Spatial Polariton Dynamics In Optical Micro-Cavities [1.0 ed.]

Citation preview

_vKQM/ M/ "2p2`Hv a+FH2` 6+mHiv Q7 1t+i a+B2M+2b a+?QQH Q7 S?vbB+b M/ bi`QMQKv

aTiBH SQH`BiQM .vMKB+b AM PTiB+H JB+`Q@*pBiB2b h?2bBb bm#KBii2/ BM T`iBH 7mH}HHK2Mi Q7 i?2 `2[mB`2K2Mib 7Q` i?2 JXa+X /2;`22 i h2H pBp lMBp2`bBiv a+?QQH Q7 S?vbB+b M/ bi`QMQKv

#v :2Q`;B :`v _Qx2MKM

h?Bb rQ`F rb +``B2/ Qmi mM/2` i?2 bmT2`pBbBQM Q7 .`X hH a+?r`ix CmM2 kyRd

+FMQrH2/;K2Mib 6B`bi Q7 HH- A rQmH/ HBF2 iQ i?MF Kv i?2bBb /pBbQ` .`X hH a+?r`ix Q7 i?2 a+?QQH Q7 *?2KBbi`v i h2H pBp lMBp2`bBivX h?2 /QQ` iQ .`X a+?r`ix Q{+2 rb Hrvb QT2M r?2M2p2` A `M BMiQ  i`Qm#H2 bTQi Q` ?/  [m2biBQM #Qmi Kv `2b2`+? Q` r`BiBM;X >2 +QMbBbi2MiHv HHQr2/ i?Bb TT2` iQ #2 Kv QrM rQ`F- #mi bi22`2/ K2 BM i?2 `B;?i /B`2+iBQM r?2M2p2` ?2 i?Qm;?i A M22/2/ BiX Jv T2`bQMH /2p2HQTK2Mi b  b+B2MiBbi ?b #22M bi`QM;Hv BM~m2M+2/ #v i?2 +QMiBMmQmb ;mB/M+2bmTTQ`i M/ BKK2Mb2 FMQrH2/;2 Q7 .`X a+?r`ix M/ A K /22THv i?MF7mH 7Q` i?iX A rQmH/ HbQ HBF2 iQ i?MF i?2 2tT2`ib r?Q r2`2 BMpQHp2/ BM i?2 pHB/iBQM bm`p2v 7Q` i?Bb `2b2`+? T`QD2+i, .`X u2H GB#2b S22` M/ .`X /BM :QHQK#2FX qBi?Qmi i?2B` TbbBQMi2 T`iB+BTiBQM M/ BMTmi- i?2 pHB/iBQM bm`p2v +QmH/ MQi ?p2 #22M bm++2bb7mHHv +QM/m+i2/X A i?MF Kv 72HHQr H# Ki2b- l`B _QbbKM - KB` P?/ - Ei?2`BM2 FmHQp M/ _QHB o2`K 7Q` i?2 biBKmHiBM; /Bb+mbbBQMb M/ KmimH ?2HTX Gbi #mi MQi i?2 H2bi- A rQmH/ HBF2 iQ i?MF Kv JQi?2`- A`BM _Qx2MKM- Kv T`iM2` -HQM JbH2MBFQp- Jv +HQb2 7`B2M/b- .Mv "2bb2`;HB+F M/ E`BM SBpMB+- 7Q` bmTTQ`iBM; K2 bTB`BimHHv i?`Qm;?Qmi r`BiBM; i?Bb i?2bBb M/ Kv HB72 BM ;2M2`HX

R

#bi`+i *pBiv TQH`BiQMb `2 +QKTQbBi2 2t+BiiBQMb Q7 HB;?i M/ Kii2`- 7Q`K2/ #v i?2 +Q?2`2Mi +QmTHBM; Q7 QTiB+HHv@+iBp2 Ki2`BHb iQ KB+`Q+pBiB2b M/ Qi?2` QTiB+H `2bQMiQ`bX .m2 iQ i?2B` ?v#`B/ Mim`2i?2v /BbTHv #Qi? T`iB+H2@HBF2 #2?pBQ`- bm+? b KmimH BMi2`+iBQMb- b r2HH b T?QiQMB+- rp2@ HBF2 +?`+i2`BbiB+bX AM Q`;MB+ +pBiB2b- +QM}M2/ T?QiQMb `2 +QmTH2/ iQ i?2 `/BiBp2 2H2+i`QMB+ i`MbBiBQM BM Q`;MB+ /v2 KQH2+mH2b- ;BpBM; `Bb2 iQ bi`QM;- +Q?2`2Mi +QmTHBM; M/ i?2 7Q`KiBQM Q7 TQH`BiQMb 2p2M i `QQK i2KT2`im`2X b bm+?- Q`;MB+ KB+`Q+pBiB2b i i?2 bi`QM; +QmTHBM; `2;BK2 ?p2 #22M 2ti2MbBp2Hv bim/B2/- b i?2v T`QpB/2  +QMp2MB2Mi THi7Q`K 7Q` bim/vBM; p`BQmb T?2MQK2M BM +QM/2Mb2/ Kii2` M/ KMv@#Q/v T?vbB+b- bm+? b "Qb2 1BMbi2BM +QM/2MbiBQM M/ bmT2`~mB/Biv- HH Q#b2`p#H2 i `QQK i2KT2`im`2X 6m`i?2`KQ`2- TQH`BiQMb +M #2 ?`p2bi2/ 7Q` mHi`@HQr i?`2b?QH/ HbBM; M/ 2H2+i`B+HHv TmKT2/- imM#H2 Q`;MB+ G1.bX JQbi MQi#Hv- Bi rb `2+2MiHv /2KQMbi`i2/ i?i bi`QM; +QmTHBM; M/ i?2 7Q`KiBQM Q7 M2r- TQH`BiQMB+ [mMimK bii2b +M #2 mb2/ iQ +QMi`QH +?2KB+H `2+iBQMb BM KQH2+mH2b b r2HH b Qi?2` Ki2`BH T`QT2`iB2bX q?2M Q`;MB+ KQH2+mH2b `2 bi`QM;Hv +QmTH2/ iQ T?QiQMb BM +pBiB2b- HQM; `M;2 i`MbTQ`i T`QT2`iB2b KB;?i #2 Q#b2`p2/- h?Bb MQiBQM Bb bmTTQ`i2/ #v `2+2Mi 2tT2`BK2Mib- r?B+? b?Qr2/ i?i i?2 bTQMiM2Qmb 2KBbbBQM 7`QK KQH2+mH2b mM/2` bi`QM; +QmTHBM; /BbTHvb bTiBH +Q?2`2M+2 Q7 b2p2`H KB+`QMb- p2`v `2+2MiHv bi`QM; +QmTHBM; rb b?QrM iQ 2M?M+2 i?2 2H2+i`B+ +QM/m+iM+2 Q7 Q`;MB+ b2KB+QM/m+@ iQ`b- BM+`2bBM; i`MbTQ`i `M;2 7`QK KQH2+mH` `M;2 iQ KB+`QM `M;2X >Qr2p2`- i?2b2 `2bmHib QMHv ;p2 BM/B`2+i 2pB/2M+2 iQ HQM; `M;2 i`MbTQ`i T`QT2`iB2bX AM i?Bb i?2bBb- r2 rMi2/ iQ ;Bp2 i?2 /B`2+i 2tT2`BK2MiH 2pB/2M+2 i?i bi`QM; +QmTHBM; Q7 Q`;MB+ Ki2`BHb iQ HB;?i BM +pBiB2b +M BM+`2b2 i`MbTQ`i `M;2 BM Q`;MB+ Ki2`BHb #v K2bm`BM; i?2 bTiBH /vMKB+b Q7 TQH`BiQMb BM Q`;MB+ +pBiB2b /B`2+iHvX q2 #mBHi  /2/B+i2/ iBK2 `2bQHp2/ BK;BM; b2imT #b2/ QM TmKT T`Q#2 KB+`Qb+QTv i2+?MB[m2bX h?2 mMB[m2 QTiB+H b2imT HHQr2/ mb iQ K2bm`2 i?2 bTiBH /vMKB+b Q7 TQ@ H`BiQMb 7Q`K2/ BM Q`;MB+ +pBiB2b i `QQK i2KT2`im`2 7Q` i?2 }`bi iBK2X h?2 Q#b2`piBQM b?Qr2/ i?i TQH`BiQMb +M BM/22/ T`QT;i2 Qp2` KB+`Qb+QTB+ /BbiM+2bX "v 7QHHQrBM; i?2 2tTMbBQM Q7 M QTiB+HHv@2t+Bi2/ TQH`BiQM +HQm/ b  7mM+iBQM Q7 iBK2 r2 2ti`+i2/ i?2 p2HQ+Biv Q7 i?2 2tTM/BM; TQH`BiQM +HQm/ M/ bim/B2/ TQH`BiQM i`MbTQ`i K2+?MBbK BM Q`;MB+ +pBiB2bX q2 #2HB2p2 i?i i?2 #BHBiv iQ K2bm`2 i?2 bTiBH /vMKB+b Q7 TQH`BiQMb QT2Mb  M2r }2H/ Q7 +QMi`QHHBM; i?2 i`MbTQ`i Q7 TQH`BiQMb #v mbBM; ?v#`B/ Q`;MB+@T?QiQMB+ bi`m+im`2b rBi? bT2+BHHv@iBHQ`2/ ;2QK2i`B2b- r?B+? 7Q`Kb  M2r rv Q7 miBHBxiBQM Q7 TQH`BiQMb 7Q` Q`;MB+ 2H2+i`QMB+ /2pB+2bX k

*QMi2Mib R AMi`Q/m+iBQM

9

k h?2Q`v Q7 SQH`BiQMb BM JB+`Q+pBiB2b

e

kXR

h?2 `2bQMMi 6#`v@S2`Qi +pBiv X X X X X X X X X X X X X X X X X X X X X X X X X X X X

kXk

ZmMimK i?2Q`v Q7 HB;?i X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Rk

kXj

1t+BiQMb X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Re kXjXR

kX9

h?2 [mMimK i?2Q`v Q7 6`2MF2H 1t+BiQMb X X X X X X X X X X X X X X X X X X X X Re

*pBiv 2t+BiQM@TQH`BiQMb @ CvM2b @ *mKKBM;b KQ/2H X X X X X X X X X X X X X X X X X R3

