1. Introduction

Phased array radar is a radar system that realizes target detection and tracking, which is an important part of strategic early warning system, and beamforming is the core technology of phased array radar. There are two main beamforming methods: electronically controlled beamforming and optically controlled beamforming. Among them, the electronically controlled beamforming is realized by regulating the phases of radiated signals of the phased array antennas (PAAs) through phase shifters, which has a narrow bandwidth, and the beam squint problems occur in wideband scenarios. Optically controlled beamforming is realized based on optical true time delay (OTTD) technology, which has the characteristics of large instantaneous bandwidth, light system weight, and anti-electromagnetic interference, and it can avoid the beam squint problems of the electronically controlled beamforming systems [1]. At present, most of the proposed optically controlled beamforming schemes are realized based on optical fibers or optical waveguides. Among them, the beamforming schemes based on optical fibers are highly favored by researchers due to the low loss and simple operation characteristics of optical fibers. The applied methods are diversified, including the use of fiber gratings with wavelength selectivity to change the relative time delays between channels by adjusting the wavelength of lasers [2–5]; the utilize of dispersive fiber technology to produce different time delays for optical carriers of different wavelengths [6–9]; the use of wavelength-division multiplexing (WDM) technology to transmit optical carrier signals of multiple different wavelengths [10,11]; the adoption of the slow-light effect to achieve a wide range of tunable time delay [12], etc. However, for the above systems using single-mode fibers (SMFs) for space-division multiplexing, the number of applied true-time delay lines (TTDLs) increases exponentially when expanded into large PAA systems, which is technically and cost-undesirable.

Few-mode fiber (FMF) supports parallel transmission of multiple spatial modes, and different LP modes have different transmission speeds, resulting in different group delays [13]. By regulating the group delays of different modes, an optically controlled beamforming system based on mode channels can be realized. Compared with the systems using SMF TTDLs, the systems using FMF TTDLs have good integration characteristics. In recent years, it has aroused great interest, and some few-mode beamforming networks have been proposed [14–16]. However, these studies stop at the design and simulation analysis of FMF TTDLs. In 2023, the experimental demonstration of a one-dimensional (1D) beamforming system using FMFs was first reported in [17], but it could not be applied to the realistic planar PAA system. Due to the small differential chromatic dispersion between neighboring modes, a length of 1 km of the FMF was used, leading to an increase in the volume of the system. In this paper, the first experimental demonstration of a two-dimensional (2D) PAA beamforming system based on mode diversity is presented. At the same wavelength, different high-order modes are obtained by using few-mode long-period fiber gratings (FM-LPFGs) for mode conversion. By using few-mode fiber Bragg gratings (FM-FBGs) and 2 × 2 optical switches, the propagation paths of optical signals are changed to achieve time delay difference control of different modes. Based on the response time limits of the magneto-optical switches, we use optical switches to select the loop structures composed of the optical circulators (OCs) to experimentally validate and performance test the 2D PAA beamforming system based on mode diversity. The far-field radiation patterns of 2 × 3 PAA system are tested, and the feasibility of 2D PAA beamforming system based on mode diversity is verified. The experimental results show that the simulation and test results of the signals at 4 GHz, 4.25 GHz, 5.53 GHz and 5.7 GHz are in good agreement when the beam pointing angles are (11°, 17°) and (16°, 23°).

