High-efficiency and full-space manipulation of electromagnetic wave-fronts with metasurfaces

Transcription

1 High-efficiency and full-space manipulaion of elecomagneic wave-fons wih measufaces Tong Cai 1,, GuangMing Wang, ShiWei Tang 3, HeXiu Xu 1,, JingWen Duan 4, HuiJie Guo 1, FuXin Guan 1, ShuLin Sun 4, Qiong He 1, 5, * 1, 5, * and Lei Zhou 1 Sae Key Laboaoy of Suface Physics, Key Laboaoy of Mico and Nano Phoonic Sucues (Minisy of Educaion), and Depamen of Physics, Fudan Univesiy, Shanghai 00433, China Ai and Missile Defend College, Ai foce Engineeing Univesiy, Xi' an, , China 3 Depamen of Physics, Faculy of Science, Ningbo Univesiy, Ningbo, 31511, China 4 Shanghai Engineeing Reseach Cene of Ula-Pecision Opical Manufacuing, Geen Phoonics and Depamen of Opical Science and Engineeing, Fudan Univesiy, Shanghai 00433, China 5 Collaboaive Innovaion Cene of Advanced Micosucues, Nanjing, 10093, China. *Coesponding Auhos: Qiong He, qionghe@fudan.edu.cn; Lei Zhou, phzhou@fudan.edu.cn 1

2 Absac Measufaces offeed gea oppouniies o conol elecomagneic (EM) waves, bu cuenly available mea-devices ypically wok eihe in pue eflecion o pue ansmission mode, leaving half of EM space compleely unexploed. Hee, we popose a new ype of measuface, composed by specifically designed mea-aoms wih polaizaion-dependen ansmission and eflecion popeies, o efficienly manipulae EM waves in he full space. As a poof of concep, hee micowave mea-devices ae designed, fabicaed and expeimenally chaaceized. The fis wo can bend o focus EM waves a diffeen sides (i.e., ansmission/eflecion sides) of he measufaces depending on he inciden polaizaion, while he hid one changes fom a wave bende fo efleced wave o a focusing lens fo ansmied wave as he exciaion polaizaion is oaed, wih all hese funcionaliies exhibiing vey high efficiencies (in he ange of 85%-91%) and oal hickness ~ /8. Ou findings significanly expand he capabiliies of measufaces in conolling EM waves, and can simulae high-pefomance muli-funcional mea-devices facing moe challenging and divesified applicaion demands.

3 I. Inoducion As he basis of nealy all opical devices, manipulaing elecomagneic (EM) wave-fon as desied is cucial in moden phoonic eseach. Naual maeials exhibi limied vaiaion anges of pemiiviy and pemeabiliy, so ha EM devices made by hem ae ypically oo bulky in size and of esiced funcionaliies, boh being unfavoable fo EM inegaion [1-3]. Recenly, meamaeials (aificial maeials made by subwavelengh micosucues wih ailoed EM popeies) and paiculaly hei plana vesion, measufaces, have demonsaed song capabiliies o manipulae EM waves, geneaing many fascinaing effecs such as anomalous efacion/eflecion [4-6], popagaing wave o suface wave coupling [7-10], plana hologams [11-13], focusing lens [14-18], phoonic spin Hall effec [19-1], and many ohes [-37]. These poweful wave-manipulaion abiliies have led o many measufacebased funcional EM devices [14, 5, 8, 38-41], which ae usually hin, fla, and exhibi divesified and muliple funcionaliies, all being vey pomising fo moden inegaionopics applicaions. Despie of he gea successes so fa achieved, we noe ha he wave-manipulaion capabiliies of measufaces ae fa less exploed, which also limi he applicaion poenials of hem. Fo example, high-efficiency measufaces usually wok eihe in pue eflecion mode [4-6, 0-5] (see Fig. 1(a)) o pue ansmission mode [5-8, 34, 35, 39], which means ha hey can only efficienly manipulae eihe he efleced wave-fon o ansmied one, leaving half of EM space oally unuilized. While some measufaces could in pinciple conol he wave-fons of boh ansmied and efleced waves [5, 6, 36], he phase gadiens povided fo ansmied and efleced waves ae usually idenical leading o locked wave-manipulaion funcionaliies a wo sides of he measufaces, no menioning he low efficiencies of hese devices due o he undesied muli-mode geneaions (see Fig. 1(b)). Alhough many muli- 3

4 funcional measuface-based devices have been poposed, hey ypically inegae diffeen funcionaliies woking fo eihe ansmission o eflecion mode [5, 8], no fo boh. I is highly desied o expand he wave-manipulaion capabiliies of measufaces o he full EM space, offeing he measufaces independenly conolled funcionaliies a hei wo diffeen sides. In his pape, we popose a new saegy o design measufaces ha can manipulae he wave-fons of EM waves in full space and wih vey high efficiencies (see Figs. 1(c-d)). The key sep is o design a collecion of mea-aoms which ae pefecly anspaen o eflecive fo inciden waves polaized along wo ohogonal diecions, ye exhibiing ailoed (ansmission/eflecion) phases coveing he whole 360 ange. We can hus uilize hese se of mea-aoms o consuc measufaces o efficienly and independenly conol he wavefons of EM waves a diffeen sides of he measufaces, dicaed by he inciden polaizaion. As a poof of concep, we expeimenally ealized hee micowave mea-sufaces: he fis wo can bend o focus EM waves a wo sides of he measufaces while he hid one combines he funcionaliies of wave-bending (fo efleced wave) and focusing (fo ansmied wave) ino one single device. In paicula, all hese devices exhibi vey high woking efficiencies fo all funcionaliies (in he ange of 85%-91%). Ou findings open up new possibiliies o ealize high-efficiency muli-funcional mea-devices woking in he full space, which can lead o many exciing applicaions in diffeen fequency domains. 4

5 FIG. 1 (colo online). Woking pinciple and advanages of he full-space measuface. Convenional measufaces woking in (a) eflecion o (b) ansmission geomeies suffe fom he issues of esiced woking space, low efficiency due o muli-mode geneaions and locked phase gadiens fo ansmied and efleced waves. (c) The newly poposed full-space measuface can efficienly manipulae elecomagneic wave-fons a boh sides of he device wih independen funcionaliies, iggeed by inciden waves wih diffeen polaizaions. II. Concep and mea-aom design We descibe ou saegy o ealize he full-space wave-fon conol, saing fom discussing how o design appopiae mea-aoms. Conside a mea-aom exhibiing mio symmey, hen is EM chaaceisics can be descibed by wo diagonal Jones maices R 0 0 and T 0 0 wih,, and denoing he eflecion/ansmission coefficiens fo waves polaized along wo pinciple axes ˆx and ŷ. In lossless sysems, we have 1 and 1 due o he enegy consevaion. To achieve independen ye highly efficien conols on boh ansmied and efleced waves, we equie ou mea-aoms o be pefecly eflecive fo ˆx -polaized inciden wave (i.e., 0, 1), 5

