPGA), the equivalent phase shift accuracy to each metasurface unit can be improved and the SLLs of the metasurface are thus reduced correspondingly. The time-modulated design strategy is verified both numerically and experimentally, and the transmissive programmable metasurface could obtain an aperture efficiency over 34% and reduced SLLs of about −20 dB, much superior to the conventional programmable metasurfaces. The proposed design could offer a novel approach of a programmable metasurface framework in low sidelobe beam scanning for radar detection and secure communication applications.

Time-Modulated Metasurface Theory
The overall schematic and architecture of the timemodulated transmissive programmable metasurface is illustrated in Figure 1. A sinusoidal signal is passing through the transmissive metasurface, and harmonic beams with different frequencies are stimulated and pointing in different directions after implementing periodic time modulation. To improve the equivalent phase shift accuracy and reduce the relative SLLs, time-modulated theory is introduced and combined with the designed 1-bit transmissive programmable metasurface through the high-speed modulation of the real-time periodic coding sequences by the programmable bias circuit along with the FPGA, Xilinx Kintex-7.
Consider a 1-bit transmissive programmable metasurface with M × N elements, and the horn antenna is exploited to transmit and receive RF signals with the carrier frequency F c . The unit spacing along both x and y axes is D, and the horn antenna is located on the z axis with the coordinate ½ 0, 0,−F in a three-dimensional Cartesian coordinate system, where F is the focal length of the feed phase center.
Assume that the transmissive metasurface works on the receiving state, and the far-field incident RF signal is incident on the metasurface from the direction ðθ, φÞ. The reconfigurable metasurface unit is composed of two patches placed on the front and back sides. The RF signals are received by the front patch and radiated out by the patches on the back, where the signal phases could be dynamically controlled through the 1-bit phase modulator using PIN diodes. The horn antenna receives the power from all the patches on the back layer, which is related to the direction of vector ðθ m,n , φ m,n Þ and distance l m,n from the ðm, nÞ th patch on the back side of the metasurface to the horn antenna. Here, Assume that the patterns of the patches on both sides are u f ðθ, φÞ and u b ðθ, φÞ, respectively. The loss and phase shift of the ðm, nÞ th patch caused by the distance l m,n are aðl m,n Þ and exp ðj2πl m,n /λÞ, correspondingly. The array factor of the transmissive metasurface on the receiving state is thus theoretically modeled as where ω m,n is the programmable weight and selected from the binary states f0, 1g and d m,n is the distance from the ðm, nÞ th patch antenna on the front layer to the plane 2 Research passing through the origin and perpendicular to the incident direction, which is calculated by In practical, the array pattern depicted by (2) can be furtherly simplified. For example, the pattern of the patch on either side is approximately equal to cos θ, and aðl m,n Þ is roughly proportional to 1/l 2 m,n ; thus, the array factor can be rewritten as By setting the ð1, 1Þ st unit as reference, the added periodic modulation sequence is designed as follows. In the first half of a modulation period T p , the phase shift is set as 0°, while in the second half, the phase shift is set as 180°. Then, the modulation sequence added to the ð1, 1Þ st unit can be described by The period function U 1,1 ðtÞ can then be unfolded by the Fourier series as where F p = 1/T p is the modulation frequency and α 1,1,k is the Fourier coefficient corresponding to the k th harmonic component: Assume that the received signal in the ð1, 1Þ st unit is A 0 e j2πF c t . After modulation, the output can be written as Referring to (7), we see that only odd harmonic components appear after the periodic modulation and symmetric spectra with opposite harmonics exist on both sides of the carrier frequency F c . Among all existing harmonic components, the ±1 st ones are the strongest. Therefore, we choose the +1 st harmonic component to implement pattern synthesis. However, the −1 st harmonic component may cause a power waste even interference to other electronic systems. The suppression of the −1 st harmonic component requires a more complicated structure with 2-bit phase shift units. However, through the power suppression in other harmonic components, the gain of the time-modulated metasurface phase array can be higher than the one without modulation, owing to the effective improvement on the aperture efficiency caused by the higher phase shift accuracy.
According to (7), if a sinusoidal signal with the amplitude A 0 = 1 is input to the modulation unit, the output signal would contain the +1 st harmonic component with the amplitude 2/π. The modulation sequence applied to the ðm, nÞ th unit is U m,n ðtÞ = U 1,1 ðt − τ m,n Þ, where τ m,n is the delay of U m,n ðtÞ corresponding to U 1,1 ðtÞ. According to the properties of the Fourier series, U m,n ðtÞ can be unfolded by We see that all the time-modulated reconfigurable units would generate harmonic components at F c + kF p . For the k th harmonic component, the phase difference between the ðm, nÞ th unit and the ð1, 1Þ st one is decided by time delay τ m,n . Therefore, the phase shifts of the +1 st harmonic components for all the metasurface units can be controlled parallelly by setting different time delays τ m,n through the FPGA.
