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Space-Time Medium Functions As a Perfect Antenna-Mixer-Amplifier

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Space-Time Medium Functions As a Perfect Antenna-Mixer-Amplifier Space-Time Medium Functions as a Perfect Antenna-Mixer-Amplifier Transceiver Sajjad Taravati and George V. Eleftheriades The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario M5S 3H7, Canada Email: [email protected] We show that a space-time-varying medium can function as a front-end transceiver, i.e., an antenna-mixer-amplifier. Such a unique functionality is endowed by space-time surface waves as- sociated with complex space-time wave vectors in a subluminal space-time medium. The proposed structure introduces pure frequency up- and down-conversions and with very weak undesired time harmonics. In contrast to other recently proposed space-time mixers, a large frequency up-/down conversion ratio, associated with gain is achievable. Furthermore, as the structure does not operate based on progressive energy transition between the space-time modulation and the incident wave, it possesses a subwavelength thickness (metasurface). Such a multi-functional, highly efficient and compact medium is expected to find various applications in modern wireless telecommunication systems. I. INTRODUCTION an antenna per se. Such an interesting functional- ity of the space-time medium is endowed by space- Reception and transmission of electromagnetic waves time surface waves. Other recently proposed space- is the essence of wireless telecommunications [1,2]. Such time antenna systems are formed by integration a task requires various functions, such as power am- of the space-time-modulated medium with an an- plification, frequency conversion, and wave radiation. tenna [3, 35, 45], and hence suffer from a number These functions have been conventionally performed by of drawbacks, i.e., requiring long structures, low ef- electronic components and electromagnetic structures, ficiency and narrow-band operation. such as transistor-based amplifiers, semiconductor-based • The proposed antenna-mixer-amplifier introduces diode mixers, and resonance-based antennas. The ever large frequency up- and -down conversion ratios. increasing demand for versatile wireless telecommuni- This is very practical, because in real-scenario wire- cation systems has led to a substantial need in multi- less telecommunication systems, a large frequency functional components and compact integrated circuits. conversion is required, i.e., a frequency conversion In general, each natural medium may introduce a sin- from a microwave/millimeter-wave frequency to an gle function, e.g., a resonator may operate as an antenna intermediate frequency in receivers. In contrast, at a specific frequency. To contrast this conventional ap- recently proposed space-time frequency converters proach, a single medium exhibiting several functions con- suffer from very low frequency conversion ratios currently could lead to a disruptive evolution in telecom- (up-/down-converted frequency is very closed to munication technology. the input frequency) [3, 17, 35, 45]. Recently, space-time-modulated media have attracted a surge of scientific interest thanks to their capabil- • Recently proposed space-time systems operate ity in multifunctional operations, e.g., mixer-duplexer- based on a progressive coupling between the inci- antenna [3], unidirectional beam splitters [4], nonrecip- dent wave and the space-time modulation [3, 33, rocal filters [5,6], and signal coding metagratings [7]. 46{48], and hence a thick (compared to the wave- In addition, a large number of versatile and high effi- length) slab is required. In contrast, the proposed ciency electromagnetic systems have been recently re- antenna-mixer-amplifier does not work based on arXiv:2005.00807v1 [physics.app-ph] 2 May 2020 ported based on the unique properties of space-time mod- progressive coupling between the incident wave and ulation, including space-time metasurfaces for advanced the space-time modulation and hence is formed by wave engineering and extraordinary control over electro- a thin (sub-wavelength) slab. As a result, the pro- magnetic waves [8{25], nonreciprocal platforms [26{32], posed structure is classified among metasurface cat- frequency converters [17, 33], and time-modulated an- egories and is compatible with the compactness re- tennas [34{39]. Such strong capability of space-time- quirements of modern wireless telecommunication modulated media is due to their unique interactions with systems. the incident field [21, 28, 40{44]. This paper reveals that a space-time medium can func- • The proposed medium inherently operates as a tion as a full transceiver front-end, that is, an antenna- band-pass filter, i.e., a pure frequency down- and mixer-amplifier-filter system. Specific related contribu- up-conversions occurs so that the undesired time tions of this study are as follows. harmonics are highly suppressed. Such a property is governed by the subluminal operation of space- • We show that the space-time medium operates as time modulation. 