Helsinki University of Technology Publications in Engineering Physics Teknillisen korkeakoulun teknillisen fysiikan julkaisuja Espoo 2000 TKK-F-A804 ANALYSIS AND MODELING OF SURFACE-ACOUSTIC WAVE RESONATORS Julius Koskela Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics for public examination and debate in Auditorium F1 at Helsinki University of Technology (Espoo, Finland) on the 12th of January, 2001, at 12 o clock noon. Helsinki University of Technology Department of Engineering Physics and Mathematics Materials Physics Laboratory Teknillinen korkeakoulu Teknillisen fysiikan ja matematiikan osasto Materiaalifysiikan laboratorio
Distribution: Helsinki University of Technology Materials Physics Laboratory P.O. Box 2200 FIN-02015 HUT Tel. +358-9-451 3150 Fax. +358-9-451 3164 E-mail: julius@focus.hut.fi Julius Koskela ISBN 951-22-5276-7 ISSN 1456-3320 Otamedia Oy Espoo 2000
T $$$ T _ Ps{ qy$r bb, bsr {s $ I BZ $t Y s $sjr _YkR${R NsAB sb k s < jr$t,$ =t$% R$k BP q {YtBjBk $t {BjjsAB s$bt b$y ${ BtsR 7 8${BtIZ{B 7V sti b$y qyb8rbt ${ BRBt${RW Z{Y s j7b$9 jsti sti 7B}Y$sTVt$}Bj$R3 st{ qy$r bb, RZ88s $9 R s bb,$t } $BI BP PBZ k s RIZ $t by${y y Ys% { $% I RZ}}B sti t{bz s 8 t P B8 8stk } RBtR *$R{ZRR$BtR b$y V $ VjsRsjBq B < $,,$j[sq 8Z _BY`Bjs* 7 $ _B}B%7$8B 7[s[sR,$jsY$_ BP RRB Fst G R T YBj8stI * _,,s Vk [sr [ Ys% A t 8BR t`bksaj sti Y k s bs 8jk {Bt$9 I y b$ry B Yst, Y } RBtt j s Y s $sjr _YkR${R NsAB sb k PB s }j srst bb,t $t t%$ Bt8 t qy {Yt${sj I$R{ZRR$BtR b$y * FZYs 3s YBj8* 7 $ BtI sk %* *s%$i B stfstt 7sjB* s { 7BjsjstI * qyb qyb %sjirrbt Ys% A t 8BR A t h{$sj y $R 8k }j srz sti YBtBZ B Yst, ]j$tbt <s 8stt_ BP RT RB ttks <sry$8bb s $ <Bt,st tfbzt$ tzz$js7s,z N YBt tqs}st$ s,,bt tsti _sr$ q$,,s PB P Z$PZj {BjjsAB s$bt sti {BsZYB $t y s8 I }jk s PZjsR s } RBt sti sr s R{$ t$rb 8k $tr Z{B _ BP RRB z${b _j RR,kPB RYs $t Y$R $tr$y Bt Y I$R{$}j$t BP RZ Ps{ s{bzr${sti PB Y$R A j$ P sti I %B$Bt Bt BZ R s {Y y $R s } $%$j I B Ys% bb, I b$y Y$8 sjj Y$R $8 y s8 I }jk $ti A I B 8k RZ} %$RB _ BP RRB s $ 7sjB8ssPB Y B}}B T Zt$k B bb, $t Y h ji sti PB Y -{ jj t bb,$t {BtI$$BtR G$YBZ Y$R I 8$ts$Bt Y R s {Y BZ} bbzji tb -$R <$R bb YPZj ZR sti }s$ t{ Bt 8 s Y$Yjk s}} {$s I 7{YBjs RY$}R sti htst{$sj RZ}}B P B8 < jr$t,$ =t$% R$k BP q {YtBjBk$T { BtsR 7 8${BtIZ{B 7Vqe e7sti W! yv 3BZtIs$Bt s s PZjjk s{,tbbjt I I er} {$sjjky Yst, Y V{sI 8k BP 3$tjstI PB s P jjbbry$} b$y$t Y sit Zs R{YBBj $t q {Yt${sj _YkR${R 3$tsjjky bbzji j$, B Yst, 8k Ps8$jk8k P $ tirv$t{jzi$t YBR sj sik 8 t$bt IvstI Vtt PB Y $ } R t{ $t 8k j$p
T$%T N$R BP _ZAj${s$BtR qy$r I$RR s$bt $R s %$ b BP Y szyb :R bb, $t Y h ji BP RZ Ps{ Ts{BZR${ bs% {YtBjBk y {BtR$RR BP st B% %$ b sti Y PBjjBb$t R j {$Bt BP }ZAj${s$BtR $t Y$R h jiu y F BR, jsz j RR,kstI 7sjB8ss"7Z}} RR$Bt BP Y j s,k 7VG s tzs$bt b$y Y s%k 8 {Yst${sj jbsi$t" yeee q strs{$btr Bt =j srbt${r 3 B j { ${R sti 3 JZ t{k ]Bt Bj ;x;nt;; wdmd yy F BR, js7 N YBt tz j RR,kstI 7sjB8ss"7Z Ps{ st% R bs% R Bt jstsr$ " V}}j$ I _YkR${R N R 11EExT1EE wdmd yyy F BR, jsz j RR,kstI 7sjB8ss"7VG\N7VG ]! }s s8 - s{$bt P B8 {B8}Z -} $8 tr b$y Ys 8Bt${ si8$st{ BP s } $BI${ s sk BP j { BI R" yeee q strs{$btr Bt =j srbt${r 3 B j { ${R sti 3 T JZ t{k ]Bt Bj ;EM(ETMdE wdd yz F BR, jsz j RR,kstI 7sjB8ss"qY B k PB RY s YB $9Btsj RZ Ps{ s{bzr${ bs% R $t ht$ Rkt{Y BtBZR RBtsB R" yeee q strs{$btr Bt =j srbt${r 3 B j { ${R sti 3 JZ t{k ]Bt Bj ;dxx(tdxe( w1(((d z F BR, jsf z tzz$js_ q q$,,s] 7 <s 8sttz j RR,kstI 7sjB8ss" {Yst$R8 PB s{bzr${ j s,s $t RZ Ps{ Ts{BZR${ bs% RT BtsB R Bt Bs I OT{Z j$y$z8 stsjs RZAR s " V}}j$ I _YkR${R N R x1emnt1emx wdd zy F BR, jsf z tzz$jsq s,,bt tz j RR,kstI 7sjB8ss "V{BZR${ jbrr 8 {Yst$R8R $t j s,k 7VG RBtsB R Bt j$y$z8 stsjs " i T }B q T3TVM(dy7 W xdt11txd;1terza8$ I B yeee q strs{$btr Bt =j srbt${r 3 B j { ${R sti 3 JZ t{k ]Bt Bj w1(((d qy BZYBZ Y B% %$ by R }ZAj${s$BtR s P I B Ak Y $ ib8st tz8 sjr
T%T VZYB :R ]Bt $AZ$Bt qy RZI$ R $t Y$R I$RR $Bt s Y RZj BP bb, {s $ I $t Y s $sjr _YkR${R NsAB sb k s < jr$t,$ =t$% R$k BP q {YtBjBk w<=qd IZ $t Y k s R det1((( _s} R ytyyy b {BtIZ{ I $t {BjjsAB s$bt b$y ${ BtsR 7 8${BtIZ{B 7V T %s$-7b$9 jstiby$j }s} R yztzy $t%bj% {BB} s$bt b$y qyb8rbt ${ BRBt${R 7VG * R$t Z szw Z{Y s j7b$9 jsti _s} z RZjR P B8 I$R{ZRR$BtR b$y ]j$tbt 7 <s 8stti3 7VG ]B8}Bt tr*sjjsrq -sr=7v qy szyb YsR RZARst$sjjk {Bt $AZ I B Y R s {Y $t _s} R ytzy < YsR I % jb} I sti PB 8Zjs I s R$t$h{st }s BP Y Y B ${sj 8 YBIR $t _s} R yyy yzsti zy Vjj Y B ${sj {sj{zjs$btr} B s88$tsti tz8 ${sj {B8}Zs$BtR $t _s} R ytzy b {s $ I BZ Ak Y$8 qy szyb s{$% jk }s ${$}s I $t Y b $$t BP _s} yy _s} R yyyytzy b b $ t 8s$tjk Ak Y$8 ]BtR$I saj }s BP Y RZjR {B% I $t _s} R ytzy YsR A t } R t I $t $t ts$btsj {BtP t{ R Y RZjR $t _s} R yyy sti yz Ak Y szyb sti YBR $t _s} R z sti zy Ak Y szyb sti {BjjsAB sb R
T%$T ]Bt tr _ Ps{ $$$ N$R BP _ZAj${s$BtR $% VZYB :R ]Bt $AZ$Bt % ]Bt tr %$ d yt BIZ{$Bt d 1 _ $BI${ ej { BI V sk x 1d <s 8Bt${stIZZsjVI8$st{ R x 11 V}}j${s$BtRBP<s 8Bt${VI8$st{ 1n <s 8Bt${VI8$st{ $ty _ R tgb, M n i$b BZR 7$8Zjs$Bt nd 3$ jitqy B ${sj3b 8Zjs$Bt n1 WZ8 ${sj7bjz$btbpy 3$ jiejzs$btr dd nn 7 Z{Z ]Ys s{ $9s$Bt d1 n; ]BZ}j$tTBPTBI R_s s8 e- s{$bt dn ; BI jpb 7Y s <B $9BtsjGs% R dx ;d _ B}ss$Bt $t Y _ $BI${ ej { ${ V sk dx ;1 VAABT<sRY$8BB]BZ}j$tTBPTBI RBI j d ;n _Y tb8 tbjb${sji RBtsB BI j dm x V{BZR${ NBRR R $t N s,k 7VG i RBtsB R Bt N$qs! n 1d xd V{BZR${N s,s {Yst$R8R 11 x1 N s,s stiy ej { ${_ PB 8st{ 1x E *$R{ZRR$Bt sti ]Bt{jZR$BtR 1E i P t{ R VAR s{r BP _ZAj${s$BtR ytzy e ss PB _ZAj${s$BtR ytzy 1M nx n
TdT d yt BIZ{$Bt qy jsr bb I {si R Ys% b$t RR I s PZ $BZR BbY BP Y j {B88Zt${s$Bt $tt IZR k V8Bt Y {Yt${sj } JZ$R$ R PB 8BI t { jjzjs sti {B Ij RR RkR 8R s si$btp JZ t{k wi3d hj R b$y % k R8sjj R$9 sti 8$t$8sj jbrr R qb 8 Y$R I 8stIs tb% j {jsrr BP {B8}Bt tr AsR I Bt Y RZ Ps{ Ts{BZR${ bs% w7vgd {YtBjBk YsR 8 I V bb, BP s $t 8$t$sZ $9s$BtY 7VG {YtBjBk {B8T A$t R RB}Y$R${s I t$t $t b$y Y $ty t 8s $sjr }YkR${sj } B} $ R BP Y {B%sj t { krsjr,tbbt sr }$ 9B j { ${R 7Z Ps{ Ts{BZR${ bs% R s s{bzr${ bs% R } B}ss$t $t st jsr${ RZAR s 8 I$Z8 yt {BtR sr B }jst Tbs% j$, AZj,Ts{BZR${ bs% R w VGRD7VGR s jb{sj$9 I B Y RZ Ps{ BP Y RZAR s b$y 8BR BP Y $ t k {Btht I B b$y$t s P b bs% T j tyr P B8 Y RZ Ps{ 7$t{ Y $ I$R{B% k $t dmmx Ak NB I iskj $Y >dhy RZ Ps{ Ts{BZR${ bs% R Ys% A t BP $t R B }YkR${RR $R8BjBkstI {B8}Bt t {YtBjBk b$y$t 8$j$s k sti {$%$j s}}j${s$btr *Z B Y $ jb{sj$9s$bt B Y RZ Ps{ Y RZ Ps{ Ts{BZR${ bs% R s R tr$$% BvstIY PB U sr$jk t s I sti 8st$}Zjs I AkvR Z{Z R Bt Y RZ Ps{ BP Y RZAR s G$Y$t Y$R bb,}$ 9B j { ${ { krsj RZAR s R s {BtR$I I $t }$ 9B j { ${ 8s $sjry j { ${sj sti 8 {Yst${sj h jir s 8ZZsjjk {BZ}j I >1H V k}${sj 7VG I %${ {BtR$RR BP s }s t BP j { BI R PsA ${s I sb} s }$ 9B j { ${ { krsj bsp ZR$t j$yb s}y${ } B{ RR R R$8$js B YBR ZR I $t Y R 8${BtIZ{B $tizr k qy AsR${ j 8 t BP s 7VG I %${ $R st $t I$$sj striz{ wy*qd >nh $jjzr s I $t 3$ dd qy B} s$bt BP Y y*q $R AsR I Bt Y }$ 9B j { ${ & {U sr s %Bjs $R s}}j$ I A b t Y AZRAs R BP Y y*qy j { ${ h ji A b t Y j {T BI R } t s R $tb Y RZAR s stiiz B Y }$ 9B j { ${ {BZ}j$ts{BZR${ bs% R s -{$ I i {$} B{sjjkY s{bzr${ bs% R s{{z8zjs j { ${ {Ys Bt busbars drive voltage electrodes SAW piezoelectric substrate 3$Z ddu yt I$$sj striz{ wy*qd R % R sr st st tts PB jszt{y$t sti { $%$t RZ Ps{ Ts{BZR${ bs% R qy I %${ $R A$I$ {$BtsjU bs% R s jszt{y I ABY B Y j P sti B Y $Y P B8 Y y*q
