# An Advanced Beamforming Mechanism Based on Programmable Plasma Prisms

Fatemeh Sadeghikia, Kazem Zafari, Mohamed Himdi, Mahmoud T. Noghani, Ali K. Horestani

► To cite this version:

Fatemeh Sadeghikia, Kazem Zafari, Mohamed Himdi, Mahmoud T. Noghani, Ali K. Horestani. An Advanced Beamforming Mechanism Based on Programmable Plasma Prisms. IEEE Access, 2024, 12, pp.182062-182072. 10.1109/access.2024.3506821. hal-04817249

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Received 4 November 2024, accepted 17 November 2024, date of publication 26 November 2024, date of current version 12 December 2024.

Digital Object Identifier 10.1109/ACCESS.2024.3506821

RESEARCH ARTICLE

# An Advanced Beamforming Mechanism Based on Programmable Plasma Prisms

FATEMEH SADEGHIKIA<sup>1</sup>, KAZEM ZAFARI<sup>1,2</sup>, MOHAMED HIMDI<sup>3</sup>, (Member, IEEE), MAHMOUD T. NOGHANI<sup>1,3</sup>, AND ALI KARAMI HORESTANI<sup>1,3</sup>, (Senior Member, IEEE)

Corresponding author: Fatemeh Sadeghikia (sadeghi_kia@ari.ac.ir)

**ABSTRACT** This paper examines the feasibility of a novel programmable beam-shaping mechanism based on plasma prisms for advanced beamforming applications. The proposed mechanism offers versatile control over the direction, width, and splitting of electromagnetic beam by independently activating plasma prisms and adjusting their plasma frequencies. Through comprehensive numerical simulations, we demonstrate the feasibility and effectiveness of the proposed mechanism in achieving precise and controllable beam shaping. The simulations showcase various operational modes, including beam steering, beam divergence, and beam splitting, with potential applications in wireless communication systems and radar technologies. Furthermore, we investigate the implementation of the beam-shaping mechanism using commercially available fluorescent lamps, providing insights into its practical realization. The proposed mechanism contributes to the field of antenna engineering by opening up new possibilities for advanced beamforming technologies.

**INDEX TERMS** Beamforming, intelligent beamforming, plasma, programmable prism.

## I. INTRODUCTION

Beam steering techniques have revolutionized wireless communication and antenna systems by enabling dynamic control over the direction and shape of transmitted and received signals. This capability finds wide applications in wireless networks, satellite communications, radar systems, and autonomous vehicles. Various methodologies, including phased array antennas [1], [2], [3], [4], [5], parasitic-based antennas [6], [7], and metamaterial-based structures [5], [8], [9], have been explored for beam steering, each offering unique advantages and limitations. Phased arrays provide fast and precise beam steering but suffer from fixed beamwidth, limited scanning angles, and susceptibility to grating lobes. Parasitic-based antennas offer simplicity and low cost but have limited steering range and challenges in achieving precise beam shaping. Metamaterial-based structures utilize engineered artificial materials with extraordinary

electromagnetic (EM) properties but face complexity in design, fabrication, and integration with practical systems.

Recent technological advancements have significantly improved beam steering mechanisms, enabling enhanced performance and adaptability. Real-time adjustment of EM properties of materials such as liquid crystals [10], [11], [12] or ferrites [13], [14], has opened new possibilities for implementing steerable antennas. By incorporating these materials in an antenna structure and dynamically changing their permittivity or permeability, it becomes possible to adjust the radiation characteristics of the antenna and control the direction and shape of the radiated beam. This approach is particularly valuable for applications that require fast and accurate beam steering, providing a simple and reliable technique, although it may introduce limitations in terms of bandwidth and the range of steering angles.

Along these lines, several types of steerable antennas based on plasma material have been developed in the literatures [15], [16], [17], [18], [19], [20], [21], and [22]. These antennas can bridge the gap between compact electronically

The associate editor coordinating the review of this manuscript and approving it for publication was Tutku Karacolak<sup>1</sup>.

