Novel Beam Scan Method of Fabry–Perot Cavity (FPC) Antennas

: A new beam scanning method of a Fabry–Perot cavity (FPC) antenna is proposed. To obtain high gain in a target direction with a reduced sidelobe level (SLL), we devised a tapered partially reﬂective surface (PRS) as a superstrate. Moreover, to attain various beam scanning directions, a phase-controllable artiﬁcial magnetic conductor (AMC) ground plane with a broad reﬂection phase range and high reﬂection magnitudes was introduced. In the proposed method, a new formula to satisfy an FP resonance condition in a cavity for a scanned beam is also suggested. According to the formula, the FPC antenna can precisely scan the main beam in designed target directions with well-maintained high gain, which has been hardly achievable. In addition, our method demonstrates the potential of electrical beam-scanning antennas by employing active RF chips on the AMC cells. To validate the method, we fabricated a prototype FPC antenna for a scanned beam at θ = 30 ◦ . Furthermore, we conducted an additional simulation for a different beam scanning angle as well. Good agreement between the expected and experimental results veriﬁes our design approach.


Introduction
In state-of-the-art communication technologies, high gain antennas with a beamscanning ability have been receiving considerable interest to secure a longer and broader communication area. Among various high gain antennas, phased-array [1,2] and reflectarray [3][4][5] antennas are especially renowned due to their beam-forming abilities. In [2,3], for instance, discrete beam-steering and continuous beam-scanning capabilities are realized, respectively. However, the phased-array antennas demand not only complex feeding networks but also phase shifters because of the many radiating elements, which causes high complexity and high expense. On the other hand, the reflect-array antennas do not require complex feeding networks as they usually employ only a single excitation source. Moreover, considering electrical beam-scanning [5], the reflect-array antenna is more favorable than the phased-array antenna because a bias network controlling each active element in the reflect-array is much simpler than the phase shifting of the phased-array antenna. However, the reflect-array antenna requires quite a long feeding distance between a reflect-array and a feeding antenna to guarantee high illumination and accurate reflection behaviors of each cell [3][4][5], making the antenna too bulky for commercial applications.
Meanwhile, a Fabry-Perot cavity (FPC) antenna, consisting of a partially reflective surface (PRS) and a single excitation source, has also been actively studied as it can provide 1.
A predictable beam-scan direction based on a newly introduced design formula; 2.
A wide beam-scan range with a well-maintained high gain; 3.
A continuously changeable beam-scan direction.
To validate our idea, we fabricated and measured a prototype FPC antenna for a scanned beam at θ = 30 • . Moreover, we performed an additional simulation of a normal radiation (θ = 0 • ) case as well. Consequently, by comparing simulation and measurement results, we have successfully proven the validity of our design proposal.
All simulations have been conducted using CST Microwave Studio [18].

Operation Principle of the Proposed Antenna
Overviews of the FPC antenna based on the proposed design method and its beamscanning scheme are presented in Figure 1. The proposed antenna consists of a tapered PRS superstrate and an AMC ground plane, forming an FP cavity. By satisfying an FP resonance condition in the cavity and adequately adjusting the reflection phase of each AMC cell, the antenna can successfully produce a scanned beam with fairly high gain in the desired target direction of θ = 30 • on the xz-plane (φ = 0 • ). For a feeding antenna, a y-polarized microstrip patch antenna is employed instead of a slot antenna or others for easy fabrication [19].    2 describes the conventional and the proposed operation principles of an FPC antenna for a scanned beam. For the FPC antenna, there are two kinds of fields distinguished by the PRS; one is being transmitted through, the other is being reflected. By carefully utilizing the reflected fields to generate an FP resonance in the cavity, the antenna can obtain high gain in a target direction [6].  Figure 2 describes the conventional and the proposed operation principles of an FPC 78 antenna for a scanned beam. For the FPC antenna, there are two kinds of fields distin-79 guished by the PRS; one is being transmitted through, the other is being reflected. By care-80 fully utilizing the reflected fields to generate an FP resonance in the cavity, the antenna 81 can obtain high gain in a target direction [7]. 82 Then, now we are going to discuss how to scan a main beam in the FPC antenna. To 83 obtain the scanned beam in the target direction, all fields transmitted through the PRS 84 should be in-phase on the tilted target wavefront. For that, we can consider the following 85 two methods: 86

2.