T1T Y j { BI R $ Y k t s {Z tr qy s{{z8zjs I {Ys R j si B s R {T BtIs k -{$s$bt BP s{bzr${ bs% R < t{ Y y*q 8sk R$8Zjst BZRjk B} s sr s str8$ s { $% sti s 4 {B BP s{bzr${ bs% R q si$$btsjjkrz Ps{ Ts{BZR${ bs% I %${ R Ys% A t ZR IPB -s8}j $t Y$YT } PB 8st{ I jsk j$t R sti str% Rsj hj R >;H RBtsB R >xud(hs{bzr${ {BtT %Bj% R >ddd1h sti 4 {$% s sk {B8} RRB R >;H qy {Bt% t$btsj 7VG hj {Bt{ } $R AsR I Bt Y P JZ t{kti } ti t {Bt% R$Bt BP Y j { ${ R$tsj $tb st s{bzr${ bs% b$y st y*qpbjjbb I Ak s {Bt% R$Bt $tb st j { ${ R$tsj b$y stby y*q *Z B Y A$I$ {$Btsj$k BP Y y*qy {Bt% t$btsj 7VG hj R Ys% s 8$t$8Z8 $tr $Bt jbrr BP E I VII$$Btsj jbrr R B{{Z IZ B I R$t$t PB B}$8sj P JZ t{k {Ys s{ $R${R RZj$t $t s k}${sj jbrr j % j BP dxt1x I NBRR R Y }BB }Bb Bj st{ sti Y sy - ti I I %${ j ty ti str% Rsj hj R Bsjjk Zth PB s}}j${s$btr b$y$t 8BA$j RkR 8R W b 8 $t s}}j${s$btr BP Y 7VG {YtBjBk $t{jzi 7VG R trb R >dnh sti sr >d;h AZ$tI I { t si%sts R $t 7VG {YtBjBk Ys% A t I $% t Ak Y %sr -}str$bt BP Y { jjzjs }YBt 8s, R qb 8 Y R $t t JZ$ 8 tr R Ak Y $tizr ks t b t s$bt BP 7VG hj R YsR 8 I BI t i3 7VG hj R k}${sjjk P sz 8$tZR{Zj R$9 st $tr $Bt jbrr b$y$t P b I sti st B} s$t P JZ t{k Z} B 1 p<9 sti sab% qy s %s $BZR I R$t s}} Bs{Y R PB jbbt jbrr I %${ RAZ RB8 8s$t s}} Bs{Y R 8sk A {jsrr$h IU $8} Ist{ j 8 t hj R >dxudh wye3rd{bz}j I RBtsB hj R >1(u11H str% Rsjjk {BZ}j I RBtsB hj R >1nu1xHstI $t I$$s I y*q R Z{Z R >1E1H qy bb,$t } $t{$}j R BP Y R 8BI t i3 7VG I %${ R I$& RR t$sjjk P B8 YBR BP Y {Bt% t$btsj str% Rsj hj R *Z B Y Y$Y B} s$t P JZ t{$ R Y j { BI Y${,t RR $R tb t j$$aj $t {B8}s $RBt B Y s{bzr${ bs% j ty ]BtR JZ tjky 8sRR jbsi$t Ak Y j { BI R $R R$t$h{st RZj$t $t RjBb$t BP Y bs% sti8br $8}B stjk$t 4 {$BtR GY t Y bs% j ty BP st s{bzr${ bs% $R {jbr B s 8Zj$}j BP Y s$t } $BI${$ks R Bt $t s{$bt A b t Y {BZt } B}ss$t bs% R s, R }js{ sti Y s{bzr${ h ji $R B% t I Ak Y s $R$t s 4 {$BtR qy R R % B s} Y s{bzr${ t k $tr$i Y I %${ 3B Y$R srbtu$t {Bt sr B Y str% Rsj hj RuY ht$ 4 {$%$k BP Y j { BI R $R PZtIs8 tsj B Y I %${ B} s$bt qy I R$t BP Y$YT} PB 8st{ 7VG I %${ R JZ$ R } {$R R$8Zjs$Bt 8BI jr qy$r bb, $R {Bt{ t I sabz Y R$8Zjs$Bt BP Y -{$s$bt sti } B}ss$Bt BP RZ Ps{ Ts{BZR${ bs% R $t } $BI${ j { BI R Z{Z R!P R} {$sj $t R $R Y Rkt{Y BtBZR Zt$PB 8 Bt T}B 7VG RBtsB $jjzr s I $t 3$ d1wyd y{btr$rrbp s wk}${sjjk jbtd y*q sti bb j { ${sjjk RYB I s$trby${y R % sr sii$$btsj 4 {B R qy 8s$t j { ${sj {Ys s{ $R${ BP Y I %${ $R s R Bt RBtst{ T st$ RBtst{ }s t $t Y P JZ t{k R}BtR R 3$ d1wkd *Z B Y js $8} Ist{ I$& t{ A b t Y RBtst{ sti Y st$ RBtst{ Y R Z{Z bb,r sr s P JZ t{kt{bt Bjj I Rb${Yvst $8} Ist{ j 8 t wyed =R$t RZ{Y yer sr AZ$jI$t AjB{,R $t j { ${sj t bb,r%s $BZR $8} Ist{ j 8 t hj R wye3rd 8sk A {BtR Z{ I >1MH srrybbt $t3$dn
TnT reflectors (a) IDT Y( f ) [1/Ω] 10 10 10 0-1 -2-3 (b) resonance antiresonance 10 800 900 1000 1100 1200 f [MHz] 3$Z d1u wyd 7{Y 8s${sj Rkt{Y BtBZR Zt$PB 8 7VG RBtsB sti wkd s8 srz I P JZ t{k R}BtR P sz $t s RBtst{ s M( <9st st$ RBtst{ s d(dn <9 stia b t Y R st $8} Ist{ j % j I$& t{ BP sabz Y 8st$ZI R Zs Z 1 s2 Z 1 in Zp Zp Zp out in Z 2 Z 2 out (a) (b) Z 1 3$Z dnu 7{Y 8s${ $8} Ist{ j 8 t hj RU wyd jsii hj sti wkd Asjst{ IT A $I hj es{y {B8}Bt t RYBbt $t Y t bb, $R st $8} Ist{ j 8 tu s Rkt{Y BtBZR Bt T}B 7VG RBtsB b$y P JZ t{kti } ti t $8} Ist{.wW D yt R $t $B BZR ]V* BBjR PB I %${ I R$t $R $t{ sr$t AZs Y 8B8 t RZ{Y 8 YBIR s BB RjBb B A ZR I sr Y } $8s k 8 str BP I R$t <Bb % $tht$ } $BI${ j { BI s skr 8sk A R$8Zjs I sy &B j RRjk yt _s} R ytyyy BP Y$R bb, b Ys% $8}j 8 t I RZ{Y s R$8ZjsB sti s}}j$ I $ B RZIk j s,k RZ Ps{ Ts{BZR${ bs% RBtsB R Bt j$y$z8 t$bas sti j$y$z8 stsjs RZAR s R sti RZ Ps{ str% R bs% RBtsB R Bt jstsr$ RZAR s qy {B8}Z R$8T Zjs$BtR } B%$I st $t -} tr$% sti j$saj 8 YBI PB Y {Ys s{ $9s$Bt sti B}$8$9s$Bt BP Y RZAR s T j { BI {B8A$ts$BtR qy stsjkr R s AsR I Bt Y {Bt{ } BP Ys 8Bt${ si8$st{ I % jb} I Ak j,` sj >1n(H sti PB 8ZT js I Ak Yst sj >ndh qy $ Y B k $R %$ b I $t ]Ys} 1bY$j ]Ys} n {Bt{ t s R Bt Y _s} R ytyyy 7$t{ $B BZR R$8Zjs$BtR {sttb A ZR I sr Y 8s$t BBj $t I %${ I R$t}Y T tb8 tbjb${sj 8BI jr RZ{Y sr Y {BZ}j$tTBPT8BI R w]!d 8BI j >n1hy _T8s $- PB 8sj$R8 >nnhsti JZ$%sj t {$ {Z$ 8BI jrs {B88Btjk RB I B qy R s j RR s{{z s Yst $B BZR 8BI jr AZ {BtR$I saj PsR stiy t{ Y k 8sk A ZR I b$y B}$8$9s$Bt sjb $Y8R qy {B8}s $RBt BP Y R }Y tb8 tbjb${sj 8BIT jr >n;h % sjr YsZtI Y Rs8 {BtI$$BtRsj8BR $I t${sj RZjR s BAs$t Iu
T;T sti Y Rs8 I$^{Zj$ R s t{bzt Iub$Y sjj BP Y 8 G$Y$t Y$R bb,btjk Y ]! PB 8sj$R8 $R -}j${$jk P I B qy {BZ}j$tTBPT8BI R PB 8sj$R8 YsR A t - tr$% jk ZR I R$t{ dx(:r $t %s $BZR } BAj 8R js I B B}${R sti j { B8st $R8 >nxneh y } B% I s}} B} $s PB Y stsjkr$r BP 7VG s$tr >nnmh Zt$PB 8 striz{ R >nu;1h sti R}s$sjjk %s k$t R Z{Z R >n1h qy s{{z s{k BP Y ]! Y B k wsti BY }Y tb8 tbjb${sj 8BIT jrd I } tir { Z{$sjjk Bt -}j${$ 8BI j }s s8 RbY${Y I R{ $A } B} $ R RZ{Y sr bs% % jb{$k 4 {$%$k P B8 Y j { BI RY R ty BP Y j { B8 {Yst${sj {BZ}j$tstI Y {s}s{$st{ BP Y R Z{Z 3B RZ{{ RRPZj I %${ I R$t Y R }s s8 R 8ZR A,tBbt B Y$Y s{{z s{k qy }s s8 R 8sk A s{y$ % I $t %s $BZR bskr qy j { ${sj 8 srz 8 tr P B8 R} {$sj R R Z{Z R >;n;;h R 8 B A Y 8BR j$saj 8 YBI =tpb ZT ts jkr$t{ Y }s s8 R Ys% B A $ti$%$izsjjk I 8$t I PB s{y RZAR s b$y % k 8s $sjr$9 RYs} sti R Z{Z BP Y j { BI RY -} $8 tsj s}t } Bs{Y $R ABY -} tr$% sti $8 T{BtRZ8$t B B% Zt{ s$t$ R $t Y } B} T $ R sti Y B8 k BP Y j { BI R IZ B Y 8stZPs{Z $t {YtBjBk j$8$ Y s{{z s{k BP Y RZjR BAs$t I 3B Y$R srbttz8 ${sj {Yt$JZ R PB }s s8 - s{$bt Ys% { tjk A t I % jb} I yt _s} yyy BP Y$R bb, b } B}BR st sjb $Y8 