NONLOCAL HOMOGENIZATION MODEL FOR THE ANALYSIS OF ABSORBING PROPERTIES OF MUSHROOM STRUCTURES WITH GRAPHENE PATCHES AT MICROWAVES

Transcription

1 NONLOCAL OMOGENIZATION MODEL FOR TE ANALYSIS OF ABSORBING PROPERTIES OF MUSROOM STRUCTURES WIT GRAPENE PATCES AT MICROWAVES A. B. Yovlev, Y. R. Pdoou, S. Kbsi, G. W. nson, nd A. Mfi SPECIAL SESSION: OMOGENIZATION OF METASURFACES AND BULK METAMATERIALS AT MICROWAVES, TZ, AND OPTICAL FREQUENCIES WEDNESDAY, JULY 14, 21

2 Outline Intoduction nd Motivtion Nonlocl omoenition Model fo Mushoom Stuctues with Thin Metl/Gphene Ptches Genelied Additionl Bound Condition Mushoom IS with Gphene Ptches s Absobin Stuctues t Micowves Numeicl Results Conclusion 2

3 Intoduction Mushoom-Tpe IS E L = L = Gound plne (PEC) di( ) d L In tems of mcoscopic field components: de d 2 L 1 L Additionl bound condition fo the micoscopic cuent t the vi-ound plne connection ( ) nd vi-ptch connection ( L ): d d L M. Silveiinh et l., New J. Phs., 1, 28 In mushoom-tpe IS stuctues with shot vis, the pesence of id sinificntl educes the sptil dispesion in the wie medium slb esultin in the unifom cuent lon the vis A. Demetidou et.l., J. Phs.: Condens. Mtte, 2, , 28 O. Luuonen et.l., IEEE Tns. Micowve Theo Tech., 57, Nov. 29 A. B. Yovlev et.l., IEEE Tns. Micowve Theo Tech., 57, Nov. 29 3

4 Nonlocl nd Locl omoenition Models E L Gound plne (PEC) L 1 L 2 The esults of eflection popeties nd ntul modes [sufce wves nd le wves] bsed on non-locl (SD+ABC) nd locl (ENG) homoenition models e in ecellent eement 4 O. Luuonen et l., IEEE Tns. Micowve Theo Tech., 57, Nov. 29 A. B. Yovlev et.l., IEEE Tns. Micowve Theo Tech., 57, Nov. 29

5 Mushoom IS Thin Metl Ptch R, db E Metl ptches 2 L PEC TM polition: Metl Thicness: 6nm ABC - PEC FSS Fequenc (G) 5 M. Silveiinh et l., New J. Phs., 1, 28 O. Luuonen et l., IEEE Tns. Micowve Theo Tech., 57, Nov. 29

6 Two-Sided Mushoom Stuctue - Thin Metl Ptch R, db T, db E Metl ptches 2 2L Reflection, db Metl Thicness: 6nm Tnsmission, db -5 TM polition: R, ABC - PEC R, FSS Fequenc (G) M. Silveiinh et l., New J. Phs., 1, 28 T, ABC - PEC T, FSS Fequenc (G) 6

7 Mushoom IS Thin Metl Ptch R, db E Metl ptches 2 L PEC ABC - PEC FSS TM polition: 3 Metl Thicness: 1nm Fequenc (G) 7 M. Silveiinh et l., New J. Phs., 1, 28 O. Luuonen et l., IEEE Tns. Micowve Theo Tech., 57, Nov. 29

8 Two-Sided Mushoom Stuctue - Thin Metl Ptch R, db T, db E Metl ptches 2 2L Reflection, db Metl Thicness: 1nm Tnsmission, db R, ABC - PEC R, FSS Fequenc (G) TM polition: 3-25 M. Silveiinh et l., New J. Phs., 1, 28 T, ABC - PEC T, FSS Fequenc (G) 8

9 Genelied Additionl Bound Condition (GABC) Thin Metl/Gphene Ptch E L J c nˆ PEC int 2D t 2 2 e BT j2γ Leontovitch Bound Condition: E t J, metl 1 E t J 2D Sufce Conductivit of Gphene j c c c 2ln e BT c, metl 1 2D 3D t B T 1 3D j Good conducto S. A. Tetov, Anlticl Modelin in Applied Electomnetics, Atech ouse: Nowood, MA, 23 -e: che of n electon B : Boltmnn s constnt μ c : chemicl potentil (electosttic bis) Γ : electon scttein te (1 12 ) T : tempetue (3 K) ћ : modified Plnc s constnt G. W. nson, J. Appl. Phs., 13, 28 Thin metl 9