A phase-controllable AMC ground plane (see Figure 2(b)). 88 First, let us consider method 1 that is used in previous works. In [11]- [14], a phase-89 controllable PRS is devised to make transmitted fields constructively interfere on the in-90 clined target wavefront. However, there is a critical problem that a beam scan direction is 91 unpredictable as there is no precise design formula. Moreover, method 1 is not suitable 92 for commercial applications requiring wide beam scan capability due to the limitation of 93 a PRS: the narrow reflection and transmission phase ranges. In fact, in method 1, the PRS 94 should have wide reflection and transmission phase ranges with a high reflection magni-95 tude to provide various beam scan directions as well as high gain [7]. However, in general, 96 it is extremely difficult for an ordinary PRS to realize broad phase ranges while maintain-97 ing high reflection magnitudes [11]- [14]. Though we can use a stacked PRS consisting of 98 two or three layers for the wide ranges, it is obviously unfavorable in obtaining high gain 99 (or high efficiency) due to high material losses [16]. 100 To overcome these problems, we propose method 2 that introduces a phase-control-101 lable AMC ground plane. The phase-controllable AMC is far desirable than the phase-102 controllable PRS for various beam scan directions because the AMC generally provides a 103 much wider reflection phase range with very low loss compared with the PRS [17]. More-104 over, another strong point of the AMC is its biasing configuration for electrical beam scan-105 ning. To understand this, we need to revisit the configuration of electrical beam-scanning 106 antennas. As we know well, they employ active RF chips such as varactor-or PIN-diodes 107 that require DC bias lines. Varactor-diodes, for example, are usually selected for continu-108 ous beam scanning as their electrical properties are continuously varied according to the 109 applied reverse DC voltage. When installing the varactor-diodes on the PRS, bias lines 110  Now we are going to discuss how to scan a main beam in the FPC antenna. To obtain the scanned beam in the target direction, all fields transmitted through the PRS should be in-phase on the tilted target wavefront. For that, we can consider the following two methods:
A phase-controllable AMC ground plane (see Figure 2b).
First, let us consider method 1 which is used in previous works. In [11][12][13][14][15], a phasecontrollable PRS is devised to make transmitted fields constructively interfere on the inclined target wavefront. However, there is a critical problem that a beam-scan direction is unpredictable as there is no precise design formula. Moreover, method 1 is not suitable for commercial applications, requiring wide beam-scan capability due to the limitations of a PRS: the narrow reflection and transmission phase ranges. In fact, in method 1, the PRS should have wide reflection and transmission phase ranges with a high reflection magnitude to provide various beam scan-directions as well as high gain [6]. However, in general, it is extremely difficult for an ordinary PRS to realize broad phase ranges while maintaining high reflection magnitudes [12][13][14][15]. Though we can use a stacked PRS consisting of two or three layers for the wide ranges, it is obviously unfavorable in obtaining high gain (or high efficiency) due to high material losses [20].
To overcome these problems, we propose method 2 which introduces a phase-controllable AMC ground plane. The phase-controllable AMC is far more desirable than the phasecontrollable PRS for various beam-scan directions because the AMC generally provides a much wider reflection phase range with very low loss compared with the PRS [21]. Moreover, another strong point of the AMC is its biasing configuration for electrical beam-scanning. To understand this, we need to revisit the configuration of electrical beam-scanning antennas. As we know well, they employ active RF chips such as varactor-or PIN-diodes that require DC bias lines. Varactor-diodes, for example, are usually selected for continuous beam-scanning as their electrical properties are continuously varied according to the applied reverse DC voltage. When installing the varactor-diodes on the PRS, bias lines will be in the cavity, as described in Figure 3a. In this case, the fatal problem is that the FP resonance becomes extremely difficult to be considered as the bias lines significantly affect the fields in the cavity, which ultimately harms the antenna's radiation. Even if PIN-diodes were applied for a discrete beam-steering, bias lines would still be located in the radiation area, which would also adversely affect the antenna performance.
vides a much wider reflection phase range with very low loss compared with the PRS [21]. Moreover, another strong point of the AMC is its biasing configuration for electrical beamscanning. To understand this, we need to revisit the configuration of electrical beam-scanning antennas. As we know well, they employ active RF chips such as varactor-or PINdiodes that require DC bias lines. Varactor-diodes, for example, are usually selected for continuous beam-scanning as their electrical properties are continuously varied according to the applied reverse DC voltage. When installing the varactor-diodes on the PRS, bias lines will be in the cavity, as described in Figure 3a. In this case, the fatal problem is that the FP resonance becomes extremely difficult to be considered as the bias lines significantly affect the fields in the cavity, which ultimately harms the antenna's radiation. Even if PIN-diodes were applied for a discrete beam-steering, bias lines would still be located in the radiation area, which would also adversely affect the antenna performance.
