This paper presents a novel class of (space)time-modulated metasurfaces, namely (space)time meta- surfaces that are modulated by pseudo-random sequence (PRS) waveforms. In contrast to their harmon- ically or quasi-harmonically modulated counterparts, these metasurfaces massively alter the temporal spectrum of the waves that they process; as a result, they exhibit distinct properties and o/uniFB00er com- plementary applications. These metasurfaces are assumed here to operate in the ‘slow-modulation’ regime, where the /uniFB01xed-state time between state-transition is much larger than the transient time asso- ciated with the dispersion of the media involved, which allows safe separation of the time-variance and frequency-dispersive e/uniFB00ects of the system. Thanks to the special properties of their modulation, which are generally assumed to have a staircase shape and to be periodic in addition to being pseudo-random, the PRS (space)time-modulated metasurfaces can perform a number of unique operations, such as spec- trum spreading, interference suppression, and row/cell selection. These properties, combined with mod- ern microwave CMOS technologies, lead to applications with unique performance or/and features, such as electromagnetic stealth, secured communication, direction of arrival estimation, and spatial multi- plexing. /one.pnum Introduction After hardly a decade of intensive worldwide research, metasurfaces have become a revolutionary advance in microwave, terahertz and optical technologies (/one.pnum), and this area is far from being exhausted at the time of this writing. Metasurfaces may be considered as dramatic generalizations of Fresnel-zone plate re/uniFB02ec- tors (/two.pnum), re/uniFB02ect/transmit arrays (/three.pnum), frequency/polarization selective surfaces (/four.pnum), di/uniFB00raction gratings (/five.pnum) and spatial light modulators (/six.pnum), given the unprecedented versatility provided by their /three.pnum/six.pnum bianisotropic de- grees of freedom/one.pnum(/one.pnum); alternately, they may be considered as the two-dimensional reductions of voluminal metamaterials (/nine.pnum), with the bene/uniFB01ts of lower form factor, lower loss, along with – amazingly! – far greater wave transformation capabilities. They have already led to a myriad of applications with unprecedented functionality or/and performance, including refraction and wavefront transformation (/one.pnum/zero.pnum; /one.pnum/one.pnum; /one.pnum/two.pnum; /one.pnum/three.pnum; /one.pnum/four.pnum), ab- sorption (/one.pnum/five.pnum; /one.pnum/six.pnum; /one.pnum/seven.pnum), polarization transformation (/one.pnum/eight.pnum), hologrpahy (/one.pnum/nine.pnum; /two.pnum/zero.pnum), analog computing (/two.pnum/one.pnum), optical force carving (/two.pnum/two.pnum; /two.pnum/three.pnum), and cloaking (/two.pnum/four.pnum; /two.pnum/five.pnum; /two.pnum/six.pnum; /two.pnum/seven.pnum). While the vast majority of the metasurfaces reported until /two.pnum/zero.pnum/one.pnum/eight.pnum were static, i.e., invariant in time, the past lustrum has witnessed an explosion of interest for time-modulated and spacetime-modulated metasur- faces. In these metasurfaces, the time dimension is introduced as an extra degree of freedom to manip- ulate electromagnetic waves, both by breaking the fundamental bounds of linear time-invariant systems and by bringing about the possibility to engineer the temporal spectrum of waves in addition to just their spatial spectrum (/two.pnum/eight.pnum; /two.pnum/nine.pnum). These time/spacetime-modulated metasurfaces have quickly given rise to their own range of applications, extending those of static metasurfaces, with the main applications including simpli/uniFB01ed front-end wireless communication (/three.pnum/zero.pnum; /three.pnum/one.pnum; /three.pnum/two.pnum), spatial frequency conversion (/three.pnum/three.pnum; /three.pnum/four.pnum; /three.pnum/five.pnum), and generalized nonreciprocitity (/three.pnum/six.pnum; /three.pnum/seven.pnum; /three.pnum/eight.pnum; /three.pnum/nine.pnum; /four.pnum/zero.pnum; /four.pnum/one.pnum), and