6 and pefecly anspaen fo ŷ -polaized inciden wave (i.e., 1, 0 ). Moeoeve, he phases associaed wih hei wo non-zeo coefficiens and, denoed by and especively, can be feely uned by vaying he sucual deails of he mea-aoms. If hese mea-aoms can be designed, we can hus ulilize hem o consuc a measuface exhibiing he desied phase disibuions (i.e., ( x, y) and ( x, y) ) o ealize ceain pe-deemined funcionaliies fo conolling efleced and ansmied wave-fons, unde ˆx - and ŷ - polaized exciaions, especively. Figue (a) shows he designed mea-aom ha can exhibi he menioned polaizaiondependen EM chaaeisics. As shown in he inse o Fig. (a), he mea-aom consiss of fou meallic layes sepeaed by hee 1.5 mm-hick F4B diecic spaces (wih i ). The fis wo layes ae ansioopic meallic cosses consising of wo meallic bas wih lenghs caefully adjused, while he boom wo layes ae opologically diffeen which ae coninuous meallic sipes (along x diecion) decoaed wih small pependicula meallic bas (along y diecion). Now he advanages of design ae clea. Those x-oienaed coninuous meallic sipes a he boom wo layes essenially wok as an effecive opical gaing o efficienly block he ˆx -polaized wave and leave only he ŷ - polaized waves o pass hough, in he fequency egime ( aound 10 GHz) sudied in his pape. The oles of he op wo meallic cosses ae o fuhe une he phases and ampliudes of he ansmied and efleced waves, fo wo diffeen polaizaions. Conside fis he ˆx - polaizaion. The coupling beween op meallic esonaos wih he boom coninuous sipes geneaes wo magneic esonances, which can damaically change he eflecion phase as a funcion of fequency. Figue (c) depics he simulaed speca of eflecion ampliude and, phase of a ypical mea-aom (peiodically eplicaed) unde ˆx -polaizaion exciaion. Indeed, wihin he fequency ineval (7-13 GHz) of inees, ou mea-aom can nealy oally eflec 6

7 ˆx -polaized wave wih eflecion-phase vaying fom -180 o 180 as fequency passes hough he magneic esonance a 9.1 GHz [8,, 3]. In his paicula example, only one magneic esonance appeas since he ba in he second laye is also coninuous ( d 11 mm ) which does no geneae a esonance. Two magneic esonances can appea if he ba in he second laye also exhibis a finie lengh (i.e., d 11 mm ). Theefoe, we can have an expanded feedom o design ou mea-aom by seing boh d1 and d feely adjusable (see Secion A of Suppoing Infomaion [4]). Fo he ŷ -polaizaion, howeve, EM waves can only see he y-oienaed meallic bas in each laye. Since all y-oienaed meallic bas ae of sho lenghs, hei Loenz esonances ae a fequencies much highe han he fequency egion ha we ae ineesed in, and heefoe, EM waves of his polaizaion can easily pass hough each laye. The coupling beween diffeen layes can fuhe enhance he ansmission by foming a seies of Faby-Peo (FP) ansmission modes (see Suppoing Infomaion A [4]). Via adjusing he geomeical paamees, we can appopiaely cascade he geneaed ansmission esonances o ge a wide-band anspaen window wih conollable ansmission phase. Figue (d) shows he simulaed speca of ansmission ampliude and phase fo a ypical sample, whee we find ha 0.84 wihin he fequency band 7-13 GHz while he vaiaion ange of can cove he whole 360 ange. We fabicaed a micowave sample (wih a size of 330 mm 330 mm ) consising of a peiodic aay of a ypical mea-aom. Figue (b) shows he op-view and boom-view picues of he sample. We hen expeimenally chaaceized is ansmission/eflecion chaaceisics, and compaed he measued esuls wih he simulaed speca in Figs. (c) and (d). Excellen ageemen is noed beween measued and simulaed speca. 7

8 FIG.. (colo online) Design and chaaceizaion of he poposed mea-aom. (a) Schemaics of he poposed mea-aom composed by fou meallic layes sepaaed by hee F4B spaces ( i, h =1.5 mm ). The following geomeical paamees ae fixed: widh of each y-oienaed ba is w1 5 mm, widh of each x-oienaed ba/sipe is w 4 mm, lenghs of he x-oienaed sipes in he hid and fouh layes ae fixed o he peiodiciy d3 d4 P 11 mm. Ohe paamees ( d1, d and lenghs of all y-oienaed bas a) ae uned appopiaely in designing each mea-aom. (b) Top view (lef) and boom view (igh) picues of a fabicaed measuface consising of a peiodic aay of mea-aoms wih a 6.3 mm, d1 9 mm and d 11 mm. Measued and FDTD simulaed ampliude/phase speca of eflecion (c) and ansmission (d) fo he peiodic measuface unde exciaions wih diffeen polaizaions. Figue illusaes ha such a mea-aom sucue is an ideal building block o consuc ou mea-sufaces o achieve he full-space wave-fon conol. Now ha he eflecion and ansmission phases ( and ) ae dicaed by he magneic esonances (fo ˆx - polaizaion) and he ansmission esonances (fo ŷ -polaizaion), especively, we undesand ha changing he geomeic sucual deails of ou mea-aom can significanly une he wo phases via vaying he coesponding esonance-mode posiions. In addiion, we undesand ha hese geomeical paamees have diffeen oles in affecing he wo phases. 8

9 Obviously, sucual paamees d1, d ae mainly esponsible fo while he paamee a mainly changes. These nealy delinked conol abiliies make ou ealisic design elaively easy, and we can design measufaces wih abiay disibuions of ( x, y) and ( x, y) accoding o hei desied funcionaliies, via choosing mea-aoms wih caefully adjused geomeical paamees based on he paamee maps ecoded in Suppoing Infomaion B [4]. We noe ha in adjusing hese geomeical paamees, he eflecion/ansmission ampliides of he mea-aoms ( x, y ) and ( x, y ) can emain a vey high values, which ensue he high-efficiency of he ealized funcionaliy (see Suppoing Infomaion B [4]). We noe ha ou mechanism is obviously diffeen fom pevious aemps of making muli-funcional devices exploing only half of he EM space [1, 14, 15, 1, 4-7], and hose aemps uilizing he full EM space bu exhibiing locked and low-efficiency funcionaliies [4, 5]. In he following secions, we will discuss seveal examples o illusae ou concep. III. Expeimenal esuls and discussions A. Full-Space Beam Defleco As he fis example, we employ ou mea-aoms o design a high-efficiency beam defleco woking in he full space. To achieve his goal, we equie ha and exhibi he following disibuions = C0+ 1 x, (1) = C1+ x whee C 0 and C 1 ae wo consans, 1 and ae wo phase gadiens which deemine he bending angles of he anomalously efleced and efaced beams, especively [4-7]. Se he woking fequency as f GHz, we chose six mea-aoms o fom a supecell fo ou measuface, and hen opimized hei geomeical paamees o make Eq. (1) saisfied wih 9