j P`;MB+ JB+`Q+pBiB2b @ S`2T`iBQM M/ *?`+i2`BxiBQM jXR

jXk

e

kj

J2i?Q/b X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X kj jXRXR

P`;MB+ QTiB+H +pBiB2b T`2T`iBQM X X X X X X X X X X X X X X X X X X X X X X X kj

jXRXk

.BbT2`bBQM K2bm`2K2Mib, M;H2@`2bQHp2/ i`MbKBbbBQM X X X X X X X X X X X X k9

jXRXj

.BbT2`bBQM K2bm`2K2Mib, M;H2@`2bQHp2/ `2~2+iBQM KB+`Qb+QTv X X X X X X X X ke

jXRX9

LmK2`B+H bBKmHiBQMb X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X kN

_2bmHib X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X jR

9 hBK2@_2bQHp2/ AK;BM; #v SmKT@S`Q#2 JB+`Qb+QTv

jj

9XR

AMi`Q/m+iBQM X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X jj

9Xk

S`BM+BTH2b Q7 mHi`7bi SmKT@S`Q#2 JB+`Qb+QTv X X X X X X X X X X X X X X X X X X X X j8

9Xj

h?2 2tT2`BK2MiH b2imT X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X jd

9X9

_2bmHib X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 9y

8 amKK`v

9e j

*?Ti2` R AMi`Q/m+iBQM *pBiv TQH`BiQMb ?p2 +m;?i i?2 ii2MiBQM Q7 KMv b+B2MiBbib BM i?2 Hbi 72r /2+/2b- /m2 iQ i?2B` `2K`F#H2 T`QT2`iB2b M/ i?2B` ?H7 T?QiQM ?H7 2t+BiQM HBF2 Mim`2X h?2 Q`B;BM Q7 +pBiv TQH`BiQMb +QK2b 7`QK i?2 }2H/ Q7 *pBiv ZmMimK 1H2+i`Q/vMKB+b- r?B+? ?b 2pQHp2/ BMiQ  ;2M2`H bim/v Q7 HB;?i@Kii2` BMi2`+iBQM BM i?2 bi`QM; +QmTHBM; `2;BK2- r?2`2 i?2 +Q?2`2Mi +QmTHBM; Q7 iQKb rBi? i?2 }2H/ /QKBMi2b HH `2HtiBQM T`Q+2bb2b (R)X 1tT2`BK2Mib QM iQKb BM +pBiB2b BMbTB`2/ b+B2MiBbib iQ bim/v i?2 bi`QM;Hv +QmTH2 2t+BiQMb BM b2KB+QM/m+iQ`b iQ +pBiB2b- r?B+? BMBiBi2/ i?2 }2H/ Q7 2t+BiQM TQH`BiQMb (k)X 6QHHQrBM; i?i- KMv 2tT2`BK2Mib +QM}`K2/ i?i i?2 +QM+2Ti Q7 TQH`BiQMb im`M2/ Qmi iQ #2  p2`v T`Q7QmM/ M/ 7`mBi7mH QM2 BM Q`/2` iQ BMi2`T`2i QTiB+H 2tT2`BK2Mib BM /B`2+i@;T b2KB+QM/m+iQ`b BM i?2 `2;BQM Dmbi #2HQr i?2 7mM/K2MiH ;T (j)X hQ/v- +pBiv TQH`BiQMb Qz2`  mMB[m2 THi7Q`K 7Q` bim/vBM; 7mM/K2MiH bT2+ib Q7 +QM/2Mb2/ Kii2` M/ +?2KB+H T?vbB+bX Ai rb `2+2MiHv b?QrM i?i bi`QM; 2t+BiQM@T?QiQM +QmTHBM; +M HbQ #2 K2bm`2/ BM M Q`;MB+ KB+`Q@+pBiv- r?B+? BMBiBi2/ i?2 }2H/ Q7 bi`QM; +QmTHBM; #2ir22M Q`;MB+ KQH2+mH2b bi`QM;Hv +QmTH2/ iQ +QM}M2/ HB;?i }2H/b BM KB+`Q@+pBiB2b (9)X SQH`BiQMb +M HbQ 2K2`;2 7`QK bi`QM; +QmTHBM; #2ir22M b2KB+QM/m+iQ`b iQ HB;?i BM KB+`Q@+pBiB2bX >Qr2p2`- 2t+BiQMb BM b2KB+QM/m+iQ`b ?p2  p2`v HQr #BM/BM; 2M2`;v M/ b  `2bmHi i?2v /BbbQ+Bi2 iQ 7`22 2H2+i`QMb M/ ?QH2b i `QQK i2KT2`im`2X b QTTQb2/ iQ i?i- KQH2+mH` 2t+BiQMb ?p2  ?B;?2` #BM/BM; 2M2`;v M/ i?2`27Q`2 `2 bi#H2 i `QQK i2KT2`im`2 (8)X h?2`27Q`2- TQH`BiQMb BM Q`;MB+ +pBiB2b TQb2 ;`2i BKTQ`iM+2 7Q` KMBTmHiBQM Q7 HB;?i +QmTH2/ iQ Kii2` i MMQb+H2 `2;BK2b M/ `QQK i2KT2`im`2b (e- d)X JQ`2Qp2`- Bi rb `2+2MiHv b?QrM i?i bi`QM; +QmTHBM; BM~m2M+2b i?2 2M2`;v HM/b+T2 Q7 Q`;MB+ Ki2`BHb r?B+? +QMi`QHb i?2 +?2KB+H `2+iBQMb- r?B+? Bb  /B`2+i miBHBxiBQM Q7 TQH`BiQMb 7Q` +?2KB+H TTHB+iBQMb (3)X

9

q?BH2 bB;MB}+Mi T`Q;`2bb ?b #22M K/2 BM mM/2`biM/BM; i?2 bT2+i`Qb+QTB+ T`QT2`iB2b M/ i2K@ TQ`H FBM2iB+b Q7 TQH`BiQMb 7Q`K2/ BM Q`;MB+ +pBiB2b- i?2 BMi2`2bi BM bTiBH 2z2+ib- bm+? b i?2B` BM~m2M+2 QM i?2 i`MbTQ`i `M;2 BM Q`;MB+ Ki2`BHb ?b ;BM2/ ii2MiBQM QMHv BM `2+2Mi v2`bX JQH2+mH` 2t+BiQMb ?p2  bi`QM;Hv HQ+HBx2/ rp2 7mM+iBQM r?B+? `2bmHib BM  b?Q`i i`MbTQ`i `M;2 Q7 72r MMQK2i2`bX >Qr2p2`- Bi ?b #22M `2+2MiHv b?QrM i?i i?2B` rp2 7mM+iBQM +M #2 /2HQ+HBx2/ r?2M Bi Bb bi`QM;Hv +QmTH2/ iQ  HB;?i KQ/2 BM  +pBivX b  `2bmHi- i?2B` rp2 7mM+iBQM Bb bTiBHHv 2ti2M/2/ Qp2`  72r KB+`QMb M/ i?2B` i`MbTQ`i `M;2 BM+`2b2b #v b2p2`H Q`/2`b Q7 K;MBim/2X h?2`27Q`2- TQH`BiQMb 7Q`K2/ BM Q`;MB+ Ki2`BHb im`M2/ Qmi iQ #2 p2`v BKTQ`iMi 7Q` 2M?M+BM; i?2 2H2+i`B+ +QM/m+iM+2 Q7 Q`;MB+ b2KB+QM/m+iQ`b (N)X AM //BiBQM iQ T`+iB+H TTHB+iBQMb- HQM; `M;2 +QM/m+iM+2 +QmH/ b2`p2 b bmTTQ`iBM; 2pB/2M+2 i?i TQH`BiQMb +M T`QT;i2 Qp2` KB+`Q@ b+QTB+ /BbiM+2b (Ry)X h?2`27Q`2- r2 #2HB2p2 i?i `2p2HBM; i?2 i`MbTQ`i K2+?MBbK Q7 TQH`BiQMb BM Q`;MB+ bvbi2Kb KB;?i QT2M  M2r rv Q7 bim/vBM; p`BQmb T?2MQK2M BM +QM/2Mb2/ Kii2` M/ KMv@#Q/v T?vbB+b M/ ;Bp2 mb i?2 #BHBiv iQ +QMi`QH i?2 i`MbTQ`i T`QT2`iB2b Q7 Q`;MB+ Ki2`BHb BM i?2 7mim`2X

8

*?Ti2` k h?2Q`v Q7 SQH`BiQMb BM JB+`Q+pBiB2b h?2 T?vbB+H bvbi2K bim/B2/ BM i?Bb rQ`F +QMbBbib Q7  6#`v@S2`Qi +pBiv rBi? Q`;MB+ KQH2+mH2b TH+2/ BM #2ir22MX AM bm+? bvbi2Kb i?2 HB;?i +QM}M2/ BM i?2 +pBiv BMi2`+ib rBi? KQH2+mH2bp`BQmb /v2 KQH2+mH2b #bQ`# M/ 2KBi HB;?i M/ i?2 +pBiv KQ/2 BMi2`+ib M/ 2t+?M;2b 2M2`;vX Ai Bb r2HH FMQrM i?i r?2M HB;?i BMi2`+ib rBi? Kii2`- Bi +M #2 b2T`i2/ BM irQ +b2b, bi`QM; M/ r2F +QmTHBM; `2;BK2bX AM i?2 bi`QM;@+QmTHBM; `2;BK2- i?2 2M2`;v 2t+?M;2 #2ir22M HB;?i M/ KQH2+mH2b #2+QK2b 7bi2` i?M Mv /BbbBTiBQM Q` /2+Q?2`2M+2- M/ i?2 2M2`;v #QmM+2b #+F M/ 7Q`i?- BM r?i Bb FMQrM b p+mmK _#B Qb+BHHiBQMbX GB;?i BM  bBM;H2 +pBiv KQ/2 Bb pB2r2/ b T?QiQMb- r?BH2 KQH2+mH2b +M #2 i`2i2/ b KQH2+mH` 2t+BiQMb- r?2M bi`QM;Hv +QmTH2/ iQ 2+? Qi?2`  bTHBiiBM; BM i?2 +pBiv bT2+i`H `2bTQMb2 2K2`;2b M/ irQ M2r 2M2`;v #`M+?2b BM i?2 +pBiv /BbT2`bBQM `2 Q#b2`p2/- i?2 bvbi2K Bb i`2i2/ b  M2r [mbB@T`iB+H2 +HH2/, 2t+BiQM TQH`BiQMX

kXR h?2 `2bQMMi 6#`v@S2`Qi +pBiv M B/2H 6#`v@S2`Qi +pBiv +M #2 +QMbB/2`2/ b irQ THM`- T`iBHHv i`MbKBiiBM; M/ MQM #bQ`#BM; KB``Q`b M1 M/ M2 - r?B+? `2 K/2 ++m`i2Hv T`HH2HX am+? bvbi2K b?HH #2  `2bQMMi +pBiv 7Q` HB;?iX q2 /2b+`B#2 i?2 BM+B/2Mi }2H/ b  bmK Q7 +QmMi2` T`QT;iBM; 2H2+i`QK;M2iB+ rp2b r`Bii2M BM i?2 7Q`K, Ei (⃗r, t) = εˆEi ei(kz−ωt) + c.c

UkXRV

q?2`2 Ei Bb i?2 +QKTH2t KTHBim/2 Q7 i?2 BM+B/2Mi 2H2+i`B+ }2H/ M/ bm`7+2 Q7 M1 Bb i z = 0X q2 /2MQi2 i?2 bK2 rv- #v Ec M/ Ec′ i?2 KTHBim/2b Q7 i?2 `2~2+i2/ M/ i`MbKBii2/ }2H/b T`QT;iBM; #2ir22M i?2 irQ KB``Q`bX h?2 KTHBim/2b Er M/ Et /2b+`B#2 i?2 `2~2+i2/ M/ i`MbKBii2/ }2H/b 7`QK M/ Qmi Q7 i?2 +pBivX h?2b2 rp2b `2 b?QrM BM 6B; kXRX e

6B;m`2 kXR,  bF2i+? Q7  ivTB+H 6#`v@T2`Qi +pBiv +QMbBbiBM; Q7 irQ T`HH2H KB``Q`b M1 , M2 b2T`i2/ #v /BbiM+2 L0 X h?2 `2;BQM #2ir22M irQ KB``Q`b ?b  `27`+iBp2 BM/2t nX Er , Ei `2 i?2 i`MbKBii2/ M/ `2~2+i2/ }2H/b `2bT2+iBp2HvXEc , Ec′ `2 i?2 T`QT;iBM; }2H/b r?B+? `2 BMbB/2 i?2 +pBivX qBi?Qmi i?2 HQbb Q7 i?2 ;2M2`HBiv r2 +M +?QQb2 i?2 T?b2b i i?2 KB``Q` M1 Q7 bm+? i?i i?2 }2H/b biBb7v i?2 `2HiBQMb, Ec = t1 Ei + r1 Ec′

UkXkV

Er = −r1 Ei + t1 Ec′

UkXjV

6Q` KB``Q` M2 i?2 2tT`2bbBQMb 7Q` i?2 KTHBim/2b `2, Et = t2 Ec exp(ikL0 )

UkX9V

Ec′ = r2 Ec exp(2ikL0 )

UkX8V

7`QK 2[miBQMb UkXk-kX9V r2 /2`Bp2 i?2 `2HiBQM, Et t1 t2 Ec exp(ikL0 ) = Ei Ec − r1 Ec′

UkXeV

6m`i?2`KQ`2- #v bm#biBimiBM; UkX8V BMiQ UkXeV r2 ;2i i?2 7QHHQrBM; `2HiBQM, Et t1 t2 exp(ikL0 ) = Ei 1 − r1 r2 exp(2ikL0 )

UkXdV

"v +H+mHiBQM i?2 `2HiBQM #2ir22M i?2 i`MbKBii2/ 2M2`;v ~mt Pt - i?2 BMi2MbBiv i`MbKBbbBQM M/ `2~2+iBQM Q7 i?2 +pBiv `2, d