this /uniFB01eld is currently evolving at a spectacular pace. /one.pnumBianisotropy is a weak form of spatial dispersion (or spatial nonlocality) occurring in complex media, whereby the response of the medium at a point of space does not depend on the excitation only at this point but also in the neighbourhood of it (/one.pnum; /seven.pnum; /eight.pnum). It is the dominant form of spatial dispersion in subwavelength structures, such as typical metamaterials and metasurfaces, but mesocopic structures, whose unit cells are notmuch smaller than the wavelength, involve higher-order spatial dispersion, with even more degrees of freedom that could be leveraged for further engineering opportunities (/one.pnum). 1 The time/spacetime-modulated metasurfaces mentioned in the applications of the previous paragraph are based on modulation waveforms that are fully deterministic. Speci/uniFB01cally, these waveforms are either si- nusoidal or exhibiting shapes that are causally related by the required metasurface operation. Such meta- surfaces induce relatively light alterations, typically limited to harmonic generation and frequency con- version, of the spectrum of the waves they process. We present here an overview of a di/uniFB00erent class of time/spacetime-modulated, namely metasurfaces whose modulation is a Pseudo-Random Sequence (PRS) , typically of staircase shape and periodic nature. In contrast to their deterministic-modulation counterparts, these metasurfaces induce major alterations of the temporal spectrum of the waves that they process. As a result, they o/uniFB00er complementary applications, such as electromagnetic stealth (/four.pnum/two.pnum), direction of arrival (DoA) estimation (/four.pnum/three.pnum), and spatial multiplexing (/four.pnum/four.pnum). The paper is organized as follows. Section /two.pnum presents a general description of time-modulated metasur- faces, their operation principle, and their modulation regimes. Then, Sec. /three.pnum establishes the key proper- ties of PRS modulation waveforms in terms of autocorrelation, power spectral density, and orthogonality. Next, Sec. /four.pnum overviews the fundamental operations of PRS time-modulated metasurfaces, namely spec- trum spreading, interference suppression. and signal selection. This concludes the theoretical part. From that point, the paper goes on with a practical part. Section /five.pnum discusses technological aspects for microwave implementations, speci/uniFB01cally the realization of a binary metaparticle and the design of a fully addressable modulation array. Then, Sec. /six.pnum presents four applications, namely electromagnetic stealth, secured com- munication, direction of arrival estimation, and spatial multiplexing. Finally, Sec. /seven.pnum provides conclusions and invokes possible future developments of the /uniFB01eld. /two.pnum Time-Modulated Metasurfaces Figure /one.pnum depicts a generic (space)time-modulated metasurface, assuming a staircase modulation, and its operation principle. A time-harmonic wave, iptq, of frequency f0!0{p2q, and hence of period T0 1{f0, impinges on the metasurface, which is typically modeled by a bianisotropic susceptibility tensor during a /uniFB01xed-state time interval of the staircase modulation. In order to e/uniFB03ciently process this wave, the metasurface must strongly interact with it; it is therefore designed to be at all times resonant near the frequency of the incident wave ( f0). As a result, its impulse response during the nth/uniFB01xed-state time interval, Tf;n, of the modulation, Tf;npt1q, rings at the frequency 0;nr!2 0;np n{2q2s1{2, where!0;n(!0) and nare respectively the resonance frequency and the damping of the metasurface during the interval Tf;n(/four.pnum/five.pnum), and features a time constant of dn2{ nand hence a memory time of Td;n3 d;n6{ n. The metasurface is modulated, via a proper electronic control of its scattering particles, by the modulation waveformmptq(Fig. /one.pnum). This waveform is typically periodic, with Ntime intervals of