PB ^{$ t ]! }s s8 - s{$bt P B8 Y Ys 8Bt${ si8$st{ BP st $tht$ j { BI s sk qy 8 YBI $R sjrb I$R{ZRR I $t ]Ys} n * R}$ Y $ $t $tr${ R$8}j${$kb$Y s{{z s jk 8 srz I }s s8 R Y ]! Y B k sti Y stsjbbzr 8BI jr {st A srbt$ry$tjk } {$R PB ts BbTAstI I %${ R 8}jBk$t {jsrr${sj 7VGR BtPB -s8}j 7qT{Z JZs 9 <Bb % Y 8BI j $R {BtR$I sajk j RR s{{z s PB RY s TYB $9Btsjjk }Bjs $9 I RZ Ps{ Ts{BZR${ bs% R w7<t 7VGRDRZ{Y sr RZ Ps{ str% R bs% R w7qgrdsti Y j s,k RZ Ps{ Ts{BZR${ bs% R wn7vgrd Bt Bs I N$WA! n sti N$qs! n RZAR s R qy js s 8}jBk I - tr$% jk $t 8BI t i3 7VG hj R yt _s} yz b {BtR Z{ s }Y tb8 tbjb${sj Y B k PB Y R$8Zjs$Bt BP Rkt{Y BtBZR Zt$PB 8 7<T7VG RBtsB R qy$r 8BI j $R %$ b I $t ]Ys} ; 3Z Y I$R{ }st{$ R A b t R$8Zjs$BtR sti -} $8 tr s $R IZ B tz8 T BZR s{bzr${ }Y tb8 ts RZ{Y sr I$R} R$BtR{s $t $tb AZj,Ts{BZR${ bs% RstI bs% Z$I$t & {RstI IZ B }s sr$${ & {R RZ{Y sr R$R$% jbrr RR sk {s}s{t $st{ RstI Y $tiz{st{ R BP Y ABtI$t b$ R yt _s} R z sti zy b Ys% stsjk9 I s{bzr${ jbrr 8 {Yst$R8R $t Rkt{Y BtBZR N7VG RBtsB R $t Bs I OT{Z N$qs! n RZAR s R qy RZjR s %$ b I $t ]Ys} x *$R{ZRR$Bt sti Y {Bt{jZR$BtR s } B%$I I $t ]Ys} E
TxT 1 _ $BI${ ej { BI V sk qy } $BI${ s sk BP j { BI R $jjzr s I $t 3$ 1d {BtR$Z R st s {Y k}sj } T $BI${ R Z{Z qy j { ${sj {Btt {$BtR 8sk A s A$ s ku Y -{$s$bt sti } B}ss$Bt BP s{bzr${ bs% R $t Y s sk sti Y j { ${ R}BtR BP Y R Z{Z RZA` { B %s $BZR j { ${ {BthZ s$btr s BP PZtIs8 tsj $t R $t Y B ${sj 7VG stsjkr$r Yst sj >ndh b saj B RYBb Ys Y {B8}j I R{ $}$Bt BP Y j { ${ R}BtR $R {Bts$t I $t s R$tj PZt{$BtY Ys 8Bt${ si8$st{ BP Y j { BI s sk qy {Bt{ } bsr B $$tsjjk $t BIZ{ I sr "R $} si8$st{ " Ak j,` sj >1n(H Yst sj j stjk PB 8Zjs I Y Y B k sti jsa j I Y PZt{$Bt "Ys 8Bt${ si8$st{ " qy Ys 8Bt${ si8$st{ $R 8}jBk I - tr$% jk $t Y$R bb, qy$r ]Ys} R % R sr st $t BIZ{$Bt B Y {Bt{ }h R %$ b$t Y Y B k BP Yst sti {BbB, R sti Y t BZj$t$t YBb Y PZt{$Bt 8sk A s}}j$ I $t Y stsjkr$r sti R$8Zjs$Bt BP 7VG I %${ R 1d <s 8Bt${ sti ZZsjVI8$st{ R 3BjjBb$t i P >ndhj ~ z I tb Y j { ${ }B t$sj Bt j { BI zi ht I b$y R} { B RB8 P t{ j % jsti j { E I tb Y RZj$t {Z t Bt j { BI E qy BZYBZ Y$R bb,ys 8Bt${ $8 I } ti t{ s Y stzjs P JZ t{k )1$W $R srrz8 Ib$Y Y Ps{B 70 A $t RZARZ8 I qy {Z tr s j$t s jk js I B Y j { BI }B t$sjr qy } B}B $Btsj$k {B ^{$ tr r Ez wwd ) ({ z w1dd (~ E s {sjj I 8ZZsj si8$st{ R *Z B Y strjs$btsj $t%s $st{ BP Y s sk Y 8ZZsj si8$st{ R {sttb I } ti Bt Y sarbjz j { BI jb{s$btr E sti zu Y k 8ZR A PZt{$BtR BP Y I$& t{ Ez * tb r Ez Ak r Ez!b$t B {$} B{$k r E )r E >ndh vacuum V -1 V0 I -1 I 0 electrode p z y V I 1 1 a h V I 2 2 x piezoelectric substrate crystal 3$Z 1dU _ $BI${ s sk BP j { BI R Bt s }$ 9B j { ${ RZAR s { krsj
TET 7$t{ Y s sk 8ZR 8s$t {Ys t Z sj ZtI s A$ s k -{$s$bty 8ZZsj si8$st{ R Rs$RPk L 3 E) r E )(3 w11d ]BtR JZ tjky P t{ j % j PB j { BI }B t$sjr 8sk A {YBR t s A$ s $jk qy {Z tr RZj$t P B8 st s A$ s k %Bjs {BthZ s$bt s BAs$t I ZR$t j$t s RZ} }BR$$BtU { z ) L 3 E) r Ez wwd~ E 3 w1nd < t{ Y 8ZZsj si8$st{ R r E PZjjk {Ys s{ $9 Y j { ${ R}BtR BP Y R Z{T Z yt } $t{$}j Y 8ZZsj si8$st{ R {BZjI A I 8$t I P B8 Y j { BI {Z tr ZtI s Zt$s k -{$s$bt BP Y s skr 3$ 11wyD <Bb % Y Zt$s k -{$s$bt A s,r Y strjs$btsj Rk88 k BP Y $tht$ j { BI s skby${y bbzji A A t h{$sj PB ^{$ t tz8 ${sj {B8}Zs$BtR Yst sj I$R{B% I Ys Y Rs8 $tpb 8s$Bt {st A I IZ{ I P B8 Y R}BtR BP Y s sk B Y Ys 8Bt${ -{$s$btr 3$ 11wKD =ti TYs 8Bt${ -{$s$bty j { BI }B t$sjr srrz8 Y PB 8 ~ z ) ~ ( 71$z 3 w1;d 7ZAR$Z$t Y %Bjs R P B8 ej w1;d $tb ej w1nd$ $R PBZtI Ys Y {Z tr sjrb Ys% TYs 8Bt${ PB 8 qy s$b KV w,wd ) { z ~ z ) { ( ~ ( ) L 3 E) r E wwd 71$E w1xd $R {sjj I Y Ys 8Bt${ si8$st{ e%$i tjk$ $R s } $BI${ PZt{$Bt BP b$y Y } $BI${$k K V wld,wd) K V w,wd 7$t{ s {BtRst %Bjs IB R tb -{$ bs% RY PZt{$Bt %st$ry R PB $t %sjz R BP 3Z Y 8B Bb$t B Y {$} B{$k BP Y 8ZZsj si8$st{ RY Ys 8Bt${ si8$st{ $R Rk88 ${ sabz )(3x sr I Bt ej w1xdy Ys 8Bt${ si8$st{ 8sk A $t } I sr s I$R{ 3BZ $ strpb 8 BP Y 8ZZsj si8$st{ R i {$} B{sjjkY 8ZZsj si8$st{ R (a) I -1 V I 0 0 I 1 I 2 x (b) V e i2πγ V 0 0 V e -i2πγ V e -i4πγ I e i2πγ 0 0 0 I I 0 e -i2πγ I 0 e -i4πγ 0 x 3$Z 11U wyd =t$s k sti wkd Ys 8Bt${ -{$s$bt BP Y } $BI${ j { BI s sk
TT 8sk A {B8}Z I P B8 Y Ys 8Bt${ si8$st{ sr r E wwd ) 8 d ( KV w,wd 71$E Q3 w1ed yt {Bt sr B Zt$s k -{$s$btys 8Bt${ -{$s$bt $R 8BR RZ$sAj PB tz8 ${sj {B8}Zs$BtR qy s8 t $R s}}j${saj PB s A$ s k s} Z R sti $ 8sk A t sj$9 I PB 8B {B8}j${s I } $BIR >;xh 11 V}}j${s$BtR BP <s 8Bt${ VI8$st{ ]Bt{ }Zsjjk8 YBIR PB Y stsjkr$r BP } $BI${ j { BI R Z{Z R 8sk A {jsrr$t h I $tb bb } $t{$}sj {s B $ RU Y stsjkr R BP Y $ t8bi } BAj 8R sti YBR BP Y t s$bt } BAj 8R yt Y $ t8bi } BAj 8Rbs% R } B}ss$t ZtI Y ABZtIs k {BtI$$BtR BP j { ${sjjk B} t B RYB I j { BI R s RBZY qy }YsR RY$P $ bs% tz8a $t Y jsr${ sti j { ${ h jir A b t Y RZ{{ RR$% } $BIR $R B A PBZtI sr s PZt{$Bt BP P JZ t{k sr s RZjY I$R} R$Bt {Z % R s BAs$t I V j$8$s$bt BP Y$R 8 YBI $R Ys Y {BZ}j$t B st s}}j$ I %Bjs {st A stsjk9 I Btjk $ti$ {jk >;1H B B% {B8}j -T%sjZ I bs% tz8a R Ys% B A {BtR$I IbY${Y JZ$ R s RB8 bys {B8}j${s I {B8}j -Tstsjk${ s8 t >;EH Vt sj ts$% B Y $ t8bi stsjkr$r $R Y t s$bt stsjkr$r qy t s$bt s}} Bs{Y 8sk A ZtI RBBI sr s R$8Zjs I -} $8 tu Y RkR 8 8BI j I $R I $% t Ak s %Bjs RBZ { sti Y $t R j$ R $t Y {Z tr Bt Y j { BI R 7$t{ Y t s$bt PB 8Zjs$Bt {jbr jk R 8Aj R -} $8 try RZjR BAs$t I s sr$ B $t } Yst YBR BP Y $ t8bi R{Y 8 3B -s8}j Y si8$st{ BP s jbt Rkt{Y BtBZR Bt T}B RBtsB 8sk A R$8Zjs I sr st $tht$ j { BI s sk ZtI ht$ j { ${ -{$s$bt >;;MHR 3$ 1n ]jbr B Y RB}AstI P JZ t{$ R Y s{bzr${ h ji $t Y RBtsB $R jb{sj$9 I B Y y*q s s sti Y 4 {B R s b jj s}} B-$8s I Ak $tht$ s$tr qy si8$st{ BP Y {BtR Z{ I $tht$ RBtsB 8sk A BAs$t I P B8 ej w1nd Ak RZ88$t Y {Z tr $t Y j { BI R Bt Bt BP Y bb AZRAs R 3B tz8 ${sj R$8Zjs$BtR$ $R {Bt% t$ t B Z$j$9 ej w1ed sti B -} RR Y si8$st{ sr s b $Y I $t sj B% Y Ys 8Bt${ si8$st{ 3B Y -s8}j $t 3$ 1nBt htir V ]} wwd ) ] 3 } ] 3 } z)d E)d r 1E1z ) 8 d ( KV w,wd R$t1 w1$] } D R$t 1 w1$d Q3 w1d qy R$8}j$ R sti } Ys}R Y 8BR $8}B st t s$bt } BAj 8 $R Ys BP Ys T 8Bt${ -{$s$bt b$y )d\1 qy }B t$sjr $t Y {BtR JZ$% j { BI R s BP Y PB 8 ~ z ) wdd z < t{ Y R Z{Z 8sk A $t } I sr st $tht$ RBtsB s Y j$8$ BP st $tht$ R$tj T j { BI striz{ U KV w d 1,W W ) j$8 ] } 1V ]} wwdb] } 3 w1md 7$t{ j { ${sjjk s{$% $ t8bi R {Bt $AZ B Y R}BtR BP Y s sk B st j { ${ -{$s$bty $ t8bi sti t s$bt s}} Bs{Y R s tb $ti } ti t yt