T =

Pt Et 2 =| | Pi Ei

UkX3V

R=

Pr Er 2 =| | Pi Ei

UkXNV

6`QK r?B+? r2 /2/m+2 i?2 i`MbKBbbBQM +Q2{+B2Mi Q7 i?2 6#`v@S2`Qi +pBiv, T =|

Et 2 T1 T2 √ |= Ei 1 + R1 R2 − 2 R1 R2 cos(2kL0 )

UkXRyV

1tT`2bbBQM UkXRyV `2+?2b KtBKmK i i?2 +QM/BiBQM, kL0 = πm

2L0 = λm m

UkXRRV

r?2`2 m = 1, 2, 3, ... Bb M BMi2;2`X h?Bb KtBKmK Bb  `2bmHi Q7  +QMbi`m+iBp2 BMi2`72`2M+2 Q7 HH i?2 `2~2+iBQMb BM i?2 +pBivX h?2 M;mH` 7`2[m2M+v ω Bb, ω = ωp = πm

c L0

UkXRkV

r?2`2 + Bb i?2 bT22/ Q7 HB;?i BM p+mmKX AM //BiBQM- Bi Bb BKTQ`iMi iQ MQiB+2 i?i 7Q` m = 1 r2 ;2i i?2 7QHHQrBM; `2HiBQM 7Q` i?2 7mM/@ K2MiH KQ/2 Q7 i?2 +pBiv, λm=1 = 2L0 X h?2 7`2[m2M+B2b ωp `2 i?2 `2bQMMi 7`2[m2M+B2b Q7 i?2 +pBivX ++Q`/BM; iQ UkXRRV- i?2v +Q``2bTQM/ iQ i?2 bBimiBQM r?2`2 i?2 +pBiv H2M;i? L0 Bb  KmHiBTH2 Q7 i?2 ?H7 rp2H2M;i? Q` i?2 `QmM/@i`BT +pBiv H2M;i? Bb  KmHiBTH2 Q7 i?2 rp2H2M;i?X am#biBimiBM; i?2 `2HiBQM Q7 `2bQMMi 7`2[m2M+B2b Q7 i?2 +pBiv UkXRRV BMiQ UkXRyV r2 ;2i, Tmax =

T1 T2 √ (1 − R1 R2 )2

UkXRjV

r?2`2 Tmax Bb i?2 KtBKH i`MbKBbbBQM +Q2{+B2Mi i  `2bQMMi 7`2[m2M+vX AM /2`BpBM; i?2 #Qp2 2tT`2bbBQMb r2 +QMbB/2`2/ i?2 HB;?i T`QT;iBM; T`HH2H iQ i?2 zˆ tBb- ?Qr2p2` i?2 bK2 /2`BpiBQM +M #2 2ti2M/2/ iQ Mv T`QT;iBQM M;H2 #v `2TH+BM; k rBi? i?2 HQM;Bim/BMH +QKTQM2Mi Q7 i?2 rp2 p2+iQ` kz X 6Q` HB;?i HmM+?2/ rBi? BM+B/2Mi M;H2 θ rBi? `2bT2+i iQ i?2 z tBb i?2 i`Mbp2`b2 KQK2MimK Bb, k∥ =

2π sinθ λ 3

UkXR9V

AM bm+? +b2- i?2 kz +QKTQM2Mi Q7 i?2 KQK2MimK Bb ;Bp2M #v, kz =

! k 2 − k∥2

UkXR8V

lbBM; i?2b2 `2HiBQMb r2 ;2i M;H2 /2T2M/2Mi +pBiv `2bQMM+2 r?B+? +M #2 2tT`2bb2/ b  /BbT2`@ bBQM `2HiBQM `2HiBM; i?2 2M2`;v Q7 T?QiQMb r?B+? i`Mbp2`b2 KQK2MimKX c kc c! 2 !c Eph (k∥ , kz ) = h =h =! k∥ + kz2 = λn 2πn n n

"

k∥2 + (

π 2 ) L0

UkXReV

q?2`2 ! Bb SHM+FǶb +QMbiMi- n Bb i?2 `27`+iBp2 BM/2t Q7 i?2 +pBiv Ki2`BH M/ k∥2 = kx2 + ky2 Bb i?2 i`Mbp2`b2 KQK2MimKX 6Q` T`+iB+H TTHB+iBQMb- i?Bb /BbT2`bBQM `2HiBQM +M #2 +QMp2`i2/ 7`QK KQK2MimK /2T2M/2M+2 BMiQ M;H2 M/ H2M;i? /2T2M/2M+2(9)X 6Q`  bvbi2K rBi? HB;?i b?BM2/ i  +2`iBM /2;`22 Q7 BM+B/2M+2 θ HQM; i?2 t tBb M/ }t2/ +pBiv H2M;i? L0 r2 +M /2}M2 ky = 0X h?Bb +?`+i2`BbiB+ /2T2M/2M+2 Bb BKTQ`iMi bBM+2 b θ BM+`2b2b Eph b?B7ib iQr`/b ?B;?2` 2M2`;v ++Q`/BM; iQ, Eph (θ) = q?2`2 E0 =

hc L n 0

E0 cos(θ)

UkXRdV

Bb i?2 #`2 +pBiv `2bQMM+2 i θ = 0◦ X 2.5

Photons 2.4

![#$]

2.3

2.2

2.1

2.0 -10

-8

-6

-4

-2

&' =

0

2

4

6

8

10

2* 1 sin(0) + 34

6B;m`2 kXk,  THQi Q7  ivTB+H /BbT2`bBQM Q7 T?QiQMb BM  6#`v@S2`Qi +pBiv ++Q`/BM; iQ UkXRdV 1 rBi? E0 = 2.11eV M/ M/ −10 < kx < 10 µm N

b 2p2`v `2bQMiQ`- QTiB+H `2bQMiQ`b ?p2  +?`+i2`BbiB+ [mHBiv 7+iQ` `2T`2b2MiBM; i?2 2M2`;v biQ`;2 iBK2 +QKT`2/ iQ i?2 HQbb `i2X Ai Bb /2}M2/ b i?2 2M2`;v biQ`2/ BM i?2 bvbi2K T2` /BbbBTi2/ 2M2`;v T2` T2`BQ/- KmHiBTHB2/ #v 2π, Q = 2π

Esystem Eper−period

UkXR3V

"v /2}MBM; i?2 HQbb T2` mMBi H2M;i? αr - i?2 Z 7+iQ` Q7 M QTiB+H `2bQMiQ` Kv #2 /2i2`KBM2/ #v Q#b2`pBM; i?i biQ`2/ 2M2`;v Bb HQbi i i?2 `i2 cαr UT2i mMBi iBK2V- r?B+? Bb 2[mBpH2Mi iQ i?2 r `i2 cα UT2` +v+H2VX bQ i?i, ν0 Q = 2π

1 cαr /ν0

Ry

UkXRNV

aBM+2 i?2 `2HiBQM #2ir22M i?2 `2bQMM+2 HBM2@rB/i? M/ i?2 `2bQMiQ` HQbb Kv #2 pB2r2/ b  KMB72biiBQM Q7 i?2 iBK2@7`2[m2M+v mM+2`iBMiv `2HiBQM, δν =

cαr 2π

UkXkyV

"v bm#biBimiBM; kXky BMiQ kXRN QM2 +M ;2i i?2 7QHHQrBM; 2tT`2bbBQM 7Q` Z 7+iQ`, Q=

ν0 δν

UkXkRV

AM KQ`2 T`+iB+H K2Mb- i?2 Z@7+iQ` 7Q` +pBiB2b rBi?  `2bQMM+2 BM i?2 QTiB+H 7`2[m2M+v i?2 7QHHQrBM; `2HiBQM Kv #2 mb2/, Q=

2π ν0 Tround−trip Pl

UkXkkV

r?2`2 ν0 Bb i?2 7`2[m2M+v- Pl Bb i?2 7`+iBQMH TQr2` HQbb T2` `QmM/ i`BT M/ Tround−trip Bb i?2 iBK2 Bi iF2b  T?QiQM iQ +QKTH2i2 QM2 `QmM/ i`BT BM i?2 +pBivX 6Q` 2tKTH2,  ivTB+H THM` +pBiv r?B+? ?b  `2bQMMi 7`2[m2M+v i λ0 = 588nm - `QmM/ i`BT Q7 Tround−trip = 1f s - `QmM/ i`BT HQbb Q7 Pl = 10W ?b  Z@7+iQ` Q7 jkX

RR

kXk ZmMimK i?2Q`v Q7 HB;?i AM i?2 T`2pBQmb +?Ti2` r2 pB2r2/ i?2 2H2+i`QK;M2iB+ }2H/ BMbB/2  +pBiv b  +HbbB+H }2H/X q?BH2 Bi Bb i`m2 i?i +HbbB+H 2H2+i`QK;M2iB+ i?2Q`v /2b+`B#2b KMv 7mM/K2MiH QTiB+H T?2MQK2M- Bi 7BHb r?2M r2 +QMbB/2`  bvbi2K BM r?B+? p2`v 72r T?QiQMb `2 T`2b2MiX AM bm+? +b2b i?2 }2H/ M22/b iQ #2 i`2i2/ [mMimK K2+?MB+HHv M/ [mMimK 2H2+i`Q/vMKB+b `2 +QMbB/2`2/X AM i?Bb +?Ti2` r2 b?HH #`B2~v /2b+`B#2 i?2 [mMiBxiBQM Q7 HB;?i BM  +pBiv- 7QHHQrBM; `272`2M+2 (RR)X h?2 G;`M;BM /2MbBiv Q7 i?2 2H2+i`QK;M2iB+ }2H/ Kv #2 r`Bii2M b, 1 L= 2

#

1 ϵ0 E + B 2 µ0 2

$

UkXkjV

⃗ M/ B ⃗ `2 i?2 2H2+i`B+ M/ K;M2iB+ }2H/X 6QHHQrBM; +HbbB+H }2H/ i?2Q`v E ⃗ M/ B ⃗ +M q?2`2 E #2 2tT`2bb2/ BM i2`Kb Q7 i?2 +HbbB+H 2H2+i`QK;M2iB+ 7Qm` TQi2MiBH }2H/ Aα - Bi Bb +QMp2MB2Mi iQ /2}M2 Bi BM i?2 7QHHQrBM; rv, φ ⃗ Aα = ( , A) c ⃗ Bb i?2 i`22 TQi2MiBH }2H/X r?2`2 Aα Bb i?2 7Qm` TQi2MiBH }2H/- φ Bb i?2 2H2+i`B+ TQi2MiBH M/ A ⃗ M/ B ⃗ BM i?2 7QHHQrBM; rv, h?2b2 }2H/b `2 `2Hi2/ iQ E ⃗ =∇ ⃗ ×A ⃗ B

UkXk9V

⃗ ⃗ = −∇φ ⃗ − ∂A E ∂t

UkXk8V

Ai Bb TQbbB#H2 iQ b?Qr i?i Jtr2HHǶb 2[miBQM 7QHHQrb /B`2+iHv 7`QK L- #v `2TH+BM; UkXk9-kXk8V M/ T2`7Q`KBM;  p`BiBQM QM L rBi? `2bT2+i iQ +QKTQM2Mib Q7 Aα X h?2 FMQrM `2bmHi b?HH #2, ⃗ ·E ⃗ =0 ∇ ⃗ ⃗ ×E ⃗ = − ∂B ∇ ∂t

⃗ ·B ⃗ =0 ∇

UkXkeV

⃗ ⃗ ×B ⃗ = 1 ∂E ∇ c2 ∂t

UkXkdV

q2 +QMbB/2` i?i i?2 2H2+i`QK;M2iB+ }2H/ Bb +QM}M2/ rBi?BM  pQHmK2 Q7 bT+2 L3 rBi? /B2H2+i`B+ ⃗ ·A ⃗ = 0) i?2 p2+iQ` TQi2MiBH A ⃗ biBb}2b M Q`/BM`v rp2 +QMbiMi ε0 X AM *QmHQK# ;m;2 U∇ 2[miBQM ;Bp2M BM i?2 7Q`K, ⃗− ∇2 A

⃗ 1 ∂ 2A =0 2 c ∂t Rk

UkXk3V

⃗ BM T`QT;iBM; THM2 rp2b r2 ;2i, "v TTHvBM; 6Qm`B2` i?2Q`v BM i?2 7Q`K Q7 2tTM/BM; A ⃗ r, t) = √ 1 A(⃗ ε0 V