2. 2D PAA beamforming system architecture based on mode diversity

2.1 System design and theoretical analysis

The 2D PAA beamforming system based on mode diversity is shown in Fig. 1. The tunable laser emits an optical carrier at a wavelength of 1550 nm, which is fed into the Mach-Zehnder modulator (MZM). The MZM modulates the radio frequency (RF) signal onto the optical carrier to realize the conversion of the electrical signal to the optical signal. Then, the beam splitter divides the optical signal into three channels, and each channel constitutes a few-mode true time delay (FM-TTD) subnetwork. In each FM-TTD subnetwork, the polarization controller (PC) adjusts the optical signal to the state of maximum output optical power, the two FM-LPFGs excite LP₁₁ and LP₂₁ modes, respectively, and the OC prevents the return of the optical signal from the right side of the optical switch loop from damaging the laser. Then, the optical signals enter the cross-state optical switch loops from the right side. In the optical switch loops, three FM-FBGs are set at different positions to achieve the self-coupled reflections of LP₀₁, LP₁₁, and LP₂₁ modes at the wavelength of 1550 nm, respectively. Hence, the first time delay difference ΔT_x1 is formed between LP₀₁, LP₁₁ and LP₂₁ modes by reflections from the FM-FBGs. The 2 × 2 optical switches are changed into parallel states before the optical signals return, and then the optical signals enter the optical switch loops from the left side. After re-reflections by the FM-FBGs, the second time delay difference -ΔT_x2 is formed between LP₀₁, LP₁₁ and LP₂₁ modes. The schematic diagram of an optical signal makes one round trip in the optical switch loop is shown in Fig. 2, and the time delay regulation of LP₀₁, LP₁₁, and LP₂₁ modes is realized by controlling the switching time of the optical switches to change the number of round trips of the optical signals in the loops. In order to form equal time delay difference between LP modes, we design the lengths of the FMF TTDLs for FM-TTD subnetworks. For the FM-TTD subnetwork 1 in Fig. 1, the distances between FBG1 and FBG2, FBG2 and FBG3 in the optical switch loop are l₁ and l₂, respectively, the distance from FBG1 to the optical switch is h₁, and the distance from FBG3 to the optical switch is h₂. Take the time delay of LP₀₁ mode as the benchmark, and set the time delays for LP₀₁ mode to pass through h₁ and h₂ as t₁ and t₂, respectively. When the optical signals make one round trip in the optical switch loops, the time delays T_f01, T_f11 and T_f21 of the LP₀₁, LP₁₁, and LP₂₁ modes are denoted as:

 

Fig. 1. 2D PAA beamforming system based on mode diversity.

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Fig. 2. Schematic diagram of the optical signal makes one round-trip in the optical switch loop.

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At the wavelength of 1550 nm, the time delay differences between LP₀₁ and LP₁₁, LP₀₁ and LP₂₁ modes of the step-refractive index FMF are Δτ_11,01= 2.8 ps/m, and Δτ_21,01= 5.9 ps/m, respectively, and the effective refractive indices of LP₀₁, LP₁₁ and LP₂₁ modes are n_eff01= 1.4488, n_eff11= 1.4474 and n_eff21= 1.4456, respectively. Thus, when the optical signals make n round trips in the optical switch loops, the time delay difference between LP_01, LP₁₁ and LP₂₁ modes should satisfy:

We set h₁ = h₂= h = 1 m to obtain l₁ = 15.1 cm and l₂ = 30 cm. When the optical signals make n round trips in the optical switch loops, the time delay difference between the different LP modes is n(ΔT_x1 - ΔT_x2)= 6.99n ps.

In each FM-TTD subnetwork, the lengths of LPFG1 and LPFG2 from the mode selective photonic lantern (PL) are l₃ and l₄, respectively. Therefore, since the FM-LPFGs excite modes at different positions, the time delay difference between LP_01, LP₁₁ and LP₂₁ modes satisfy:

Set l₃= 3.1 m and l₄= 2.8 m, the third time delay difference ΔT_x3= 8.68 ps is formed between LP₀₁, LP₁₁ and LP₂₁ modes. Then, the time delay difference between different LP modes corresponds to Δτ_x = n(ΔT_x1 - ΔT_x2) + ΔT_x3= 6.99n + 8.68 ps when the optical signals make n round trips in the optical switch loops. For the FM-TTD subnetworks 2 and 3, the distances of the FM-FBGs at the two ends in the optical switch loops from the optical switches are 1.00025 m and 1.0005 m, respectively, and the lengths of the other FMF TTDLs are the same as those of the FM-TTD subnetwork 1. Thus, in the adjacent FM-TTD subnetworks, the time delay difference Δτ_y = 4.82n ps is introduced between the same LP modes in the vertical direction of the PAA. Then, the optical signals of LP₀₁, LP₁₁ and LP₂₁ modes are demultiplexed by mode selective PL. The variable optical attenuators (VOAs) are utilized to equalize the optical power of the signal in each mode channel, and then the photodetectors (PDs) are used for photoelectric conversion to restore the RF signals. The RF signals are emitted by the PAA and interfere in space to form an accurate beam pointing.