10 Genelied Additionl Bound Condition (GABC) Thin Metl/Gphene Ptch E L J c nˆ PEC t Sufce che densit fo thin metl/phene t the connection point, L : nˆ E s s J 2D c Pinciple of Consevtion of Sufce Che s j s J c s 1 djc( ) j d Thin wies Genelied Additionl Bound Condition (GABC) t the vi-thin metl/phene connection, L : 2D djc( ) Jc( ) L j d 1

11 Mushoom A with Thin Metl/Gphene Ptches E Nonlocl Model SD + ABC Thin metl/gphene ptches 2 L Gound plne (PEC) Wie medium slb s uniil continuous mteil chcteied b tenso effective pemittivit Sptil dispesion 1 ˆˆ ˆˆ eff ˆˆ 2 p 2 2 / c p is the plsm wvenumbe 2 p 2 2 / ln M. Silveiinh et l., IEEE Tns. Antenns Popt., 56, Feb. 28

12 SD + ABC Model TM-polied incident plne wve ecites TEM nd TM modes in the wie medium slb cos e e e j cosh B B e TEM TM TM Two-sided impednce bound condition t L : In tems of field components: In tems of field components: E E Z L L L L j i eion wie medium slb Genelied dditionl bound condition t the vi-thin metl/phene ptch connection, L : 2D djc( ) Jc( ) L j d j E 2D L d d Additionl bound condition t the vi-ound plne connection, : dj ( ) c d de d de d d d 12

13 Gid Impednce of Thin Metl/Gphene Ptches E Thin metl/gphene ptches 2 L PEC Z eff eff j 2 2D eff eff eff eff lncsc 2 eff S. A. Tetov, Anlticl Modelin in Applied Electomnetics, Atech ouse: Nowood, MA, 23 O. Luuonen et l., IEEE Tns. Micowve Theo Tech., 57, Nov. 29

14 Reflection Coefficient Reflection coefficient R coth coth cot TM L L K j Z cot whee 1 2D TM 1 tnh TM L TM j K 1 2D TM 1 coth TM j TM L L K j Z 1 1 2D 1 1 tn L j TM 2D L cot L TM j TM 1 2 p 2 2 p TM p 2 2 In the limitin cse 2 D (tnspent ptches) it tuns to wie-medium slb: M. Silveiinh et l., IEEE Tns. Antenns Popt., 56, Feb. 28 In the limitin cse 2D (PEC ptches) it tuns to mushoom IS: 14 O. Luuonen et l., IEEE Tns. Micowve Theo Tech., 57, Nov. 29 A. B. Yovlev et.l., IEEE Tns. Micowve Theo Tech., 57, Nov. 29

15 J c ()/J c () Micoscopic Cuent Alon the Vis fo Thin Metl Ptches PEC 2d =.58 S; t = 1nm 2d =.1 S; t =.17 nm 2d =.25 S; t =.43 nm 2d =.1 S; t =.17 nm 2d = S /L 2D 3D t 7 3D 5.81 S / m s It should be noted tht fo thin metl (t = 1nm), the micoscopic cuent lon the wies is close to unifom, howeve, t the connection point (vi-thin metl) the enelied ABC hs to be consideed in the nonlocl homoenition model 2D J c 15

16 Mushoom IS Thin Metl Ptch R, db E Metl ptches 2 L PEC TM polition: 3 Metl Thicness: 6nm Genelied ABC GABC FSS Fequenc (G)

17 R, db T, db Two-Sided Mushoom Stuctue - Thin Metl Ptch E Metl ptches 2 2L Metl Thicness: 6nm Genelied ABC Reflection, db TM polition: 3 Tnsmission, db R, GABC R, FSS T, GABC T, FSS Fequenc (G) Fequenc (G)

18 Mushoom IS Thin Metl Ptch R, db E Metl ptches 2 L PEC GABC FSS TM polition: 3 Metl Thicness: 1nm Genelied ABC Fequenc (G) 18