(a) (b) Figure 3. Overviews of FPC antennas consisting of (a) an active PRS and (b) an active AMC. It is desirable for the bias lines to be placed beneath the ground plane as they hardly affect the FP resonance in the cavity.
However, when using the active AMC instead of the active PRS, all bias lines can be placed beneath the ground plane (see Figure 3b), which hardly affects the radiation performance. Therefore, in these regards, we can conclude that the AMC ground plane is far more favorable than the PRS in respect to numerous future phase-control applications.
So far, we have described the reason why the AMC ground plane is introduced. From now on, we are going to explain how to define a proper reflection phase of each AMC cell to obtain a desired scanned beam. For a scanned beam, each phase of fields transmitted through the PRS should be equal on the tilted target wavefront. These phases, ÐR−n to ÐRn in Figure 2b, can be derived as where β is the propagation constant in free space, h is the height of the PRS, p is the period of each PRS and AMC cell, l is the length of a ray path between the AMC and PRS, ϕ±xn is the reflection phase of each ±n th AMC cell, and ÐΓn and ÐΤn are the reflection and transmission phases of the ±n th PRS cell, respectively. The cell number n is represented in Figure  2. However, when using the active AMC instead of the active PRS, all bias lines can be placed beneath the ground plane (see Figure 3b), which hardly affects the radiation performance. Therefore, in these regards, we can conclude that the AMC ground plane is far more favorable than the PRS in respect to numerous future phase-control applications.
So far, we have described the reason why the AMC ground plane is introduced. From now on, we are going to explain how to define a proper reflection phase of each AMC cell to obtain a desired scanned beam. For a scanned beam, each phase of fields transmitted through the PRS should be equal on the tilted target wavefront. These phases, ∠R −n to ∠R n in Figure 2b, can be derived as where β is the propagation constant in free space, h is the height of the PRS, p is the period of each PRS and AMC cell, l is the length of a ray path between the AMC and PRS, φ ±xn is the reflection phase of each ±n th AMC cell, and ∠Γ n and ∠T n are the reflection and transmission phases of the ±n th PRS cell, respectively. The cell number n is represented in Figure 2. Equation (1) means that we can control all the transmitting rays' phases by adequately changing each AMC cell's reflection phase. However, there are three phase-uncontrollable rays directly passing through the PRS without any reflection by the AMC, which are depicted as red short-dashed lines in Figure 2b. Among the phase-uncontrollable rays, the blue-dashed one (see Figure 2b) must be the most influential on beam-scanning as they are normally bouncing between the PRS and the ground plane, which yields the strongest radiation power. Therefore, we set the strongest ray's phase as the reference ∠R ref when designing a target wavefront, which is obtainable through a simulation where there is a superstrate of three PRS cells that the phase-uncontrollable fields pass through. According to the simulation, ∠R ref is about −130 • above 1 mm from the center of the PRS at the design frequency. Now, the relationship among the phases ∠R ±n on the inclined target wavefront (see Figure 2b) can be derived with regard to ∠R ref as follows: Finally, by combining the Equations (1) and (2), the required reflection phase of each AMC cell can be derived as where φ ±xn and φ ±yn are the reflection phases of the ±n th AMC cell along the xand y-axis, respectively, and the superscript Pol. means the polarization mode of fields incident on the PRS. Since both the reflection and transmission coefficients of the PRS are highly dependent on the incident angle and polarization [20], it is very important to consider the incident conditions when determining the coefficients, which will be further elucidated in Section 2.3.