10 1 0.43k0 and 0.43k0, whee k 0 f 0 / c wih c being he speed of ligh. The sucual deails of he opimized mea-aoms ae summaized in Secion C of Suppoing Infomaion [4]. To validae ou design, we depic in Figs. 3(c-d) he finie-diffeence-imedomain (FDTD) simulaed disibuions of eflecion/ansmission ampliude/phase of he designed mea-suface. We find ha he wo phase disibuions mach well wih he heoeical cuves, meanwhile hese mea-aoms exhibi compeiive values of ansmission/eflecion ampliudes ( >0.93 and >0.86), which can guaanee he highefficiency opeaions of ou mea-devices. FIG. 3. (colo online) Design/fabicaion of he full-space beam defleco. (a) Top-view and (b) boom view picues of he fabicaed full-space beam defleco. FDTD simulaed pofiles of (c) ( x), ( x ), (d) and fo he designed full-space beam-defleco, compaed wih he heoeically equesed lines = C0 0.43k0 x and = C10.43k0 x (black lines). Hee he woking feqeuncy is f GHz. We fabicaed a measuface sample accoding o he design (see Figs. 3(a-b) fo is opview and boom-view picues), which conains mea-aoms wih a oal size of mm, and hen expeimenally chaaceized is wave-manipulaion pefomances. We fis chaaceized he ˆx -polaizaion popeies of he mea-suface. Shining an ˆx - 10

11 polaized micowave nomally ono ou mea-suface, we measued he angula disibuions of scaeed waves a boh eflecion and ansmission sides of he measuface. As shown in Figs. 4(a-b), wihin a fequency ineval (10.35 o GHz), mos inpu powe is efleced 1 o an oblique angle deemined by he genealized Snell s law sin ( / k ) (solid sas in Fig. 4(a)) [4-7]. The bes pefomance appeas a 10.6 GHz whee all undesied modes in he full space ae suppessed leaving only he anomalous eflecion suvived. This aleady implied he good woking efficiency of ou device. We nex chaaceized he ŷ -polaizaion popeies of he mea-suface following he same pocedues. Figues 4(d) and 4(e) show, especively, he measued angula powe disibuions of he scaeed waves in eflecion and ansmission sides fo ou mea-suface unde he illuminaion of ŷ -polaized micowaves. As expeced, wihin he fequency ineval (10. o 11.0 GHz), mos inpu powe is now edieced o he ansmission chanel a he angle deemined by he genealized Snell s law sin ( / k0) (solid sas in Fig. 4(d)), wih he bes pefomance again appeaing a he woking fequency 10.6 GHz. We quaniaively chaaceized he woking efficiencies of ou device. A each fequency, we compued he woking efficiency as he aio beween he powe caied by he desied anomalously defleced mode (eihe a eflecion o ansmission side) and a efeence value epesening he oal powe caied by he inpu beam [8, 0, 4]. The fome value is obained by inegaing ove an appopiae angle egion occupied by he desied mode, while he efeence is obained via inegaing ove he angle egion of he speculaly efleced mode when he mea-suface is eplaced by a meallic plae of he same size (see Secion E of he Suppoing Infomaion fo moe deails [4]). Figs. 4(c) and 4(f) depic he woking efficiencies of ou device (eieved fom he expeimenal daa shown in Figs. 4(a-b) and 4(de)) as funcions of fequency, fo wo polaizaion-dependen funcionaliies. We also 11

12 pefomed FDTD simulaions o compue he angula disibuions of he scaeing paens a each fequency fo wo polaizaions (see Suppoing Infomaion D [4]), fom which we successfully obained he heoeical values of woking efficiencies fo ou device. As shown in Figs. 4(c) and 4(f), he expeimenally eieved efficiencies mach well wih hei coesponding heoeical ones. In paicula, ou expeimens indicae ha he woking efficiencies of he fabicaed device can be as high as 91% (eflecion-side) and 85% (ansmission-side), while hese values ae 93% and 88% esimaed fom FDTD simulaions. The sligh diffeence beween he measued and simulaed esuls can be aibued o ineviable fabicaion eos and impefecions of he incoming wave-fons geneaed by ou micowave hons. FIG. 4. (colo online) Chaaceizaions of he full-space beam defleco unde nomal incidence. Measued scaeed-field inensiy (colo map) vesus fequency and deecing angle a (a) eflecion and (b) ansmission sides of he measuface shined by ˆx -polaized micowaves. (c) Simulaed and measued absolue efficiencies of he eflecive beam-bending 1

13 funcionaliy of he device. Measued scaeed-field inensiy (colo map) vesus fequency and deecing angle a (d) eflecion and (e) ansmission sides of he measuface shined by ŷ -polaized micowaves. (f) FDTD simulaed and measued absolue efficiencies of he ansmissive beam-bending funcionaliy of he device. Inses o (c) and (f) depic he measued (symbols) and simulaed scaeing paens of ou measuface illuminaed by ˆx - and ŷ - polaized waves, especively, a he fequency f GHz. All signals ae nomalized agains a efeence value obained by eplacing he mea-device wih a meallic plae of he same size. B. Full-Space Mea-Lens As anohe example, we designed a full-space mea-lens, which can focus EM waves a is eflecion and ansmission sides fo ˆx and ŷ -polaized inciden waves, especively (see Figs. 5(a) and 5(e)). To achieve his end, he wo phase funcions ( and ) of ou meadevice should exhibi he following disibuions ( x, y) k0( F1 x y F1 ) ( x, y) k0( F x y F ) () whee F 1 and F ae wo focal lenghes which can be feely seleced. Hee, sill se he woking fequency as f GHz, we designed a full-space mea-lens wih wo focal lenghs F1 F 80 mm. Diffeen fom he defleco ealized in he las sub-secion, hee he mea-lens does no exhibi a supe cell, and hus evey mea-aom should be caefully opimized such ha he wo phase disibuions can saisify Eq. (). We fixed he sucual deails of all mea-aoms adoped based on he paamee maps ecoded in Suppoing Infomaion B [4], and hen fabicaed a mea-lens sample accoding o he design, which conains mea-aoms and has a oal size of mm. Figues 5(b) and 5(f) depic he op-view and boom-view picues of he fabicaed sample. To validae ou design, we calculaed he disibuions of wo elavan phases ( and ) and ampliudes ( and 13