For the planar 2D PAA shown in Fig. 1, the far-field radiation pattern is expressed as :

When the spacing of the antenna elements along the x-axis and y-axis is the same, d_x= d_y= d. The beam pointing angle (θ₀, φ₀) is denoted as:

We have customized a 4 × 4 PAA with the operating frequency of 4-6 GHz and the array element spacing d_x= d_y= d = 26 mm. When the maximum radiation angle ψ_max= 60°, it satisfies $d \le \frac{\lambda }{{1 + |{\sin {\psi_{\max }}} |}}$. For the RF signal at 5 GHz, the time delay difference Δτ_x between different LP modes, the time delay difference Δτ_y between the same LP modes and beam pointing angle (θ₀, φ₀) versus n round trips of the optical signals in the optical switch loops are shown in Table 1. When the optical signals make 1-7 round trips in the loops, the beam pointing angle (θ₀, φ₀) turns from (10.90°, 17.10°) to (50.38°, 30.36°). Obviously, a larger beam pointing angle can be formed without changing the states of the optical switches. In addition, Fig. 3 gives the far-field radiation pattern results of the beam pointing angles of (10.90°, 17.10°), (16.51°, 23.05°), (22.37°, 26.00°) and (28.54°, 27.75°) when the optical signals make 1-4 round trips in the optical switch loops.

 

Fig. 3. When the optical signals make 1-4 round trips in the optical switch loops, the beam pointing angles correspond to (a) (10.90°,17.10°), (b) (16.51°,23.05°), (c) (22.37°,26.00°) and (d) (28.54°,27.75°).

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Table 1. The Time Delay Difference Δτ_x between Different LP modes, the Time Delay Difference Δτ_y between the Same LP Modes and Beam Pointing Angle (θ₀, φ₀) Versus n Round Trips of the Optical Signals in the Optical Switch Loops.

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Moreover, the results of the 2D PAA beamforming system based on mode diversity compared with other beamforming networks are given in Table 2. In terms of operating bandwidth, our system is the same as the optical beamforming network based on chirped fiber Bragg grating and high dispersive specialty fiber element for S-band (2-4 GHz) proposed in [18], but smaller than the PAA system based on highly dispersive photonic crystal fibers for X-band (8-12 GHz) proposed in [19]. In terms of time delay range, as long as the reflection efficiencies of the FM-FBGs are high enough, not changing the state of the optical switches will result in the largest possible time delay between adjacent TTDLs of the 2D PAA beamforming system based on mode diversity. In Table 2, the time delay ranges of adjacent TTDLs along the y-axis (Δτ_y) of the 2D PAA are taken as the comparison results, and the time delay ranges of our system are much larger than those of the systems in [18] and [19].

Table 2. Performance Comparison of Beamforming Systems

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2.2 Composition of the experimental system