19 R, db T, db Two-Sided Mushoom Stuctue - Thin Metl Ptch E Metl ptches 2L 2 Metl Thicness: 1nm Genelied ABC Reflection, db TM polition: 3 Tnsmission, db R, GABC R, FSS T, GABC T, FSS Fequenc (G) Fequenc (G)

20 Gphene Gphene is mono-tomic le of phite A sinle-wll cbon nnotube is olled-up sheet of phene Althouh phene hs been lon studied to eplin the popeties of cbon sstems, it ws lon thouht tht phene itself did not eist 24 phene found! Gphene is chcteied b unique electicl, theml, nd mechnicl popeties: hih electicl conductivit opticl tnspenc bein stenth much ete thn steel 2

21 Mushoom A with Gphene Ptches Gphene ptches 2 L E Gound plne Peiod (): 2 mm Gp () :.2 mm Rdius of vis ( ):.5 mm Substte thicness (L): 1 mm Dielectic pemittivit ( ):

22 R, db Compison of Diffeent omoenition Models nd FSS Reflection, db -5 TM polition: 45-1 μc =.5185 ev σ2d f 11.96G.34 j.11 S GABC FSS Locl Model ABC - PEC Fequenc(G) Nonlocl model with the enelied ABC is in ood eement with the full-wve FSS esults, howeve, nonlocl nd locl models (with the ABC deived fo PEC ptches nd vis) pedict ve diffeent behvio fo the eflection coefficient 22 O. Luuonen et l., IEEE Tns. Micowve Theo Tech., 57, Nov. 29

23 J c ()/J c () Micoscopic Cuent Alon the Vis fo Gphene Ptches TM polition: c =.5 ev [ 2D =.29 - j.12 S] f = 14 G c =.25 ev [ 2D =.14 - j S] c =.1 ev [ 2D = j S].2 c = ev [ 2D = j S] /L It should be noted tht fo the le chemicl potentil [μc =.5 ev] the micoscopic cuent lon the vis is close to unifom, howeve, t the connection point (vi-phene ptch) the enelied ABC hs to be consideed in the nonlocl homoenition model 23

24 J c ()/J c () Micoscopic Cuent Alon the Vis fo Gphene Ptches J c ()/J c () f = 11.5 G f = 14 G μc =.5 ev c =.5 ev GABC COMSOL μc = ev c = ev GABC COMSOL σ 2D.293 j.16 S.5 σ 2D.21 j S /L /L Nonlocl model with enelied ABC is in ood eement with the full-wve COMSOL esults 24 (Comsol Multiphsics,

25 R, db Mushoom IS with Gphene Ptches Compison of Nonlocl Model with FSS Reflection, db TM polition c =.5185 ev = Solid lines: Nonlocl model Dot-dsh lines: FSS = 3 = 45 = Fequenc, G Mushoom IS with phene ptches esults in stble esonnce fequencies (in the vicinit of the plsm fequenc) fo diffeent nles of incidence 25

26 R, db Tunble Mushoom IS with Gphene Ptches Compison of Nonlocl Model with FSS Reflection, db TM polition Solid lines: Nonlocl model Dot-dsh lines: FSS =, c =.5185 ev = 45, c =.6785 ev = 6, c =.467 ev Fequenc, G Reflection minim cn be obtined t diffeent incident nles b djustin the chemicl potentil 26

27 Conclusions The peviousl used ABC t the connection of metllic vis to metllic ptches is no lone pplicble in the cse of thin metl/phene ptches A Nonlocl (SD+ABC) homoenition model with enelied ABC is poposed fo the nlsis of mushoom stuctues with thin metl/phene ptches Fo the cse of thin metl/phene ptches the micoscopic cuent lon the wies is close to unifom, howeve, the enelied ABC hs to be consideed t the connection point (vi-thin metl/phene) in the nonlocl homoenition model Absoption popeties of mushoom stuctues with phene ptches e studied. The eflection minim cn be obtined t diffeent incident nles b djustin the chemicl potentil (electosttic bis field) 27

28 Acnowledement The uthos e thnful to Máio G. Silveiinh fo helpful discussions edin the Additionl Bound Condition 28