TMT W V N λ p 0 3$Z 1nU Vt $tht$ Bt T}B RBtsB U st y*q b$y ] } j { BI }s$ R sti bb $tht$ 4 {B RPB 8 I P B8 s } $BI${ j { BI s sk Ak ht$ j { ${ -{$T s$bt yt Y$R -s8}j Y 4 {B R s {Btt { I B Y jbb AZRAs by${y 8sk A {BtR$I I BZtI I }s ${Zjs Y $ t8bi R BP Y j { ${sjjk RYB T{$ {Z$ I wr{d sti B} tt{$ {Z$ I wb{d s skr 8st$P R Y 8R j% R sr Y }Bj R sti 9 BR BP Y Ys 8Bt${ si8$st{ R} {$% jk ]BtR JZ tjky Ys 8Bt${ si8$st{ 8sk A $t } I sr Y s$b BP Y I$R} R$Bt js$bt PB B} t sti RYB I s$tru V w,wd ) ; B{w,WD ; R{ w,wd 3 w1d qy {BtI$$BtR ; B{ )( sti ; R{ ) ( R} {$% jk I ht Y I$R} R$Bt js$btr PB Y B} tt{$ {Z$ I sti RYB T{$ {Z$ I R Z{Z R V $B BZR 8sY 8s${sj } BBP BP Y$R Y B 8 bsr { tjk PBZtI Ak $ kz,b% >;H qy PZt{$BtR ; B{ w,wd sti ; R{ w,wd 8sk A BAs$t I sr Y I 8$tstR BP s}} B} $s jk I ht I RkR 8R BP JZs$BtR BAs$t I P B8 tz8 ${sj {B8}Zs$BtR b$y Y ABZtIs kt j 8 t 8 YBI qy A st{y }B$tR BP Y Ys 8Bt${ si8$st{ 8sk A $I t$h I b$y AZj,Ts{BZR${ bs% R b$y Y $ t k } B}ss$t sjbt Y RZ Ps{ 1n <s 8Bt${ VI8$st{ $t Y _ R t GB, qy {Bt{ }R BP } $BI${ j { BI s sk sti Ys 8Bt${ si8$st{ s s}}j$ I -T tr$% jk $t Y$R bb, G Ys% PB 8Zjs I s $B BZR R$8ZjsB PB s skr b$y st $tht$ s} Z w_s} R y sti yyyd sti s}}j$ I $ B {Ys s{ $9 7VG -{$s$bt $t %s $BZR RZAR s R w_s} R y sti yyd _ B{ IZ PB - s{$t }Y tb8 tbjb${sj }s s8 R AsR I Bt Y $B BZR R$8Zjs$BtR YsR A t I % jb} I w_s} yyyd V }Y T tb8 tbjb${sj 8BI j PB ht$ RZ Ps{ str% R bs% w7qgd RBtsB R $R PB 8 I Ak h R {BtR Z{$t s PB 8sj$R8 PB 7qGR $t s } $BI${ j { BI s sk stirzar T JZ tjkak s,$t $tb s{{bzt Y 4 {$BtR P B8 Y I R BP Y 4 {B R w_s} yzd e- ti$t Y } $BI${ 7qG 8BI j PB ht$ s} Z R sti 8}jBk$t ej w1d tsaj R JZst$s$% stsjkr R BP Y jbrr 8 {Yst$R8R $t $tht$ bs% Z$I RBtsB R w_s} zyd
TT n i$b BZR 7$8Zjs$Bt qy } B} $ R BP RZ Ps{ Ts{BZR${ bs% I %${ R R Btjk I } ti Bt Y R j {$Bt BP Y RZAR s 8s $sj{ krsj {ZstI Y Y $Yb$IYstI RYs} BP Y j {T BI RstI sjrb Bt 8} sz * 8$ts$Bt BP Y 7VG {Ys s{ $R${R P B8 RTR Z{Z 8 srz 8 tr >;n;;h $R jsab BZR$8 T{BtRZ8$t sti$p s B tt $ jk t b RZAR s R s $t%bj% I% k -} tr$% 3B Y$R srbt IZ{$t Y tz8t A BP -} $8 tr %$s tz8 ${sj R$8Zjs$BtR R 8R s s{$% G Ys% $8}j 8 t I s R$8Zjs$Bt BBj PB $tht$ } $BI${ j { BI s skr sti 8}jBk I $ B RZIk Y 7VG {Ys s{ $R${R Bt %s $BZR RZAR s R!t }s ${Zjs jk $8}B st PB 8 BP R Z{T Z {Ys s{ $9s$Bt $R Y - s{$bt BP Y }s s8 R ZR I $t Y }Y tb8 tbjb${sj I R$t 8BI jr G Ys% I % jb} I st ^{$ t 8 YBI PB Y - s{$bt BP Y ]! }s s8 R P B8 Y $B BZRjk {B8}Z I Ys 8Bt${ si8$st{ nd 3$ jitqy B ${sj 3B 8Zjs$Bt _YkR${sjjkY R Z{Z $t 3$ 1d 8sk A s, t B {BtR$R BP Y }$ 9B j { ${ RZAR s { krsjy 8 sj j { BI R Bt Y { krsj RZ Ps{ sti Y RZ BZtI$t %s{zz8 VR R$8}j$Pk$t s}} B-$8s$BtRY RZAR s $R srrz8 I R 8$T$tht$ B PZjhjj Y jbb YsjPR}s{ F (sti Y j { BI R s srrz8 I $tht$ jk Y$t P B8 Y j { ${ }B$t BP Y %$ b qy RZAR s sti Y j { BI R 8sk A s I ZR$t Y Y B k BP jsr${$k >x(xdhy Y 8BIkts8${sj Y B k BP }$ 9B j { ${$k >x1h sti s-b jj:r JZs$BtRbY$j Btjk s-b jj:r JZs$BtR s JZ$ I PB Y %s{zz8 qy Y B k BP jsr${$k {BtR$I R s YB8B t BZR {Bt$tZBZR 8 I$Z8 qy h ji JZst$$ R BP $t R s Y 8 {Yst${sj I$R}js{ 8 t h ji ǹ Y j { ${h ji n o sti Y 8st ${ h ji n 4 yt j$t s }$ 9B j { ${ 8 I$sY R RR trb sti Y j { ${ I$R}js{ 8 t h ji n ; s j$t s jk {BZ}j I B Y R s$t trb sti B Y j { ${ h ji no *Z B Y jbb % jb{$k BP Y s{bzr${ bs% R$t {B8}s $RBt B Y R} I BP j$y Y 8st ${ h ji 8sk $t } s{${ A t j { I ]BtR JZ tjky j { ${ h ji 8sk A s}} B-$8s I sr Y si$ t BP st BR{$jjs$t j { ${ }B t$sj *U no ) n*3 wndd qy$r $R,tBbt sr Y JZsR$Rs${ s}} B-$8s$Bt G$Y$t Y JZsR$Rs${ s}} B-$8sT $BtY {BtR$Z$% js$btr s >x1h T z Z x 7i ) ; 7 ) n3 >,q)d n3 i,>)d o (`> 7i>q L (? q 7i> (`i (? > n3 >)d n3 C 7i i)d >7i (* (? >, (* 3 (? i wn1d <? d? 1? n I tb Y ]s R$st {BB I$ts R?, r, F R} {$% jkx 7i s Y {B8T }Bt tr BP Y R {BtIT st, R RR trb 7i>q s Y {B8}Bt tr BP Y PBZ YT st,
Td(T R$&t RR trb 7i> s Y {B8}Bt tr BP Y Y$ IT st, }$ 9B j { ${ trb sti 7i s Y {B8}Bt tr BP Y R {BtIT st, } 8$$%$k trb qy RZ} R{ $}R o sti C $ti${s Ys Y {B8}Bt tr BP Y trb R s B A 8 srz I ZtI {BtRst j { ${ h ji sti ZtI {BtRst R s$t R} {$% jk qy B% t$t JZs$BtR $t Y RZAR s sti $t Y j { BI R s Y JZs$BtR BP 8B$Bt ww bbt:r jsbd n3 (x ' 1`7 7i ), wnnd (? i sti s-b jj:r JZs$Bt i)d nn n ; )(3 wn;d < ' I tb R Y 8sRR I tr$ksti Ys 8Bt${ $8 I } ti t{ s Y stzjs P JZ t{k $R srrz8 I yt %s{zz8y j { ${ I$R}js{ 8 t h ji $R $% t Ak n ;) ( n o by ( $R Y } 8$$%$k BP %s{zz8sti Y s-b jj JZs$Bt IZ{ R B n 1 * )(3 wnxd qy 8 {Yst${sj ABZtIs k {BtI$$BtR s YsU wdd Y 8 {Yst${sj I$R}js{ 8 t h ji $R {Bt$tZBZR s{ BRR Y j { BI TRZAR s $t Ps{ R w1d Y tb 8sj {B8}Bt t BP Y R RR trb $R {Bt$tZBZR s{ BRR Y j { BI TRZAR s $t Ps{ R sti wnd Y tb 8sj {B8}Bt t BP Y R RR trb %st$ry R Bt P RZ Ps{ R $ Bt RZ Ps{ R RZ BZtI I Ak %s{zz8 qy I$R{Bt$tZ$k BP Y tb 8sj {B8}Bt t BP Y j { ${ I$R}js{ 8 t s{ BRR Y j { BI TRZAR s $t Ps{ k$ jir Y RZ Ps{ {Ys I tr$k U w?d ) ; %s{zz8 F w?, (D ; RZAR s F w?, (D3 wned qy j { ${sj ABZtIs k {BtI$$BtR s YsU w;d Y j { ${ }B t$sj $R {Bt$tZBZR % kby wxd Y j { ${ }B t$sj $R {BtRst Bt Y j { BI R *w?, (D ) * z,? ; > z yb1,z Lyb1H, wnd sti Y }B t$sj I$& t{ A b t stk bb j { BI R z sti E 8ZR s b$y Y {B R}BtI$t %Bjs I$& t{ I ht I Ak Y j { ${ -{$s$bt BP Y s sk * z * E ) ~ z ~ E, wnmd wed Y RZ Ps{ {Ys I tr$k 8ZR %st$ry s RZAR s T%s{ZZ8 $t Ps{ R sti wd Y RkR 8 8s$tR {Ys t Z sj qy si$s$bt {BtI$$Bt Rs R YsU wmd sjj t k B $$ts R P B8 Y { krsj RZ Ps{ sti Y j { BI RU Y h jir {sttb Bb Bbs IR F sti t k {sttb A si$s I P B8 Y $tht$$ R B Y RZ Ps{!t{ Y B8 k BP Y j { BI RY %Bjs I$& t{ RstI Y 8s $sjr }s s8 R wy 8sRR I tr$k sti Y {B8}Bt tr BP Y R$&t RR trb }$ 9B j { ${ trb sti } 8$$%$k trb D s R} {$h IY I ht$$bt BP Y } BAj 8 $R {B8}j yt } $t{$}j $ Btjk 8s$tR B RBj% Y h jir ZtI Y TYs 8Bt${ -{$s$bt sti B $t s Y RZ Ps{ {Ys I tr$k B% Y j { BI TRZAR s $t Ps{ B BAs$t Y BR{$jjs$t t {Ys stirzar JZ tjky Ys 8Bt${ si8$st{