%

UkXkNV

⃗⃗ (t)ei⃗k·⃗ri A k

⃗k

r?2`2 i?2 bmKKiBQM Qp2` ⃗k K2Mb bmKKiBQM Qp2` i = x, y, z M/ ni = 0, 1, 2, ... `2 [mMimK i MmK#2`b bbQ+Bi2/ iQ 2+? ⃗k +QKTQM2Mi, ki = 2πn X 6`QK ;mbb Hr Bi Bb /2/m+i2/ i?i UkXkeV, L UkXjyV

⃗k · A ⃗⃗ = 0 k

⃗ BM i?2 h?2`27Q`2- i?2 }2H/ Bb i`Mbp2`bHX 6QHHQrBM; UkXkNV r2 +M 2tT`2bb i?2 p2+iQ` TQi2MiBH A 7QHHQrBM; rv, %&

⃗ r, t) = √ 1 A(⃗ ε0 V

u⃗k,s (t)⃗ ϵs e

i⃗k·⃗ r

+

⃗ u⃗∗k,s (t)⃗ ϵs ∗ e−ik·⃗r

⃗k,s

'

UkXjRV

r?2`2 u⃗k,s (t) = u⃗k,s (0)e−iω⃗k,s t #v mbBM; UkXk8-kXk9V Bi +M #2 b?QrM i?i i?2 2H2+i`B+ M/ K;M2iB+ }2H/b +M iF2 i?2 7QHHQrBM; 7Q`K, ⃗ r, t) = √ 1 E(⃗ ε0 V ⃗ r, t) = √ 1 B(⃗ ε0 V

% ⃗k,s

%& ⃗k,s

& ' ⃗ ⃗ iω⃗k,s u⃗k,s (t)⃗ ϵs eik·⃗r + u⃗∗k,s (t)⃗ ϵs ∗ e−ik·⃗r

UkXjkV

⃗ ⃗ u⃗k,s (t)(⃗k × ϵ⃗s )eik·⃗r + u⃗∗k,s (t)(⃗k × ϵ⃗s ∗ )e−ik·⃗r

'

UkXjjV

"v TTHvBM; G2;2M/`2 i`Mb7Q`K QM UkXkjV M/ bmKKBM; Qp2` bT+2 d3 r i?2 >KBHiQMBM Q7 i?2 }2H/ iF2b i?2 7Q`K, 1 H= 2

ˆ

L3

#

1 ⃗2 ⃗ 2 (⃗ ε0 E r,t) + B (⃗r, t) µ0

$

UkXj9V

⃗ M/ B ⃗ i?Bb >KBHiQMBM iF2b i?2 7Q`K, "v mbBM; i?2 `2HiBQMb 7Q` E H=2

%

UkXj8V

2 ω⃗k,s |u⃗k,s (t)|2

⃗k,s

hQ r`Bi2 i?2 >KBHiQMBM BM  +MQMB+H 7Q`K r2 mb2 i?2 7QHHQrBM; +MQMB+H i`Mb7Q`KiBQM, q⃗k,s (t) = u⃗k,s (t) +

u⃗∗k,s (t)

&

p⃗⃗k,s (t) = −iω⃗k,s u⃗k,s (t) −

h?2 >KBHiQMBM i?2M iF2b i?2 7QHHQrBM; 7Q`K, Rj

u⃗∗k,s (t)

'

UkXjeV

H=

1% 2 2 2 (p⃗k,s (t) + ω⃗k,s q⃗k,s (t)) 2

UkXjdV

⃗k,s

h?Bb 7Q`K b?Qrb i?i i?2 2H2+i`QK;M2iB+ }2H/ Kv #2 2tT`2bb2/ BM i?2 7Q`K Q7 BM/2T2M/2Mi ?`KQMB+ Qb+BHHiQ`bX 1+? Qb+BHHiQ` ?b  +Q``2bTQM/BM; 7`2[m2M+v ω ⃗ ⃗k,s X hQ i?Bb TQBMi r2 +QMbB/2`2/ +HbbB+H }2H/ i?2Q`v QMHv- iQ [mMiBx2 i?Bb >KBHiQMBM i?2 +MQMB+H [mMiBxiBQM T`Q+2/m`2 +M #2 mb2/X r2 +QMbB/2` i?2 7QHHQrBM; +QKKmiiBQM `2HiBQMb, (

) qˆ⃗k,s (t), pˆ⃗k,s (t) = i!δ⃗k,⃗k′ δs,s′

(

) qˆ⃗k,s (t), qˆ⃗k,s (t) = 0

(

) pˆ⃗k,s (t), pˆ⃗k′ ,s′ (t) = 0

UkXj3V

r?2`2 i?2 QT2`iQ`b qˆ M/ pˆ `2 bbQ+Bi2/ iQ +HbbB+H p`B#H2b q M/ pX aBKBH` iQ [mMiBxiBQM Q7 ?`KQMB+ Qb+BHHiQ` r2 +M /2}M2 i?2 +`2iBQM M/ MMB?BHiBQM QT2`iQ`b a ˆ⃗k,s (t) M/ a ˆ⃗∗k,s (t) a ˆ⃗k,s (t) =

a ˆ⃗†k,s (t) =

1

&

1

&

1 (2!ω⃗k,s ) 2 1 (2!ω⃗k,s ) 2

ω⃗k,s qˆ⃗k,s (t) + iˆ p⃗k,s (t)

'

UkXjNV

'

UkX9yV

ω⃗k,s qˆ⃗k,s (t) − iˆ p⃗k,s (t)

"v mbBM; i?2b2 QT2`iQ`b i?2 >KBHiQMBM iF2b i?2 7QHHQrBM; [mMimK 7Q`K, ˆ = H

%

!ω⃗k,s

⃗k,s

#

1 n ˆ⃗k,s + 2

$

UkX9RV

r?2`2 r2 /2}M2/ i?2 MmK#2` QT2`iQ` b, n ˆ⃗k,s = a ˆ⃗†k,s a ˆ⃗k,s - r?2`2 a ˆ⃗†k,s Bb `2 +`2iBQM M/ a ˆ⃗k,s `2 i?2 MMB?BHiBQM QT2`iQ`b Q7 T?QiQMbX h?2 T`Q/m+i Q7 +`2iBQM M/ MMB?BHiBQM QT2`iQ`b Bb i?2 MmK#2` QT2`iQ` Q7 T?QiQMb rBi? i?2 +Q``2bTQM/BM; [mMimK bii2b, n ˆ⃗k,s |n⃗k,s ⟩ = n⃗k,s |ˆ n⃗k,s ⟩

R9

UkX9kV

PM2 Q7 i?2 KQbi BKTQ`iMi `2bmHib Q7 i?Bb /2`BpiBQM +M #2 2pHmi2/ 2bBHv- +QMbB/2` i?2 +b2 BM r?B+? i?2`2 `2 MQ T?QiQMb ,ˆ n⃗k,s = 0X +QKKQM b2Mb2 BM i?2 7Q`K Q7 +HbbB+H T?vbB+b rQmH/ i2HH mb i?i 7Q` y T?QiQMb i?2`2 Bb MQ 2M2`;vX >Qr2p2`- BM b2+QM/ [mMiBxiBQM bm+? +b2 Bb +HH2/ i?2 p+mmK bii2 |vac⟩ = |0⟩ M/ BibǶ 2M2`;v Bb, Evac =

1% !ω⃗k,s 2

UkX9jV

⃗k,s

AM RN93- i?2 /mi+? T?vbB+Bbib >2M/`BF "X :X *bBKB` M/ .B`F SQH/2` T`2/B+i2/ i?2 2tBbi2M+2 Q7  iBMv ii`+iBp2 7Q`+2 #2ir22M +HQb2Hv TH+2/ K2iH THi2b U +pBivV /m2 iQ `2bQMM+2b BM i?2 p+mmK 2M2`;v BM i?2 bT+2 #2ir22M i?2KX r?B+? Bb FMQrM b i?2 dz*bBKB` SQH/2` 2z2+iǴ r?B+? ?b #22M 2tT2`BK2MiHHv p2`B}2/ BM RNNd (Rk)X b r2 rBHH b?Qr Hi2`- i?2 2tBbi2M+2 Q7 p+mmK 2M2`;v HB2b i i?2 ?2`i Q7 bi`QM; +QmTHBM; i?2Q`vbBM+2 bBM;H2 iQKb Q` KQH2+mH2b +M #2 bi`QM;Hv +QmTH2/ iQ bBM;H2 KQ/2b Q7 p+mmK 2M2`;v BM +pBiB2b(Rj)X

R8

kXj 1t+BiQMb AM bQHB/ bii2 T?vbB+b M 2t+BiQM Bb  [mbBT`iB+H2 `2bmHiBM; 7`QK  #QmM/ bii2 Q7 M 2H2+i`QM@ ?QH2 TB` r?B+? `2 ii`+i2/ iQ 2+? Qi?2` #v i?2 2H2+i`QbiiB+ *QmHQK# 7Q`+2X h?2 2t+BiQM Bb M 2H2+i`B+HHv M2mi`H [mbBT`iB+H2 i?i 2tBbib BM BMbmHiQ`b- b2KB+QM/m+iQ`b M/ BM bQK2 HB[mB/bX h?2 2t+BiQM Bb `2;`/2/ b M 2t+BiiBQM Q7 +QM/2Mb2/ Kii2` i?i +M i`MbTQ`i 2M2`;v rBi?Qmi i`MbTQ`iBM; M2i 2H2+i`B+ +?`;2 (R9)X PM2 +M /BbiBM;mBb? #2ir22M 6`2MF2H M/ qMMB2`Ĝ JQii 2t+BiQMb- i?2 7Q`K2` ?pBM; Km+? H`;2` #BM/BM; 2M2`;B2b M/ Km+? bKHH2` "Q?` `/Bmb i?M i?2 Hii2` (R8)X MQi?2` KDQ` /Bz2`2M+2 Bb i?i rMMB2` 2t+BiQMb `2 +QMbi`m+i2/ QM /2HQ+HBx2/ 2H2+i`QMb 2t+Bi2/ 7`QK i?2 pH2M+2 #M/ iQ i?2 +QM/m+iBQM #M/X h?2b2 b2KB+QM/m+iQ` #M/b `2bmHi 7`QK i?2 T2`BQ/B+ BQMB+ bi`m+im`2 Q7 i?2 b2KB+QM/m+iQ` HiiB+2 (Re)X b QTTQb2/ iQ i?i- i?2 T?vbB+H TB+im`2 Q7 i?2 KQH2+mH` 2t+BiiBQMb ;BpBM; `Bb2 iQ 6`2MF2H 2t+BiQMb Bb  b2i Q7 2H2+i`QMb iB;?i iQ i?2B` BQMb- i?2b2 2H2+i`QMb brBi+?BM; 7`QK i?2 KQH2+mH` ;`QmM/ bii2 iQ i?2 KQH2+mH` }`bi 2t+Bi2/ H2p2H (Rd)X AM i?Bb rQ`F r2 b?HH KBMHv 7Q+mb QM 6`2MF2H 2t+BiQMb 2K2`;BM; BM CĜ;;`2;i2b Q7 Q`;MB+ /v2bX h?2 C@;;`2;i2b `2 +`vbiHHBi2b Q7 /v2 BM r?B+? i?2 i`MbBiBQM /BTQH2b Q7 i?2 +QMbiBim2Mi KQH2+mH2b bi`QM;Hv +QmTH2 iQ 7Q`K  +QHH2+iBp2 M``Qr HBM2rB/i? QTiB+H i`MbBiBQM TQbb2bbBM; Qb+BH@ HiQ` bi`2M;i? /2`Bp2/ 7`QK HH i?2 ;;`2;i2/ KQMQK2`b (R3)X

kXjXR h?2 [mMimK i?2Q`v Q7 6`2MF2H 1t+BiQMb h?2 T?vbB+H TB+im`2 Q7 i?2 2t+BiiBQMb ;BpBM; `Bb2 iQ 6`2MF2H 2t+BiQMb Bb  b2i Q7 2H2+i`QMb iB;?i iQ i?2B` BQMb- i?2b2 2H2+i`QMb brBi+?BM; 7`QK i?2 KQH2+mH` ;`QmM/ bii2 iQ i?2 }`bi KQH2+mH` 2t+Bi2/ H2p2H (R8)X q?BH2 #2BM; 2tT2`BK2MiHHv bim/B2/ Qp2`  rB/2 `M;2 Q7 2tT2`BK2Mib- 6`2MF2H 2t+BiQMb 7Q`KBM; BM #Qi? KQH2+mH2b M/ b2KB+QM/m+iQ`b ?p2 HbQ #22M  ?Qi iQTB+ Q7 i?2Q`2iB+H bim/B2bX AM i?Bb rQ`F r2 b?HH /2b+`B#2 6`2MF2H 2t+BiQMb BM i?2 irQ 2M2`;v H2p2H iQK TT`QtBKiBQM M/ /2`Bp2 Bib T`QT2`iB2b 7QHHQrBM; _27 (Re)X >Qr2p2`- Ai Bb BKTQ`iMi iQ `2K2K#2` i?i i?Bb TT`QtBKiBQM pB2rb i?2 KQH2+mH2 b  k 2M2`;v bii2 bvbi2KX q?BH2 BM `2HBiv KQbi KQH2+mH2b ?p2 KmHiBTH2 2M2`;v H2p2Hb r?B+? `2 M2;H2+i2/ BM i?Bb KQ/2HX