2 Incoming propagating wave at ω 0 Radiated up-converted wave at ω0=ωIF+ωm x Input wave z x d Down-converted atωIF and amplified wave z ω at IF =ω0−ωm (a) (b) Radiate and receive: ω0 ωIF < ωm < ω0 BPF at ω Amplifier ω IF ω IF 0 Received signal at ω ωm IF Modulation:ω ω ω m 0 m Transmitted ω signal at ω 0 ωIF IF BPF at ω0 (c) FIG. 1. Functionality of the antenna-mixer-amplifier space-time surface wave medium. (a) Down-link (reception) state, where a strong transition between a space-wave at !0 to a space-time surface wave at !IF = !0 − !m occurs. (b) Up-link (transmission) state, where a transition between a space-time surface wave at !IF to a space-wave at !0 = !IF + !m occurs. (c) Circuital representation of the combined antenna-mixer-amplifier space-wave medium in (a) and (b). • In contrast to conventional mixers that introduce II. OPERATION PRINCIPLE a significant conversion loss, here a conversion gain may be achieved in the down-link or up-link. In Consider the antenna-mixer-amplifier slab in Fig. 1(a), addition, the radiation from the antenna-mixer- with the thickness of d and a spatiotemporally-periodic amplifier is very directive. electric permittivity as (z; t) = av + m cos(βmz − !mt); (1) The paper is organized as follows. Section II presents with av being the average electric permittivity of the the operation principle of the antenna-mixer-amplifier. background medium, and m representing the modula- Then, Sec. III investigates the theoretical aspects of the tion amplitude. In Eq. (1), !m denotes the temporal work, and provides an analysis of the wave propagation in frequency of the modulation, and βm is the spatial fre- the antenna-mixer-amplifier space-time medium. Next, quency of the modulation represented by Sec.IV presents the design procedure of the structure, !m !m and gives an approximate closed-form solution to calcu- β = = ; (2) m v Γ v late the thickness and receive/transmit power gain of the m b structure. SectionV gives the time and frequency domain where vm and vb are the phase velocity of the mod- numerical simulation results for the designed antenna- ulation and the background medium, respectively, and mixer-amplifier. Finally, Sec.VI concludes the paper. Γ = vm=vb is the space-time velocity ratio [28]. 3 The slab in Fig. 1(a) is obliquely illuminated by a y- Ei , ω 0 polarized incident electric filed under an angle of inci- dence of θi, as θ θ E (x; z; t) = ^yE ei(kxx+kz z−!0t); (3) i rn i i ω IF =ω0−ωm x ESW ε = ε + ε β −ω where Ei is the amplitude of the incident wave, and !0 (z,t) av m cos( m z mt) ω =ω −ω p 2 2 p 2 2 IF 0 m and k0 = kx + kz = (k0 sin(θi)) + (k0 cos(θi)) are z θn Em,ωn respectively temporal and spatial frequencies of the inci- Received surface-wave dent wave. Here, k0 = !0=c, with c being the velocity of ω =ω −ω ESW light in vacuum. IF 0 m θ In the receiving state (down-link) in Fig. 1(a), strong tn transition between a space-wave, with temporal fre- FIG. 2. Operation principle of the antenna-mixer-amplifier quency !0, to a space-time surface wave, with temporal frequency ! = ! − ! , occurs. In the transmission space-time medium. Transition of the incident space-wave to IF 0 m space-time surface waves at the two boundaries of the medium state (up-link) in Fig. 1(b) a transition between a space- ◦ ◦ (θr;−1 = θt;−1 = 90 ) as well as inside it (θ−1 = 90 )). time surface wave at !IF to a space-wave at !0 = !IF+!m occurs. Figure 1(c) shows an equivalent circuit representation harmonics outside of this interval represent imaginary of the antenna-mixer-amplifier in Figs. 1(a) and 1(b). k and hence propagate as space-time surface waves Thanks to the unique properties of space-time-modulated z;n along the two boundaries of the slab at z = 0 and z = d. media, that will be described later in this study, such The scattering angles of the space-time harmonics in- a medium introduces the functionality of a highly di- side the space-time-modulated medium read rective antenna, a pure frequency up-converter, a pure frequency down-converter, up-link and down-link filters, −1 kx −1 k0 sin(θi) and a down-link amplifier. Such a rich functionality has θn = tan = tan : (6) not been experienced in other media unless several com- βz;n βz;0 + nβm ponents and media are integrated, as shown in Fig. 1(c). However, here we show that a single medium can offer Figure2 shows the structure of the antenna-mixer- such versatile and useful operation. amplifier space-time medium. We aim to design the As the slab is periodic in both space and time, the spa- structure such that the first lower space-time harmonic, n = −1, outside the medium scatters along the boundary tial and temporal frequencies of the space-time harmon- ◦ ics inside the structure are governed by the momentum of the medium, i.e., θr;−1 = θt;−1 = 90 .
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