TddT n1 WZ8 ${sj 7BjZ$Bt BP Y 3$ ji ejzs$btr *Z B Y 8 {Yst${sj } $BI${$k BP Y s sk sti Y } B} $ R BP Ys 8Bt${ -{$st $BtY {B8}Zs$BtR 8sk A IZ{ I B Btjk Bt P t{ } $BI yt sii$$bty R Z{Z sti Y h jir s %$ Zsjjk sjbskr srrz8 I $t%s $st sjbt rrz{y Ys Y } BAj 8 IZ{ R $tb s bbti$8 tr$btsj Bt W % Y j RRRBj%$t PB Y 8 {Yst${sj sti j { ${sj h jir JZ$ R RB}Y$R${s I tz8 ${sj {Yt$JZ R qy -$RR st $88 tr s8bzt BP j$ sz Bt Y tz8 ${sj s}} Bs{Y R <BbT % b$y$t Y 8BR } %sj t 8 YBIR {Z tjk $t ZR Y h jir $t Y RZAR s s 8BI j I b$y Y ht$ T j 8 t w3ed 8 YBI >xnx;h R}s{ Ys 8Bt${R -}stt R$Bt >xxhp t:r PZt{$Bt {Yt$JZ R >xexh ZR$t Y ABZtIs kt j 8 t 8 YBI w ed >xmx;e(uexhb ABY 3e sti Y R}s{ Ys 8Bt${R -}str$bt >EEH p tt sj$9s$bt BP Y p t:r PZt{$Bt 8 YBIR PB RZAR s R {B% I Ak Y$t hj8r $R R s$ypb bs I >EH *Z B Y js js$% j { BI Y${,t RR R ZR I $t 8BIT t i3 7VG hj RY R RR R $t Y j { BI TRZAR s $t Ps{ 8ZR A sjrb {B8}Z I sy } {$R jk qy 8BR }B}Zjs s}} Bs{Y $R } BAsAjk Y % Rs$j 3e >xnx;x;e(ueneeh sjybzy ABY Y R}s{ Ys 8Bt${ -}str$bt >xxh sti Y tb 8sj 8BI -}str$bt >E;H Ys% sjrb A t }B I V 3e\ etasr I R$8ZjsT B {s}saj BP s$t 8Zj$T j { BI Zt$ } $BIR YsR A t I % jb} I sti t BZRjk 8sI s%s$jsaj B 7VG R s {Y R Ak <sry$8bb >;xh G Ys% PB 8Zjs I sti $8}j 8 t I s 3e\ etasr I 8 YBI PB {B8}Z$t Y Ys 8Bt${ si8$st{ w_s} R y sti yyyd PB st s A$ s k RZAR s { krsj{ krsj {ZstI Y b$iyy${,t RRstI 8s $sj BP Y s} 9B$Isj j { BI RR 3$ nd qy$r {BI PB 8R Y As{,ABt BP Y stsjkr R sti s}}j${s$btr $t _s} R ytyyy z Electrode: FEM model Unit period y T(x), σ(x), Interface Substrate: Green's function formalism + u(x,z) GuT(x-x',z) Guσ (x-x',z) T(x') ( φ(x,z) ) = [ G φ T (x-x',z) Gφ σ(x-x',z) ]( σ(x') )dx' 8 8 - φ n x 3$Z ndu yt 3e\ e 8BI jr Y RZAR s $R I R{ $A I Y BZY Y p t:r PZt{$Bt PB 8sj$R8bY$j Y 8 {Yst${sj h jir $t Y j { BI R s 8BI j I ZR$t Y ht$ T j 8 t 8 YBI w3ed qy RZ Ps{ R RR n x sti Y RZ Ps{ {Ys } R t s Y j { BI TRZAR s $t Ps{ R s{ sr RBZ { R BP Y bs% h jir
Td1T nn 7 Z{Z ]Ys s{ $9s$Bt yt _s} yy $B BZR 3e\ e R$8ZjsB $R 8}jBk I B RZIk j s,k RZ Ps{ T s{bzr${ bs% R wn7vgd Bt Bs I OT{Z N$WA! n sti N$qs! n RZAR s R qy R {Bts$t s b s, AZ tbtt j$$aj RjBb RY s AZj,Ts{BZR${ bs% w77t VGD {B8}BT t tby${y RZjR $t Y s tzs$bt BP Y N7VG qy {BZ}j$t $R R tr$$% B P JZ t{ky { krsj {Z stj sti Y 8s $sj sti I$8 tr$btr BP Y j { BI R $t$8$9$t Y jbrr R BP N7VG RBtsB R $R BP {BtR$I saj {Yt${sj sti {BtB8${sj $8}B st{ 7$t$h{st IZ{$Bt $t Y } B}ss$Bt jbrr Bt N$qs! n bsr s{y$ % I b$y Y I$R{B% k >EMEH Ys Y {BZ}j$t B Y RjBb RY s VGR 8sk A I$8$tT $RY I Ak st B}$8sj {B8A$ts$Bt BP Y { krsj {Z stj sti Y Y${,t RR BP Y sjz8$tz8 j { BI R yt _s} yb Ys% PZ Y RZI$ I Y & { Bt N$qs! n sti I$R{B% I R$8$js B}$8sj { krsj B $ ts$btr Bt N$WA! n yt sii$$bt$ $R I 8BtR s I Ys Y jbrr R IZ B 77T VG si$s$bt 8sk A RZ}} RR I Ak ZR$t % k Y s%k j { BI R qy }Y tb8 tbt $R $jjzr s I $t 3$ n1 yt Y R I %${ b$y Y Y s%$ R j { BI R Y RBtst{ B{{Z R s sabz d1 <9 7$t{ Y$R $R A jbb Y Y RYBjI P JZ t{k ded <9 PB Rkt{Y BtBZR VG t s$bty jbrr R IZ B 77T VG -{$s$bt s RZ}} RR I sti Y I %${ P sz R Y A R JZsj$k Ps{B b$y$t Y -} $8 t VjRB RYBbt s Y R$8Zjs$BtR BP Y R I %${ RBAs$t I b$y Y 3e\ e R$8ZjsB sti Y $tht$ RBtsB 8BI j P B8 ej w1d qy } I${ I P JZ t{$ R sti JZsj$k Ps{B R BP Y RBtst{ R sti st$ RBtst{ R {jbr jk PBjjBb Y -} $T 8 tsjjk BAR % I ti t{$ R BR BP Y 8s$t$t I$R{ }st{$ R 8sk A -}js$t I Ak Y ht$ j ty sti s} Z R sk {s}s{$st{ RstI PsA ${s$bt Bj st{ R qy } I${ I jbrr R {jbr B Y st$ RBtst{ s BB R8sjj 3Z Y 8B Y -} $8 t b$y 0 j { BI Y${,t RR sjrb RYBbR Zt,tBbt $}}j R $t Y si8$st{ sab% Y RBtst{ P JZ t{k <Bb % Y {B8}s $RBt RYBbR Ys Y B% sjj s{{z s{k BP Y R$8ZjsB $R RZ^{$ t PB JZsj$s$% sti % t JZst$s$% R Z{Z {Ys s{ $9s$Bt Y( f ) [1/Ω] 10 0 10-1 10-2 (a) 9% 10-3 850 900 950 1000 1050 1100 f [MHz] 3% 6% Re Y( f ) [1/Ω] 0.03 0.025 0.02 0.015 0.01 0.005 0 850 900 950 1000 1050 1100 f [MHz] 3$Z n1u wyd st$zi sti wkd sj }s BP Y si8$st{ PB R R Z{Z R b$y _b1 )n0 E0stI 0 Y${, sjz8$tz8 j { BI R Bt E; H O T{Z N$WA! n 7Bj$I sti IsRY I {Z % RU -} $8 tsj RZjR sti 3e\ e R$8Zjs$BtR R} {$% jk i R$R$%$k sti s tzs$bt Ys% A t $t BIZ{ I B Y 8BI j }Y tb8 tbjb${sjjk (b) 9% 3% 6%
TdnT *Z B s%s$jsa$j$k sti } ${ R ${$BtRR$8Zjs$BtR s BP t Y Btjk bsk B {Ys s{ $9 t b RZAR s { krsjr sti B $ ts$btr 3B -s8}j Y YsR A t 8Z{Y $t R $t Y { krsj jstsr$ R i P >(H qy s%s$jsa$j$k BP Y 8s $sj $R JZ$ j$8$ I s Y 8B8 taz Y 8s $sjr }s s8 R s,tbbt s{{z s jk tbzy PB } j$8$ts k RZI$ R >d1h yt _s} yy Y 3e\ e R$8T ZjsB $R s}}j$ I B {Ys s{ $9 RZ Ps{ str% R bs% R w7qgrd Bt Bs I OT{Z jstsr$ sr I Bt Y RZjRs 8} sz R tr$$%$k R$8$js B Ys $t JZs 9 sti st j { B8 {Yst${sj {BZ}j$t {B ^{$ t R % sj $8 R Y$Y Yst PB 7qGR Bt 7qT{Z JZs 9 $R -} { I <Bb % $t {BtR sr B 7qG RBtsB R Bt JZs 9YBR Bt jstsr$ s}} s B Ys% -{ jj t 8stZPs{Z sa$j$k n; ]BZ}j$tTBPTBI R _s s8 e- s{$bt V }s ${Zjs jk $8}B st sti I 8stI$t PB 8 BP Y R Z{Z {Ys s{ $9s$Bt $R Y - s{$bt BP Y }s s8 R ZR I $t }Y tb8 tbjb${sj I %${ 8BI jrrz{y sr Y {BZ}j$tTBPT8BI R w]!d PB 8sj$R8 >n1h qy 8BR R s$ypb bs I Y B ${sj s}} Bs{Y $R B I IZ{ Y }s s8 R P B8 Y I$R} R$Bt {Z % R PB RYB IT sti B} tt s$t $ t8bi R yt } $t{$}j Y I$R} R$Bt {Z % R 8sk A PBZtI I$ {jk Ak hti$t Y }Bj R sti 9 BR BP Y Ys 8Bt${ si8$st{ <Bb % $t } s{${ Y$R $R Zts s{$% R$t{ Y $ t8bi R ti B Ys% {B8}j - bs% tz8a R sti Y {Bt$tZs$Bt BP Y Ys 8Bt${ si8$st{ PB {B8}j -T%sjZ I JZ$ R s {Z8A RB8 } B{ IZ >;EH yt Y } B{ IZ RZ R I Ak Yst sj >ndh Y {Bt $AZ$Bt BP Y RYB T {$ {Z$ I $ t8bi R B Y Ys 8Bt${ si8$st{ $R I { $A I b$y s R$8}j }s s8 T $9 I 8BI j qy I$R} R$Bt {Z % R s BAs$t I $ti$ {jk Ak h$t Y }s s8 T $9 I 8BI j B Y $B BZRjk {B8}Z I Ys 8Bt${ si8$st{ s s{y P JZ t{k BP $t R ]BtR JZ tjkzr$t s {B8}j -T%sjZ I $R s%b$i I <Bb % Y 8 YBI JZ$ R JZ$ $t tr$% {B8}Zs$Bt sti $ $R,tBbt >;MH B Zt $tb I$^{Zj$ R PB N7VGR by t Y RZ Ps{ TR,$88$t AZj, bs% R w77 GRD {Bt $AZ R Btjk B Y Ys 8Bt${ si8$st{ B $t s{ b$y Y N7VG >nh yt _s} yyyb $t BIZ{ s t b } B{ IZ PB Y PsR - s{$bt BP ]! }st s8 R P B8 $B BZR R$8Zjs$BtR PB 7VGR sti N7VGR $t A$ {$Btsj R Z{Z R yt Y$R s}} Bs{YY Ys 8Bt${ si8$st{ PB (3x $R I R{ $A I b$y$t Y ]! PB 8sj$R8 qy PBjjBb$t -} RR$BtBP Y PB 8 BP ej w1d8sk A I $% IU KV ]! w ) dlr W 1,W ) 7g R$t{wRD ƒ B{wWDR 1 1, /R/ (3 wnd ƒ R{wWDR 1 1 < R 8 srz R Y I %$s$bt BP P B8 Y %sjz (xy {s}s{$st{ } j { BI }s$ g $R s ]! }s s8 sti ƒ B{ sti ƒ R{ s tb 8sj$9 I bs% tz8a R PB $ t8bi R BP B} tt{$ {Z$ I sti RYB T{$ {Z$ I j { BI s skr R} {$% jk yt Y ]! 8BI jy I$R} R$Bt js$bt PB s RYB T{$ {Z$ I s sk $R BP Y PB 8 > ƒ R{ wwd ) : w W N 1 W 1 X ~ 1 8 d 7 y // 3 wnd(d $ $