In the previous paragraphs, we described how the phase-uncontrollable rays passing directly through the PRS are considered for building a target wavefront; the phase of the most influential rays (blue-dotted line in Figure 2b) is selected as the reference. However, another phase of two rays (red dashed lines in Figure 2b) is still out of control, which may adversely affect beam-scanning. Thus, their transmission through the PRS should be suppressed, which is achievable by increasing the reflection magnitude of the PRS cells. On the other hand, at the same time, high reflection magnitudes of the PRS make impedance matching difficult for an FPC antenna. Therefore, the reflection magnitudes of the PRS cells, where the phase-uncontrollable rays pass through, should be determined based on a trade-off relationship between the beam-scan ability and the good impedance matching property. In this work, when the corresponding reflection magnitude is 0.86, the proposed antenna provides a well-scanned beam in the target direction with acceptable impedance matching performance. Figure 4 shows the deployment of the proposed PRS superstrate and the AMC ground plane. As we can see in Figure 4a, the strip lines of the PRS are symmetric to the y-axis, which is intended for a symmetrical beam-scan performance on the H-plane (xz-plane). Moreover, they are tapered toward the edges so as to suppress an SLL [17]. By tapering the widths of the strip lines, their reflection magnitudes are lowered to the edges. Thus, while fields in the cavity propagate to lateral openings experiencing multiple reflections between the PRS and the AMC, most of them should be transmitted through the PRS before leaking out of the openings. Consequently, the SLL gets decreased thanks to the reduced leaky components contributing to the undesirable sidelobe. In our work, the proposed PRS has three tapering reflection magnitudes of 0.86, 0.72, and 0.50 toward the edges.   Table 1.

Deployment of a PRS Superstrate and an AMC Ground Plane
Now, we move on to the AMC ground plane in Figure 4b, which is employed for the aforementioned phase control. The AMC ground plane consists of 76 unit cells arranged with a period p of 35 mm. Each AMC cell has the required reflection phase calculated by (3) and (4) at the design frequency, and their corresponding lengths are listed in Table 1. In Figure 4b, the same-colored cells have the same reflection coefficients, and there are eleven different colors in total. In addition, since the proposed antenna is designed for a scanned beam along the x-axis, the phase distribution of the cells is symmetric with respect to the x-axis. In Figure 4, the regions enclosed by the red and the blue lines are related to polarization modes incident on the cells, which will be explained in the following subsection in more detail. 25.98 Figure 5 shows the geometry of the source feeder that is a y-polarized U-slot microstrip patch antenna, whose feeding point is fp far from the center. The U-slot is introduced to improve impedance matching of our antenna, which is difficult due to the strong influence of reflected fields in the cavity.  Table 1. Now, we move on to the AMC ground plane in Figure 4b, which is employed for the aforementioned phase control. The AMC ground plane consists of 76 unit cells arranged with a period p of 35 mm. Each AMC cell has the required reflection phase calculated by (3) and (4) at the design frequency, and their corresponding lengths are listed in Table 1. In Figure 4b, the same-colored cells have the same reflection coefficients, and there are eleven different colors in total. In addition, since the proposed antenna is designed for a scanned beam along the x-axis, the phase distribution of the cells is symmetric with respect to the x-axis. In Figure 4, the regions enclosed by the red and the blue lines are related to polarization modes incident on the cells, which will be explained in the following subsection in more detail. Figure 5 shows the geometry of the source feeder that is a y-polarized U-slot microstrip patch antenna, whose feeding point is fp far from the center. The U-slot is introduced to improve impedance matching of our antenna, which is difficult due to the strong influence of reflected fields in the cavity.    