Feasibility of a Plasma-Based Intelligent Reflective Surface

Gaseous Plasma Antennas are devices in which an ionized gas (i.e., plasma) is exploited to transmit and receive Electromagnetic waves. Their main advantage over metallic systems is the possibility to reconfigure the antenna performance (e.g., radiation pattern) by electronically varying the plasma parameters (e.g., density). Recently, Intelligent Reflecting Surfaces (IRSs) have been proposed to control the environment between transmitting and receiving antennas manipulating the signals reflected. In this work, the feasibility of a plasma-based IRS is investigated. A theoretical model has been developed to assess the use of plasma as a reflecting medium. Numerical simulations have been performed to preliminary design plasma-based IRSs. Two designs of IRSs, relying on plasma properties consistent with the technology at the state-of-the-art, are proposed. The former enables beam steering operations depending on the continuous control of the phase of the reflected wave. The latter exploits a 1-Bit coding strategy to produce specific diffraction patterns. The main advantage of a plasma-based IRS with respect to the metallic counterpart is the possibility to control the phase of the reflected wave, maintaining the magnitude of the reflection coefficient close to the unit. The main drawback of plasma-based systems is the necessity of using thick plasma elements (in the order of the wavelength in the air) to control the phase of the reflected wave over 360 deg. This constraint can be relaxed if digital plasma elements are adopted.

operated in the Ultra High Frequency (UHF) range rely- 46 ing on custom-build Cold Cathodel Fluorescence Lamps (CCFL). Numerical designs of both transmit-arrays [10], constitute the surfaces. Each unit cell can independently control the phase of the reflected wave by varying the plasma 103 density electronically [16]. Using a plasma panel to accom-104 plish beam steering operations is not new [16]. Nonetheless, 105 this study introduces relevant advances to the state-of-the-art. 106 First and differently from previous works [16], the proposed 107 design relies on realistic plasma properties. The assumed val-108 ues of plasma density, electron temperature, and neutral gas 109 pressure are coherent with the experimental data available in 110 the literature of GPAs [4]. Specifically, for each configuration 111 proposed dedicated experimental works have been referenced 112 to demonstrate the feasibility of the design. Therefore, the 113 results discussed in the following are more robust with respect 114 to previous works in which aspirational plasma properties 115 have been assumed [28] (e.g., inconsistent plasma density and 116 neutral pressure). Second, we derive quantitative design rules 117 valid for a generic plasma panel operated as a reflector. This 118 result improves the state-of-the-art since past configurations 119 address only peculiar architectures (e.g., the incident wave 120 produced by a horn antenna [16]). Specifically, a simplified 121 theoretical model has been developed to assess the use of 122 plasma as a reflecting medium.

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Eventually, the remainder part of this paper is organized 124 as follows. Section II discusses the adopted theoretical-125 numerical methodology. Section III and Section IV present 126 the derivation of the quantitative design rules and the numer-127 ical design of two plasma-based IRSs, respectively. Finally, 128 Section V draws the conclusions and discusses the next steps 129 toward realizing a plasma-based IRS.

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A theoretical model has been developed to assess the use of 132 plasma as a reflecting medium, and numerical simulations are 133 performed to preliminary design plasma-based IRSs. In both 134 cases, the EM response of the plasma, namely its capability 135 to control the phase of the reflected wave, is described via 136 the relative permittivity ε r . The latter is derived according to 137 the cold plasma model [29]. The motion of the ions has been 138 neglected provided the frequencies of interest are in the GHz 139 range [29]. Namely, ε r reads: where ω is the wave angular frequency in rad/s, ω p is the 142 plasma frequency in rad/s, ν is the collision frequency in Hz, 143 and j is the imaginary unit. The plasma frequency is given 144 where k B is the Boltzmann constant, and T 0 is the neutral gas 167 temperature in K. Second, the plasma impedance