For the 2D PAA beamforming system based on mode diversity in Fig. 1, the switching times of the 2 × 2 optical switches are less than 4.8 ns. We can choose electro-optical switches with the response time of ns level, and use a computer to control the electro-optical switches so as to realize the tuning of the number of round trips of the optical signals in the loops of the system of Fig. 1. Based on the 7.5-µs response time limits of the existing magneto-optical switches, we use optical switches to select the loop structures composed of the OCs to build a 2 × 3 PAA beamforming experimental system based on mode diversity, as shown in Fig. 4. The tunable laser (ID Photonics, CoBrite-DX) is set to emit an optical carrier signal at a wavelength of 1550 nm, which is fed into the MZM (Conquer, KG-AM-15-10 G). Then, the MZM is controlled by a voltage source to work at the orthogonal bias point, and the RF signal emitted by the vector network analyzer (VNA, Rohde & Schwarz, ZNB 40) is modulated onto the optical carrier signal. The beam splitter divides the modulated optical signal into two paths, each of which is adjusted by the PC to output the maximum optical power. Then, LP₁₁ and LP₂₁ modes are excited by FM-LPFGs. When the 2 × 2 optical switches work in the cross state, the optical signals of LP₀₁, LP₁₁ and LP₂₁ modes are transmitted to the branches a and c, which corresponds to the case that the optical signals make one round trip in the optical switch loops in the system of Fig. 1. When the 2 × 2 optical switches are switched to the parallel state, the optical signals of LP₀₁, LP₁₁ and LP₂₁ modes are transmitted to the branches b and d, which corresponds to the case that the optical signals make two round trips in the optical switch loops in the system of Fig. 1. Then, the optical signals of LP₀₁, LP₁₁ and LP₂₁ modes enter the loops formed by OCs. In each of the loops, three FM-FBGs are cascaded sequentially to achieve self-coupled reflections of LP₀₁, LP₁₁, and LP₂₁ modes at the wavelength of 1550 nm, respectively. As a result, two regulation of the time delays of LP₀₁, LP₁₁ and LP₂₁ modes are achieved by the reflections of FM-FBGs. The optical signals of LP₀₁, LP₁₁ and LP₂₁ modes are demultiplexed by mode selective PL (Phoenix Photonics, 6PLS). Then, LP₀₁, LP_11a and LP_21a modes are selected as transmission channels, and the power of the optical signal of each mode channel is equalized by a VOA. The optical signals are detected by PDs (Conquer, KG-APD-10G-A-SM-FC) and the resulting RF signals are emitted by the PAA, and the beam pointing angle is formed after spatial interference. Then, the VNA is used to test the signal received by the pyramid horn antenna. To be consistent with the lengths of the FMF TTDLs in the system of Fig. 1, the distances of the first and second FM-LPFGs from the optical switches in the paths after the beam splitter are set to be equal to l₃= 3.1 m and l₄= 2.8 m, respectively. In addition, the distances between the first and second, and the second and third FM-FBGs in each loop are equal to l₁= 15.1 cm and l₂= 30 cm, respectively. As shown in Fig. 4, the branches a-d after the 2 × 2 optical switches correspond to s₁+ s₂ = s₃+ s₅ = s₄ = 1 m, u₁ + u₂ = u₃ + u₅ = u₄ = 1 m, v₁ + v₂ = v₃ + v₅ = v₄= 1.00025 m and w₁ + w₂ = w₃ + w₅ = w₄= 1.0005 m, respectively, and should also satisfy s₂+ s₃ = 1 m, u₂ + u₃= 1 m, v₂ + v₃ = 1.00025 m and w₂ + w₃ = 1.0005 m. respectively.

 

Fig. 4. 2 × 3 PAA beamforming experimental system based on mode diversity.