Figure 6 represents the configuration of the PRS and the AMC unit cell. Both of them employ a Taconic RF-35 substrate of thickness 1.52 mm with dielectric constant ε r = 3.5 and loss tangent tan δ = 0.0025. The PRS cell consists of a copper strip parallel to the y-axis and a fully etched opposite backside. On the other hand, the AMC cell is comprised of a square patch etched on the substrate whose backside is entirely covered with copper. In both cells, the required reflection or transmission phases can be obtained by changing the widths of the patches (w and a in Figure 6). Figure 5. The U-slot microstrip patch antenna used as a source antenna. The design parameters are wx1 = 30 mm, wx2 = 15 mm, wy1 = 25.5 mm, wy2 = 1 mm, ly1 = 20 mm, g1 = 1 mm, g2 = 2 mm, and fp = 3 mm. Figure 6 represents the configuration of the PRS and the AMC unit cell. Both of them employ a Taconic RF-35 substrate of thickness 1.52 mm with dielectric constant εr = 3.5 and loss tangent tan δ = 0.0025. The PRS cell consists of a copper strip parallel to the yaxis and a fully etched opposite backside. On the other hand, the AMC cell is comprised of a square patch etched on the substrate whose backside is entirely covered with copper. In both cells, the required reflection or transmission phases can be obtained by changing the widths of the patches (w and a in Figure 6). The unit cell simulations for two different incident modes of a transverse electric (TE) and a transverse magnetic (TM) with the incidence angle α are illustrated in Figure 7. As briefly aforementioned in Section 2.1, when determining the reflection or transmission phases of the PRS and the AMC cell, we should take into account both the incident angle and polarization. In our antenna, the incidence angle is fixed at 19° by the antenna height The unit cell simulations for two different incident modes of a transverse electric (TE) and a transverse magnetic (TM) with the incidence angle α are illustrated in Figure 7. As briefly aforementioned in Section 2.1, when determining the reflection or transmission phases of the PRS and the AMC cell, we should take into account both the incident angle and polarization. In our antenna, the incidence angle is fixed at 19 • by the antenna height h = 50 mm and the unit cells' period p = 35 mm. When it comes to the incident polarization, we have supposed that a TE field is incident on the cells in the region surrounded by the red lines in Figure 4, whereas a TM field is incident in the region enclosed by the blue lines according to the y-polarized feeder antenna. The reflection or the transmission coefficients of the proposed PRS and the AMC unit cell are plotted in Figure 8. As the incidence angle is low enough, the reflection and transmission behaviors are pretty similar to each other. When we see the reflection phases, we can confirm that the AMC has much wider phase coverage than the PRS, which is favorable for various beam-scan directions. Moreover, the reflection magnitudes of the PRS are varied from 0.50 to 0.86 while those of the AMC are maintained as fairly high from 0.9 to 1.0, which are desirable to reduce an SLL and to obtain high gain, respectively.

Design of the AMC and the PRS Unit Cell
(a) (b) Figure 7. Unit cell simulations for two different incident modes of (a) a transverse electric (TE) and (b) a transverse magnetic (TM) with the incidence angle α.
The reflection or the transmission coefficients of the proposed PRS and the AMC unit cell are plotted in Figure 8. As the incidence angle is low enough, the reflection and transmission behaviors are pretty similar to each other. When we see the reflection phases, we can confirm that the AMC has much wider phase coverage than the PRS, which is favorable for various beam-scan directions. Moreover, the reflection magnitudes of the PRS are varied from 0.50 to 0.86 while those of the AMC are maintained as fairly high from 0.9 to 1.0, which are desirable to reduce an SLL and to obtain high gain, respectively.

Results
To prove the proposed beam-scan method in an FPC antenna, we fabricated and measured a prototype antenna for a scanned beam at θ = 30˚ and ϕ = 0˚, which is presented in Figure 9. The total volume of the antenna excluding the four acrylic supports measures 380 mm × 300 mm × 53.04 mm. Here, we could not help but fabricate the y-axis length

Results
To prove the proposed beam-scan method in an FPC antenna, we fabricated and measured a prototype antenna for a scanned beam at θ = 30°and φ = 0°, which is presented in Figure 9. The total volume of the antenna excluding the four acrylic supports measures 380 mm × 300 mm × 53.04 mm. Here, we could not help but fabricate the y-axis length shorter than that of the x-axis due to the limited fabrication facilities. However, it does not matter for proving our idea because the antenna is designed to scan the beam on the xz-plane (φ = 0°) where the x-axis length plays a crucial role rather than that of the y-axis.
Appl. Sci. 2021, 11, 11005 9 of 13 shorter than that of the x-axis due to the limited fabrication facilities. However, it does not matter for proving our idea because the antenna is designed to scan the beam on the xzplane (ϕ = 0˚) where the x-axis length plays a crucial role rather than that of the y-axis.