Re

AM i?Bb KQ/2H r2 +QMbB/2`  irQ H2p2H bvbi2K rBi? i?2 7QHHQrBM; k. #bBb

|↑⟩ =

*

1 0

+

⟨↓|=

*

0 1

+

UkX99V

AM bm+? +b2 i?2 KQH2+mH` >KBHiQMBM Bb  bmK Qp2` ++2bbB#H2 2M2`;B2bX ˆ exciton = Eg |↑⟩⟨↑| +Ee |↓⟩⟨↓| H

UkX98V

"v bm#biBimiBM; UkXjNV BMiQ UkX9yV r2  bBKTHB}2/ p2`bBQM Q7 i?2 >KBHiQMBM,

ˆ exciton = H

*

Ee 0 0 Eg

+

UkX9eV

6QHHQrBM; i?Bb bBKTHB}+iBQM -i?2 >KBHiQMBM +M #2 2tT`2bb2/ BM i?2 7Q`K Q7 TmHB Ki`Bt, ˆ exciton = 1 (Ee + Eg )Iˆ + 1 ∆E σ H ˆz UkX9dV 2 2 * + 1 0 q?2`2 Iˆ Bb i?2 B/2MiBiv Ki`Bt - ∆E = Ee − Eg M/ σ ˆz = Bb i?2 FMQrM TmHB Ki`BtX 0 −1

hQ ;2M2`HBx2 i?Bb ?KBHiQMBM 7Q`  KMv #Q/v bvbi2K UKmHiBTH2 6`2MF2H 2t+BiQMbV b2+QM/ [mM@ iBxiBQM T`Q+2/m`2 Bb +QMbB/2`2/ M/ i?2 >KBHiQMBM iF2b i?2 7Q`K,(RN), 1 ˆ exciton = 1 ∆Eˆ H e† eˆ = !ω0 eˆ† eˆ 2 2

UkX93V

r?2`2 ∆E Bb i?2 2t+BiiBQM 2M2`;v Q7 i?2 6`2MF2H 2t+BiQM- 7Q`  T?QiQM rBi? ∆E = !ω0 - eˆ† Bb i?2 +`2iBQM QT2`iQ` M/ eˆ Bb i?2 MMB?BHiBQM QT2`iQ` Q7 i?2 2t+BiQMX

Rd

kX9 *pBiv 2t+BiQM@TQH`BiQMb @ CvM2b @ *mKKBM;b KQ/2H h?2 CvM2b *mKKBM;b KQ/2H rb T`QTQb2/ BM RNej #v 1/rBM CvM2b M/ 6`2/ *mKKBM;bX h?2 Q`B;BMH Tm`TQb2 Q7 i?Bb KQ/2H rb i?2 bim/v i?2 `2HiBQMb?BT #2ir22M i?2 [mMimK i?2Q`v Q7 HB;?i 2KBbbBQM M/ i?2 b2KB@+HbbB+H i?2Q`v BM /2b+`B#BM; i?2 T?2MQK2MQM Q7 bTQMiM2Qmb 2KBbbBQM r?B+? Bb MQi T`2/B+i2/ BM i?2 b2KB@+HbbB+H i?2Q`v (R)X hQ /2`Bp2 i?Bb KQ/2H r2 b?HH /2}M2 i?2 +?`+i2`BbiB+b Q7 i?2 >KBHiQMBMX q2 +QMbB/2` i?2 7QHHQrBM; >KBHiQMBM BM i?2 b2+QM/ [mMiBxiBQM 7Q`K, ˆ P olariton = H ˆ f ield + H ˆ matter + H ˆ interaction H

UkX9NV

h?2 }2H/ QT2`iQ` b?HH #2 +QMbB/2`2/ b  [mMimK QT2`iQ` Q7 HB;?i- b /2`Bp2/ BM +?Ti2` UkXkV ˆ f ield = H

%

!ω⃗k,s

⃗k,s

#

a ˆ⃗†k,s a ˆ⃗k,s

1 + 2

$

UkX8yV

AM CvM2b *mKKBM;b KQ/2H- r2 +?QQb2 iQ M2;H2+i i?2 p+mmK 2M2`;v bbmKBM; r2 ?p2  p2`v ?B;? MmK#2` Q7 T?QiQMb BM i?2 +pBivX h?Bb `2/m+2b i?2 }2H/ i2`K iQ, ˆ f ield = H

%

!ωk a ˆ†k a ˆk

UkX8RV

k

"b2/ QM b2+iBQM UkXjXRV Qm` Kii2` Bb  6`2MF2H @ 1t+BiQM +?`+i2`Bx2/ #v  irQ bii2 bvbi2K BM b2+QM/ [mMiBxiBQM M/ BibǶ >KBHiQMBM Bb ;Bp2M #v, 1 ˆ exciton = 1 ∆Eˆ H e† eˆ = !ω0 eˆ† eˆ 2 2

UkX8kV

r?2`2 ω0 Bb  7`2[m2M+v Q7  T?QiQM `2[mB`2/ iQ #2 #bQ`#2/ BM Qm` irQ bii2 Kii2` iQ +`2i2 i?2 2t+BiiBQM- eˆ† Bb i?2 +`2iBQM QT2`iQ` M/ eˆ Bb i?2 MMB?BHiBQM QT2`iQ` Q7 i?2 2t+BiQMX

R3

ˆ interaction /2b+`B#2b i?2 BMi2`+iBQM #2ir22M HB;?i M/ Kii2` M/ iF2b i?2 7QHHQrBM; h?2 Hbi i2`K H 7Q`K mM/2` `QiiBM; rp2 TT`QtBKiBQM, ˆ interaction = H

%

!Ω(ˆ a†k eˆ + a ˆk eˆ† )

UkX8jV

k

q?2`2 ! Bb THM+FǶb +QMbiMi- Ω Bb i?2 p2`;2/ 2t+BiQM@T?QiQM /BTQH2 BMi2`+iBQM +QMbiMi Qp2` HH bTiBH /Bbi`B#miBQM M/ TQbBiBQM Q7 KQH2+mH` /BTQH2 KQK2MibX h?2 /BTQH2 BMi2`+iBQM +QMbiMi Bb /2`Bp2/ 7`QK i?2Q`v Q7 BMi2`+iBQM #2ir22M KQH2+mH` 2t+BiQMb rBi? i?2 2H2+i`B+ }2H/ KQ/2 BM i?2 +pBiv- Bi Bb +QMp2MB2Mi Ki2`BH T`K2i2` i?i +?`+i2`Bx2b i?2 2t+BiQM@T?QiQM +QmTHBM;- /2}M2/ MHQ;Qmb iQ i?2 iQK@T?QiQM BMi2`+iBQM BM  +pBiv (ky))X AM ;2M2`H i2`Kb- i?2 +QmTHBM; T`K2i2` Ω(⃗r) Bb  T`Q/m+i Q7 i?2 _#B 7`2[m2M+v Ω0 -  TQbBiBQM /2T2M/2Mi T`i ψ(⃗r) - M/  TQH`BxiBQM /2T2M/2Mi T`i cos(ξ)(R9), Ω(⃗r) = Ω0 ψ(⃗r)cos(ξ)

UkX89V

r?2`2 Ω0 Bb i?2 #bB+ +QmTHBM; T`K2i2`-ψ(⃗r) Bb i?2 MQ`KHBx2/ bTiBH T`i Q7 i?2 2H2+i`B+ }2H/ BM +pBiv- cos(ξ) Bb i?2 M;H2 #2ir22M M;mH` KQK2MimK M/ TQH`BxiBQM Q7 i?2 }2H/- ⃗rM /2MQi2b i?2 TQBMi r?2`2 i?2 }2H/ BMi2MbBiv UI = ϵ(⃗r) | E(⃗r) |2 ) Bb KtBKmK M/ ϵM Bb i?2 /B2H2+i`B+ +QMbiMi i i?Bb TQBMiX +QM+Hm/BM; i?i ϵM = ϵ(⃗rM )X 1H2+i`B+ }2H/ Q`B2MiiBQM i i?2 HQ+iBQM ⃗r Bb /2MQi2/ b eˆ- ⃗µ Bb i?2 i`MbBiBQM Ki`Bt /BTQH2 2H2K2Mi #2ir22M i?2 2t+Bi2/ M/ ;`QmM/ bii2 Q7 i?2 2t+BiQMX Ω0 Bb /2}M2/ BM i?2 7QHHQrBM; rv, |µ| Ω0 = !

"

!ω 2ϵM V

UkX88V

h?2 +pBiv KQ/2 pQHmK2 V Bb ;Bp2M #v,

V =

ϵ(⃗r) | E(⃗r) |2 d3⃗r ϵM | E(⃗rM ) |2

´´´

UkX8eV

h?2 MQ`KHBx2/ bTiBH T`i Q7 i?2 2H2+i`B+ }2H/ Bb ;Bp2M #v, ψ(⃗r) =

E(⃗r) | E(⃗rM ) |

RN

UkX8dV

am#biBimiBM; HH Q7 i?2 #Qp2 ;Bp2b i?2 7QHHQrBM; >KBHiQMBM 7Q`K Q7 i?2 TQH`BiQM ?KBHiQM- r?B+? Bb FMQrM b i?2 CvM2b@*mKKBM;b >KBHiQMBM, ˆ J.C = H

% k

% 1 !ωk a ˆ†k a ˆk + !ω0 eˆ† eˆ + !Ω(ˆ a†k eˆ + a ˆk eˆ† ) 2 k

h?Bb >KBHiQMBM Bb /B;QMHBx2/ #v mbBM; >QT}2H/ i`Mb7Q`KiBQM(RN), pˆk = Xk eˆk + Ck a ˆk

UkX83V

qˆk = −Ck eˆk + Xk a ˆk

UkX8NV

r?B+? biBb}2b i?2 MQ`KHBxiBQM +QM/BiBQM U| Xk |2 + | Ck |2 = 1V

h?2 +Q``2bTQM/BM; 2B;2Mbii2b `2 M2r TQH`BiQM bii2b- r?B+? ;2M2`H 7Q`K Bb(d), UkXeyV

| P± ⟩ = Ck | n, g⟩ ± Xk | n − 1, e⟩

r?2`2 M Bb i?2 MmK#2` Q7 T?QiQMb- | g⟩ `2T`2b2Mib i?2 ;`QmM/ bii2 M/ | e⟩ 2t+Bi2/ bii2 Q7 i?2 2t+BiQMX Ck , Xk `2 T`Q##BHBiv +Q2{+B2Mib Q7 HQr2` M/ mTT2` TQH`BiQM bii2bX PM2 +M /2}M2 ∆E(k) b /2imMBM; #2ir22M T?QiQMB+ M/ 2t+BiQMB+ KQ/2b BM i?2 7QHHQrBM; rv, UkXeRV

∆E(k) = Eexciton − Ecavity (k) 6QHHQrBM; i?Bb /2}MBiBQM- i?2 +Q2{+B2Mib Xk M/ Ck `2 ;Bp2M #v(RN- kR), 1 | Xk |2 = 2

*

1 | Ck | = 2

*

2

∆E(k)

+

UkXekV

∆E(k)