<footnote n="1">¹Wireless Telecommunication Group, Khayyam Research Institute, Ministry of Science, Research and Technology, Tehran 14657-74111, Iran</footnote>

<footnote n="2">²Department of Electrical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran</footnote>

<footnote n="3">³Institute of Electronics and Telecommunications of Rennes (IETR), UMR-6164, University of Rennes 1, 35042 Rennes, France</footnote>
steerable antennas and bulky mechanically steerable antennas [23], [24], [25], [26], [27]. Beam steering using plasma offers greater flexibility compared to other techniques while remaining relatively cost-efficient [28], [29], [30], [31]. An additional advantage is that plasma components can be electrically switched ON/OFF, therefore the entire or some parts of the antenna can be concealed [32], [33], [34], [35]. Moreover, plasma elements can operate in either a conductive or a dielectric mode, depending on the operating frequency [36], [37]. At frequencies above the plasma frequency, they act as relatively good dielectrics [38], [39], [40], while at frequencies below the plasma frequency, they behave as conductors, reflecting incident EM waves [41], [42], [43], [44]. These advantages make plasma components attractive for application in programmable or intelligent antenna systems with capabilities such as real-time beam-steering and beam-forming.

Building on these advancements, this paper presents an innovative approach for manipulating an EM beam using a programmable structure based on plasma materials. The novelty of this work lies in the development of a fully programmable and multifunctional beam-shaping mechanism based on a plasma structure capable of performing beam steering, beamwidth control, and beam splitting within a single architecture. Unlike conventional approaches that either focus on static beam splitting or beam steering independently [45], [46], [47], [48], our proposed system offers dynamic and simultaneous control over both. This is achieved by adjusting the plasma frequencies of the plasma elements forming the prism, thus achieving real-time and flexible manipulation of the EM beam.

The remainder of this paper is organized as follows: Section II presents the structure and analytical design equations of a steerable plasma prism. Section III proposes a programmable beam-shaping mechanism based on a plasma cube composed of multiple plasma prisms. Section IV investigates the development and implementation of the programmable beam-shaping structure using cylindrical plasma tubes. Finally, Section V provides a summary and brief conclusion.

## II. PLASMA PRISM

In this section, we present the structure and formulation of a reconfigurable plasma prism, followed by an analytical and numerical investigation of its performance.

As illustrated in Fig. 1(a), the proposed plasma prism is a right triangular prism with square sides, each having a side length of a. In this figure, $\vec{z}$ represents the propagation direction coordinate and $\vec{n}$ is the normal axis to the hypotenuse. When an incident EM wave interacts with a cold, homogeneous, and isotropic plasma prism, it experiences a complex permittivity $\epsilon_p$, given by [49]:

$$ \epsilon_p = 1 - \frac{\omega_p^2}{\omega(\omega - j\nu)} = \left[ 1 - \frac{\omega_p^2}{\omega^2 + \nu^2} \right] - j \left[ \frac{\nu\omega_p^2}{\omega(\omega^2 + \nu^2)} \right] \quad (1) $$

<figure><img src="image_2.png" /><figcaption>FIGURE 1. (a) The 3D view of the proposed plasma prism. (b) Ray-tracing in a dielectric plasma prism.</figcaption></figure>

Here, $\omega$ represents the angular frequency of the incident EM wave in rad/s, $\nu$ denotes the electron-neutral collision frequency in Hertz, and $\omega_p$ corresponds to the plasma angular frequency in rad/s, which is an inherent property of the plasma medium. The plasma angular frequency is calculated as:

$$ \omega_p = \sqrt{\frac{ne^2}{m_e\epsilon_0}} \quad (2) $$

In this relation, $e$ and $m_e$ denote the electron charge and mass, respectively, $n$ represents the plasma density, and $\epsilon_0$ signifies the free space permittivity.

For incident EM waves with frequencies higher than the plasma frequency, the plasma prism functions as a dielectric with a positive permittivity, where the real part of the permittivity falls within the range of 0 and 1. Consequently, the incident wave can propagate through the prism, although the extent of propagation loss is directly proportional to the imaginary part of the permittivity. Conversely, when the frequency of the incident wave is lower than the plasma frequency, the prism exhibits a negative permittivity, leading to the reflection of the incident wave. It is important to note that by adjusting the plasma frequency, which can be achieved by modifying certain plasma characteristics like density, the frequency band where the plasma prism behaves as a dielectric or conductor can be altered.