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In order to build the 2 × 3 PAA beamforming experimental system based on mode diversity, the femtosecond laser direct writing method are used to fabricate FM-LPFGS and FM-FBGs. The step-index FMFs for fabricating fiber gratings and fiber TTDLs are provided by YOFC company, which support four modes: LP₀₁, LP₁₁, LP₂₁ and LP₀₂. The diameters of the core and cladding of the FMF are 18.5 µm and 125 µm, respectively, and effective refractive indices of the core and cladding are 1.4498 and 1.4440, respectively. At the wavelength of 1550 nm, the effective refractive indices of LP₀₁, LP₁₁, LP₂₁ and LP₀₂ modes are n_eff01 = 1.4488, n_eff11 = 1.4474, n_eff21 = 1.4456 and n_eff02 = 1.4451, respectively. In fabricating gratings, the femtosecond laser (Light Conversion, PH1-10W) emits optical pulses with a wavelength of 1030 nm and a width of 290 fs. The 515 nm femtosecond laser is obtained by frequency-doubling the optical pulse with β-BaB₂O₄ crystal, and the laser is focused in the fiber core through the oil-immersed objective lens to form a refractive index modulation region. To realize the excitation of higher-order modes, the femtosecond laser with the pulse energy of 70 nJ is used to write first-order FM-LPFGs by scanning a 12-µm trajectory perpendicular to the fiber core. At the wavelength of 1550 nm, the periods Λ_LPFG of the FM-LPFGs for the mode conversions of LP₀₁ to LP₁₁ and LP₁₁ to LP₂₁ are 1107.14 µm and 861.11 µm, respectively. In addition, a FM-LPFG with the period Λ_LPFG of 484.38 µm is inscribed for the mode conversion of LP₀₁ to LP₂₁. During the construction of the system, it is observed that it can be converted from LP₀₁ to LP₁₁ and LP₂₁ modes simultaneously. Therefore, only this FM-LPFG is connected in the lower branch of the beam splitter. The FM-LPFG is at a distance of 3 m from the optical switch, which is between the range of distances of the two FM-LPFGs from the optical switch in the upper branch of the beam splitter. For the unequal time delay difference between the modes caused by the FMFs inside the optical devices and the FM-LPFG that achieves the mode conversion from LP₀₁ to LP₁₁ and LP₂₁, the SMF TTDLs are used to compensate. In order to achieve efficient self-coupled reflections of LP₀₁, LP₁₁ and LP₂₁ modes at the wavelength of 1550 nm, respectively, the single laser pulse with the pulse energy of 200 nJ is used to form three refractive-index modulation points with the interval of Δr in the fiber core to fabricate FM-FBGs, as shown in Fig. 5 (b). The Δr is set to 3 µm, 5 µm, and 7 µm, respectively, so that the positions of the refractive index modulation points match the optical field energy of each mode. Due to the small difference in the effective refractive indices of LP₀₁, LP₁₁ and LP₂₁ modes, the periods of the first-order FM-FBGs are relatively close to each other. Thus, it is difficult to distinguish each mode. In order to effectively distinguish the modes and to satisfy the resonant condition mλ = 2n_effΛ_FBG for the mth order FM-FBG to realize self-coupled reflection, where n_eff is the effective refractive index of the mode. We choose to inscribe third-order FM-FBGs with periods Λ_FBG of 1604.78 nm, 1606.33 nm, and 1608.33 nm, respectively. Then, a broadband optical source (Connet Fiber Optics, VASS-C-B) and a spectrum analyzer (Anritsu, MS9710B) are used to test the transmission spectra of the FM-LPFGs and the reflection and transmission spectra of the six FM-FBGs connect to branches a and c behind the optical switches. As shown in Figs. 6 (a)-(c), due to transmission depths η (in dB) at the wavelength of 1550 nm of the FM-LPFGs for the mode conversions of LP₀₁ to LP₁₁, LP₁₁ to LP₂₁ and LP₀₁ to LP₁₁ and LP₂₁ are -5.67 dB, -3.87 dB and -7.82 dB, respectively. Therefore, according to the conversion efficiency $\gamma = 1 - {10^{\frac{\eta }{{10}}}}$, their mode conversion efficiencies γ are 72.90%, 58.98% and 83.48%, respectively. Furthermore, the tunable laser is set to emit an optical signal at the wavelength of 1550 nm, which is fed into the FM-LPFG for LP₀₁ to LP₁₁ and LP₂₁ mode conversion and a mode-demultiplexed PL. Then, LP₁₁ and LP₂₁ modes are measured by an optical power meter to obtain 57.7% and 42.3% power, respectively. As demonstrated in Figs. 6 (d)-(f) and (h)-(j), for the fabricated FM-FBGs, LP₀₁, LP₁₁ and LP₂₁ modes achieve self-coupled reflections at a wavelength of 1550 nm, respectively. Moreover, it is informed from Fig. 6(g) that at the wavelength of 1550 nm, the transmission depths of the FM-FBGs connect to branch a achieving self-coupled reflections of LP₀₁, LP₁₁, and LP₂₁ modes are -12.52 dB, -10.63 dB, and -10.14 dB, respectively, and thus the reflection efficiencies are 94.40%, 91.35%, and 90.32%, respectively. From Fig. 6(k), at the wavelength of 1550 nm, the transmission depths of the FM-FBGs connect to branch c achieving self-coupled reflections of LP₀₁, LP₁₁, and LP₂₁ modes are -14.33 dB, -11.38 dB, and -10.62 dB, respectively, and thus the reflection efficiencies are 96.31%, 92.72%, and 91.33%, respectively. In addition, the mode-field propagation results of LP₀₁, LP₁₁ and LP₂₁ modes along the three FM-FBGs connect to branch a behind the optical switch at the wavelength of 1550 nm are given in Fig. 7, respectively. Due to the reflection efficiencies of the FM-FBGs are more than 90%, there is a small portion of the power of LP₀₁, LP₁₁, and LP₂₁ modes of the system that do not achieve self-coupled reflection may cause a slight interference with the time delay difference between the different LP modes. However, the power is too small to affect the final beam pointing angle results.