Td;T < 8 $R bs% % jb{$ky {BZ}j$t {B ^{$ t 8 srz R 4 {$%$k } Zt$ j tysti Y }s s8 y I R{ $A R }Y tb8 tbjb${sj s tzs$bt V R$8$js T RZj $R BAs$t I PB st B} tt{$ {Z$ I s$t AZ Y }s s8 R s b s,jk P JZ t{k I } ti t >;1H yt Zt$I$ {$Btsj R Z{Z RY I R BP Y RB}AstIR PB RYB I sti B} t s skr s R} {$% jk 8st$P R I sr bb RBtst{ R sti st$ RBtst{ R $t Y si8$st{ BP st $tht$ striz{ < t{ Y I R BP Y RB}AstIR 8sk A I 8$t I P B8 Y PZt{$Bt K V w(3x,wdr i P >;H <Bb % $t A$I$ {$Btsj R Z{Z R Y RB}AstIR PB B} t sti RYB I s$tr Ys% Bt {B$t{$I$t I >xhrz{y Ys Bt }Bj sti Bt 9 B $t Y si8$st{ {st{ j s{y BY sti 8B $tpb 8s$Bt $R JZ$ I B I 8$t Y ]! }s s8 R yt Y - s{$bt } B{ IZ I R{ $A I $t _s} yyyy P JZ t{k {B R}BtI$t B Y {B$t{$I$t I BP Y RB}AstIR $R jb{s I b$y s R} {$sjjk {BtR Z{ I }YsR T RY$P sjb $Y8 3 B8 ej wnd $ PBjjBbR Ys$tB $t Y R$t{TPs{B Y I$R} R$Bt js$bt 8sk A -} RR I YBZY Y Ys 8Bt${ si8$st{ sr PBjjBbRU ƒ 1 R{wWD R 1 V K w(3xwdlrd,wd 7g KV w(3xwdlrd,wd V K, R (3 wnddd w(3x,wd VR $t Yst:R sjb $Y8Y - tr$bt BP Y Ys 8Bt${ si8$st{ PB {B8}j -T %sjz I $R s%b$i I 7$t{ Y PZt{$Bt t IR B A %sjzs I PB Btjk bb sj %sjz R BP s s{y P JZ t{ky } B{ IZ $R tz8 ${sjjk % k ^{$ t qy } ${ B }sk $R Ys Y I$R} R$Bt js$bt $R {BtR s$t I B Y PB 8 BP ej wnd(d 7$t{ ej wnd $R s{{z s b$y$t Y ]! PB 8sj$R8Y } B{ IZ sjrb R % R sr s R PB Y %sj$i$k BP Y ]! Y B k yp Y } B{ IZ Ps$jRY 8BI j IB R tb I T R{ $A Y R Z{Z b$y RZ^{$ t } {$R$Bt 3B iskj $YTk} RZ Ps{ Ts{BZR${ bs% R $t s ts Bb P JZ t{k st {jbr B Y RB}AstIY ]! Y B k sti ej wnd ZRZsjjk s}}jk b jj <Bb % I$^{Zj$ R s t{bzt I b$y N7VGR Bt Bs I OT{Z N$WA! n sti$t }s ${Zjs N$qs! n!b$t B Y $t s{$bt b$y PsRTRY s AZj,Ts{BZR${ bs% R Y N7VGR BP t P sz R Bt I$R} R$Bt R} {$sjjk $t Y s tzs$bt sti Y j { B8 {Yst${sj {BZ}j$t {B ^{$ t qy R Bt Y I$R{ }st{$ R A b t Y ]! 8BI j sti Y $B BZR R$8Zjs$BtY Ys I $ $R B hti st B}$8sj R BP }s s8 R yt Y }YsR TRY$P sjb $Y8 $ $R srrz8 I Ys Y }s s8 R s {BtRst sti Ys Y 8s$t$t si8$st{ 8sk A t$ jk I R{ $A I Ak s Rs${ {s}s{$st{ V P JZ tt {$ R A jbb Y Y RYBjI PB 37T VG t s$bty sjb $Y8 ZRZsjjk bb,r AZ Y I$R{ }st{$ R A b t Y R$8Zjs$Bt sti Y 8BI j RjBbjk $t{ sr b$y P JZ t{k qy BtR BP Y Rkt{Y BtBZR VG si$s$bt {szr R Y }YsR TRY$P sjb $Y8 B ZT jk Ps$j 3B Zts jkpb Y j { BI Y${,t RR R _b1 ); M0{Z tjk ZR I $t i3 7VG AstI}sRR hj RY$R Y RYBjI YsR s RZ^{$ tjk Y$Y P JZ t{k RZ{Y Ys Y I R BP Y RB}AstIR 8sk A I 8$t I qy I % jb}8 t BP s }Y tb8 tbjb${sj PB 8sj$R8 8B s}}j${saj B Rkt{Y BtBZR RBtsB R 8}jBk$t N7VGR Bt Bs I OT{Z N$qs! n $R Y B}${ BP _s} yz I$R{ZRR I $t 7 { ;
TdxT ; BI jpb 7Y s <B $9BtsjGs% R qy {BZ}j$tTBPT8BI R 8BI j YsR A t 8s,sAjk RZ{{ RRPZj $t I R{ $A$t I %${ R AsR I Bt {Bt% t$btsj iskj $YTk} RZ Ps{ s{bzr${ bs% RRZARst$sjjk RjBb Yst AZj,Ts{BZR${ bs% R sti b$y 8s$tjk Rs$sj }Bjs $9s$Bt <Bb % Y 8BI j $R {BtR$I sajk j RR si JZs PB IB8$tstjk RY s YB $9Btsj RZ Ps{ Ts{BZR${ bs% R w7<t7vgrdrz{y sr RZ Ps{ str% R bs% R w7qgrdsti j s,k RZ Ps{ Ts{BZR${ bs% R wn7vgrd Bt Bs I OT{Z N$WA! n sti N$qs! n V}} Bs{Y R B I R{ $A RY s TYB $9Btsj bs% R k}${sjjk {BtR$I 7qG } B}ss$Bt $t s } $BI${ s$t Bt s JZs 9 RZAR s sti Z$j$9 Y 3jBJZ -}str$bt sti s}} B-$8s ABZtIs k {BtI$$BtR RZ{Y sr Y *sst<ztr$t ABZtIs k {BtI$$BtR >EHR i PR >MH *st${,$ >H I $% I s }Y tb8 tbjb${sj 8BI j PB Y Ys 8Bt${ si8$st{ qy {Ys s{ $R${R BP Y 7<T7VG } B}ss$Bt $t s } $BI${ s$t s b jj I R{ $A I Ak s }Y tb8 tbjb${sj 8BI j IZ B _j RR,k >M(H %$ b I A jbb yt _s} yz b Ys% - ti I _j RR,k:R I$R} R$Bt 8BI j PB Y -{$s$bt BP 7<T7VGR $t ht$ j { BI R Z{Z RYZR BAs$t$t s 8BI j PB Rkt{Y BtBZR 7<T7VG RBtsB R ;d _ B}ss$Bt $t Y _ $BI${ ej { ${ V sk V {Ys s{ $R${ BP RY s YB $9Btsj RZ Ps{ Ts{BZR${ bs% R $R Ys Y $ % jb{$k $R {jbr B Ys BP PsR RY s AZj,Ts{BZR${ bs% R w37t VGRD 7<T7VGR 8sk A $t T } I sr 37T VGR jb{sj$9 I B Y RZ Ps{ Ak RB8 }YkR${sj 8 {Yst$R8RZ{Y sr st $t s{$bt b$y Y j { ${ h jir $t }$ 9B j { ${ RZAR s R w j ZR $ttpzjks % bs% R >MdHN7VGR $t N$WA! n >M1H sti N$qs! n >MnHD8sRR jbsi$t wnb% bs% R >M;HD B jbsi$t Ak } $BI${ j { BI R Z{Z R w7qgr >MxMEHD qy jb{sj$9s$bt I }Y BP Y 7<T7VG $R I 8$t I Ak Y R8sjj I$& t{ $t Y % jb{$$ R BP Y RZ Ps{ sti AZj, bs% RstI w$t {Bt sr B iskj $Y bs% RD $ R Btjk I } tir Bt Y R ty BP Y RZ Ps{ } Z As$Bt yt I %${ R 8}jBk$t 7<T7VGR Y$R 8sk RZj $t R Bt I$R} R$Bt sti R{s $t $tb 37T VGRRB8 $8 R {sjj I 7VGT VG $t s{$btr sti $t s }s sr$${ -{$s$bt BP Y 37T VGR ]BtR$I Y R Z{Z $t 3$ 1d yt _j RR,k:R I$R} R$Bt 8BI j >M(H Y 7<T 7VG $ t8bi R BP Y } $BI${ s$t s RBZY b$y$t Y {BZ}j$tTBPT8BI R s}} B-$8s$Bt$t Y PB 8 `w?, FD ) `L 7<? LF L ` 7wdD<? F 3 w;dd < Y I ht$$btr s sr $t 3$ 1dstI `L sti ` } R t Y s8}j$zi R BP Y $t{$i t sti 4 { I bs% R R} {$% jk< ) 1$b $R Y s$t bs% tz8a sti ) wd L RDb1 $R Y tb 8sj$9 I bs% tz8a BP Y $t{$i t bs% qy Ps{B R
TdET I R{ $A Y jb{sj$9s$bt BP Y bs% B Y RZ Ps{ U w< W 1 ) wd RD 1 1 > 1 3 w;1d < > ) b8 sti 8 I tb R Y % jb{$k BP Y 37T VG qy VG RjBbt RR {Z % R $R srrz8 I $RB B}${ $t Y?FT}jst qy {Zj$t PB Y RJZs BB $t ej w;1d $R {YBR t RZ{Y Ys Y RZ Ps{ Tk} bs% R I {sk sti Y AZj,Tk} bs% R } B}ss sr F 3B j ZR $ttpzjks % bs% R } B}ss$t Bt s 8 sjj$9 I RZ Ps{ b$y s } $BI${ 8sRR I tr$kabztis k {BtI$$BtR $t Y PB 8 T X < L ( z Z > 1 < 1 wdlrd 1 ( X < ( 1 wdrd 1 > 1 ( < ~ `L )1 d > 1 ~ ` )1 d > 1 < `, < `L3 w;nd 8sk A I $% I >MH < ( $R Y }$ 9B j { ${ {BZ}j$t {BtRst sti Y }s s8 R ( sti d I R{ $A Y Zt$PB 8 8sRR jbsi$t sti Y {BZ}j$t A b t Y {BZt T } B}ss$t bs% R R} {$% jk qy I$R} R$Bt JZs$Bt $R BAs$t I Ak R $t Y I 8$tst > ;w,wd) X 1 > L ( <1 ( ~X ( wdd<1 ( ~;/ 1 d / 1 >; w;;d < < < 1 B%st$RYVts}} B-$8s RBjZ$Bt$t{jBR IPB 8$RI $% I$ti P>M(H qy -s{ RBjZ$Bt 8sk A PBZtI Ak {Bt% $t Y I$R} R$Bt JZs$Bt $tb s JZs ${ }BjktB8$sj sti hti$t Y BBR BP Y }BjktB8$sj < t{ Y I$R} R$Bt $R $t } $t{$}j s%s$jsaj $t {jbr I PB 8 AZBb$t B Y j ty BP Y RZj$t -} RR$BtRY -s{ s}} Bs{Y $R } s{${sj PB tz8 ${sj %sjzs$bt Btjk G$Y Y } $BI${ jbsi $t } I sr st & {$% I R{ $}$Bt BP st j { BI s sk Y I$R} R$Bt js$bt BAs$t I R % R sr s 8BI j PB Y 7<T7VG } B}ss$Bt $t s } $BI${ s$tr 3$ ;d 3B P JZ t{$ R Ps A jbb Y AZj,Tbs% Y RYBjI W ) 8 b1 Y $ t8bi {Ys s{ $R${R s R$8$js B YBR BP iskj $YTk} RZ Ps{ T s{bzr${ bs% R $t } $BI${ s$tr <Bb % Y jb{sj$9s$bt I }Y BP Y bs% BbR w I { sr D b$y $t{ sr$t P JZ t{k Zt$j Y 4 { I bs% A {B8 R t$ jk I jb{sj$9 IU $ $R {Bt% I $tb s AZj, bs% sti si$s I $tb Y RZAR s qy$r R{s $t BP Y 7<T7VG $tb VGR RZjR $t } BtBZt{ I s tzs$bt BP Y $t{$i t bs% stisr $jjzr s I $t 3$ ;d$ 8sk {szr s } 8sZ {Bjjs}R BP Y RB}AstI 3B N7VGR $t N$WA! n Y jb{sj$9s$bt I }Y $R I 8$t I Ak Y Y$Y }$ 9BT {BZ}j$t sti Y RB}AstI $R b jj R }s s I P B8 P JZ t{k $Bt b$y AZj,Tbs% t s$bt <Bb % PB N7VGR $t N$qs! n Y Z}} I BP Y RB}AstI 8sk - ti {jbr B Y AZj,Tbs% Y RYBjIstI PB 7qGR $t JZs 9 $ 8sk % t -{ I $ ]BtR JZ tjk % t R8sjj {Yst R $t Y % jb{$k $tr$i Y RB}AstI RZj $t s R Bt {Yst BP Y jb{sj$9s$bt I }Y