As shown in Fig. 1(b), when an EM wave with a frequency higher than the plasma frequency is incident perpendicular to one side of a plasma prism, it undergoes refraction at the prism's front side. According to Snell's Law, the refraction angle $\theta_{out}$ can be expressed as:

$$ \theta_{out} = \sin^{-1}(n_p \sin(\alpha)), \quad (3) $$

where, $n_p$ denotes the refractive index of the plasma medium, which is the square root of the real part of the plasma relative permittivity. Thus, $n_p$ can be derived from equation (1) as:

$$ n_p = \sqrt{\left(1 - \frac{\omega_p^2}{\omega^2 + \nu^2}\right)} \quad (4) $$
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>FIGURE 2. (a) Analytically calculated refraction angle of the dielectric plasma prism versus plasma frequency for different operating frequencies, (b) Comparison between the analytical and numerical refraction angles versus operating frequency for a dielectric plasma prism with a plasma frequency of $f_p = 8$ GHz and a collision frequency of $v = 0.5$ GHz.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>FIGURE 3. Distribution of the electric field within the dielectric plasma prism at an operating frequency of 10 GHz, with a plasma frequency of $f_p = 8$ GHz and collision frequency of $v = 0.5$ GHz: (a) phase, (b) magnitude.</figcaption></figure>

Equations (3) and (4) show that the angle of refraction is a function of the plasma frequency. To gain a better understanding, Fig. 2(a) illustrates variations in the refraction angle of the plasma prism with respect to the plasma frequency for different operating frequencies. In this figure, the plasma frequency is adjustable between 1 GHz and 8 GHz, while the collision frequency is assumed constant at $v = 0.5$ GHz.

The figure clearly demonstrates that the refraction angle can be controlled by manipulating the plasma frequency of the prism.

Fig. 2(b) provides a comparison between the numerically investigated and analytically calculated refraction angles of a plasma prism with a side length of $a = 165$ mm across the operating frequency. In this case, the plasma frequency and collision frequency are set at 8 GHz and 0.5 GHz, respectively. The dimensions of the port in the simulation are $W_{feed} = 50$ mm and $L_{feed} = 165$ mm. The results demonstrate good agreement between the analytical and numerical approaches.

Figures 3 depict the phase and magnitude of the E-field distribution of EM wave passing through the dielectric plasma prism at the operating frequency of $f = 10$ GHz. The incident wave is a linearly TE-polarized plane wave with an electric field component in the x-direction. From the figures, it can be observed that the refracted wave is steered towards an angle of $\theta_{out} = 21^{\circ}$.

The adjustable plasma frequency in this prism provides a mechanism for beam steering. For example, as illustrated in Fig. 4(a), when the plasma prism is switched OFF, at the

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>FIGURE 4. (a) Normalized gain of the plasma prism at the operating frequency of 10 GHz for different plasma frequencies using an ideal waveguide port feed, (b) Normalized gain of the prism versus the collision frequency for a plasma frequency of $f_p = 8$ GHz and an operating frequency of $f = 10$ GHz.</figcaption></figure>
operating frequency of 10 GHz, the incident wave passes through the prism without any refraction which means $\theta_{out} = 0°$. By exciting the prism and controlling the plasma frequency up to 8 GHz, the refracted angle can be altered from $\theta_{out} = 0°$ to $\theta_{out} = 21°$. It is noticeable to mention that all gain plots in this investigation are normalized to the gain of the bare feed, which is 20 dBi in this study. It represents the “plasma OFF” mode of the prism. Due to the plasma loss and beam steering, the maximum normalized gain for other states is smaller than 0 dB. In summary, increasing the plasma frequency in the plasma prism increases the steering angle of the incident wave.

To investigate the influence of the collision frequency on the performance of the plasma prism, the simulated normalized gain of the prism as a function of the collision frequency is presented in Fig. 4(b). In this simulation, we consider a plasma frequency of $f_p = 8$ GHz and an operating frequency of $f = 10$ GHz. Note that an increase in the collision frequency leads to a relative permittivity with a larger imaginary part. Therefore, as can be observed in the figure, an increase in the collision frequency leads to a higher loss in the plasma prism. Conversely, decreasing the collision frequency results in lower losses for the plasma prism, as depicted in the figure. This can be achieved by using low-pressure plasmas.