 

Fig. 5. Fabrication methods of (a) FM-LPFG and (b) FM-FBG.

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Fig. 6. Transmission spectra of FM-LPFGs, the mode conversions of: (a) LP₀₁ to LP₁₁, (b) LP₁₁ to LP₂₁, (c) LP₀₁ to LP₁₁ and LP₂₁. Reflection spectra of the FM-FBGs connect to branch a behind the optical switch: at the wavelength of 1550 nm, self-coupled reflections of (d) LP₀₁, (e) LP₁₁ and (f) LP₂₁ modes, and (g) the corresponding transmission spectra of the three FM-FBGs. Reflection spectra of the FM-FBGs connect to branch c behind the optical switch: at the wavelength of 1550 nm, self-coupled reflections of (h) LP₀₁, (i) LP₁₁ and (j) LP₂₁ modes, and (k) the corresponding transmission spectra of the three FM-FBGs.

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Fig. 7. At the wavelength of 1550 nm, mode-field propagation results of (a) LP₀₁, (b) LP₁₁ and (c) LP₂₁ modes along the three FM-FBGs connect to branch a behind the optical switch, respectively.

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3. Experimental results

We test the voltage standing wave ratio (VSWR) parameters of the 4 × 4 PAA and far-field radiation patterns of the individual antenna elements, respectively, and select the four operating frequencies with the most similar radiation capabilities of the six antenna elements. Then, the performance of the 2 × 3 PAA beamforming experimental system based on mode diversity is demonstrated.

The VSWR is the ratio of the reflected wave amplitude to the incident wave amplitude, which represents the energy reflected by the antenna. Based on the high requirements of calibration kits of VNAs in a wide frequency range, we divide the 4-6 GHz operating frequency of the PAA into four frequency bands, 4-4.5 GHz, 4.5-5 GHz, 5-5.5 GHz and 5.5-6 GHz for VSWR test. Firstly, the VNA is calibrated by a calibration kit and generates RF signals in the corresponding frequency ranges. Then each antenna element is connected to port 1 of the VNA, and the S₁₁ parameter Γ is read by selecting VSWR test item. The VSWR results are obtained based on the formula $\textrm{VSWR = }{{({1 + |\varGamma |} )} / {({1\textrm{ - }|\varGamma |} )}}$, and then six antenna elements with the most similar VSWR parameters are selected. A photograph of the 4 × 4 PAA is exhibited in Fig. 8(a), the six antenna elements with the most similar VSWR parameters correspond to elements 5, 6, 7, 9, 10, 11 in the 4-4.5 GHz band and elements 2, 3, 4, 6, 7, 8 in the 5.5-6 GHz band. Moreover, the VSWR test results of the selected antenna elements are demonstrated in Figs. 8(b) and (c), respectively.

 

Fig. 8. (a) Photograph of the 4 × 4 PAA. Red curves: antenna elements with the most similar VSWR parameters selected in the 4-4.5 GHz band. Blue curves: antenna elements with the most similar VSWR parameters selected in the 5.5-6 GHz band. The VSWR test results of six antenna elements selected in the (b) 4-4.5 GHz band and (c) 5.5-6 GHz band.