duration Tf;nper period and with period Tm(°N n1Tf;nTm). This wave modulates the metasurface by varying its dispersive (!) susceptibility in time ( t), in possible addition to space ( )/two.pnum, i.e., as  p;t;!q. This modulation transforms the incident wave into a scattered wave, sptq, which may be either a wave that is transmitted through the metasurface (as in the /uniFB01gure) or a wave that is re/uniFB02ected from it. The scattered wave exhibits a transient response during the time Tt;n, withTt;n"T0, following the transition from the pn1qthto thenthmodulation intervals, as illustrated in Fig. /one.pnum. This transient time is proportional to the dispersion di/uniFB00erence between the modulation states pn1qandn, and is limited to Td;n. If the modulation has a smooth (rather than a staircase) form, which is also quite common, we have Tf;nÑ0, andTt;nÑ0since the di/uniFB00erence between the modulation states pn1qandnvanishes. One may distinguish two modulation regimes depending on the ratio between the time scales of the mod- ulation, which is related to the /uniFB01xed-state time ( Tf;n) if the modulation is of staircase form, and of the dispersion of the metasurface, which is related to the transient time ( Tt;n). In this paper, we are mostly concerned with the regime pT0!Tt;n!Tf;n(case of Fig. /one.pnum), which we shall refer to as the slow-modulation regime . In this regime, the transient part of the response can be neglected, since it is much shorter than the steady-state part of the modulation states (see sptqin Fig. /one.pnum), and the polarization density response of the metasurface can hence be safely written in terms of a multiplication product in the time domain, as Pptq0 p;t;!qEptq(temporal locality), where the transients due to dispersion ( !) may be simply ig- nored. In contrast, for Tt;nTf;n, orTt;n¡Tf;n, which we shall refer to as the fast-modulation regime , the temporal e/uniFB00ects due to the modulation and to the dispersion (or memory) of the system are intertwined, /two.pnumThe spatial modulation may be either intrinsic to the metasurface, i.e., consisting in di/uniFB00erent metaparticle shapes, or induced by the modulation, for instance via di/uniFB00erent varactor capacitance levels, in which case the modulation would be indexed as mijptq, withiandjreferring to the rows and columns of the structure, assuming a rectangular lattice. /two.pnum mptq (modulation)ψiptq (incident wave)ψsptq (scattered wave) χpρ,t;ωq (susceptibility) (ﬁxed state)Tf,n (ﬁxed state) Tf,nTt,n (transients) T0 (incident period) Tm (modulating period)metasurface χTf,npt1q t1(impulse response) Td,n (dispersion time)2π ν0,n n“ 1n“ 2n“ 3n“ Nnx yzFigure /one.pnum: (Space)time-modulated metasurface, processing a harmonic incident electromagnetic wave using a modulation mptq, which will be a staircase periodic Pseudo-Random Sequence (PRS) in this paper. The metasurface is generally dispersive ( !-dependent) and space-varying ( x^ xy^ y-dependent) in addition to time-varying ( t-dependent), and may be characterized by the susceptibility tensor function p;t;!qin the slow modulation regime. and the polarization response cannot anymore be expressed in terms of a susceptibility function (/two.pnum/eight.pnum). In the case of a smooth modulation, the situation is even more complicated. If the modulation is periodic, as in Fig. /one.pnum, the slow- and fast-modulation regimes would rather correspond to the regimes Tm!Tdand Tm;¡Td, respectively, where Tdwould now refer to the maximal dispersion time within one period/three.pnum. Note that the regime TmT0, which belongs the fast regime, is the regime that typically prevails in para- metric ampli/uniFB01ers (/four.pnum/seven.pnum; /four.pnum/eight.pnum). /three.pnum Pseudo-Random Sequence (PRS) Modulation The term ‘pseudo-random sequence’ (PRS) refers to a sequence of values that are generated by an algo- rithm whose properties approximate the properties of a sequence of random numbers. Such a sequence has therefore, per se, a white-noise spectrum. However, we shall consider here that