TdT 0.54 0.02 0.52 0.01 Re γ sc ( f ) 0.5 0.48 0-0.01 Im γ sc ( f ) 0.46-0.02 0.44 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04-0.03 f 2p / v B 3$Z ;du *$R} R$Bt {Z % R PB 7<T7VGR $t } $BI${ s$tr sr PZt{$BtR BP Y tb 8sj$9 I P JZ t{kb$y }s s8 R I 8$t I B k$ ji {B$t{$I$t I R BP Y RB}AstI 7{s $t $tb VGR A $tr s Y P JZ t{k W { sti {szr R s {BjT js}r BP Y RB}AstI 7Bj$I {Z % RU ( )(1E ( )(sti d )(dn *sry I {Z % RU ( )( ( )(1xstI d )(ded *srytib I {Z % RU Y s}} B-$8s RBjZ$Bt P B8 i P >M(H f c ;1 VAABT<sRY$8BB ]BZ}j$tTBPTBI R BI j VAAB sti <sry$8bb RZ{{ I I $t {B8A$t$t Y s}} B-$8s {jbr ITPB 8 I$R} T R$Bt js$bt b$y Y ]! P s8 bb, >MMMH qy $ {BtR Z{$Bt $R A $jj$st $t Ys Y ]! PB 8sj$R8} B%$I$t {jbr ITPB 8 PB 8ZjsR PB Y {B8}Bt tr BP Y _T8s $-8sk A ZR I stir$8zjst BZRjkY 7<T7VG I$R} R$Bt {Ys s{ $R${R s si JZs jk I R{ $A I <Bb % s P b } BAj 8R 8s$t tb RBj% I qy s}} B-$8s I$R} R$Bt js$bt sr Y Zt} Z A I bs% R sr RZ Ps{ T R,$88$t AZj, bs% R w77 GD qy$r s}} B-$8s$Bt YBjIR Btjk $P Y }$ 9B j { ${ {BZ}j$t sti Zt$PB 8 jbsi$t 8s$t R8sjj W s Y RB}AstI Y jb{sj$9s$bt I }Y $R I 8$t I Ak Y s 4 {$BtRAZ PB js P JZ t{k I Zt$tR % t s b s, Zt$PB 8 jbsi 8sk jb{sj$9 Y 77 G qy$r {szr R s 8$tB AZ RkR 8s${ B $t Y % jb{$kr 3$ ;d qy I$R{ }st{k YsR A t % $h I AsR I Bt tz8 ${sj R$8Zjs$BtRstI s {B {$Bt {BtRst B A $t{jzi I $tb Y Y B k YsR A t RZT R I >M(H *Z B {Yst R $t Y jb{sj$9s$bt BP Y {BZt } B}ss$t {B8}Bt tr BP Y $ t8bi R sr PZt{$BtR BP P JZ t{ky tb 8sj$9s$Bt BP Y bs% s8}j$zi R $R I$PT h{zj qy I$ { -{$s$bt BP AZj,Ts{BZR${ bs% R $R t$ jk $tb I ]BtR JZ t{ jk Y I R{ $}$Bt BP Y j { B8 {Yst${sj {BZ}j$t $R ZtRs$RPs{B k >Md1H
TdMT 3$tsjjksjYBZY Y Y B k I R{ $A R Y R{s $t BP Y 7<T7VG $tb AZj, bs% R $t s } $BI${ s$ty sii$$btsj 8BI {Bt% R$Bt B{{Z $t s I$R{Bt$T tz$$ RRZ{Y sr s}r >(H sti Y I R BP Y R Z{Z $R tb s, t $tb s{{bzt qy 8BI {Bt% R$Bt $R R} {$sjjk R Bt PB 7qGR R$t{ Y R Z{Z BP Y bs% $tr$i Y j { BI s$t sti Bt s P B 8 sjj$9 I RZ Ps{ {st A {BtR$I sajk I$& tvrb8 $8 R s 7qG IB R tb % t -$R Bt s P RZ Ps{ ;n _Y tb8 tbjb${sj i RBtsB BI j yt _s} yzb Ys% {BtR Z{ I s }Y tb8 tbjb${sj 8BI j PB Rkt{Y BtBZR RT BtsB R 8}jBk$t 7<T7VGR qy s}} Bs{Y $R AsR I Bt - ti$t _j RR,k:R I$RT } R$Bt 8BI j PB Y -{$s$bt BP 7<T7VGR $t ht$ j { BI R Z{Z R G$Y RB8 bys Y$Y {B8}Zs$Btsj {BR$ $ty tjk {B} R b$y 8BR BP Y I$^{Zj$ R I$R{ZRR I sab% qy } $t{$}sj {BtR$Z tr BP Y Y B k s Y }Y tb8 tbjb${sj R{sjs p t:r PZt{$Bt tw?dby${y js R Y R{sjs I$R}js{ 8 t h ji Bt Y RZ Ps{ `w?d B Y R{sjs RZ Ps{ R RR h ji x w?d %$s `w?d ) 8 L sti Y }Y tb8 tbjb${sj ABZtIs k {BtI$$Bt tw?? I Dx w? I DQ? I, x w?d ) '_w?d 1`w?D L Cw?D3 w;xd w;ed < '_w?d $R & {$% 8sRR I tr$k Bt Y RZ Ps{ by$j Cw?D $R s RBZ { 8 R}BtR$Aj PB Y -{$s$bt BP Y s{bzr${ h jir ]BtR$R t{k b$y ej w;nd JZ$ R s p t:r PZt{$Bt BP Y PB 8 Ktw#D ) sti st & {$% 8sRR I tr$k '_w?d ) 1 w <8 1 ( L1/ d / {BRw<?L D } # 1 > 1 ( # wld ] d, w;d W w] 1/?/D 3 w;md VAB% # wld I tb R # b$y Y R$t BP Y sj }s {YBR t }BR$$% sti $R Y }YsR BP Y }s s8 d Y }YsR I 8$t R Y jb{s$bt BP Y 4 {$%$k { t $tr$i s{y } $BI w?d $R Y < s%$r$i R } PZt{$Bt sti ] $R Y tz8a BP } $BIR $t Y s sk yt Y j$8$ BP st $tht$ s$t w] DPZjj JZ$%sj t{ b$y _j RR,k:R 8BI j $R BAs$t I Ak B8$$t Y RBZ { 8 Cw?D qb I R{ $A j { ${ -{$s$bt sti {Z t t s$bts ht$ RBZ { 8 $R sjjbb I sti s{bzr${ {Z tr } B}B $Btsj B Y I$R}js{ 8 t s Y j { BI { t R s srrz8 I yt BIZ{$t st -{$s$bt 8 BP Y Ys 8Bt${ PB 8st stsjk${ 8BI j PB Y Ys 8Bt${ si8$st{ 8sk A BAs$t IU KV 7< w,wd ) 7gwD ; B{w,WD ; R{ w,wd 3 w;d
TdT < Y PZt{$Bt gwd I R{ $A R Y RjBbjk %s k$t {s}s{$$% {Bt $AZ$Bt B Y Ys 8Bt${ si8$st{ by$j Y I$R} R$Bt PZt{$BtR ; B{ sti ; R{ s BP Y PB 8 BP ej w;;d qy I$R} R$Bt JZs$BtR PB B} tt{$ {Z$ I sti RYB T{$ {Z$ I s skr s BAs$t I Ak R $t Y R} {$% I$R} R$Bt PZt{$BtR JZsj B 9 B V 8BI j PB s ht$ Rkt{Y BtBZR RBtsB $R BAs$t I Ak j$8$$t Y -{$s$bt B ] } j { BI }s$ R sti Ak R $t ] )1w] L] } DbY ] $R Y tz8a BP j { BI R $t s{y 4 {B R 3$ ;1 qy$r RZjR $t st $t sj JZs$Bt PB Y RZ Ps{ R RR s sy R$8$js 8 YBI YsR A t ZR I s j$ Ak itt,j $% >nh G$Y {B8}j -Tstsjk${ {Yt$JZ RY RBjZ$Bt $R PBZtI B {BtR$R BP Y RBjZ$Bt PB Y {B R}BtI$t $tht$ Bt T}B RBtsB sti BP 8R I R{ $A$t Y 4 {T $BtR sti 8BI {Bt% R$Bt B{{Z $t s Y 4 {B I R e%sjzs$t Y 4 { I AZj,Ts{BZR${ bs% R b$y Y R } R I R{ t 8 YBIs}} B-$8s RZ Ps{ R RR $t sj A s${ PB 8 $R PBZtI qy RZj $t ej w;d sjjbbr Y - s{$bt BP Y }s s8 R BP Y Y B k P B8 $B BZR 3e\ e R$8Zjs$BtR qy I 8$ts$Bt BP Y }s s8 ( $R RB8 bys {Bt si${b ku A R$I R $t4z t{$t Y $ t8bi R $tr$i s s$t$ sjrb I R{ $A R Y 7<T7VG {Ys s{ $R${R BZR$I Y R Z{Z wk}${sjjkbt P B 8 sjj$9 I { krsj RZ Ps{ D ]BtR JZ tjk$ RYBZjI sjrb 4 { Y 8BI {Bt% R$Bt B{{Z $t s Y I R BP s ht$ R Z{Z V{{B I$t B Y$R srbt$tbb R }s s }s s8 R ( RYBZjI A $t{b }B s I $tb Y 8BI ju Bt $t Y p t:r PZt{$Bt B I R{ $A Y RZ Ps{ BZR$I Y I %${ Y BY Bt $t Y ABZtIs k {BtI$$Bt B I R{ $A Y s$tvaz Y$R YsR tb A t IBt b$y$t Y$R bb, VhBPY 8BI j $tejw;d B $B BZR {B8}Z I Ys 8Bt${ si8$st{ Bt ;1 H O T{Z N$qs! n $R I$R}jsk I $t 3$ ;nwyd V Rs$RPs{B k JZst$s$% s 8 t $R s{y IsjYBZY RB8 I$R{ }st{$ R 8sk sjrb A BAR % I 7$t{ Y bs% Bt Y$R {Z $R tb t$ jk 7<T7VG AZ N7VGY 8BI j B% R$8s R Y si$s$bt BP PsRTRY s AZj,Ts{BZR${ bs% R s P JZ t{$ R {jbr B sti sab% Y Y RYBjI W qy -{$s$bt BP RjBb RY s AZj,Ts{BZR${ bs% R R}BtR$Aj PB Y jbrr R s jbb P JZ t{$ R sti {j s jk tbtt j$$aj $t Y RB}AstI P JZ t{$ R$R tb PZjjk {B% I Ak Y 8BI j VR s {BtR JZ t{ Y } I${ I st$ RBtst{ sti Y } s, s Y Z}} I BP Y RB}AstI s Ps BB RYs } λ 0 =2p W V N gp Npλ 0 N g p 3$Z ;1U 7{Y 8s${sj Rkt{Y BtBZR RBtsB
T1(T ~ Y(γ = 0.499,f) [1/Ω] 0.20 0.15 0.10 0.05 0 (a) Re Im -0.05 0.90 0.92 0.94 0.96 0.98 1.00 1.02 f 2p/v B Re Im 0.9280 0.9285 0.9290 Y( f ) [1/Ω] 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 (b) Im 0.4 Im 0.2 Re 0-0.2 480 490 500 Re 0 440 460 480 500 520 540 560 f [MHz] 3$Z ;nu ]B8}s $RBt BP Y 8BI j wisry I {Z % RD B wrbj$i {Z % RUD wyd Y Ys 8Bt${ si8$st{ K V w(3;,wd sti wkd Y 8 srz I R}BtR BP s R RBtsB < _b ( )M0 yb )(EstI Y RZAR s $R ;1 H O T{Z N$qs! n yt Y R RT BtsB ); 8 ] } )x ] )n sti G)dE ( V R$8Zjs I RBtsB R}BtR $R {B8}s I B s R R Z{Z 8 srz 8 t >;H $t 3$ ;nwkd _Y tb8 tbjb${sj s tzs$bts R $ R R$Rst{ BP d; sti RB8 sit I$$Btsj {s}s{$st{ b $t BIZ{ I B Y 8BI jaz BY b$r Y }s s8 R s YBR I IZ{ I P B8 Y 3e\ e R$8Zjs$Bt qy RBtst{ P JZ t{k $R Rj$Yjk RY$P I sti Y $R R8sjj B $t Y I$R} R$Bt {Ys s{ $R${R qy R & {R 8sk A -}js$t I Ak bs% Z$I$t sti I %$s$btr $t Y I %${ B8 k <Bb % Y s{y$ % I B% sjj s{{z s{k -{ IR Ys BP {Bt% t$btsj ]! Y B k R} {$sjjk {BtT { t$t Y RYs} BP Y RBtst{ VR -} { I AsR I Bt 3$ ;nwydy } I${ I jbrr R s Y RB}AstI s RB8 bys BB jbb sti Y VG si$s$bt s Y$Y P JZ tt {$ R $R B% R$8s I <Bb % Y -} $8 tsj {Z % sjrb P sz R st Zt -} { I $t{ sr $t Y {BtIZ{st{ $t Y YR BP Y RBtst{ qy 8 {Yst$R8 ZtI jk$t Y js I jbrr RvN7VG si$s$bt B Y AZRAs R BP Y RBtsB v$r Y B}${ BP _s} R z sti zyi$r{zrr I $t 7 { x