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Nevertheless, similar VSWR parameters of antenna elements cannot indicate similar radiation capabilities. Thus, we measure the individual far-field radiation patterns of elements 5, 6, 7, 9, 10, and 11 in the 4-4.5 GHz band and elements 2, 3, 4, 6, 7, and 8 in the 5.5-6 GHz band of each frequency point with 0.01 GHz frequency interval. Then, four operating frequencies with the most similar radiation capabilities are selected in the 4-4.5 GHz and 5.5-6 GHz bands, which are 4 GHz, 4.25 GHz, 5.53 GHz and 5.7 GHz, respectively. The test results of the individual far-field radiation patterns of the antenna elements corresponding to the four frequencies are given in Fig. 9. Due to the smoother VSWR parameters in the 5.5-6 GHz band than in the 4-4.5 GHz band, the individual far-field radiation patterns of the antenna elements are better at 5.53 GHz and 5.7 GHz than at 4 GHz and 4.25 GHz.

 

Fig. 9. Individual far-field radiation patterns at (a) 4 GHz, (b) 4.25 GHz, (c) 5.53 GHz and (d) 5.7 GHz.

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We take the infinite averaging method of VNA to measure the time delay of the signal of each mode channel. To reduce the noise effect, the intermediate frequency (IF) bandwidth of the VNA is set to 300 Hz, and RF signals are generated in the 4-4.5 GHz and 5.5-6 GHz bands, respectively. Then the option of infinite averaging is selected and time delays of all the frequency points are averaged by the VNA. The averaged result corresponds to the actual transmission time of the signal for each mode channel. When the 2 × 2 optical switches work in the cross state, the time delay difference between different modes is measured to be Δτ_x = 16 ps, and the time delay difference between the same modes is Δτ_y = 5 ps. When the 2 × 2 optical switches work in the parallel state, the time delay difference between different modes is measured to be Δτ_x = 22 ps, and the time delay difference between the same modes is Δτ_y = 9 ps. Besides, we find that the time delay of each frequency point of the VNA deviates from the average time delay, which is the error that occurs in the test. Hence, as demonstrated in Fig. 10, the errors of the time delays deviation from the average time delays of the signals of six mode channels at 4 GHz, 4.25 GHz, 5.53 GHz and 5.7 GHz are recorded when the optical switches are operated in different states, respectively.

 

Fig. 10. The time delay distortion errors for the signals of six mode channels at 4 GHz, 4.25 GHz, 5.53 GHz and 5.7 GHz when the optical switches operate in the (a) cross state and (b) parallel state.

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At last, we test the far-field radiation patterns of the system outdoors. To meet the far-field test conditions, the test distance between the PAA and the pyramid horn antenna is not less than 2.5 m. The VNA is set to emit RF signals at 4 GHz, 4.25 GHz, 5.53 GHz, and 5.7 GHz with the power of 10dBm, and then the six antenna elements with the most similar radiation capabilities are selected to transmit the signals. In testing the azimuth angle, the PAA is rotated -60° ∼ + 60° in the horizontal direction, and the S₂₁ parameters of the VNA are recorded every 5°. In testing the elevation angle, the PAA and the pyramid horn antenna are rotated 90 ° clockwise to keep the polarization directions the same, and then test in the same way. Based on the results of the measured time delay differences between modes, the beam pointing angles of the system correspond to (θ₀, φ₀) = (11°, 17°) and (θ₀, φ₀) = (16°, 23°), respectively. When the beam pointing angle (θ₀, φ₀) = (11°, 17°), three-dimensional (3D) far-field radiation patterns simulated at 4 GHz, 4.25 GHz, 5.53 GHz and 5.7 GHz are exhibited in Figs. 11(a) and (b) and Figs. 12(a) and (b), respectively. The comparative results of the simulations and tests for the elevation angle θ₀ = 11° are given in Figs. 11(c) and 12(c), and the comparative results of the simulations and tests for the azimuth angle φ₀ = 17° are given in Figs. 11(d) and 12(d). When the beam pointing angle (θ₀, φ₀) = (16°, 23°), 3D far-field radiation patterns simulated at 4 GHz, 4.25 GHz, 5.53 GHz and 5.7 GHz are exhibited in Figs. 13(a) and (b) and Figs. 14(a) and (b). The comparative results of the simulations and tests for the elevation angle θ₀= 16° are given in Figs. 13(c) and 14(c), and the comparative results of the simulations and tests for the azimuth angle φ₀ = 23° are given in Figs. 13(d) and 14(d). The experimental results show that the simulated and tested far-field radiation patterns are in good agreement, and no beam squint is generated.