+

UkXejV

1+ , ∆E(k)2 + 4!2 Ω2

1− , ∆E(k)2 + 4!2 Ω2

h?2b2 +Q2{+B2Mib `2 i?2 `2HiBQMb #2ir22M i?2 T?QiQMB+ M/ 2t+BiQMB+ KQ/2b BM i?2 +pBiv- 7Q` BMbiM+2- 7Q` | Ck |= 0 i?2 TQH`BiQM #`M+?2b rBHH #2 +QKTH2i2Hv T?QiQMB+ M/ 7Q` | Xk |= 0 +QKTH2i2Hv 2t+BiQMB+X 7Q` x2`Q /2imMBM; U∆E = 0V i?2 TQH`BiQMb `2 2[mHBiv r2B;?i2/ bmT2`TQbBiBQMb Q7 T?QiQMb M/ 2t+BiQMb, ky

1 | Xk |=| Ck |= √ 2

UkXe9V

6QHHQrBM; i?2 T`Q+2/m`2- i?2 2M2`;B2b Q7 i?2 TQH`BiQMb `2 ;Bp2M #v /B;QMHBxiBQM Q7 i?2 M2r >KBHiQMBM M/ `2 ;Bp2M #v, $ ! Eexciton + Ecavity − 4!2 Ω2 + (Eexciton − Ecavity )2

1 ELP (k) = 2

#

1 EU P (k) = 2

#

$ ! Eexciton + Ecavity + 4!2 Ω2 + (Eexciton − Ecavity )2

UkXe8V

UkXeeV

b b?QrM BM 6B; kXj- r2 +QKT`2 i?2b2 /BbT2`bBQM `2HiBQMb iQ i?2 /BbT2`bBQM Q7 T?QiQMb BM  2KTiv 6#`v@S2`Qi +pBiv M/ iQ #`2 KQH2+mH2bX h?2 /2T2M/2M+2 QM i?2 rp2 p2+iQ` k TT2`b iQ #2 bB;MB}+Mi- r?B+? rBHH #2 /Bb+mbb2/ M/ p2`B}2/ 2tT2`BK2MiHHv BM i?2 M2ti +?Ti2`X PM2 +M b22 i?i i `2bQMM+2 Eexciton = Ecavity i?2 TQH`BiQM 2M2`;B2b iF2 i?2 7Q`K, ELP,U P = Eexciton ± !Ω

UkXedV

6Q` i?Bb +QM/BiBQM- i?2 HQr2` M/ mTT2` TQH`BiQM 2M2`;B2b ?p2 KBMBKmK b2T`iBQM- EU P −ELP = 2!Ω- r?B+? Bb i?2 FMQrM dz_#B bTHBiiBM;Ǵ 2M2`;vX q?BH2 #2BM; M ++m`i2 KQ/2H 7Q` +H+mHiBM; 2M2`;v H2p2Hb 7Q` TQH`BiQMB+ bvbi2Kb- i?2 CvM2b@ *mKKBM;b >KBHiQMBM /Q2b MQi BM+Hm/2 Mv +QmTHBM; iQ M 2MpB`QMK2Mi H2/BM; iQ /2+vX AM Q`/2` iQ BM+Hm/2 i?2 irQ HQbb@K2+?MBbKb r2 +M ;2M2`HBx2 i?2 KQ/2H #v //BM; i?2 /2+v `i2b Γ, k b M BK;BM`v T`ib iQ i?2 2M2`;B2b Q7 i?2 +pBiv M/ i?2 KQH2+mH2 `2bT2+iBp2HvX AM Q`/2` iQ ;2i `2H 2M2`;B2b ++Q`/BM; iQ `2HiBQMb UkXee-kXe8V r2 Kmbi `2[mB`2 Ω ≫ Γ, κ- r?B+? Bb i?2 +b2 Q7 i?2 bi`QM; +QmTHBM; `2;BK2X AM i?Bb +b2 i?2 2M2`;v 2t+?M;2 `i2 #2ir22M i?2 KQH2+mH2b M/ i?2 +pBiv Bb 7bi2` i?M i?2 `i2 Q7 /BbbBTiBQMX

kR

2.5

Photons Excitons U-Polaritons L-Polaritons

2.4

![#$]

2.3

2.2

2.1

2.0 -10

-8

-6

-4

-2

&' =

0

2* +

2

sin(0)

4

6

8

10

1 34

6B;m`2 kXj,  THQi Q7  ivTB+H /BbT2`bBQM Q7 T?QiQMb BM  6#`v@S2`Qi +pBiv ++Q`/BM; iQ UkXRdV1 rBi? E0 = 2.11eV M/ −10 < kx < 10 µm

kk

*?Ti2` j P`;MB+ JB+`Q+pBiB2b @ S`2T`iBQM M/ *?`+i2`BxiBQM jXR J2i?Q/b jXRXR P`;MB+ QTiB+H +pBiB2b T`2T`iBQM h?2 T`2T`iBQM Q7 +pBiv bKTH2b ?/ i?`22 KBM bi;2bX 6B`bi- r2 bi`i2/ rBi? bTmii2`BM;  30nm bBHp2` Hv2` QM  +H2M ;Hbb bm#bi`i2X a2+QM/- r2 //2/  Hv2` Q7 L0 ≈ 150nm i`MbT`2Mi UBM pBbB#H2 HB;?iV TQHvK2` /QT2/ rBi? C@;;`2;i2 KQH2+mH2b Uh."*VX h?Bb rb /QM2 #v bTBM@+QiBM; Ui 810rpmV  TQHvK2`fh."* bQHmiBQMX h?2 bQHmiBQM rb K/2 #v /BbbQHpBM; SQHvpBMvH H+Q?QH U205, 000M w) BM ri2` U5wtW) i 80◦ 7Q` 7 ?Qm`b- +QQHBM; iQ `QQK i2KT2`im`2 M/ KBtBM; i 1 : 1 `iBQ rBi? h."* /BbbQHp2/ BM ri2` U0.5wtW VX S`BQ` iQ bTBM +QiBM; i?2 bQHmiBQM rb }Hi2`2/ #v mbBM;  0.2µm MvHQM K2K#`M2 }Hi2`X 6BMHHv- r2 /2TQbBi2/  b2+QM/ i?BM KB``Q` Hv2` QM i?2 +pBiv UrBi?  i?B+FM2bb Q7 30nmVX AM Q`/2` iQ ;2i i?2 2t+i i?B+FM2bb r?B+? +Q``2bTQM/b iQ ?H7 Q7 i?2 rp2H2M;i? BM i?2 +pBiv- r2 p`v i?2 2t+i i?B+FM2bb Q7 i?2 KQH2+mH` Hv2` #v }M2@imMBM; i?2 bTBM `TKX AM Q`/2` iQ T`Q#2 TQH`BiQMb rBi? MQM2@x2`Q KQK2MimK M/ bBKBH` T?QiQMB+ M/ 2t+BiQMB+ +QKTQM2Mib- i?2 +pBiB2b r2`2 imM2/ iQ #2 i `2bQMM+2 rBi? i?2 2t+BiQM 7Q` θ = 45◦ X hQ T`2p2Mi i?2 #bQ`TiBQM Q7 ?mKB/Biv 7`QK i?2 B`- r?B+? z2+ib bT2+i`H T`QT2`iB2b- i?2 bKTH2b r2`2 biQ`2/ BM  p+mmK +?K#2`X 7i2` i?2 bKTH2b `2 mb2/ 7Q` b2p2`H ?Qm`b BM 2tT2`BK2Mii?2v `2 Tmi BM  b+B2MiB}+ Qp2M M/ `2 ?2i2/ iQ 80◦ 7Q` 10 − 15 KBMmi2bX h?2b2 +QM/BiBQMb `2 2MQm;? iQ 2pTQ`i2 i?2 ri2` KQH2+mH2b M/ /Q MQi /2bi`Qv i?2 bKTH2X

kj

Empty cavity Transmission [%]

ABS

1.0

0.5

0 500

550

600

650

700

Wavelength[nm]

UV

750

15

30

Transmission [%]

Molecular layer

10

5

0

500

550

600

650

700

Wavelength[nm]

U#V

750

Strong Coupling: Cavity + Molecules 20° 0° ! =45°

15

0

500

550

600

650

700

750

Wavelength[nm]

U+V

6B;m`2 jXR, h`MbKBbbBQM bT2+i` /2KQMbi`iBM; bi`QM; +QmTHBM; #2ir22M HB;?i +QM}M2/ BM KB+`Q@ +pBiv M/ KQH2+mH` 2t+BiQMbX h?2 KB+`Q@+pBiv M/ KQH2+mH` 2t+BiQMb TQbb2bb `2bQMMi 7`2[m2M@ +B2b Q7 ωcav M/ ωexciton X q?2M bi`QM; +QmTHBM; Q++m`b- i?2 +QKTQbBi2 bvbi2K b?Qrb M2r `2bQMM+2b i ωLP M/ ωU P X h?2 +pBiv Bb imM2/ iQ #2 i `2bQMM+2 i 45◦ - 7Q` `272`2M+2- Qz `2bQMM+2 U20◦ , 0◦ ) i`MbKBbbBQM bT2+i` `2 /2KQMbi`i2/X 6B; jXR b?Qrb  K2bm`2K2Mi Q7 M #bQ`TiBQM bT2+i`mK Q7 #`2 KQH2+mH2b-  i`MbKBbbBQM bT2+i`mK Q7 M 2KTiv +pBiv M/  i`MbKBbbBQM bT2+i`mK Q7  +pBiv rBi? KQH2+mH2bX h?2 K2bm`2K2Mib T`QpB/2  /B`2+i 2pB/2M+2 Q7 bi`QM; +QmTHBM; b i?2 HQr2` M/ mTT2` TQH`BiQMb +M #2 2bBHv Q#b2`p2/ BM 6B; jXR U+V i?2 bTHBiiBM; Bb +H2`Hv Q#b2`p2/ M/ i?2 bi`QM;@+QmTHBM; +QM/BiBQM Bb biBb}2/- r2 b22 i?i i?2 `2bQMM+2 Bb bi`QM;Hv /2T2M/2Mi QM i?2 M;H2 Q7 BM+B/2M+2X h?2 `2bmHib HbQ b2`p2 b  p2`B}+iBQM Q7 Qm` +?QB+2 Q7 Ki2`BHb M/ K2i?Q/b Q7 T`2T`iBQMX

jXRXk .BbT2`bBQM K2bm`2K2Mib, M;H2@`2bQHp2/ i`MbKBbbBQM  ivTB+H +QKK2`+BH mpfpBb i`MbKBbbBQMf#bQ`TiBQM bT2+i`QK2i2` K2bm`2b  bT2+i`mK #v BHHm@ KBMiBM; HB;?i i  bBM;H2 rp2H2M;i?- +H+mHiBM; i?2 `2HiBp2 [mMiBiv 7Q` i`MbKBbbBQMf#bQ`TiBQM rBi? `2bT2+i iQ i?2 `272`2M+2 bKTH2 M/ `2T2ib i?Bb T`Q+2bb KmHiBTH2 iBK2b 7Q` i?2 /2KM/2/ `M;2 Q7 rp2H2M;i?bX h?Bb T`Q+2bb Bb p2`v bHQr M/ KQbi +QKK2`+BH bT2+i`QK2i2`b /Q MQi HHQr iQ K2@ bm`2 i KmHiBTH2 M;H2b Q7 BM+B/2M+2X h?2 }`bi ;QH BM #mBH/BM; i?Bb QTiB+H b2imT rb iQ Qp2`+QK2 i?2 Q#bi+H2b K2MiBQM2/ #Qp2X AM //BiBQM iQ i?i- +QKT`2/ rBi? +QKK2`+BH bT2+i`QK2i2`bi?Bb b2imT HbQ HHQr2/ mb iQ iF2 K2bm`2K2Mib rBi? T`2+Bb2 /DmbiK2Mib BM M;H2 Q7 BM+B/2M+2TQH`BxiBQM M/ K2+?MB+H TQbBiBQM /DmbiK2Mi Q7 i?2 bKTH2 M/ T2`7Q`K [mB+F K2bm`2K2MibX  bF2i+? Q7 i?2 QTiB+H b2imT mb2/ iQ K2bm`2 i?2 M;H2@`2bQHp2/ i`MbKBbbBQM bT2+i` TT2`b BM 6B; jXkX  }#2`@+QmTH2/ >HQ;[email protected]`BmK HB;?i bQm`+2 Bb mb2/ 7Q` ;2M2`iBM;  #`Q/#M/ bT2+i`mK- +Qp2`BM;  `M;2 Q7 k8y@Rk8yMKX h?2 HB;?i 2tBiBM; i?2 }#2` Bb +QHHBKi2/ mbBM;  H2Mb Q7 8yKK 7Q+H H2M;i? M/ i?2M T`QD2+i2/ BMiQ i?2 bKTH2 i?`Qm;? M B`Bb- r?B+? Bb mb2/ iQ HBKBi i?2 #2K /BK2i2` iQ RKK- bm+? i?i  `2HiBp2Hv bKHH `2 Q7 i?2 bKTH2 Bb K2bm`2/- `2/m+BM; i?2 2z2+i Q7 BM?QKQ;2M2BiB2bX aBM+2 i?2 +pBiv /BbT2`bBQM /2T2M/b QM i?2 TQH`BxiBQM Q7 HB;?ik9