According to (4) and (9), after time modulation, the transmissive metasurface array factor of the k th harmonic component can be deduced as By substituting (7) and (9) into (11), the array factor of the +1 st harmonic component can be rewritten as Next, the phase shift accuracy for the metasurface under time modulation would be discussed thoroughly. For the FPGA device used in the programmable metasurface, there is a system clock frequency f clk , which defines the minimum time interval as 1/f clk in all programs. That is, all the delays generated by the FPGA are an integral multiple of 1/f clk . Therefore, the phase shift resolution of the period time modulation is Δφ = 2πF p /f clk . For example, if the system clock frequency of the FPGA is 64 MHz and the modulation frequency is 1 MHz, the equivalent phase shift accuracy under time modulation would be equal to that of a 6-bit digital phase shifter. If the required phase shift is π/4, the time delay of the modulation sequence should be set as 8 times of the FPGA system clock period. It is worth noting that the transmissive metasurface would operate at F c + F p through time modulation, and the frequency stepping among the harmonic components is 2F p . Therefore, in order to avoid aliasing, the bandwidth of the received signal should be less than 2F p .
Considering the designed 1-bit transmissive metasurface with 20 × 20 units working at 7.5 GHz, the unit spacing along both x and y axes is λ/2, and the feed horn antenna is placed on the z axis with the coordinate ½0, 0,−5λ. The exploited pattern synthesis method is to generate an equiphase surface perpendicular to the incidence direction. By substituting the above parameters into (4), the array pattern could be rewritten as Assume that the required phase for the ðm, nÞ th unit is ϕ m,n in order to generate equiphase surface perpendicular to ðθ, φÞ. For the situation without time modulation, ω m,n in (13) is selected from the binary states f0, 1g and decided by ω m,n = mod ϕ m,n − 2π l m,n + d m, where b⋅c is the floor function. For the situation with time modulation in our study, the system clock frequency of the FPGA is 64 MHz and the modulation frequency is 1 MHz. Therefore, the phase shift accuracy is equivalent to 6-bit at the +1 st harmonic component. The required phase shift ϕ m,n is mapped to the time delay τ m,n between the modulation sequence applied to the ðm, nÞ th unit and that of the reference unit. Thereafter, τ m,n is generated by the control FPGA, and the number of delays over the system clock can be calculated by ω ′ m,n = 2 5 × mod ϕ m,n − 2π l m,n + d m,n ð Þ /λ ð Þ , 2π À Á π " # : ð15Þ As described above, in the pattern synthesis with time modulation, ω ′ m,n defines the approximate ratio between τ m,n and the system clock period.
In order to validate the effectiveness of the proposed time-modulated transmissive programmable metasurface for low SLL beam scanning, the normalized 2D patterns both with and without time modulation are calculated based on the above theory and examined further with the measured results of the fabricated transmissive programmable metasurface for four scanning directions, including ð0°, 0°Þ, ð15°, 0°Þ, ð30°, 0°Þ, and ð45°, 0°Þ. Detailed procedures along with the results are provided in the following section.

Time-Modulated Metasurface Design and Verification
The established transmissive programmable metasurface is designed by combining a receiving patch, a transmission patch, and a 1-bit phase modulator in a single reconfigurable unit. The presented 1-bit transmissive reconfigurable unit is constructed by four metal layers along with two substrates and one bonding film, as shown in Figure 2. The two substrates are Rogers RO4003C (dielectric constant of 3.55, loss tangent of 0.0027) with a thickness of 1.524 mm, while the middle bonding film layer is Rogers 4450F (dielectric constant of 3.52, loss tangent of 0.004) with a thickness of 0.203 mm. The metal layers include, from top to bottom, the receiving layer, the bias layer, the ground, and the transmission layer. The transmission layer is designed with an elliptical patch integrated by an O-slot and two PIN diodes, while the supernatant receiving layer is with the same-size elliptical patch integrated by a U-slot, and both layers are connected at the center by a metallized via-hole through the ground for energy transferring. Besides, the receiving layer is connected with two crescent-shaped distributed capacitors in the bias layer through two symmetric distributed via-holes for biasing purposes, while the transmission layer is connected with the ground plane in a similar way.
To choke the high-frequency signals ulteriorly, the bias line is designed with a very narrow linewidth, which is placed very close to the ground and integrated with two symmetric zigzag inductances along with the distributed capacitors. The 1-bit phase resolution of the transmissive metasurface unit is obtained by integrating two PIN diodes with an antisymmetry configuration for current inversion, thus achieving the uniform amplitudes but inverse phase states    [50], is chosen to acquire lower transmission losses within the designed band and modeled by the equivalent lumped components for the two biasing states. For positive biasing, the series resistor R ON = 2:1 Ω and inductor L ON = 30 pH are adopted for the PIN diode, while for negative biasing, the series capacitance C OFF = 0:05 pF and inductor L OFF = 30 pH are employed for the PIN diode.