the PRS function is periodic . This assumption does not represent a restriction of generality insofar as an aperiodic function can always be treated as the limit of a periodic function with in/uniFB01nite period. However, periodicity endows the PRS with a rich set of temporal and spectral properties that are crucial in many applications. We shall establish here the characteristics and properties of this modulation, with the help of Fig. /two.pnum.In this paper, we will restrict our attention to binary polar staircase periodic PRS modulations, mptq, of the type plotted in Fig. /two.pnum(a). This PRS oscillates between the levels 1. It has bits of duration TbandNbits per period, corresponding to the period TpNT b, withNbeing generally odd for technological reasons (linear feedback shift register generation) (/four.pnum/nine.pnum). The autocorrelation of a function is a measurement of the similarity of this function with delayed copies of /three.pnumOne may also distinguish the ultra-slow regime TmÎTd, which corresponds to a simple regime of recon/uniFB01gurability (between di/uniFB00erent operation modes), and, at the other extreme, the ultra-fast regime TmÏTd, which prevails in attophysics (/four.pnum/six.pnum), but these regimes are not of interest in this paper. /three.pnum -101 1(a) (b) (c)ttmptq Tb smptq Tb f˜smpfq ´fb fbN`1 N2 fp“1 Tp´Tp Tp´1 NTp“NT b (period) 1 N2 0Figure /two.pnum: Characteristics of the periodic Pseudo-Random Sequence (PRS) used as the modulation, mptq, in the time-modulated metasurface of Fig. /one.pnum. (a) Waveform. (b) Autocorrelation function, obtained by Eq. (/one.pnum). (c) Power spectral density, obtained by Eq. (/two.pnum). itself versus the delay. In the case of the periodic PRS function mptqin Fig. /two.pnum(a), it is found as (/four.pnum/nine.pnum) smptq1 Tp»t0Tp t0mp qmpt qd 1 NN1 N8¸ n8tnNT b Tb ;(/one.pnuma) wheret0is an arbitary time and pqis the triangular function ptq# 1|t|ift¤1; 0 ift¡1;(/one.pnumb) This function is plotted in Fig. /two.pnum(b). It shares the periodicity ( Tp) ofmptq, since copies of the PRS that are delayed by an integer number of the period perfectly superimpose with each other. Moreover, it is composed of triangular pulses of width 2Tb, corresponding to the correlation of rectangular pulses of width Tb, with a small negative o/uniFB00set of 1{Nthat is due to the excess, by one unity, of the number of 1’s compared to the number of 1’s, due to the odd nature of N. Note that the larger is N, and hence the /four.pnum more random is mptq, the larger is the spacing between the triangles ( Tp), and of course the smaller is the o/uniFB00set|1{N|; in the limit NÑ8 of an aperiodic PRS, smptqreduces to the triangle at the origin since there is then no delay anymore that leads to perfect superposition, and in the further limit TbÑ0,smptq reduces to a unit impulse at the origin, corresponding to a perfectly random wave, which superimposes only with the non-delayed copy of itself. The Fourier transform of the autocorrelation function is called the Power Spectral Density (PSD) . In the case of the PRSmptqin Fig. /two.pnum(a), the PSD is (/four.pnum/nine.pnum) ~smpfq1 N2pfqN1 N28¸ n8 n0sinc2n N  fn Nfb ; (/two.pnum) and is plotted in Fig. /two.pnum(c). This function has a sinc2pq-form envelope, corresponding to the Fourier trans- form of the triangular components of smptq, whose magnitude, pN1q{N2, depends only on N. Due to the periodicity of smptq, with period Tp,~smpfqis a discrete function, with spacing of fp1{Tpbetween its im- pulses; note the small DC component, of magnitude 1{N2, due to the imperfect balance between the 1’s and1’s ofmptq, which quickly falls to zero as the length of the PRS increases. Finally, the bandwidth of smptq, de/uniFB01ned as the width of the main beam, is fb1{Tb, and includes fb{fpTp{TbNT b{TbN impulses. Some PRS-modulated metasurface applications involve, as we shall see, a set of PRSs, tmkptqu, withk 1;2;:::;K , where each of the KPRSs,mkptq, is of the type of mptqin Fig. /two.pnum(a) while composed of a distinct sequence of 1’s