 

Fig. 11. When the beam pointing angle (θ₀, φ₀) = (11°, 17°), 3D far-field radiation patterns simulated at (a) 4 GHz and (b) 4.25 GHz, (c) simulation and test results of the elevation angle at 4 GHz and 4.25 GHz, (d) simulation and test results of the azimuth angle at 4 GHz and 4.25 GHz.

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Fig. 12. When the beam pointing angle (θ₀, φ₀) = (11°, 17°), 3D far-field radiation patterns simulated at (a) 5.53 GHz and (b) 5.7 GHz, (c) simulation and test results of the elevation angle at 5.53 GHz and 5.7 GHz, (d) simulation and test results of the azimuth angle at 5.53 GHz and 5.7 GHz.

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Fig. 13. When the beam pointing angle (θ₀, φ₀) = (16°, 23°), 3D far-field radiation patterns simulated at (a) 4 GHz and (b) 4.25 GHz, (c) simulation and test results of the elevation angle at 4 GHz and 4.25 GHz, (d) simulation and test results of the azimuth angle at 4 GHz and 4.25 GHz.

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Fig. 14. When the beam pointing angle (θ₀, φ₀) = (16°, 23°), 3D far-field radiation patterns simulated at (a) 5.53 GHz and (b) 5.7 GHz, (c) simulation and test results of the elevation angle at 5.53 GHz and 5.7 GHz, (d) simulation and test results of the azimuth angle at 5.53 GHz and 5.7 GHz.

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4. Conclusion

A 2D PAA beamforming system based on mode diversity is experimentally demonstrated in this paper. At the input end of FMFs of the system, only LP₀₁ mode is input. Then, LP₁₁ and LP₂₁ modes are excited by FM-LPFGs, and the propagation paths of LP₀₁, LP₁₁ and LP₂₁ modes are controlled by FM-FBGs and 2 × 2 optical switches to realize the true time delay control of LP₀₁, LP₁₁ and LP₂₁ modes. Then we simulate the far-field radiation patterns of the beam pointing angles when the optical signals make 1-4 round trips in the optical switch loops. To demonstrate the feasibility of the 2D PAA beamforming system based on mode diversity, we experimentally validate and test the performance of the system by using optical switches to select the loop structures composed of the OCs. The VSWR parameters of the 4 × 4 PAA and far-field radiation patterns of the individual antenna elements are tested separately, and six antenna elements with the most similar radiation capabilities at 4 GHz, 4.25 GHz, 5.53 GHz, and 5.7 GHz are selected. The experiments demonstrate that the no beam squint occurs when the beam pointing angles are (11°, 17°) and (16°, 23°). The system in this paper only applies LP₀₁, LP₁₁ and LP₂₁ modes, which will lead to more complexity in the design of the whole system as more LP modes are introduced in practical applications. we can consider inscribing multiple FM-FBGs as one or a few chirped gratings with non-uniform period. Under satisfying the resonant condition for the realization of self-coupled reflection of FM-FBGs, it is speculated that different modes at the wavelength of 1550 nm will produce self-coupled reflections at different locations of the chirped grating. Then only one or a few chirped gratings can replace multiple FM-FBGs that realize self-coupled reflections of different modes, thus the complexity of the system will be appropriately reduced.