14 ) of ou designed/fabicaed mea-lens, and depic hem in Figs. 5(c, g, d, h), especively. Clealy, he phase pofiles of he fabicaed mea-lens follow well wih he paabolic disibuions dicaed by Eq. (), while he eflecion/ansmission ampliudes also exhibi high values ( >0.9 and >0.85), implying he high pefomances of ou device. FIG. 5. (colo online) Design/fabicaion of he full-space mea-lens. Schemaic illusaion of he pefomance of ou mea-device, which behaves as a (a) eflecive lens and (e) a ansmissive lens unde exciaions of ˆx - and ŷ - polaized waves, especively. Top-view (b) and boom-view (f) picues of ou fabicaed sample. FDTD simulaed pofiles of (c) ( x, y), (d) ( x, y ), (g) ( x, y) and (h) ( x, y) of he designed/fabicaed meadevice. The woking fequency is f GHz. 14

15 Wih he fabicaed sample in hand, we expeimenally chaaceized is full-space focusing pefomances, wih eflecion-mode funcionaliy consideed fis. Shining he sample wih an ˆx -polaized plane wave, we used a monopole anenna (~0 mm long) o measue he elecic field disibuions a he eflecion-side half space. To see clealy he focusing effec, we puposely deduced he inciden field fom he measued oal field, so ha he obained field is solely he scaeed one. Figue 6(a) depics he measued scaeed-field disibuions on boh xoz and yoz planes a he fequency10.6 GHz, which ae nomalized agains he maximum value in he paen. We found ha he efleced waves ae indeed well conveged o a focal poin a z 77 mm, idenified as he maximum-field poin in he E ~ z cuve along he cenal z axis (see Suppoing Infomaion G [4]). The focal lengh x idenified expeimenally agees easonably wih he heoeical value F1 80 mm. To check he qualiy of he focusing effec, we quaniaively evaluaed he full-widh-a-half-maximum (FWHM) of he focal spo on he focal plane, and found i is appoximaely 4 mm (see inse o Fig. 6(b)). Obviously, such a value songly depends on he apeue size of ou mea-lens, and can be fuhe educed by enlaging he oal size of ou lens. To idenify he woking bandwidh of ou focusing funcionaliy, we show in Fig. 6(b) how he measued and FDTD compued scaeed E -field a he focal poin vaies agains fequency, wih he inciden E - field keeping as a consan. The opeaion bandwidh of ou device, defined by he FWHM of he Ex ~ f cuve, is found as 0.85 GHz (shaded egion in Fig. 6(b)). Finally, we used he mehod epoed in efs. [4] and [37] o evaluae he woking efficiency of his funcionaliy, defined as he aio beween he powes caied by he focal spo and he inciden beam. Ou analysis shows ha he efficiency is as high as 90.6% (see Suppoing Infomaion H [4]). 15

16 FIG. 6. (colo online) Chaaceizaions of he full-space mea-lens. (a) Measued E x disibuions on boh xoz and yoz planes a he eflecion side of he mea-lens unde illuminaion of nomally inciden ˆx -polaized wave. (b) Measued/simulaed E x a he focal poin vesus fequency fo ou mea-lens unde ˆx -polaized exciaion. (c) Measued E y disibuions on boh xoz and yoz planes a he ansmission side of he mea-lens unde illuminaion of nomally inciden ŷ -polaized wave. (d) Measued/simulaed E y a he focal poin vesus fequency fo ou mea-lens unde ŷ -polaized exciaion. Inses o (b) and (d) depic he measued E x and E y disibuions on he xy planes wih z=-77 mm and z =78 mm, especively, wih he dashed-line cicles defining he sizes of he focal spos. Hee, he woking fequency is f GHz. All field values ae nomalized agains he maximum value in he coesponding specum/paen. We hen expeimenally chaaceized he focusing pefomance of ou device a he ansmission side of he measuface, which is illuminaed by an ŷ -polaized plane wave. The chaaceizaion pocedues ae essenially he same as hose fo he eflecion-mode funcionaliy, only wih he field scanning now caied a he ansmission side of he device. The measued E -field disibuions on boh xoz and yoz planes (Fig. 6(c)) a he woking 16

17 fequency clealy evealed he nice focusing effec a he ansmission side. The focal lengh is idenified as 78 mm, quie close o he designed value 80 mm (see Suppoing Infomaion G [4]). The woking bandwidh of his funcionaliy is found as 0.75 GHz, indicaed as he shaded egion in Fig. 6(d) whee he specum of he E -field measued a he focal poin is shown. We also checked he qualiy of he focusing effec, and found ha he size of he focal spo is abou 0 mm (see inse o Fig. 6(d) fo he measued field paen on he focal plane). Finally, we noe ha his focusing funcionaliy sill exhibis high woking efficiency 85%, obained wih he same pocedue as ha fo he eflecive lens (see Suppoing Infomaion H [4]). C. Full-Space Bifuncional Mea-device In pevious secions, he measufaces ha we ealized exhibi he same funcionaliies fo efleced and ansmied waves. In his secion, we fuhe demonsae ha such fullspace manipulaion is no esiced o ealizing idenical funcionaliies. As an illusaion, we design a mea-device which combines beam-bending and focusing funcionaliies in a single device, wih such wo disinc funcionaliies woking fo efleced and ansmied EM waves, especively (see Figs. 7(a) and 7(d)). To achieve his goal, we equie he wo phase funcions ( and ) of ou mea-device o saisfy he following disibuions ( x, y) C 3x ( x, y) k0( F3 x y F3 ) (3) wih C being a consan. Hee, 3 is he phase gadien o deemine he angle of he anomalously efleced wave and F 3 is he focal lengh fo he mea-lens applicaion woking fo he ansmied wave, boh of which can be feely chosen. In ou design, keeping he woking fequency sill a f GHz, we se k 0 and F3 85 mm wihou losing genealiy. Aided by he sucual map shown in Secion B of he Suppoing Infomaion [4], 17

18 we opimized each mea-aom in he measuface such ha he esuling and disibuions saisfy Eq. (3) (see Fig. S13 in Suppoing Infomaion I [4]), and hen fabicaed a sample accoding o he design. Figs. 7(c) and 7(e) depic he op-view and boom-view picues of he fabicaed sample, which conains mea-aoms and has a oal size of mm. Again, we emphasize ha all opimized mea-aoms exhibi vey high values of eflecion/ansmission ampliudes ( >0.9, >0.86, see Fig. S13 in Suppoing Infomaion I [4]), which guaanees ha ou mea-device mus exhibi high woking efficiencies. We fis expeimenally chaaceized he beam-bending funcionaliy of he device a he eflecion side. Following he expeimenal pocedues descibed in Secion 3.1, we measued he angula disibuions of scaeed waves in boh eflecion and ansmission sides of he measuface, which is shined by nomally inciden ˆx -polaized EM waves. Fig. 7(c) clealy shows ha nealy all inciden powes ae e-dieced o he anomolous-eflecion angles dicaed by he genealized Snell s laws (pink symbols), wihin a boad fequency ineval ( GHz). FDTD simulaions well epoduced he expeimenal obsevaions and he esuls ae pesened in Secion J of Suppoing Infomaion [4]. Fig. 7(c) aleady implied ha he woking bandwidh of his funcionaliy is quie boad, which is einfoced by he expeimenally measued efficiency specum of he anomolous-eflecion as shown in Fig. 7(d). Obviously, he bes beam-bending pefomance is found a abou 10.6 GHz wih a peak absolue efficiency 88% (simulaion esul: 9%), and inse o Fig. 7(d) shows ha he scaeing paen a his fequency is vey clean and conains only one single anomolous eflecion mode. We finally examined he focusing funcionaliy of ou device a is ansmission side. We expeimenally mapped ou he E y -field disibuions on wo high-symmey planes a he 18