and1’s. This set can be designed to be approximately orthogonal as 1 Tp»Tp 0mpptqmqptqdt# 1pq; 1 Npq;(/three.pnum) wherempptqandmqptqare an arbitrary pair of sequences in the set, and the 1{Nresult is due to the same reason as before. /four.pnum Operations of PRS Time-Modulated Metasurfaces PRS-modulated metasurfaces may perform three fundamental operations, which underpin their appli- cations (Sec. /six.pnum): A. spectrum spreading, B. interference suppression, and C. row/cell selection. We shall demonstrate here these operations with the help of Fig. /three.pnum. /four.pnum./one.pnum Spectrum Spreading The spectrum spreading operation is depicted in Fig. /three.pnum(a). The incident wave, iptq, is assumed to have a narrow spectrum, fi, centered at f0, and it is modulated by the binary 1PRS waveform mptqdescribed in Sec. /three.pnum. In the slow-modulation regime ( T0!Tt;n!Tf;n), which is assumed throughout the paper, temporal locality (Sec. /four.pnum) allows to write the scattered wave as sptqmptq iptq; (/four.pnum) where the symbol ‘ ’ denotes the simple multiplication product, which will be from now on omitted. The Fourier transform of Eq. (/four.pnum) expresses then the Fourier transform of the scattered wave as the convo- lution of the Fourier transforms of the modulation and of the input wave, namely ~ spfq~mpfq~ ipfq: (/five.pnum) Given the assumed narrow width of ~ ipfq,fi, and the much broader width of ~mpfq,2fb, due to the pseudo-random nature of mptq[Fig. /two.pnum(a)], this operation results in a response ~ spfqthat is much broader than ~ ipfq[Fig. /three.pnum(a)]. In other words, the PRS-modulated metasurface spreads out the spectrum of the wave that it processes by the factor 2fb{fi, which can be extremely large in practice. Note that the spreading of the spectrum by the modulation does notdecrease the envelope of the power spectral density of the scattered wave, because the spectrum envelope is essentially a translation from zero to the frequency of the incident wave ( f0) of the modulation spectrum [Fig. /three.pnum(a)], whose envelope was shown in Sec. /three.pnum to depend only on the length ( N) of the PRS. However, the spectrum spreading is /five.pnum mptqmptq ψiptqψiptqψiptq ψsptqψsptqψsptq χptqχptq ψintptqψrptqmptq χpρ,tq ψi,1ptq ψi,2ptq ψi,rptq ψi,Kptq m1ptq m2ptq mKptqmrptqArejφrmrptq şTb 0ψsptqmrptqdt∆fint∆fi∆fi ff fffN`1 N2 1 N2fp f0f0 f0f0f0|˜ψspfq|2 |˜ψipfq|2|˜ψipfq|2 f0´fbf0`fb |˜ψrpωq|2 |˜ψdpωq|2fint(a) (b) (c)Figure /three.pnum: Fundamental operations performed by a PRS-modulated metasurface. (a) Spectrum spreading. (b) Interference suppression. (c) Row/cell selection. accompanied by a dramatic reduction of the spectral power level of the wave, particularly at f0where the reduction is by the factor 1{N2, but also elsewhere, where the reduction is in the form of the sinc2pq function with maximum of pN1q{N2, which represents an overall major reduction of the power spectral level of the processed wave. /six.pnum The spectrum spreading ratio between the scattered wave and the incident wave, 2fb{fi, is particularly strong – in fact in/uniFB01nite! – when iptqtends to pure single-tone harmonic wave, i.e., iptqej2f0tand ~ ipfqpff0q. In this case, Eq. (/five.pnum) reduces indeed to ~ spfq~mpff0q; (/six.pnum) which is simply the Fourier transform of mptqshifted to the frequency of the incident wave, and the scat- tered wave has therefore exactly the same spectral width as ~mpfq. /four.pnum./two.pnum Interference Suppression The interference suppression operation is depicted in Fig. /three.pnum(b). It corresponds to a scenario where an interfering wave, intptq, which may typically be a harmonic wave or a narrow-band burst wave, escapes the metasurface and reaches unimpeded a point of space where the signal passed through the metasurface, iptq, is to be demodulated. The total wave reaching the point of interest is then rptq sptq intptqmptq iptq intptq; (/seven.pnum) and a receiver possessing there the information of mptqcan process this wave as dptq rptqmptq iptqm2ptq intptqmptq  iptq