T1dT x V{BZR${ NBRR R $t N s,k 7VG i RBtsB R Bt N$qs! n N s,k RZ Ps{ Ts{BZR${ bs% RBtsB R Bt Bs I OT{Z N$qs! n RZAR s R P sz R Btjk P JZ t{kti } ti t jbrr RsR {st A t R t $t 3$ ;n qy R j si B I $B s$bt $t Y hj } PB 8st{ sti JZ$ {B {$BtR $t I %${ I R$t >xh VjYBZY Y {Bt $AZ$BtR BP }Y tb8 ts RZ{Y sr Y As{,R{s $t $tb 37T VGR sti Y Rkt{Y BtBZR VG -{$s$bt B Y jbrr R Ys% A t RZI$ I >nhy j s,s 8 {Yst$R8R $t N7VG RBtsB R Ys% 8s$t I b s,jk ZtI RBBI i { tjkjsr T$t P B8 ${ 8 srz 8 tr Ak tzz$js sj % sj I Ys s{bzr${ bs% R s {s}saj BP R{s}$t Y RBtsB s s Y BZY Y AZRAs R >EH yt _s} z BP Y$R bb,y R{s}$t s{bzr${ A s8r Ys% A t $I t$h I sr N7VG si$s$bt sti Y $ {Ys s{ $R${ P sz R Ys% A t JZsj$s$% jk -}js$t I AsR I Bt Y { krsjj$t st$rb B}k BP Y j$y$z8 stsjs RZAR s 3Z Y 8B $t _s} zy b Ys% JZst$s$% jk stsjk9 I Y P JZ t{kti } ti t{ BP Y si$s$bt sti R$8s I Y s{bzr${ jbrr R IZ B Y & { sr b jj sr YBR IZ B N7VG } B}ss$Bt jbrr RN7VG As{,R{s $t $tb 37T VGRstI Y 37T VG -{$s$bt qy stsjkr$r $R AsR I Bt Y $tht$ } $BI${ s$t b$y s ht$ s} Z $jjzr s I $t 3$ xd *Z B Y Y$Y st$rb B}k BP Y N7VG RjBbt RR {Z % R Bt Bs I OT{Z N$qs! n RZAR s R{Bt% t$btsj R{sjs bs% Z$I Y B $ R AsR IPB -s8}j Bt Y }s s-t $sj s}} B-$8s$Bt >nmh s ZtRZ$sAj PB N7VG I %${ R yt _s} zys R 8$T }Y tb8 tbjb${sjr 8$T 8}$ ${sj 8BI j $R {BtR Z{ I PB Y Ys 8Bt${ si8$st{ BP Y $tht$ j { BI s sk b$y s ht$ s} Z qy 8BI j 8sk A {BtR$I I sr s bbti$8 tr$btsj - tr$bt BP Y 7<T7VG RBtsB 8BI j $t _s} yz Vt sj T A s${ p t:r PZt{$Bt tw?, rd $R 8}$ ${sjjk {BtR Z{ I RZ{Y Ys Y RjBbt RR {Z % R PB N7VGR ZtI Zt$PB 8 8 sjj$9s$bt Bt N$qs! n s } BIZ{ I Ak Y B k b$y s srbtsaj s{{z s{k qy -{$s$bt BP PsRTRY s VGR $R $ty tjk $t{jzi IAZ y W z X p W a 3$Z xdu _ $BI${ j { BI s sk b$y $tht$ AZRAs R
T11T Y RjBbTRY s VG {Bt $AZ$Bt $R s{{bzt I PB Btjk $t Y } B}ss$Bt jbrr BP Y N7VG 7Bj%$t Y 8BI j tz8 ${sjjk sti s}}jk$t Y stsjkr$r {Yt$JZ R %$ b I $t 7 { 1Y I$R}js{ 8 t h jir sti Y j { ${ si8$st{ $t st $tht$ RBtsB 8sk A {B8}Z I tsaj$t JZst$s$% stsjkr$r BP Y j s,s 8 {Yst$R8R xd V{BZR${ N s,s {Yst$R8R NsR T$t P B8 ${ R{stR BP Y s{bzr${ h ji $t Rkt{Y BtBZR RBtsB R Bt ne H O T N$qs! n % sj R Btjk P JZ t{kti } ti t s{bzr${ si$s$bt B Y AZRAs R BP Y R Z{Z sr RYBbt Ak Y R $ R BP $8s R $t 3$ x1 yt _s} z Y }Y tb8 tbt $R JZsj$s$% jk -}js$t I AsR I Bt Y RjBbt RR {Z % R sti Y }Bjs $9s$Bt PB N7VGR Bt Zt$PB 8jk 8 sjj$9 I N$qs! n RZ Ps{ yt Y RB}AstI Y s{bzr${ h ji $t Y s$t s s $R B% t I Ak Y s 4 {$BtR V { s$t P JZ t{$ R Y AZRAs R wby${y 8sk A {BtR$I I sr 8 sjj$9 I { krsj RZ Ps{ D RZ}}B N7VG $ t8bi R by${y s Rkt{Y BtBZRjk {BZ}j I B Y s{bzr${ h ji $t Y s$t N s,k bs% Z$I 8BI R Ys% A t RZI$ I s j$ Bt dd1 H TN$qs! n >MH stibt7qt{zjzs 9>d((H V I s$j I stsjkr$r BP 8sRRTjBsI I RjBbt RR {Z % R $t _s} zy {Bth 8R Ys Y } I${ I P JZ t{kti } ti t{ BP Y si$s$bt {jbr jk 8s{Y R ABY b$y Y jsr T$t P B8 ${ R{stR sti b$y Y j { ${sj 8 srz 8 tr 3Z Y 8B Y P JZ t{$ R 8BR } Bt B Y si$s$bt I } ti Btjk Bt Y js$% 8 sjj$9s$bt Y${,t RR *Z B Y st$rb B}k BP Y RZAR s { krsjy I { I si$s$bt $R R}s$sjjk srk88 ${ VjYBZY Y N7VG RjBbt RR {Z % R s Rk88 ${ sabz Y { krsj Ts-$RY }Bjs $9s$Bt $R tb qy srk88 k $R }s ${Zjs jk R Bt PB Y b s, RY s % ${sj {B8}Bt t by${y Y $t P B8 I {R yti I8 srz 8 tr Ys% {Bth 8 I Ys Y Ps%BZ I I$ {$Bt BP Y si$s$bt $R $ti } ti t BP Y }Bjs $k BP Y j { ${ I $% <Bb % s{{b I$t B BZ {B8}Zs$BtR Y IB8$tst RY s YB $9Btsj {B8}Bt t $R sj8br Rk88 ${ qy$r RZ RR YsI R}$ Y } BA $8s RN7VGR s s{zsjjk si$s I B Y AZRAs R sj8br Rk88 ${sjjk 3$Z xn $jjzr s R Y R$8Zjs I I$R}js{ 8 t } Bhj R BAs$t I P B8 Y $tht$ RBtsB 8BI j $t _s} zy yt {BtR sr B Y jsr T$t P B8 ${ R{stR 8 srz $t Y RY s % ${sj {B8}Bt ty R{sjs I$R}js{ 8 t h ji s I Ak Y 8BI j $R $t } I B I R{ $A Y IB8$tst RY s YB $9Btsj {B8}Bt t sti $ $R srrz8 I Rk88 ${ *Z B Y ht$ R$9 BP Y R RBtsB I$& t{ R s R t $t Y j s,s Y BZY Y 4 {B R <Bb % s {jbr R$8$js $k $R BAR % I A b t Y 8 srz I sti 8BI j I s8}j$zi I$R $AZ$BtR sti$t }s ${Zjs $t Y si$s$bt j s,$t B Y AZRAs R yt sii$$bt B N7VGRsjRB iskj $Y bs% R 8sk A si$s I Rkt{Y BtBZRjk B Y AZRAs R BY Rkt{Y BtBZR sti str% Rsjjk -{$ I iskj $Y bs% R s BAT R % I $t Y jsr T$t P B8 ${ R{stR }B I $t _s} zyaz Y k s j$, jk B A sy b s,!y s{bzr${ j s,s 8 {Yst$R8R $t{jzi Y si$s$bt BP AZj,T s{bzr${ bs% RbY${Y s $t } I B k$ ji Y b s, s{bzr${ As{, BZtI %$R$Aj $t Y R{stR
T 1n T (a) 891 MHz (b) 904 MHz (c) 907 MHz (d) 911 MHz (e) 917 MHz ( f ) 934 MHz (g) 949 MHz 3$ Z x 1U e-} $8 t sj RY s % ${sj I$R}js{ 8 t } Bhj R 8 srz I b$ Y s jsr } BA P s Z $t N7VG si$s $Bt B Y AZRAs R $t s R RBts B Bt neh O T{Z N$qs!n jbb Y RBtst{ P JZ t{k wy, KD Y si$s $Bt $R b s, AZ R Bt st I$s $Bt B{{Z R Rj$ Y jk sab% Y RBtst{ w, QD qbbs IR s JZ t{y$t P JZ t{k BP sabz d <9 Y si$s $Bt I$8$t$RY R w D sti %$ Zsjjk I$Rs}} s R ww, /D qy I$R}js{ 8 t $t Y 8 sjj$9 I sti P { kr sj RZ Ps{ R s tb $t R{sj ]BZ Rk BP FBZt$ tzz $js
T1;T (a) 891 MHz (b) 904 MHz (c) 907 MHz (d) 911 MHz (e) 917 MHz ( f ) 934 MHz (g) 949 MHz 3$Z xnu 7$8Zjs I RY s YB $9Btsj I$R}js{ 8 t } Bhj R PB Y R R Z{Z BP 3$ x1bas$t I b$y s }Y tb8 tbjb${sj 8BI j PB $tht$ RBtsB R
T1xT 10 0 10-1 Y( f ) experiment theory 2D resonator 2D periodic 1D resonator [1/Ω] Y( f ) 10-2 Re Y( f ) 10-3 10-4 860 880 900 920 940 960 f [MHz] 3$Z x;u srz I sti R$8Zjs I si8$st{ sti {BtIZ{st{ BP Y R R Z{T Z $t 3$R x1 sti xn 3B s P t{ sjrb Y R$8Zjs$BtR PB st $tht$ striz{ sti s RBtsB b$y st & {$% jk $tht$ s} Z s RYBbt x1 N s,s sti Y ej { ${ _ PB 8st{ qy 8BI j sjrb sjjbbr ZR sjrb B R$8s Y & { BP Y s{bzr${ si$s$bt Bt Y j { ${ R}BtR BP Y RBtsB 7$8Zjs$BtR {Bth 8 Ys Y N7VG AZRAs si$st $Bt $R $ti I R}BtR$Aj PB Y -} $8 tsjjk BAR % I $t{ sr $t Y {BtIZ{st{ $t Y %${$t$k BP Y RBtst{ R 3$ x; 3Z Y -} $8 tr sti R$8Zjs$BtR $t _s} zy $ti${s Ys Y R ty BP Y si$s$bt I } tir Btjk b s,jk Bt Y s{bzr${ s} Z ]BtR JZ tjky js$% jbrr R s } BtBZt{ I PB ts Bb s} T Z R Vt $t R$t P sz BP Y R{stt I $8s R sti Y R$8Zjs$BtR $R Y sj8br Bsj sar t{ BP str% Rsj RBtst{ R yt _s} zyy$r $R s $AZ I B Y Ps{ Ys PB ABY ne H sti ;1 H {Z N$qs! n Y N7VG s tzs$bt $t{ sr R I sr${sjjk b$y Y } B}ss$Bt stj B& Y { krsj Ts-$R ]BtR JZ tjky$y B I str% Rsj bs% Z$I 8BI R s j$, jk B I$R}jsk R Bt } B}ss$Bt jbrr R V{{B I$t B Y R$8Zjs$BtRY AZRAs si$s$bt sti Y N7VG s tzs$bt b jj -}js$t Y jbrr R {jbr B sti Rj$Yjk sab% Y RBtst{ qy R 8sk sjrb A R}BtR$Aj PB Y % k Y$Y %sjz R BP R $ R R$Rst{ JZ$ I $t Y 7<T7VG RBtsB 8BI j w_s} yzd V Y$Y P JZ t{$ RY -{$s$bt BP Y PsR RY s AZj,Ts{BZR${ bs% R $R Y IB8$ts$t jbrr 8 {Yst$R8 <Bb % Y R & {R {sttb -}js$t Y -} $8 tsjjk BAR % I jbrr R $t Y RB}AstI sti$t }s ${Zjs $t Y %${$t$k BP Y st$ RBtst{ qy R 8sk A IZ B Y I$ { -{$s$bt BP Y RjBb RY s AZj,Ts{BZR${ bs% R sti Y s{bzr${ jbrr R $t Y j { BI R B R s {Y $R JZ$ I Bt Y$R sr} {sr b jj sr B hti Y 8 str B B}$8$9 Y RBtsB B 8$t$8$9 Y jbrr R