19 ansmission side of ou mea-suface, which is shined by a nomally inciden ŷ -polaized EM wave a 10.6 GHz. Fig. 7(g) shows clealy ha ou mea-device now woks as a mea-lens ha can focus ansmied wave o a focal poin, wih focal lengh evaluaed as 84 mm, ageeing well wih he heoeical design ( F 85 mm ). The spo size a he focal plane is found as 19 mm (see inse o Fig. 7(h) fo he measued field paen on he focal plane). Uilizing he same appoach as in Sec. 3., we also expeimenally chaaceized he woking efficiency of he mea-lens, and found ha he efficiency is oughly 85.% (see Suppoing Infomaion J [4]). The measued E y value a he focal poin is depiced in Fig. 7(h) as a funcion of fequency, fom which we idenified he woking bandwidh of he mea-lens as 0.8 GHz ( GHz). 19

20 FIG. 7. (colo online) Design, fabicaion and chaaceizaion of a full-space bifuncional mea-device. Schemaic illusaion of he pefomance of ou mea-device, which behaves as a (a) eflecive beam-bende and (e) a ansmissive lens unde exciaions of ˆx - and ŷ - polaized waves, especively. (b) Top-view and (f) boom-view picues of ou fabicaed mea-device. (c) Measued scaeed-field inensiy (colo map) vesus fequency and deecing angle a he eflecion side of he measuface shined by nomal-incidence wave wih E x ˆ polaizaion. (d) Simulaed and measued absolue efficiencies of he eflecive beam-bending funcionaliy of he device unde ˆx -polaized exciaions. Inse shows he measued and FDTD simulaed scaeing paens of he mea-suface. (g) Measued E y disibuions on boh xoz and yoz planes a he ansmission side of he measuface unde illuminaion of nomally inciden ŷ -polaized wave. (h) Measued and simulaed E -field ampliude a he focal poin as funcions of fequency. Inse depics he measued E y disibuions on he xy plane wih z =84 mm, wih he dashed-line cicle defining he size of he focal spo. Hee, he woking fequency is 10.6 GHz and all field values ae nomalized agains he maximum value inside each specum. IV. Conclusion To summaize, we poposed a new ype of measuface ha can efficienly conol EM wave-fons in he full space, and expeimenally demonsaed he concep in he micowave egime. We designed/fabicaed hee mea-devices (wih oal hickness much less han wavelengh) and expeimenally demonsaed ha hey can simulaneously ealize he beambending and/o focusing funcionaliies in ansmission and eflecion modes wih vey high woking efficiencies (in he ange of 85%-91%), depending on he inpu polaizaions. Ou findings open he doo o ealize funcional high-efficiency mea-devices wih full-space conol abiliies in diffeen fequency domains, which ae impoan in moden inegaionopics applicaions. 0

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25 [36] P. Wang, N. Mohammad, and R. Menon, Chomaic-abeaion-coeced diffacive lenses fo ulaboadband focusing, Sci. Rep. 6, 1545 (016). [37] Z. Li, W. Liu, H. Cheng, J. Liu, S. Chen, and J. Tian, Simulaneous geneaion of highefficiency boadband asymmeic anomalous efacion and eflecion waves wih few-laye anisoopic measuface, Sci. Rep. 6, (016). [38] M. Khoasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, Mealenses a visible wavelenghs: diffacion-limied focusing and subwavelengh esoluion imaging, Science 35, 1190 (016). [39] K. Chen, Y. Feng, F. Monicone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, S. Zhang, A. Alù, and C.-W. Qiu, A econfiguable acive huygens mealens, Adv. Mae. 9, (017). [40] L. Zhang, S. Mei, K. Huang, and C.-W. Qiu, Advances in full conol of elecomagneic waves wih measufaces, Adv. Op. Mae. 4, 818 (016). [41] H.H. Hsiao, C. H. Chu and D. P. Tsai, Fundamenals and applicaions of measufaces, Small Mehods 1, (017). [4] See he Supplemenal Maeial fo moe discussions on woking mechanism of he mea-aom, design saegy of he full-space measufaces, FDTD simulaion esuls fo he full-space defleco, evaluaing he woking efficiencies of he full-space beam defleco, incidence-angle-dependen pefomance of he full-space beam defleco, esimaions on he focal lenghs of he full-space mea-lens, evaluaions of he woking efficiencies fo he full-space mea-lens, phase/ampliude disibuions of he full-space bifuncional mea-device sudied in Fig. 7 and addiional simulaion/expeimenal daa of he full-space bifuncional mea-device. 5

26 Suppoing Infomaion High-efficiency and full-space manipulaion of elecomagneic wave-fons wih measufaces Tong Cai 1,, GuangMing Wang, ShiWei Tang 3, HeXiu Xu 1,, JingWen Duan 4, HuiJie Guo 1, FuXin Guan 1, ShuLin Sun 4, Qiong He 1, 5, * 1, 5, * and Lei Zhou A. Woking mechanism of he mea-aom Ou poposed mea-aom can achieve oal eflecion and oal ansmission fo inciden eleomagneic (EM) waves wih diffeen polaizaions. In his subsecion, we illusae he undelying physics via caefully analyzing he EM ansmission/eflecion chaceisics of he mea-aom unde exciaions wih diffeen polaizaions. Conside fis he ˆx -polaizaion whee he mea-aom should be (nealy) oally eflecive bu exhibis a conollable eflecion phase. As aleady explained in he main ex, ou poposed mea-aom consiss of 4 meallic layes in which he x-oiened meallic bas in he boom wo layes ae always coninuous sipes bu hose in he op wo layes can exhibi finie lenghs. We fis conside he case (called mea-aom 1, see Fig. S1a) ha only he x- oiened meallic ba in he fis laye has a finie lengh ( d 1 8 mm P 11 mm ). Fig. S1c shows he finie-diffeence-ime-domain (FDTD) calculaed eflecion specum of such a mea-aom. A magneic esonance is geneaed by he ineacion beween he op meallic ba and he boom coninuous sipes, evidenced by he eflecion dip and he in-phase eflecion a 9 GHz and he cuen disibuion depiced in he inse o Fig. S1c. We nex conside he second example (called mea-aom ) whee he x-oienaed bas in he op wo layes ae boh of finie lenghs (d 1 =d =8.5 mm, see Fig. S1b). The addiional feedom povided by he second meallic ba makes such a mea-aom exhibi wo magneic esonances, appeaing a 7. GHz and 11.9 GHz, especively (see Fig. S1d). The calculaed cuen disibuions (see inse o Fig. S1d) eveal ha he low-fequency magneic esonance is due o he ineacion beween he uppe meallic bas and he lowe coninuous meallic sipes while he second magneic esonance is mainly geneaed by he muual ineacion beween wo meal bas in he uppe wo layes. Figue S1 implied ha we can easily ge any desied eflecion phase a a age fequency via uning he magneic esonance posiions wih he eflecion ampliude emaining nealy unchanged, fo he ˆx -polaized exciaion. 6