r2 BMb2`i  HBM2` TQH`Bx2` #27Q`2 i?2 bKTH2 M/ T2`7Q`K i?2 K2bm`2K2Mib 7Q` T E M/ T M TQH`BxiBQMb b2T`i2HvX 7i2` i?2 bKTH2 i?2 i`MbKBii2/ #2K Bb 7Q+mb2/ BMiQ M QTiB+H }#2` mbBM; M +?`QKiB+ H2Mb UL2- *QHHBKiBM; G2MbV r?B+? +``B2b i?2 HB;?i BMiQ  TQ`i#H2 bT2+i`QK2i2` UpMi2b- paT2+@lGaje93VX h?2 bKTH2 Bb KQmMi2/ QM  `QiiBQM bi;2 r?B+? HHQrb mb iQ b2i i?2 M;H2 Q7 BM+B/2M+2 rBi?BM  `M;2 Q7 ±60◦ X h?2 bT2+i` r2`2 iF2M rBi? M BMi2;`iBQM iBK2 Q7 eKb M/ p2`;2/ Qp2` kyyy +[mBbBiBQMb- r?B+? ;Bp2b  MQBb2 H2p2H Q7 yXRW BM i?2 i`MbKBbbBQM bT2+i`mK i i?2 pBbB#H2 `M;2X  #b2HBM2 7Q` i?2 i`MbKBbbBQM bT2+i` rb +[mB`2/ rBi?  KB+`Qb+QT2 ;Hbb bHB/2 B/2MiB+H iQ i?i mb2/ b  bm#bi`i2 7Q` i?2 +pBiv bKTH2bX h?2 i`MbKBbbBQM bT2+i` r2`2 `2+Q`/2/ 7Q` i?2 r?QH2 ++2bbB#H2 M;mH` `M;2- rBi? bi2Tb Q7 ±5◦ M/ 7Q` 2+? M;H2 i?2 irQ i`MbKBbbBQM T2Fb +Q``2bTQM/BM; i?2 TQH`BiQMB+ bii2b r2`2 mb2/ BM Q`/2` iQ 2ti`+i i?2 2M2`;v@KQK2MimK `2HiBQM- #v, ELP,U P =

hc

k∥ =

λLP,U P

2π λLP,U P

sinθ

UjXRV

r?2`2 λLP,U P `2 i?2 T2F rp2H2M;i? 7Q` HQr2` M/ mTT2` TQH`BiQMbX

6B;m`2 jXk,  bF2i+? Q7 i?2 QTiB+H b2imT- i?2 r?Bi2 HB;?i Bb 2KBii2/ 7`QK i?2 HB;?i bQm`+2 i`Qm;? M QTiB+H }#2` BMiQ  +QHHBKiBM; H2Mb UGRVX Ai Tbb2b iQ  TQH`Bx2` USGV iQ /2}M2 HB;?i TQH`BxiBQM (T M, T E) M/ i`Qm;? M B`Bb r?B+? +QMi`QHb i?2 /BK2i2` Q7 i?2 #2KX i?2M i?2 #2K Tbb2b i`Qm;? i?2 bKTH2- r?B+? +M #2 iBHi2/ #v M M;H2 θ Up`B2b i pHm2b 7`QK 0◦ iQ 60◦ VX h?2 i`MbKBii2/ HB;?i i?2M Tbb2b i`Qm;?  b2+QM/ +QHHBKiBM; H2Mb UGkV M/ ;Q2b i`Qm;? M QTiB+H }#2` BMiQ M pMi2b bT2+i`QK2i2`X AM Q`/2` iQ `2/m+2 MQBb2 r2 mb2 6ms K2bm`2K2Mib rBi? M p2`;BM; Q7 2000 iBK2b- r2 ;2i M 2``Q` Q7 ±0.1W rBi? ivTB+H K2bm`2K2Mi iBK2 Q7 QMHv b2p2`H b2+QM/bX

k8

jXRXj .BbT2`bBQM K2bm`2K2Mib, M;H2@`2bQHp2/ `2~2+iBQM KB+`Qb+QTv h?2 b2+QM/ TT`Q+? iQ K2bm`2 i?2 /BbT2`bBQM `2HiBQM Q7 Qm` bKTH2b rb #v #mBH/BM; MQi?2` QTiB+H b2imT r?B+? b2`p2/ b  bBM;H2 b?Qi /BbT2`bBQM `2HiBQM bT2+i`QK2i2`X *QKT`2/ iQ i?2 T`2pBQmb b2imT- i?Bb TT`Q+? Bb bmT2`BQ` bBM+2 Bi +M K2bm`2  /BbT2`bBQM `2HiBQM Q7  bKTH2 #v bBM;H2 b?Qi K2bm`2K2Mi M/ BM  p2`v bKHH bm`7+2 `2 UivTB+HHv Q7 i2Mb Q7 KB+`QMbVX S`2+Bb2 /BbT2`bBQM K2bm`2K2Mib BM bTiBH `2b Q7 i?Bb ivT2 HHQrb iQ Qp2`+QK2 i?2 Bbbm2b +`2i2/ #v MQM2@ ?QKQ;2M2Qmb bKTH2b- r?B+? +`2i2b p`BQmb +?M;2b BM i?2 i`MbKBbbBQM M/ `2~2+i2/ bT2+i`mKbX *QKT`BM; iQ i?2 T`2pBQmb TT`Q+?- i?Bb TT`Q+? 2HBKBMi2b i?2 M22/ Q7 K2+?MB+H +HB#`iBQM Q7 i?2 M;H2 Q7 BM+B/2M+2- r?B+? HHQrb iQ Q#iBM  T`2+Bb2 bBM;H2 b?Qi K2bm`2K2Mi Q7 i?2 2MiB`2 bT2+i`mK- HQM; rBi? M BK;BM; +T#BHBiv i?i 2M#H2b  HQ+H K2bm`2K2MiX h?Bb b2imT HHQrb iQ K2bm`2 i?2 `2~2+iBQM bT2+i`mKb- r?B+? `2 p2`v ?`/ iQ Q#iBM BM i?2 b2imT T`2b2Mi2/ BM i?2 T`2pBQmb bm#+?Ti2` M/ `2[mB`2 KQ/B}+iBQMb BM T`ib M/ QTiB+H /2bB;MX h?2 ;2M2`H B/2 Q7 i?Bb b2imT Bb iQ T`Q#2 i?2 bKTH2 BM  bKHH `2 r?B+? 2HBKBMi2b i?2 bTiBH 2z2+i Q7 BM?QKQ;2M2BiB2b U50 ∗ 50µm2 ) #v 7Q+mbBM; HB;?i pB Q#D2+iBp2 H2MbX h?2 HB;?i Bb 7Q+mb2/ rBi?  rB/2 `M;2 Q7 BM+B/2M+2 M;H2b- r?B+? HHQrb  bBM;H2 b?Q`i K2bm`2K2Mi Q7 /BbT2`bBQMX Ai Bb /QM2 #v BK;BM; i?2 7`@}2H/ Q7 i?2 #+F 7Q+H THM2 Q7 i?2 Q#D2+iBp2 iQ  bHBi Q7  bT2+i`QK2i2`r?B+? 2M#H2b mb iQ b2T`i2 i?2 /Bz2`2Mi M;H2b X  bF2i+? Q7 i?2 QTiB+H b2imT mb2/ iQ K2bm`2 i?2 M;H2@`2bQHp2/ `2~2+iBQM KB+`Qb+QTv TT2`b BM 6B; jX9X M BMp2`i2/ KB+`Qb+QT2 UPHvKTmb AsdRV Bb mb2/ b  #bBb 7Q`  ;2M2`B+ KB+`Qb+QTv BK;BM; b2imT +QK#BM2/ rBi? M PHvKTmb r?Bi2 HB;?i bQm`+2 Ul@G>RyyG@jVX h?2 HB;?i 2tBiBM; i?2 HB;?i bQm`+2 Bb `2~2+i2/ #v i?2 #2K bTHBii2` M/ i?2M 7Q+mb2/ iQ i?2 i?2 bKTH2 #v Q#D2+iBp2 H2Mb UPHvKTmb _JaeysVX h?2 #2K Bb i?2M `2~2+i2/ #+F BMiQ i?2 Q#D2+iBp2 H2Mb- r?B+? iQ;2i?2` rBi? im#2 H2Mb L1 +`2i2b M BK;BM; Q7 i?2 bKTH2 iQ i?2 bHBi Q7 i?2 bT2+i`QK2i2` U L1 Bb Q`B;BMHHv  im#2 H2Mb BMbB/2 i?2 BMp2`i2/ KB+`Qb+QT2VX hQ brBi+? 7`QK i?Bb KQ/2 iQ M;H2@`2bQHp2/ KB+`Qb+QTv r2 // MQi?2` H2Mb L2 r?B+? Bb iQ;2i?2` rBi? L1 +ib b M 2z2+iBp2 H2MbX h?2 2z2+iBp2 H2Mb UL1 rBi? L2V ?b M 2z2+iBp2 7Q+H H2M;i? r?B+? HHQrb i?2 BK;BM; Q7 i?2 #+F 7Q+H THM2 Q7 i?2 Q#D2+iBp2 iQ i?2 bT2+i`QK2i2` bHBiX h?2 bT2+i`QK2i2` ;Bp2b M;mH` /2+QKTQbBiBQM HQM; i?2 bHBi Ui?2 p2`iB+H /B`2+iBQMVX L2 Bb TH+2/ QM  ~BT KQmMi iQ brBi+? #2ir22M BK;BM; M/ bT2+i`Qb+QTv KQ/2bX S`BQ` iQ i?2 bHBi r2 //  TQH`Bx2` r?B+? HHQrb iQ K2bm`2 i T E M/ T M TQH`BxiBQMbX h?2 bT2+i`QK2i2` Bb 2[mBTT2/ rBi?  b*JPa +K2` Ua*hjky @ S`BM+2iQM BM/mbi`B2b- SBtB2b b*JPaVX q2 mb2/ M 2pTQ`i2/ i?BM bBHp2` KB``Q` b `272`2M+2- r?B+? Bb K/2 #v bTmii2`BM;  100nm Hv2` Q7 bBHp2` QM  +H2M ;Hbb bm#bi`i2X

ke

600

!"#

%$550

500

450

400 300

400

500

600

&[()]

6B;m`2 jXj, AK;2 Q#iBM2/ rBi? i?2 bT2+i`QK2i2` Ua*hjky @ S`BM+2iQM BM/mbi`B2b- SBtB2b b*JPaV r?2M  `272`2M+2 bKTH2 rb TH+2/- i?2 BK;2 rb iF2M rBi? T E TQH`BxiBQM AM 6B; jXj r2 +M b22  ivTB+H BK;2 Q#iBM2/ i i?2 bT2+i`QK2i2`X b b22M BM i?2 };m`2- r2 Q#iBM ?2B;?i UK2bm`2/ BM `r TBt2HbV p2`bmb rp2H2M;i? UK2bm`2/ BM nmVX AM Q`/2` iQ +HB#`i2 Qm` bvbi2K 7`QK TBt2H iQ M;H2@`2bQHp2/ bT2+i`QK2i2`  .o. rb mb2/- r2 mb2  .o. b  ?B;?@ `2bQHmiBQM ;`iBM; rBi?  FMQrM T2`BQ/B+Biv Q7 1.45µmX h?2 `2HiBQM #2ir22M i?2 `2bQHp2/ M;H2 M/ TBt2H ?2B;?i Bb ;Bp2M #v "`;;Ƕb Hr Q7 /Bz`+iBQM, θ = arctan ((s(y − y0 )))