Figure 5 illustrates variations in the radiation efficiency of the plasma prism versus the operating frequency for several plasma frequencies. It can be observed that as the plasma frequency increases, the efficiency of the prism decreases due to the increasing plasma permittivity, which affects the overall performance of the prism.

<figure><img src="image_8.png" /><figcaption>**FIGURE 5.** Radiation efficiency of the plasma prism versus operating frequency at the collision frequency of $v = 0.5$ GHz.</figcaption></figure>

It should be noted that for the numerical EM analysis in this study, an ideal waveguide port with a radiation gain of 20 dBi and a half-power beamwidth of 8.8° at 10 GHz is used. Using the waveguide port rather than a horn antenna simplifies the setup, reduces computational complexity, and decreases simulation time. To assess the validity of using a waveguide port in place of a horn feed, the normalized gain of the plasma prism at various plasma frequencies using a horn

<figure><img src="image_9.png" /><figcaption>**FIGURE 6.** Normalized gain of the plasma prism using a pyramidal horn feed, at the operating frequency of 10 GHz and collision frequency of $v = 0.5$ GHz.</figcaption></figure>

feed is presented in Fig. 6. The aperture dimensions of the horn ($W_{feed} = 50$ mm and $L_{feed} = 165$ mm) are identical to those of the waveguide port. Comparing the results shows that although the horn feed exhibits a slightly wider beamwidth, the overall behavior, such as beam steering and refraction angles, remains consistent between both feeds. Therefore, it can be concluded that the waveguide port serves as a valid and efficient approximation for the horn antenna in this study.

<figure><img src="image_10.png" /><figcaption>**FIGURE 7.** Illustration of the multifunctional beam-shaping structure: (a) 3D view, (b) top view.</figcaption></figure>

### III. PROGRAMMABLE BEAM SHAPING MECHANISM BASED ON THE PLASMA PRISM

To achieve a versatile beam-shaping mechanism, this section proposes a novel plasma structure. The section also studies the performance of the proposed structure through numerical simulations. Fig. 7 presents the 3D view and the top view of the proposed structure, which consists of four right triangular plasma prisms with square sides of length a. In this configuration, each plasma prism can be independently deactivated or activated while the plasma frequency within each prism is controllable. The capability of individually controlling the ON/OFF status of each plasma prism allows for 16 different operational states. Furthermore, by adjusting the plasma frequency within each activated prism, the operation mode can be manipulated, enabling the transition between dielectric
and conductive modes for each prism. This section discusses some operational modes of the proposed structure. In what follows, the frequency of the incident wave is set to $f = 10$ GHz.

As the first example, Fig. 8(a) illustrates a beam steering structure where prisms 1 and 2 are deactivated, while prisms 3 and 4 are excited with a plasma frequency of $f_p = 8$ GHz. In this configuration, the excited plasma prisms act as dielectrics since the plasma frequency is lower than the operating frequency. Consequently, the incident wave is refracted towards the left side, as shown in the E-field distribution of Fig. 8(b). By controlling the plasma frequency within this prism between 2 GHz and 8 GHz, the direction of the refracted wave can be adjusted, as discussed in Section II. It is clear that the beam can be steered to the right by activating prisms 1 and 4, and deactivating prisms 2 and 3.

For the second example, prisms 1 and 3 are activated in the dielectric mode, as depicted in Fig. 8(c). The plasma frequency is set to 8 GHz in each activated region. As illustrated in Fig. 8(d), this operational mode changes the beamwidth of the incident wave.

In the next examples, the selected plasma prisms are activated in their conductive (rather than dielectric) mode. To this end, the plasma frequency of the activated prisms is set at 15 GHz. In the first case, prisms 2 and 3 are activated. Since the active plasma surfaces behave as conductors, they serve as reflective surfaces for the incident EM wave. As shown in Fig. 8(f), this mode changes the direction of the wave towards the left side. Again, it is clear that the wave can be reflected towards the right side by activating prisms 1 and 2, and deactivating prisms 1 and 4.