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where Z 0 = √ µ 0 /ε 0 is the impedance of free space, and The reflected wave is described via the complex reflection 189 coefficient defined as where E ρ and E ι are the reflected and incident electric field, 192 respectively. According to the conventional transmission line 193 model [32], reads where ρ is the Fresnel's reflection coefficient at the air-196 plasma interface, and pl is the reflection coefficient within 197 the plasma medium. Specifically, pl reads where λ = c/f is the wavelength in air, and ρ reads    to plasma-based systems (see Table 1). On the other hand,

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The numerical model described in Section II has been 306 exploited to define the preliminary design of plasma-307 based IRSs. First, the behaviour of a plasma element 308 has been assessed by accounting for practical constraints 309 (e.g., L pl = L). Second, the design of two IRSs is proposed. 310 The former exploits thick plasma elements (z pl = λ) to 311 accomplish beam steering operations via a continuous control 312 of the phase. The latter relies on digital plasma elements 313 whose thickness is z pl = λ/3 to produce specific diffraction 314 patterns.

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The condition L pl = L is hardly met in practice since addi-317 tional equipment is required to confine and ignite the plasma 318 VOLUME 10, 2022    The plasma element described in Section IV-A, has been 348 exploited to design an IRS in which n e and, in turn, the phase 349 of can be controlled continuously to enable beam steer-350 ing operations. An IRS made of 10 × 10 plasma elements 351 constitutes the design (see Fig. 7) [16]. The operation fre-352 quency is f = 10 GHz, and the element periodicity has been 353 chosen as L = λ/2 = 15 mm to avoid grating lobes [44]. 354 Specifically, n e has been varied column by column to steer the 355 beam along the direction θ max = −10 deg on the x-z plane 356   Fig. 9. z pl = λ/3, n 0 = 5 × 10 22 m −3 (p 0 = 2.0 mbar), and ν = 1.6 × 10 9 Hz.
(broadside in correspondence of θ = 0). The properties of the 357 plasma elements, sorted by column, are reported in Table 2.

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In addition, the array factor rule has been adopted to design This methodology allows for designing of an IRS that per-364 fectly matches the requirement in terms of θ max (see Fig 8).

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It is worth noting that the RCS has been computed for both  Table 2). Very comparable results are obtained for 371 the two cases (differences < 0.1 dBm 2 ), confirming that neg- quency f = 10 GHz, lattice periodicity, L = λ/2 = 15 mm, 382 plasma element width, L pl = L/ √ 2, and thickness, z pl = 383 λ/3 = 10 mm. This design employs a relatively thin plasma 384 cell since there is no need to control the phase over 360 deg. 385 Indeed, the value z pl = λ/3 is a trade-off between compact-386 ness and achievable plasma properties. Provided that a plasma 387 density in the order of n e ≈ 10 19 m −3 is required for this 388 application (see Fig. 4), the neutral pressure is assumed to 389 be p 0 = 2 mbar, and ν = 1.6 × 10 9 Hz [5], [9]. In fact, 390 according to experimental evidence [4] and theoretical pre-391 diction [6], in usual GPAs higher values of n e are achiev-392 able increasing p 0 . Again, a structure of 10 × 10 plasma 393 elements constitutes the proposed IRS (see Fig. 9). The 394 ''on''-''off'' state of each column has been controlled to 395 achieve |θ max | = 30 deg; the assumed plasma properties 396 are reported in Table 3. The fulfillment of the require-397 ment imposed on θ max is demonstrated in Fig. 10 where the 398 obtained RCS is depicted. Specifically, n e = 7.3 × 10 18 m −3 399 is required for the ''on'' state, which is a value fully compat-400 ible with the technology at the state-of-the-art [5], [9]. Pro-401 vided that neutral pressure is higher with respect to the cases 402 analysed in previous sections (i.e., higher losses might occur 403 within plasma [6]), the RCS computed assuming ν = 0 has 404 been depicted in Fig. 10. The results are very comparable with 405 the collisional case (differences < 0.2 dBm 2 ) consistently 406 with a value of | | close to the unit for the plasma elements 407 adopted in this design (see Table 3).

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It is worth noting that plasma-based IRSs relying on 409 multi-Bits elements are feasible but have not been analysed 410 in this work for the sake of brevity. Specifically, multi-Bits 411 designs present a better power efficiency with respect to 1