(a) (b) Impedance matching results for different scan angles are plotted in Figure 10. To confirm that our idea is still valid for other beam-scan directions but θt = 30°, we have conducted additional simulations for θt = 0°, θt = 15°, and θt = 45°. As shown in Figure 10, the −10 dB bandwidths are well maintained for the most cases. However, we can find that the impedance matching is slightly deteriorated for θt = 45°. This is owing to the large variation of reflection phases of AMC cells compared to the other cases, which needs to be Impedance matching results for different scan angles are plotted in Figure 10. To confirm that our idea is still valid for other beam-scan directions but θ t = 30 • , we have conducted additional simulations for θ t = 0 • , θ t = 15 • , and θ t = 45 • . As shown in Figure 10, the −10 dB bandwidths are well maintained for the most cases. However, we can find that the impedance matching is slightly deteriorated for θ t = 45 • . This is owing to the large variation of reflection phases of AMC cells compared to the other cases, which needs to be further improved in future works. A little discrepancy between the simulated and the measured results for θ t = 30 • is caused by the limited fabrication tolerance, which is significantly influential for our antenna.
Impedance matching results for different scan angles are pl firm that our idea is still valid for other beam-scan directions b ducted additional simulations for θt = 0°, θt = 15°, and θt = 45°. A −10 dB bandwidths are well maintained for the most cases. How impedance matching is slightly deteriorated for θt = 45°. This is tion of reflection phases of AMC cells compared to the other further improved in future works. A little discrepancy betwe measured results for θt = 30° is caused by the limited fabricatio nificantly influential for our antenna. Sim. θ t = 30˚ Sim. θ t = 45S

[dB]
Frequency [GHz] Figure 10. Input reflection coefficients (S11) according to the frequency for each scanned beam case.
Three-dimensional radiation patterns of the proposed antenna for each target direction are also shown in Figure 11. As we can see, the FPC antenna can scan the main beam well by properly adjusting the AMC configurations. To show the beam-scan performance more clearly, we plotted the contours of the radiation patterns on both the H-and E-plane for each scanning case in Figure 12. The specific performances of the proposed antenna at the design frequency are summarized in Table 2. As is described, the antenna can scan the main beam in the target direction with well-maintained high gain and a relatively narrow half-power beamwidth (HPBW). Good agreement between expected and experimental results verifies the validity of our design approach. well by properly adjusting the AMC configurations. To show the beam-scan performance more clearly, we plotted the contours of the radiation patterns on both the H-and E-plane for each scanning case in Figure 12. The specific performances of the proposed antenna at the design frequency are summarized in Table 2. As is described, the antenna can scan the main beam in the target direction with well-maintained high gain and a relatively narrow half-power beamwidth (HPBW). Good agreement between expected and experimental results verifies the validity of our design approach.   A comparison between previous works and own is described in Table 3. Even though [11,12] can scan the main beam continuously, they are hardly applicable for real timevarying systems due to their phase-adjusting methods: mechanically rotating a PRS and injecting water into a PRS. Moreover, while [13][14][15] can electrically switch the main beam using PIN-diodes, they cannot realize continuous beam-scanning and a wide steering coverage. On the other hand, our work can electrically and continuously scan the main beam   A comparison between previous works and own is described in Table 3. Even though [11,12] can scan the main beam continuously, they are hardly applicable for real time-varying systems due to their phase-adjusting methods: mechanically rotating a PRS and injecting water into a PRS. Moreover, while [13][14][15] can electrically switch the main beam using PIN-diodes, they cannot realize continuous beam-scanning and a wide steering coverage. On the other hand, our work can electrically and continuously scan the main beam with high gain as well as a wide scan range by introducing the phase-controllable AMC ground plane, which is far favorable for commercial applications.

Conclusions
In this paper, we have proposed a novel beam-scan method in an FPC antenna providing relatively high gain with a low SLL obtained using a tapered PRS. In order to produce the desired tilted main beam, an AMC ground plane was newly introduced, which was easier and more practical to manipulate the reflection phase than modifying PRS cells. In that only changing the AMC's reflection property is enough to produce a scanned beam, our approach is innovative compared with previous works.
To verify the proposed method, we have performed several simulations for different beam-scan directions and measured the fabricated prototype antenna. Accordingly, we have successfully proved that the proposed antenna indeed provides a well-directed beam in the desired target directions with reasonably high gain.
Although we have shown only a fixed tilted beam, our method can readily expand to electrical beam-scanning applications by employing active RF components in the AMC cells. In addition, our work has also presented a good idea of separating bias networks from a crucial field-bouncing cavity area. Therefore, in the active scanning approach, the expected potential problems that the bias lines will disturb a sensitive cavity mode are already removed. Consequently, we expect our method can be utilized in many practical beam-scan applications that require beam-scanning as well as high gain.