intptqmptq;(/eight.pnum) where we used the fact that m2ptq1for the assumed unitary bipolar symmetric sequence mptq[Fig. /two.pnum(a)]. The input wave has thus been demodulated by the receiver [Fig. /three.pnum(b)]. Moreover, Fourier-transforming the /uniFB01nal result of Eq. (/eight.pnum) yields ~ dpfq~ ipfq~ intpfq~mpfq; (/nine.pnum) which shows that the spectrum of the interfering wave has been spread out, just as the wave incident on the metasurface in the previous subsection, so that its power spectral level has decreased to a very small level Fig. /three.pnum(b). The e/uniFB00ect of the interference can then be further reduced, if necessary, to quasi total suppression by applying a band-/uniFB01lter at f0so as to eliminate all of its energy contents distributed over the other spectral impulses. /four.pnum./three.pnum Row/Cell Selection The row/cell/four.pnumselection operation is depicted in Fig. /three.pnum(c). This pertains yet to another scenario, where the goal is to select out, at a given point of space where this selection is to be performed, the parts of the inci- dent wave, iptq, that impinged on the di/uniFB00erent rows/cells of the metasurface. We shall call the so-de/uniFB01ned kthpart of the wave ikptq, wherek1;2;:::;k;:::;K , for a metasurface modulated in its Kcolumns. Here, the incident wave may generally be a combination of di/uniFB00erent waves coming from arbitrary direc- tions of space. The row/cell selection operation can be performed using an orthogonal set of modulation PRSs,tmkptqu,k1;2;:::;K , i.e., a set of PRSs whose any pair satis/uniFB01es the condition (/three.pnum). Note that such a system is actually a space -time modulated system. Indeed, the di/uniFB00erent rows/cells, even if they happen to have all the same shape, are distinctly modulated, so that the incident wave actually “sees” a spatial modulation in addition to the temporal modulation when impinging on the metasurface. If theKparts of the incident wave have distinct magnitudes and phases, they may be generically expressed as ikptqAkptqejp!0t kptqq, and the global signal scattered by the metasurface is then sptqK¸ k1mkptq ikptqK¸ k1mkptqAkptqejp!0t kptqq; (/one.pnum/zero.pnum) which represents a row/cell encoded mixture of the incident wave. This scattered wave may then down- /four.pnumFor simplicity, we shall mostly restrict here our attention to the case where all the cells of the kthrow are addressed by the same modulation, mkptq, but this may be generalized to the addressing of individual cells, with a modulation mijptq, as will be shown in the design of the next section. /seven.pnum converted to base-band as /zero.pnumptq sptqej!0tK¸ k1mkptqAkptqej kptq: (/one.pnum/one.pnum) If the PRS settmkptquis known, and assuming that Akptqand kptqare slowly varying function of time with respect to the time scale of the modulation period ( Tp) (Figs. /one.pnum and /two.pnum), this wave may be processed as follows at the point of space where the selection is to be performed: dr1 Tp»Tp 0mrptq 0ptqdt1 Tp»Tp 0mrptqK¸ k1mkptqAkej kdt Arej r1 Tp»Tp 0m2 rptqdt: 1 TpK¸ k1 krAkej k»Tp 0mrptqmkptqdt Arej r1 NK¸ k1 krAkej kArej r:(/one.pnum/two.pnum) where the orthogonality relation (/three.pnum) was used in the last-but-one equality and the approximation N"K was used in the last equality. This result shows that integrating an mrptq-weighted version of the wave 0ptqselects out the magnitude and phase of the part i;rptqof the incident wave, i.e., the part of this wave that impinged on the rthrow/cell of the metasurface. /five.pnum Design The design of a time-modulated metasurface system involves a mixture of electromagnetics engineering, for the metasurface structure part, and of electronics engineering, for the time modulation part. While the former is equally mature in the microwave and optical regimes (/one.pnum), the latter still represents an insurmount- able task in the optical regime at the present time. Therefore, we shall discuss here only microwave-regime designs, with the help of the representative example described in Fig. /four.pnum. Figure /four.pnum(a) depicts a unit-cell design for the assumed binary-polar PRS modulation and for individual cell addressing, with polarity reversal following from switching between the opposite sides of the receiving (resonant, and hence {2-long) slotted-patch unit-cell particle. Figure /four.pnum(b) shows a simpli/uniFB01ed version of (a), and plots the corresponding scattering parameters, which exhibit an excellent broadband equal- magnitude and opposite-phase response. Figure /four.pnum(c) shows a modulation array for individual cell address- ing, inspired by the Thin-Film Transistor (TFT) matrices used in screen displays (/five.pnum/zero.pnum) and implementable in standard CMOS technologies (/five.pnum/one.pnum), with Field Programmable Gate Array (FPGA) control. Finally, Fig. /four.pnum(d) shows the individual-cell addressing scheme of this array, where the array refresh time, Tr, is assumed to be much larger (up to the bit duration Tb, see Fig. /two.pnum) than MT s, withMbeing the number of rows and Ts the row selection time, so that the sequential addressing cycle of all the rows of the array can be, practically, considered simultaneous. /six.pnum Applications Figure /five.pnum presents four applications of PRS (space)time-modulated metasurfaces. Figure /five.pnum(a) depicts the application of electromagnetic stealth (/four.pnum/two.pnum). Instead of altering the shape of the object to conceal, as typical stealth techniques, this technology covers the object by the PRS time-modulated metasurface and alters its spectrum. The narrow-band signal of the interrogating radar is spread out upon re/uniFB02ection and its spectral power level is reduced below the noise /uniFB02oor of that radar, according to the spectrum spreading principles established in Sec. /four.pnum./one.pnum, which makes the object undetectable. Such temporal spectrum spreading can be enhanced by spatial dispersion upon adding spatial modulation in the form of alternating PEC and PMC metasurface cells (/five.pnum/three.pnum). Figure /five.pnum(b) shows the application of secured communication . Here, the spectrum spreading (Sec. /four.pnum./one.pnum) in- duced by PRS modulation acts as an encryption mechanism of the message. Whereas an eavesdropper /eight.pnum } }(a) (b)(c) (d)t1 t1t2 t2t3 t3t4 t4t5 t5TrTs aaa aaaa aa a b bbbb bbbbb d dd dt1´t2 t2´t3 t3´t4example of state switching in one cycle Tr aON bOFF das beforeswitch ONswitch OFF switch OFFswitch ON PIN diode 1PIN diode 2double-plate enclosures =S21|S21| =S21|S21|1 ON,2 OFF 1 OFF,2 ON11 12 21 22Figure /four.pnum: Representative design example for a microwave PRS (space)time-modulated metasurface. (a) Unit-cell design, with binary-polar state switching principle and double-plate enclosure to support and isolate the electronics and bias lines from the scattering/radiating top and bottom parts. (b) Simpli/uniFB01ed version of (a), reported in (/five.pnum/two.pnum), for only row addressing, with biasing on the top plane, and corresponding measured scattering parameters. (c) Overall modulation array for individual cell addressing correspond- ing to (a). (d) Detail of the individual cell addressing scheme in 22section of (c), with state rema- nence ensured by a capacitance discharge time being much longer than the refresh time ( Tr), for the setup t11;12; 21;22ut (on,o/uniFB00), (o/uniFB00,on); (o/uniFB00,on), (on,o/uniFB00) u. receives a jammed, undecipherable version of the message, plus possible interfering burst noise, the in- tended receiver can safely demodulate the message using the modulation key in his possession while elim- inating the interfering noise, according to the interference suppression principles established in Sec. /four.pnum./two.pnum. If the position of the receiver is known, the metasurface may additionally use spatial modulation in the form of an appropriate phase gradient, possibly dynamic for motion tracking, to speci/uniFB01cally radiate in the direction of the receiver, and hence further enhance the safety of the communication link. Figure /five.pnum(c) describes