In another example depicted in Fig. 8(g), the plasma frequency is set at 15 GHz in region 2 while the other regions are deactivated, as. Using this mode, the structure functions as a splitter, dividing the incident EM wave. This is demonstrated by the computed E-field distribution as shown in Fig. 8(h).

In summary, it is demonstrated, through full-wave EM simulations, that the combination of four right plasma prisms enables electrical beam steering. However, implementing homogeneous plasma prisms is relatively complicated and as a result is costly. Therefore, in the next section, a practical method for the implementation of the proposed beam-shaping structure based on commercial fluorescent lamps is investigated.

Note that the height of the structure, (denoted by $a$ in Fig. 7(a)), is determined based on the E-plane beamwidth of the feed, with the first null beamwidth (FNBW) serving as a practical reference for this selection. To ensure that a significant portion of the feed's radiated power passes through the structure, the height is chosen such that the FNBW approximately covers the height of the front surface of the structure. The radiation pattern for the TE mode of the feed, with an FNBW of 56°, is analyzed to guide this decision. While a more conservative approach would involve increasing the height to cover the rear surface, this would result in

<figure><img src="image_11.png" /><figcaption>FIGURE 8. Illustrations of the proposed structure in four different operating configurations, namely, (a) beam-steering configuration with $f_p = 8$ GHz in prisms 3 and 4, (c) beam-width-control configuration with $f_p = 8$ GHz in prisms 1 and 3, (e) reflector configuration with $f_p = 15$ GHz in prisms 2 and 3, and (g) beam splitting configuration with $f_p = 15$ GHz in prism 2. The figure also shows E-field distributions (subfigures (b), (d), (f), and (h)) of the proposed structure in each configuration when exposed to a planar incident wave at $f = 10$ GHz.</figcaption></figure>

a much larger structure. Therefore, in this study, a height of 165 mm is selected to balance structural efficiency and size, ensuring effective interaction between the feed and the structure.

## IV. IMPLEMENTATION OF THE BEAMFORMING MECHANISM

In this section, the feasibility of the implementation of the beamforming mechanism is investigated.
<figure><img src="image_12.png" /><figcaption>**FIGURE 9.** Arrangement and dimensions of the commercial cylindrical fluorescent lamps for the implementation of the beam shaping structure: (a) 3-D view, (b) top view.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**FIGURE 10.** Block diagram of the beamforming mechanism.</figcaption></figure>

One method for the implementation of the proposed beam-shaping structure based on a plasma prism is using a sufficiently dense array of cylindrical plasma tubes. To achieve this, cylindrical commercial fluorescent lamps available in the market can be utilized. Fig. 9 illustrates the arrangement and dimensions of the array consisting of 121 lamps. Note that using this configuration, all the operating modes presented in the previous section can be realized. Moreover, since in this configuration each individual lamp can be independently switched ON or OFF, other configurations not discussed in the previous section can be achieved.

A block diagram of the system is provided in Fig. 10. As illustrated, the control system consists of several key components, with the processor and excitation circuits being the most critical. The processor manages the configuration of the beamforming mechanism by sending control commands to the excitation circuits, which then switch each plasma element ON or OFF according to the required beam shaping or steering function.

There are various methods for biasing the plasma elements, such as DC, AC, and pulsed techniques. In this design, DC biasing is preferred, based on the previous experience in [38], due to its simplicity, stability in maintaining the plasma state, and ability to precisely control the plasma

frequency. Specifically, using a controllable DC power supply paired with an electrical dimmer is recommended to energize the plasma medium. The dimmer allows for fine adjustment of the input current, which in turn fine-tunes the plasma frequency.

The fluorescent lamps considered in this study have a controllable plasma frequency ranging from $f_p = 2$ GHz to $f_p = 15$ GHz, while their collision frequency is almost fixed at $\nu = 0.5$ GHz. Each lamp has a height of $a = 165$ mm and a diameter of 14 mm, while it is covered by a dielectric material with a thickness of 0.5 mm and a relative permittivity of 2.

The simulation setup includes an ideal waveguide port with dimensions $W_{feed} = 50$ mm and $L_{feed} = 165$ mm. By varying the number and arrangement of activated lamps, the beam profiles of the incident wave can be steered. In what follows, four configurations of the structure are studied, and their characteristics are investigated using a commercial full-wave numerical modeling tool.