27 Figue S1. Schemaics of uni 1 (a) and (b) uni. FDTD simulaed eflecion phase and ampliude fo (c) uni 1 wih d 1 =8 mm and (d) uni wih d =d 1 =8.5 mm. Inses o (c) and (d) show he cuen disibuions a he esonan fequencies. We now conside he EM popeies of he mea-aom unde ŷ -polaizaion exciaion. To illusae he essenial physics, we simplify he complicaed sucue by only eaining hose y-oiened bas in each laye since y-polaized EM waves can only see he y-oiened bas unde he lowes ode appoximaion. Now he sysem is a mulilaye of meallic paches sepaaed by F4B dielecic spaces. Obviously, hee ae wo opologically diffeen unis inside such a mulilaye sysem --- a single meallic pach on a dielecic subsae (called A laye, see Fig. S(a,b)) and he same meallic pach sandwiched beween wo dielecic spaces (called A laye, see Fig. S(d,e)). We fis sudy he EM chaaceisics of hese wo layes. Solid lines in Figs. Sc and Sf depic he FDTD calculaed speca of ansmission ampliude and phase fo hese wo layes, fom which we find ha hey can be easonably A descibed by wo effecive pemiiviy 10 eff f A', 10 eff f a he fequency egion ha we ae ineesed in, evidenced by he good ageemen beween FDTD simulaions on ealisic sucues (lines) and ansfe-maix-mehod (TMM) calculaions on effecive-medium slabs (symbols). 7

28 Figue S. (a, d) Effecive-medium models and (b, e) schemaics of mea-aom A and meaaom A. Tansmission ampliude and phase speca fo (c) mea-aom A and (f) mea-aom A, calculaed by FDTD simulaions on ealisic sucues and TMM calculaions on effecivemedium slabs. (g) Geomey of a fou-laye mea-aom consising of wo layes A and wo layes A sepaaed by ai gaps wih hickness g. Tansmission (h) ampliude and (i) phase speca fo such a fou-laye mea-aom, calculaed by FDTD simulaions on ealisic sucues and TMM calculaions on model sysems. (j) Schemaics of he ealisic 4-laye mea-aom in which he gaps sepaaing diffeen layes ae F4B dielecic slabs wih hickness g 1. FDTD simulaed (k) ansmission ampliude and (l) phase speca of such a mea-aom; (m) Effecive model of he ealisic fou-laye mea-aom, and is coesponding TMM compued (n) ansmission ampliude and (o) phase speca. The paamees ae fixed as p=11 mm, h=0.1 mm, w 1 =5 mm, a=8 mm, d a =d a =0.1 mm, h=0.05 mm, g=10 mm, g 1 =1.4 mm. 8

29 Wih he EM popeies of individual A and A s layes fully undesood, we can hen sack hem o fom a mulilaye sucue and sudy he EM chaaceisics of he esuling mulilaye sysems. As shown in Fig. Sg, when he ai gap beween wo adjacen layes is lage enough, FDTD simulaions on ealisic mulilaye sucue ae in good ageemen wih he TMM calculaions on he model sysem in which each ealisic laye is eplaced by is effecive-medium laye (A o A ), boh showing ha he 4-laye sucue can exhibi a seies of pefec ansmission peaks due o he consucive inefeences of muliply scaeed waves. Designing he sucue o cascade seveal ansmission peaks appopiaely, we can find a wide fequency band wih high ansmission ampliudes and phases coveing he ange (see shaded egions in Fig. Sh). In ealisic design, he siuaion is moe complicaed, since he space beween wo adjacen layes is much hinne han he case we sudied in Fig. Sg and hus he nea-field ineacions beween adjacen layes ae moe significan. Howeve, he physics emains essenially unchanged. Figue Sk-l depic he FDTD simulaed ansmission ampliude/phase speca of a 4-laye mea-aom wih spaces in ealisic design (gap hickness 1.4 mm). While he FDTD esuls have quaniaive diffeences wih hose obained based on effecive medium models (Fig. Sn-o) due o he enhanced nea-field ineacions beween adjacen layes, we noe ha he essenial feaues of he FDTD speca ae simila o hose of he TMM ones. B. Design saegy of he full-space measufaces To fasciliae ou design, we pesen in his secion deailed paamee maps, based which we can easily fix he sucual deails of mea-aoms a difeen posiions in a measuface accoding o is desied phase disibuions. To his end, we need o calculae how he EM esponseses of he mea-aom (e.g.,,,, and ) depend on is sucual paamees. In pinciple, we need o pesen hee-dimensional (3D) maps since we have hee independen sucual paamees (e.g., a, d 1 and d ). In pacice, howeve, we found i no absoluely necessay o make d 1 and d fully independen. Insead, we found i is enough o esic ou paamee soing wihin wo pojeced paamee spaces: {5 d1 10.8, d 11} & {8 d1 d 9}. Figue S3a-3d illusae, especively, how,,, and vay agains he paamees a, d 1 and d, wih fequency fixed a f 0 =10.6 GHz. Obviously, is sensiive o d 1 and d bu insensiive o a, while behaves jus 9

30 opposiely. Changing he sucual paamees wihin he wo esiced spaces, we find ha he vaiaions of he wo phases ( and ) aleady cove he whole 360 ange, while simulaneously he eflecion/ansmission ampliudes ( and ) emain a vey high values ( 0.9, 0.84 ), which ensues he high woking efficiency of he designed measuface. Figue S3. (a) Reflecion phase and (b) he ampliude disibuions of he mea-aom as funcions of a and d 1 (d ) fo nomally inciden ˆx -polaized waves. (c) Tansmission phase and (d) ampliude disibuions of he mea-aom as funcions of a and d 1 (d ) fo nomally inciden ŷ -polaized waves. Hee, he fequency of inees is f 0 =10.6 GHz. C. Deailed sucual paamees of hee mea-devices designed in his pape Wih he sucual maps (Fig. S3) in hand, we can hen deemine he geomeical paamees (a, d 1 and d ) of all mea-aoms involved in ou full-space measufaces based on hei equied phase disibuions. Figue S4-S6 depic, especively, he disibuions of meaaom paamees of hee mea-devices ealized in his pape. 30