the application of direction of arrival (DoA) estimation (/four.pnum/three.pnum). In contrast to conventional DoA systems, which require an array of independent receive antennas with individual phase detectors, this DoA system o/uniFB00ers the advantage of requiring only one pick-up antenna, thanks to the row/cell selection principles established in Sec. /four.pnum./three.pnum. The wave impinging on the metasurface, under an angle (to determine), is modulated at each row of the metasurface by a di/uniFB00erent PRS from a set of mutually orthogonal PRSs. Then, the wave scattered by the metasurface is picked up by an antenna, down-converted to base-band and stored in a memory. Next, the phase of the waveform part originating from any rthrow of the metasurface is determined from the operation corresponding to Eq. (/one.pnum/two.pnum), and is /uniFB01nally obtained from the so obtained phases between waveforms from adjacent rows, i;rand i;r1, assin1rcp i;r1 i;rq{p!dqs, where dis the distance between adjacent rows of the metasurface. Finally, Fig. /five.pnum(d) shows the application of spatial multiplexing (/four.pnum/four.pnum), where the metasurface can operate ei- ther as a multiplexer or as a demultiplexer. In the demultiplexing mode, it receives a mixture of Qprecoded /nine.pnum mptqtarget ˜ψipfq radarff˜ψspfq f0f0(a) transmitterintended receivereavesdropper demod.mptq mptq interfererf ff ff˜ψspfq ˜ψintpfq˜ψipfq˜ψepfq ˜ψdpfqf0 f0 f0f0f0 (b) θψiptq m 1ptq,m 2ptq,...,m Nptqdemod. ∆φi,rpθq Ñ DoAAi,rejφi,re´jω0t∆d (C) (c) θ1 θ2ψi,1ptq ψi,2ptqψs,1ptq ψs,2ptqe∆φ1m1ptq e2∆φ1m2ptq en∆φ1mnptq e∆φ2m1ptq e2∆φ2m2ptq en∆φ2mnptqprecoding ˇψi,1ptq ˇψi,2ptqˇψiptq ∆dm1ptq m2ptq m3ptq m4ptq... mNptq (d) Figure /five.pnum: PRS (space)time-modulated metasurface applications. (a) Electromagnetic stealth. (b) Secured communication. (c) Direction of arrival (DoA) estimation. (d) Spatial multiplexing. messages destinated to di/uniFB00erent users,  iptq°Q q1 i;qptq, where  i;qptq i;qptq°N n1ejn qmnptq with qk0dsinqrepresenting the metasurface’s inter-row phase gradient that encodes the des- tination direction, q, of theqthmessage, i;qptq, andtmkptqurepresenting a set of orthogonal PRSs. The metasurface modulates the signal  iptqby the same PRS sequences as those used to precode the messages, which results into the scattered wave spt;q°N r1mrptq iptqejr pq, where  pqk0dsin. It may be easily veri/uniFB01ed that substituting in this expression for spt;qthe expression for  iptqand applying the PRS orthogonality relation (/three.pnum) leads to spt;q°Q q1 i;qptq°N r1ejk0rdpsinsinqq. Thus, accord- ing to basic antenna array theory (/five.pnum/four.pnum), each message i;qptqis properly radiated into its intended direction, q, and the multiplexing operation is therefore accomplished as expected. The reciprocal, multiplexing op- eration of the system is essentially identical to that of the DoA system presented in the previous paragraph, with multiple angles corresponding to the multiple messages. Using a unique antenna, this metasurface multiplexing system clearly represents a major interest for massive Multiple-Input Multiple-Output (MIMO) systems. /seven.pnum Conclusion We have presented an overview of a novel class of (space)time-modulated metasurfaces, namely (space)time- modulated metasurfaces that are modulated by pseudo-random sequence (PRS) waveforms. These meta- surfaces exhibit very distinct and complementary properties to those of other (space)time-modulated metasurfaces, and o/uniFB00er thereby a cornucopia of new application opportunities. Many future research directions may be envisioned in this area, such as for instance the exploitation of other modulation se- quences (e.g., Walsh-Hadamard, Gold and M-ary sequences), the combination of PRS time modulation /one.pnum/zero.pnum with the versatile electromagnetic transformations allowed by more sophisticated metaparticles (bian- isotropic and higher-order spatially dispersive structures), and the investigation of potential of the so far quasi-unexplored fast-modulation regime.