In the first configuration, to form a prism similar to that of Fig. 8(a), half of the fluorescent lamps of the cubic structure are excited (see Fig. 11(a)). Therefore, as expected, the incident beam is steered. This is clearly shown by the computed electric field illustrated in Fig. 11(b). Moreover, as shown in Fig. 11(c), by varying the plasma frequency in the excited lamps, the direction of the incident wave can be changed from 0° to 20°. As shown in the figure, the degradation of the radiation gain in the worst case, i.e., for the steering angle of 20° is approximately 1.7 dB.

As mentioned earlier, the realization of the structure using an array of cylindrical plasma lamps allows us to form other interesting configurations that were not possible using four prisms. For instance, when using the structure shown in Fig. 12(a), the incident wave can be steered up to around 25° when the plasma frequency is $f_p = 8$ GHz in the excited lamps. This is shown in Fig. 12(b). This mode enables the steering of the radiated wave up to $\pm 25$°, as depicted in Fig. 12(c). Other configurations, for instance activating a plasma region with a curved surface may result in a larger steering angle.

The second mode configuration, as illustrated in Fig. 13(a), involves a two-dielectric-prism structure in the form of a butterfly, similar to the mode shown in Fig. 8(c). This configuration can be used to control the radiated beamwidth, as shown in the E-field distribution of Fig. 13(b). By controlling the plasma frequency in the dielectric prisms up to 8 GHz, the beamwidth of the refracted wave can be adjusted, as shown in Fig. 13(c). Table 1 presents the simulated normalized gain and beamwidth of the diverging mode for different plasma frequencies at 10 GHz. It is noted that $f_p = 0$, which is the pattern associated with the plasma OFF, corresponds to the pattern of the feed.

Let us move to the next configuration, in which the reflective mode of the plasma is used. With this aim, the plasma frequency of the excited lamps is set to 15 GHz, while
<figure><img src="image_14.png" /><figcaption>**FIGURE 11.** (a) Beam shaping structure based on using commercial lamps for beam forming using the dielectric mode of plasma elements, (b) Simulated E-field distribution at *f* = 10 GHz when *f*<sub>p</sub> = 8 GHz, (c) Simulated beam forming at *f* = 10 GHz by controlling the plasma frequency between 2 GHz and 8 GHz.</figcaption></figure>

<table><caption>**TABLE 1.** Simulated radiation characteristics of the beamwidth control mode of the beam shaping structure at *f* = 10 GHz.</caption><thead><tr><td>f<sub>p</sub> (GHz)</td><td>Normalized Gain (dBi)</td><td>Beamwidth</td></tr></thead><tbody><tr><td>0</td><td>0</td><td>8.8°</td></tr><tr><td>2</td><td>-0.97</td><td>9.4°</td></tr><tr><td>6</td><td>-3.2</td><td>20.4°</td></tr></tbody></table>

their collision frequency is almost fixed at $v = 0.5$ GHz. Fig. 14(a) shows one of the reflective configurations that can steer the incident wave, as illustrated in the E-field distribution of Fig. 14(b). By exciting different groups of lamps in this arrangement, the steering angle can be changed from 90° to 270°, as shown in linear scaling of Fig. 15. The resolution of this steering mechanism strongly depends on the dimensions of the entire structure and the diameter of each plasma element, which in this case is a commercial fluorescent lamp. Decreasing the diameter of each element enhances the steering resolution. It is worth noting that in the reflective mode, it is not necessary to excite all the lamps in the configuration; exciting one or two rows at the front face is sufficient for reflection and steering, thereby reducing power consumption.

<figure><img src="image_15.png" /><figcaption>**FIGURE 12.** Extended steering angle in the beam forming mode introduced in Fig. 8 (a): (a) Structure providing an extended steering angle, (b) Simulated normalized gain at *f* = 10 GHz with *f*<sub>p</sub> = 8 GHz, (c) Total possible steering range.</figcaption></figure>

Finally, the splitter configuration of the structure is achieved by exciting the lamps with a plasma frequency of 15 GHz in the structure depicted in Fig. 16 (a). This configuration splits the incident wave as shown in the E-field distribution of Fig. 16(b). The direction of the split beam can also be controlled based on the position and configuration of the excited lamps.