The central operation frequency of the transmissive metasurface unit is designed at 7.5 GHz. The numerical simulation is carried out with the help of the commercial software package CST Microwave Studio by using unit cell boundary conditions along with the Floquet port excitations. Figures 2(e) and 2(f) give the simulated S parameters of the unit in magnitude and phase for both π and 0 states. For the π state with PIN diode I on and PIN diode II off, the transmission coefficient is greater than −1 dB from 7.169 to 7.791 GHz. For the 0 state with PIN diode I off and PIN diode II on, the transmission coefficient is greater than −1 dB from 7.175 to 7.805 GHz. The phase difference of the two programmable states agrees well with 180°within the designed frequency band. Besides, the radiation characteristics of patches on both sides of the metasurface unit are also simulated, which have a gain of about 6 dBi and a beamwidth over 90°.
To further validate the actual working performance of the proposed time-modulated transmissive programmable metasurface for low sidelobe beam scanning, the metasurface prototype with 20 × 20 units was manufactured based on the designed unit, with a unit spacing of d = λ/2 along both x and y axes. A pyramid horn feeder is positioned in the central axis of the metasurface with a focal length of F = 20 cm to illuminate the overall metasurface aperture, and the steering logic board is connected with the metasurface through flexible flat cables (FFCs). The metasurface along 6 Research with the horn feeder and the steering logic board is all mounted onto a designed black acrylic bracket, as shown in Figure 3. Each metasurface unit is connected and modulated with the steering logic board through the bias layer network. The FPGA, Xilinx Kintex-7, is adopted as the host processing system in order to regulate the programmable signals in parallel for all 400 PIN diodes of the metasurface within the assigned clock signals, according to the optimized timevarying coding sequences. The reconfiguration speed of the proposed time-modulated transmissive programmable metasurface depends critically on the minimum switching speed of the PIN diode employed, which is about 20 nanoseconds according to the data sheet [50].
The experimental environment and measurement setup in the microwave anechoic chamber are also presented in Figure 3. A horn antenna transmits the single-frequency signal at 7.5 GHz stimulated by the signal source from the far field. The transmissive programmable metasurface is fastened on an electronic-controlled turntable, and the power patterns were recorded by the spectrum analyzer. Firstly, the programmable metasurface is operating with time modulation. The main clock frequency of the FPGA on the control board is set as 64 MHz with modulation frequency of 1 MHz, resulting in an equivalent phase shift accuracy of 6 bits. The pattern synthesis method is to generate an equiphase surface perpendicular to the desired beam direction, and the weight ω ′ m,n is calculated by (15) and then translated to the delay of the modulation sequence compared to the reference in programs. As for the situation without time modulation, the weight ω m,n is calculated by (14).
The measured normalized 2D radiation patterns both with and without time modulation are plotted and compared with the calculated results based on the above timemodulated metasurface theory, as shown in Figure 4. It is observed that good-shaped directional pencil beams for the four scanning directions, including ð0°, 0°Þ, ð15°, 0°Þ, ð30°, 0°Þ, and ð45°, 0°Þ, are obtained with very high pointing stability. The main lobes of the scanning beams with and without time modulation are nearly the same, while the SLLs would decrease remarkably by using time modulation. The measured SLLs are lower than −12 dB for the programmable metasurface without time modulation, while that with time modulation would be lower than −20 dB for the scanning beams, reaching a −10 dB decrease on average. The measured results are basically coincident with the calculated predictions, and the relatively higher SLLs of the measured patterns are mainly caused by the assembly error along with the estimation error of the metasurface patch pattern. The beamwidth of the main lobes would be broadened as the scanning angle increases and the SLLs of the metasurface also have a little increase but still remain lower than −20 dB for the scanning beams through time modulation. The maximum measured gain of the metasurface with time modulation is over 26.31 dB with an aperture efficiency in excess of 34%, while a decreased aperture efficiency lower than 30% would be obtained for the programmable metasurface without time modulation. The aperture efficiency is improved because of the high phase accuracy created with time modulation, along with a higher energy ratio achieved for the main lobes through sidelobe suppression.
In order to further highlight the intrinsic advantage of the proposed design, a comparison of the overall performance for the proposed time-modulated transmissive programmable metasurface with some representative published works is tabulated in Table 1. Owing to the equivalent 6-bit phase accuracy created through time modulation, an increased aperture efficiency over 34% along with the reduced SLLs of about −20 dB could be obtained, which has definite improvements when compared with the conventional programmable metasurfaces without time modulation.

Conclusion
In summary, we have presented a time modulation strategy for increasing the phase shift accuracy of a 1-bit transmissive programmable metasurface and decreasing the SLLs of the scanning beams. Numerical simulations were provided, and a 20 × 20-unit transmissive programmable metasurface was fabricated and measured to validate the effectiveness of the proposed strategy. Through the high-speed modulation of the real-time periodic coding sequences on the metasurface by the programmable bias circuit, an improved 6-bit phase shift accuracy was achieved at the +1 st harmonic component for the time-modulated metasurface. We demonstrated that the aperture efficiency is improved along with the SLLs reduced owing to the high phase accuracy created through time modulation. The time-modulated transmissive programmable metasurface could obtain a measured gain over 26.31 dB along with an aperture efficiency over 34% and reduced SLLs of about −20 dB. The proposed design could offer a novel approach of a programmable metasurface framework in low sidelobe beam scanning for prospective radar detection and secure communication applications.

Data Availability
The data used to support the findings of this study are available within the article and the supplementary materials.