31 Figue S4. Disibuions of sucual paamees (a) a, (b) d 1 and (c) d of he full-space beam defleco sudied in Figs. 3-4 in he main ex. All paamees have he uni of mm. Figue S5. Disibuions of sucual paamees (a) a, (b) d 1 and (c) d of he full-space mealens sudied in Figs. 5-6 in he main ex. All paamees have he uni of mm. Figue S6. Disibuions of sucual paamees (a) a, (b) d 1 and (c) d of he full-space bifuncional me-device sudied in Fig. 7 in he main ex. All paamees have he uni of mm. D. FDTD simulaion esuls fo he full-space defleco Figue S7 depics he FDTD simulaed scaeing popeies of he full-space defeco unde exacly he same exciaion condiions as in Fig. 4 of he main ex. Obviously, FDTD esuls ae in good ageemen wih hei coesponding expeimenal esuls (Fig. 4). In paicula, a he woking fequency 10.6 GHz, simulaions show ha he inpu beams have been edieced o he anomalous-eflecion (fo ˆx -polaizaion exciaion) and he anomalous-efacion mode (fo ŷ -polaizaion exciaion) wih vey high efficiencies, since all undesied modes have been fully suppessed. 31

32 Figue S7. FDTD simulaed scaeed-field inensiies (colo map) in (a, c) eflecion and (b, d) ansmission space vesus fequency and he deecing angles of ou mea-beam-defleco shined by nomal-incidence wave wih E x ˆ (a, b) and E y ˆ (d, e) polaizaions, especively. E. Evaluaing he woking efficiencies of he full-space beam defleco 3

33 Figue S8. (a, b) Measued and FDTD simulaed angula powe disibuions of he scaeed field fo a meallic plae shined by a nomally inciden wave. (c, d) Measued and FDTD simulaed angula powe disibuions of he scaeed field fo ou measuface shined by a nomally inciden ˆx -polaized wave. (e, f) Measued and FDTD simulaed angula powe disibuions of he scaeed field fo ou measuface shined by a nomally-inciden ŷ - polaized wave. In his secion, we quaniaively esimae he woking efficiencies of ou full-space beam defleco based on boh expeimenal daa and FDTD esuls. We define he efficiency as he aio beween he powe caied by he defleced beam (anomalously efleced/efaced modes) and ha of he inciden one. The fome is evaluaed as he inegaed powe ove he angle anges occupied by anomalously efleced wave (Fig. S8c, 8d) o he anomalously efaced one (Fig. S8e, 8f), fo ou measuface illuminaed by nomally inciden waves wih diffeen polaizaions a 10.6 GHz, while he lae is obained by he same echnique bu wih he measuface eplaced by a meal plae of he same size (Fig. S10a, b). The aio beween he wo is hus he desied efficiency. Based on his echnique, we found ha he woking 33

34 efficiency of he anomalous eflecion is 91% in expeimen and 93% in simulaion, and ha of he anomalous ansmission is 85% in expeimen and 88% in simulaion. F. Incidence-angle-dependen pefomance of he full-space beam defleco In his secion, we numeically and expeimenally illusae he incidence-angle dependen popeies of ou full-space beam defleco a he fequency 10.6 GHz. Figue S9. Chaaceizaions of ou beam defleco unde oblique incidence. (a) Measued scaeed-field inensiies (colo map) in eflecion (down) and ansmission (up) sides vesus incidence angles θ i and he deecing angles θ /θ, fo ou mea-beam-defleco illuminaed by ŷ -polaized (uppe panel) and ˆx -polaized (lowe panel) waves. FDTD simulaed and measued absolue efficiencies of (b) anomalous eflecion and (c) anomalous efacion of ou mea-device unde oblique illuminaions wih ŷ - and ˆx -polaizaions a 10.6 GHz. Figue S9a shows how he measued nomalized inensiies of he anomalous eflecion/ansmission signals vay agains inciden ( θ i ) and deecing angles ( θ,θ ), fo ou beam defleco unde illuminaions of ˆx - and ŷ -polaized micowaves. We can see clealy ha he elaionships beween anomalous eflecion/ansmission angles and he inciden angles well saisfy he genealized Snell s law 1 / i k0 sin (sin θ / ) epesened by blue sas. Figues S9b and 9c fuhe compae he measued and simulaed woking efficiencies of ou device (using he echnique descibed in Sec. E) fo wo funcionaliies as funcions of he incidence angle, fom which we find he woking efficiencies emain a high values. Excellen ageemen beween measued and simulaed esuls is noed. 34

35 G. Esimaions on he focal lenghs of he full-space mea-lens Figue S10. Measued Re( E y ) (a) and Re( E ) x (c) disibuions a xoz planes a ansmission space and eflecion space fo ou mea-device illuminaed by ŷ - and ˆx -polaized waves a woking fequency of 10.6 GHz, especively. Calculaed (b) E and (d) E disibuions along hee axes fom he measued E -Field disibuions fo ou mea-lens, especively. In his secion, we descibe how o evaluae he focal lenghs of ou mea-lenses sudied in Figs. 5-6 of he main ex. Figue S10a depics he measued Re( E y ) disibuions on he xoz plane a he ansmission side of ou mea-lens, unde he illuminaion of a ŷ -polaized plane wave a f GHz. Based on such Re( E ) disibuion, we plo in Fig. S10b (black y y x line) how he measued E y vaies agains z on he cenal z axis (wih x=0), fom which we can easily idenify he focal poin (z=78 mm) whee he maximum field value appeas. Hee, Re( E y ) conains he phase infomaion, heefoe he focal plane is no a he maximum value of Re( E y ). In ode o esimae he spo size on he focal plane, we also measued he E y 35