It is worth noting that, given the periodic nature of the structure, the potential influence of Bloch band characteristics on wave propagation in the fluorescent lamp array should be investigated. The array used in this study was evaluated at a frequency that supports effective wave propagation, as confirmed by our simulation results, indicating that the chosen
<figure><img src="image_16.png" /><figcaption>**FIGURE 13.** Beam shaping structure based on using commercial lamps for controlling the beamwidth of the radiated beam using the dielectric mode of plasma elements: (a) Illustration, (b) Simulated E-field distribution at *f* = 10 GHz when *f*<sub>p</sub> = 8 GHz, (c) Simulated normalized gain based on the plasma frequency.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**FIGURE 14.** Beam shaping structure based on using commercial lamps for steering the radiated beam using the reflective mode of plasma elements: (a) Illustration, (b) Simulated E-field distribution at *f* = 10 GHz when *f*<sub>p</sub> = 15 GHz.</figcaption></figure>

frequency does not fall within a band gap of the structure. For optimal performance across the desired frequency range, analyzing the dispersion diagram of the structure's unit cell could further guide the design process.

<figure><img src="image_18.png" /><figcaption>**FIGURE 15.** Extension of the steering range in the reflective mode of the mechanism: (a) $\theta_{\text{out}} = 90^{\circ}$, (b) $\theta_{\text{out}} = 170^{\circ}$, (c) $\theta_{\text{out}} = 190^{\circ}$, and (d) $\theta_{\text{out}} = 270^{\circ}$.</figcaption></figure>

In summary, it has been demonstrated that the proposed beam shaping mechanism can be implemented using a dense array of commercial lamps, offering a simple and cost-effective solution that enhances beam steering capabilities. However, to advance this concept toward practical applications, several design challenges need to be addressed. The limitations of this work primarily relate to the development of plasma cells with optimal dimensions and properties. Addressing challenges such as collision frequency, excitation efficiency, and dielectric tube characteristics is essential for future improvements of the mechanism.

<figure><img src="image_19.png" /><figcaption>**FIGURE 16.** Beam shaping structure based on using commercial lamps for splitting the radiated beam using the reflective mode of plasma elements: (a) Illustration, (b) Simulated E-field distribution at *f* = 10 GHz, when *f*<sub>p</sub> = 15 GHz.</figcaption></figure>

## V. CONCLUSION

In this paper, a feasibility study on a novel programmable beam-shaping structure based on plasma prisms has been presented and its performance through comprehensive numerical
simulations has been investigated. The proposed struc-
ture offers multifunctional beam manipulation capabilities,
including beam steering, beamwidth control, reflecting, and
beam splitting, by independently controlling the activation
of plasma prisms and adjusting their plasma frequencies.
Through extensive simulations, we have demonstrated the
effectiveness of the proposed mechanism in achieving precise
and controllable beam shaping. The ability to dynamically
control the plasma prisms and their plasma frequencies
allows for versatile beam steering, offering potential appli-
cations in wireless communication systems, radar systems,
etc. The paper has also suggested a method of realization
using commercial fluorescent lamps. Numerical analyses of
the realizable structure based on fluorescent lamps provide
valuable insights into its potential capabilities. Overall, the
programmable beam-shaping mechanism based on plasma
prisms presents a promising avenue for advanced beamform-
ing technologies. Its ability to dynamically shape electro-
magnetic beams with high precision and flexibility opens
up new possibilities for improved communication systems
and electromagnetic applications. We believe this research
contributes to the field of antenna engineering and paves the
way for further investigations in programmable beam shaping
mechanisms.

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<figure><img src="image_20.png" /></figure>

**FATEMEH SADEGHIKIA** received the B.Eng. degree in electrical and electronics engineering from Iran University of Science and Technology (IUST), Tehran, Iran, in 2000, the M.Eng. degree in electrical and electronics engineering from the K. N. Toosi University of Technology, Tehran, in 2003, and the Ph.D. degree in telecommunication engineering (the area of plasma antennas) from IUST, in 2012.

Since 2009, she has been with the Wireless Telecommunication Group, Khayyam Research Institute, Ministry of Science, Research and Technology, Tehran, where she is currently an Associate Professor. Her research interests include reconfigurable antennas, microwave and millimeter-wave devices, and the applications of plasma technology in wireless communications. She was a recipient of the 2020 IEEE Transactions on Antennas and Propagation Best Paper Award from the IEEE Malaysia Section and the 2024 Best Paper Award from the IEEE Malaysia AP/MTT/EMC Joint Chapter.

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**KAZEM ZAFARI** received the B.S. degree in electrical engineering from Yazd University, Yazd, Iran, in 2015, and the M.S. degree in electrical engineering from Iran University Science and Technology, Tehran, Iran, in 2018. From 2018 to 2023, he was a Research Assistant with the Iran University of Science and Technology. His research interests include the development of plasma lens antennas, leaky-wave and holographic antennas, spoof surface plasmon polaritons waveguides, metasurfaces, metamaterials, and power amplifiers.

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**MOHAMED HIMDI** (Member, IEEE) received the Ph.D. degree in signal processing and telecommunications from the University of Rennes 1, France in 1990. Since 2003, he has been a Professor with the University of Rennes 1, and the Head of the High Frequency and Antenna Department until 2013, and from 2024 of IETR. He has authored or co-authored 170 journal papers and over 350 papers in conference proceedings and H-index 38. He has also co-authored 12 book

chapters. He holds 49 patents. His research activities concern passive and active millimeter-wave antennas. His research also includes the development of new architectures of antenna arrays, and new three-dimensional (3-D) antenna technologies. He was Laureate of the 2d National Competition for the Creation of Enterprises in Innovative Technologies in 2000 (Ministry of Industry and Education). In March 2015, he received the JEC-AWARD at Paris on Pure composite material antenna embedded into a motorhome roof for the Digital Terrestrial Television reception. He received the Innovation Trophy 2021 from University of Rennes 1.
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**MAHMOUD T. NOGHANI** received the B.Sc. degree in electronic engineering from the Sharif University of Technology, in 2005, and the M.Sc. and Ph.D. degrees in communication engineering from Iran University of Science and Technology (IUST), in 2008 and 2013, respectively.

He is currently an Assistant Professor and the Director of the Communications Laboratory, Khayyam Research Institute, Ministry of Science, Research and Technology, Tehran, Iran. His

research interests include the design of antennas and passive microwave devices, and microwave and RF circuits, optical communication, photonic, and nanophotonic devices and components.

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**ALI KARAMI HORESTANI** (Senior Member, IEEE) received the B.Eng. degree in electrical and electronics engineering from the University of Shiraz, in 2003, the M.Eng. degree in electrical and electronics engineering from the University of Shahid Beheshti, Iran, in 2006, and the Ph.D. degree (Hons.) in electrical and electronics engineering (the areas of microwave and millimeter-wave circuit design) from The University of Adelaide, in 2014. He was a Postdoctoral

Researcher with The University of Adelaide, for six months, where he was a Lecturer, from 2014 to 2015. He was a Postdoctoral Researcher with the University of Tehran, supported by Iran National Elites Foundation, from 2015 to 2016. Since 2016, he has been with the Khayyam Research Institute, Ministry of Science, Research, and Technology, where he is currently an Assistant Professor. He was a Visiting Scholar with GEMMA/CIMITEC, Departament d'Enginyeria Electronica, Universitat Autonoma de Barcelona, Bellaterra, Spain, hosted by Prof. Ferran Martin. He is also a Guest Researcher with Gdańsk University of Technology, Poland, hosted by Prof. Michal Mrozowski. His research interests include microwave and millimeter-wave devices and circuits, antennas, and metamaterial-inspired structures and their applications. He was a recipient of the 2014 IEEE Sensors Journal Best Paper Award, the 2020 IEEE Transactions on Antennas and Propagation Best Paper Award from the IEEE Malaysia Section, the Winner of the 2014 Gertrude Rohan Memorial Prize and Medal for the Best Ph.D. Thesis in the areas of information and communication technology from The University of Adelaide, and the 2012 Simon Rockliff Award for Outstanding Mentoring of Fellow Students.

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