36 disibuions along x and y axes on he focal plane, and depiced he esuls in Fig. S10b (ed doed line and blue dashed line). We noe ha hese wo cuves mach well wih each ohe, implying he good isoopic esponse of ou mea-lens. In addiion, we can idenify fom hese wo cuves ha he size of he focal spo is 0 mm, which is labeled by he cyan lines a he full-widh-a-half-maximum (FWHM) of he measued paens. Similaly, we can evaluae he focal lengh and spo-size of ou mea-lens woking in eflecion space, which ae 77 mm and 4 mm, especively (see Figs. S10c-10d). H. Evaluaions of he woking efficiencies fo he full-space mea-lens In his secion, we descibe how o evaluae he woking efficiency of ou mea-lens as sudied in Figs. 5-6 of he main ex. We fis evaluae he woking efficiency of he eflecive mea-lens unde he exciaion of an ˆx -polaized wave. We define he efficiency as he aio beween he powe caied by he focal spo and ha of he inciden beam. Since a diec measuemen on he mea-lens woking efficiency is echnically impossible, we use a wosep mehod o appoximaely evaluae i, following he saegy esablished in Ref. [4]. The ef foc absolue woking efficiency can be calculaed by P P foc P P. The fis em P / ef P epesens he aio beween he powe caied by he oally efleced waves and ha of he P inciden one, while he second one, Pfoc / P ef, is defined by P o foc ef ef nˆ S ds 1 nˆ S ds o, whee S is he Poyning veco, n is he nomal uni veco of he inegaion aea, and he wo inegaions un ove he aeas occupied by he focusing spo and ha of he mea-lens. The wo aios can boh be evaluaed in FDTD simulaions and expeimens, and hus he final absolue efficiencies can be obained. 36

37 Figue S11 Measued powe disibuions of he scaeed waves fo a meallic slab (a, c) wih a same size of he mea-suface and he mea-lens (b, d) illuminaed by ˆx -polaized and ŷ - polaized inciden plane wave a fequency of 10.6 GHz. Figue S1 FDTD simulaed 3D powe disibuions of he scaeed waves fo a meallic slab illuminaed by an ˆx -polaized inciden plane wave a fequency of 10.6 GHz. We esimae he em P / P fis. Fo a 3D lens, he efleced/ansmied waves go o ef o all diffeen diecions afe passing hough he focal poin. Theefoe, we should in pinciple pefom a wo-dimensional (D) inegaion ove he whole solid angle o accuaely evaluae he efficiency. Howeve, such a D inegaion is vey difficul o pefom in expeimens. Founaely, ou mea-lens has quie good isoopic esponses on he xy-plane (see inses o Figs. 6(b) and 6(d) in he man ex and Fig. S10b and 10d), and he 3D scaeing paen of a meal slab also exhibi nice isoopic esponse on he xy-plane (see Fig. S1). Theefoe, i is a easonable appoximaion o ake only one pincipal plane o pefom one-dimensional (1D) 37

38 inegaions o obain boh he inegaed efleced/ansmied powe and he efeence value. Shining he mea-lens by a nomal-incidence ˆx -polaized wave a 10.6 GHz, we measued he H-plane scaeing paen and depiced he esul in Fig. S11b. As a efeence, we hen measued he scaeing paen wih he measuface eplaced by a meallic slab of he same size, and depiced he scaeed-field disibuions in Fig. S11a. We hen pefomed inegaions ove he cuves in Fig. S11b and Fig. S11a. The aio beween he wo inegaed values is found as 95.8%. The missing powe is mainly due o dielecic losses and he ansmission. We noe ha his value is also quie close o he aveaged value (~0.96) of eflecance of all mea-aoms in ou device unde ˆx -polaized exciaion, which e-enfoced ou appoximae eamen. We hen evaluaed he em P / P. Following he saegy esablished in Ref. [5], we appoximaely eplaced he fomula foc ef P P foc ef nˆ S ds 1 nˆ S ds as E ds Pfoc 1 Pef E ds, which is easonable as ou designed mea-lens has a lage F/ D aio (F: focal lengh, D: laeal size of he lens). Shining he sample wih an ˆx -polaized inciden plane wave a f GHz, we measued he E disibuion on he focal plane (i.e., he xy-plane a z 77 mm ) and depiced he esuls in he inse o Fig. 6b of he main ex. We nex evaluaed he wo inegaions ( E ds, 1 E ds ) based on he measued field paen, whee he fis inegaion uns ove he aea occupied by he focal spo (defined by he dashed lines in he inse o Fig. 6b) and he second one uns ove he enie egion occupied by he measuface. Based on hese calculaions, we ge eflecive lens is 95.8% 94. 6% 90.6%. P P foc ef 94.6%. Thus, he final woking efficiency of ou We employed he same wo-sep chaaceizaion mehod o evaluae he woking efficiency of ou mea-lens woking on he ansmission mode, based on he fomula P P ans foc foc P o P. The fis em ans ans Po P is esimaed as 89.% based on he measued fa-field paens depiced in Fig. S11c-11d, wih he missing powe caied away by dielecic losses and he eflecions. Again, we noe ha his value is quie close o ha (0.88) esimaed based on aveaging he ansmiance of all mea-aoms inside ou mea-lens unde ŷ -polaized 38

39 P exciaion. The second em P foc ans is evaluaed as 95.3% based on he measued nea-field E disibuions a he focal plane (see inse o Fig. 6d of he main ex). Theefoe, he poduc of he wo efficiencies gives us he final woking efficiency of his funcionaliy, which is oughly 85%. I. Phase/ampliude disibuions of he full-space bifuncional meadevice sudied in Fig. 7 Figue S13 depics he disibuions of eflecion/ansmission phases ( and ampliudes ( and ) and ) of he sample sudied in Fig. 7 of he main ex, obained by FDTD simulaions. We noe ha he designed phase disibuions mach well wih he heoeical ones given in Eq. (3), while he eflecion/ansmission ampliudes of all meaaoms emain a high values ( >0.9, >0.86), which guaanees he high efficiencies of ou bifuncional mea-device. Figue S13. FDTD simulaed disibuions of efecion/ansmission phase (a/b) and ampliude (c/d) of he designed mea-device sudied in Fig. 7 of he main ex, a fequency of 10.6GHz. J. Addiional simulaion/expeimenal daa of he full-space bifuncional mea-device 39

40 Figue S14. FDTD simulaed scaeed-field inensiies (colo map) in full space vesus fequency and he deecing angles, fo ou bifuncional mea-suface unde he nomally inciden illuminaion wih polaizaion of E x ˆ. Figue S14 conains he FDTD simulaion esuls coesponding o he expeimenal esuls shown in Fig. 7. Obviously, hey mach wih each ohe well. Figue S15. Measued Re( Ey ) disibuions a xoz (a) and yoz (b) planes a ansmission space fo ou mea-device illuminaed by a ŷ -polaized wave a 10.6 GHz. (c) Calculaed E y disibuions along hee axes fom he measued E y disibuions of ou mea-lens, especively. Figue S15a and S15b show he expeimenally measued Re( E y ) disibuions on boh xoz and yoz planes, fo he mea-suface (sudied in Fig. 7 of he main ex) illuminaed by a ŷ - polaized plane wave a 10.6 GHz. To clealy idenify he focal poin, we depiced in Fig. S15c he measued E y disibuions along he z axis (black line) and found ha he focal poin is a z=84 mm whee he E y eaches a maximum. Finally, we ploed in Fig. S15c he measued E y disibuions along x and y axes on he focal plane a z=84 mm (ed do line and blue dash line), fom which we can esimae he size of he focusing spo (19 mm) on he focal plane. 40