UjXkV

r?2`2 θ Bb i?2 M;H2- y Bb i?2 TBt2H +QQ`/BMi2- y0 Bb i?2 TBt2H +QQ`/BMi2 2t+iHv i i?2 KB//H2 Q7 i?2 bT2+i`mK- 7QmM/ iQ #2 y0 = 510nm #v mbBM;  .o.- s Bb  b+HBM; 7+iQ` 7QmM/ iQ #2 s = 1/120X 6BMHHv- iQ Q#iBM /BbT2`bBQM `2HiBQMb UkXR9-kXRdV r2`2 mb2/X

kd

6B;m`2 jX9,  bF2i+? Q7 i?2 QTiB+H b2imT- irQ KBM QTiB+H Ti?b `2 T`2b2Mi2/X RV i?2 HB;?i 2KBii2/ 7`QK i?2 }`bi HB;?i bQm`+2 Ua*RV Tbb2b i?`Qm;?  50 : 50 #2K bTHBii2` U"aV- Bb 7Q+mb2/ QM i?2 bKTH2 #v mbBM;  ×60 Q#D2+iBp2 H2Mb rBi? 0.9N A M/ i?2M i?2 `2~2+iBQM 7`QK i?2 bKTH2 Tbb2b i`Qm;? i?2 Q#D2+iBp2 H2Mb iQ i?2 #2K bTHBii2` U"aV- `2~2+i2/ #v  KB``Q` UJRV iQ  H2Mb UGRV M/  TQH`Bx2` USGVX h?2 Hbi H2Mb Bb QTiBQMH M/ +M #2 `2KQp2/X A7 #b2Mi i?2M i?2 BK;BM; KQ/2 Bb QM M/ M BK;BM; Q7 i?2 bKTH2 QM i?2 bHBi Q7 i?2 bT2+i`QK2i2` Bb /QM2- B7 Gk Bb T`2b2Mi i?2M M BK;BM; Q7 i?2 6Qm`B2` THM2 Q7 i?2 KB+`Qb+QT2 Q#D2+iBp2 QM i?2 2Mi`M+2 bHBi Q7 i?2 bT2+i`QK2i2` Bb /QM2X

k3

jXRX9 LmK2`B+H bBKmHiBQMb AM Q`/2` iQ pHB/i2 Qm` 2tT2`BK2MiH K2bm`2K2Mib Q7 i?2 /BbT2`bBQM M/ iQ 2ti`+i i?2 +pBiv T`K2i2`b- T`2b2Mi2/ BM i?2 T`2pBQmb bm#b2+iBQM r2 mb2/  b2`B2b Q7 bBKmHiBQMb iQ +H+mHi2 i?2 /BbT2`bBQM `2HiBQM Q7 Qm` ?v#`B/ +pBiB2bX h?2 bBKmHiBQM r2 mb2/ rb #b2/ QM i?2 h@Ki`Bt 7Q`@ KHBbK- r?B+? +H+mHi2b i?2 i`MbKBbbBQMf`2~2+iBQM bT2+i`mK Q7 KmHiBHv2` bi`m+im`2bX h@Ki`Bt 7Q`KHBbK Bb #b2/ QM bQHpBM; Jtr2HHǶb 2[miBQMb BM 2+? Hv2`- bbmKBM; 2+? Hv2` +M #2 /2@ b+`B#2/ #v  mMB7Q`K rp2H2M;i?@/2T2M/2Mi BM/2t Q7 `27`+iBQMX lM/2` i?Bb bbmKTiBQM i?2 2H2+i`QK;M2iB+ }2H/ +M #2 /2b+`B#2/ b  bmK Q7  7Q`r`/ UEf V M/ #+Fr`/ UEb V T`QT;iBM; THM2@rp2b, . ⃗ f = eˆf fj ∗ exp kx x + k j (z − z0j ) − ωt E z

UjXjV

. ⃗ b = eˆb bj ∗ exp kx x − kzj (z − z0j ) − ωt E

UjX9V

f,b q?2`2 HB;?i TQH`BxiBQM- zoj Bb i?2 TQbBiBQM Q7 i?2 `B;?i BMi2`7+2 Q7 i?2 jth Hv2` M/ !eˆ Bb i?2 ! ωn j 2 2 kz = kj − kx = ( c j )2 − kx2 - nj Bb i?2 rp2H2M;i?@/2T2M/2Mi `27`+iBp2 BM/2t Q7 i?2 jth Hv2`X h?2 HB;?i 2Mi2`BM; i?2 bi`m+im`2 Bb M;H2 /2T2M/2Mi #v kx = ωn sinθ M/ ?b  p+mmK rp2H2M;i? c Q7 λX

h?2 2MiB`2 bi`m+im`2 rBHH #2 +QKTQb2/ Q7 N Hv2`b Q7 i?B+FM2bb lj M/ 2+? Hv2` rBHH ?p2  +Q``2bTQM/BM; `27`+iBp2 BM/2t nj X q2 iF2 i?2 bm#bi`i2 b  b2KB@}MBi2 Hv2` rBi?  `27`+iBp2 BM/2t nj M/ bbmK2 i?2 BM+B/2Mi }2H/ Bb MQ`KHBx2/ iQ R- b BHHmbi`i2/ BM 6B; jX8X

6B;m`2 jX8,  bF2i+? Q7 i?2  ivTB+H KmHiBHv2` bi`m+im`2 bQHp2/ #v h@Ki`Bt 7Q`KHBbK qBi?BM 2+? Hv2` j i?2 KTHBim/2b Q7 #Qi? bB/2b `2 `2Hi2/ #v i?2 T`QT;iQ` Ki`Bt, *

fjL bLi

+

=

Tjprop

*

fjR bR j

+

=

*

exp (−ikzj Lj ) 0 0 exp (+ikzj Lj ) kN

+*

fjR bR j

+

UjX8V

*

+ * + fjL fjR r?2`2 `2 i?2 +QKTH2t KTHBim/2b i i?2 H27i bB/2 Q7 i?2 Hv2` M/ `2 i?2 +QKTH2t bLj bR j KTHBim/2b i i?2 `B;?i bB/2 Q7 i?2 Hv2`X ⃗ ⃗ AM //BiBQM iQ i?i- * i?2 }2H/b + E∥ M/ H∥ `2 +QMiBMmQmb 7Q` i?2 }2H/b i?`Qm;? i?2 BMi2`7+2- i?2 fjL +QKTH2t KTHBim/2b `2 i`Mb7Q`K2/ #v i?2 BMi2`7+2 Ki`Bt ;Bp2M #2HQr, bLj * + * + * +* + 1 r¯ R L L fj+1 f f j j t t¯ = Tjint = UjXeV r 1 R L L bj+1 bi b ¯ j t t Ai +M #2 b?QrM i?i r?2M +`QbbBM; i 2+? THM2 i?2 i`MbKBbbBQM M/ `2~2+iBQM KTHBim/2b 7Q` T E/T M TQH`BxiBQMb `2 /2`Bp2/ 7`QK 7`2bM2H 2[miBQMb U7Q` MQM2 K;M2iB+ Ki2`BHbV (kk), tT E =

tT M =

kzj+1 − kzj kzj+1 + kzj

rT E =

2ϵ2 kzj+1 ϵ2 kzj+1 + ϵ1 kzj

ϵ2 kzj+1 − ϵ1 kzj ϵ2 kzj+1 + ϵ1 kzj

rT M =

UjXdV

2ϵ2 kzj+1 ϵ2 kzj+1 + ϵ1 kzj

UjX3V

q?2`2 ϵ1,2 `2 i?2 /B2H2+i`B+ +Q2{+B2MibX h?2 r?QH2 KmHiBHv2` bi`m+im`2 +M #2 2tT`2bb2/ b  b2`B2b Q7 BMi2`7+2 M/ T`QT;iBQM Ki`B+2b BM i?2 7QHHQrBM; rv, *

fN +1 bN +1

+

=

prop prop int int TNint × TNprop × TNint−1 × TNprop −1 × TN −2 × TN −2 × ... × T1 × T0

*

f0 b0

+

= T ML

*

+ f0 b0 UjXNV

++Q`/BM; iQ UjXNV- i?2 +Q2{+B2Mib tM L , rM L `2 ;Bp2M #v,

tM L =

1

rM L =

ML T1,1

ML T2,1 ML T1,1

UjXRyV

6`QK r?B+? i?2 BMi2MbBiv +Q2{+B2Mib +M #2 Q#iBM2/, T =

nR cosθt | tM L |2 nL cosθi

R =| rM L |2

q?2`2 T M/ R `2 i?2 i`MbKBbbBQM M/ `2~2+iBQM BMi2MbBiB2bX

jy

UjXRRV

jXk _2bmHib q2 T`2b2Mi i?2 `2bmHib Q7 /BbT2`bBQM K2bm`2K2Mib Q7 TQH`BiQMb 2K2`;BM; BM Q`;MB+ KB+`Q@+pBiB2bb2p2`H bKTH2b r2`2 7#`B+i2/ #v i?2 K2i?Q/b T`2b2Mi2/ BM +?Ti2` UjXRXRVX h?2 7mHH KB+`Q@+pBiv rb BMp2biB;i2/ i `QQK i2KT2`im`2 #v K2Mb Q7 M;H2@`2bQHp2/ i`MbKBbbBQM bT2+i`Qb+QTv b K2MiBQM2/ BM +?Ti2` UjXRXkV- r2 K2bm`2/ i?2 i`MbKBbbBQM bT2+i`mK 7Q` M;H2b `M;BM; #2ir22M −60◦ M/ −60◦ rBi? bi2Tb Q7 5◦ M/ M M;mH` b2H2+iBQM Q7 ∆θ = 1◦ - 7Q` 2+? bT2+i`mK i?2 K2M pHm2b Q7 HQr2` M/ mTT2` TQH`BiQM T2Fb `2 2ti`+i2/ BM K2Mb Q7 irQ pHm2b Q7 rp2H2M;i?bX q2 +H+mHi2 i?2 2M2`;v Q7 HQr2` M/ mTT2` TQH`BiQMb i 2+? M;mH` bi2T #v i?2 FMQrM `2HiBQM, 1239.8 E(eV ) = λ(nm) M/ i?2 pHm2 Q7 kx Bb Q#iBM2/ 7`QK `2HiBQM UkXR9VX h?2 pHm2b Q7 HQr2` M/ mTT2` TQH`BiQM 2M2`;B2b `2 T`2b2Mi2/ p2`bmb i?2 M;H2 /2T2M/2Mi kx iQ +`2i2  7mHH /BbT2`bBQM THQi b b22M BM 6B; jX8X hQ +QKT`2 2tT2`BK2MiH `2bmHib rBi? i?2Q`v r2 +H+mHi2 i?2 i`MbKBbbBQM bT2+i`mK i θ◦ = 0 #v mbBM; i?2 h@Ki`Bt K2i?Q/ T`2b2Mi2/ BM +?Ti2` UjXRX9V- 7`QK r?B+? r2 2ti`+i i?2 rB/i? Q7 i?2 +pBiv L0 = 156nmX h?2 +H+mHiBQM Q7 i`MbKBbbBQM bT2+i`mK Bb i?2M /QM2 7Q` M;H2b `M;BM; #2ir22M −60◦ M/ −60◦ M/ mTT2`fHQr2` TQH`BiQM 2M2`;B2b p2`bmb kx `2 2ti`+i2/ BM i?2 bK2 rv b 7Q` i?2 2tT2`BK2MiH /i- 7`QK r?B+?  i?2Q`2iB+H /BbT2`bBQM ;`T? Bb +H+mHi2/X 2.5

2.5

Simulation Transmission

2.3

2.3

2.2

2.2

2.1

2.1

2.0

2.0

1.9

1.9

1.8 -10

-8

-6

-4

-2

&' =

0

2

4

6

Simulation Transmission

2.4

0[23]

![#$ ]

2.4

8

1.8 -10

10

2* 1 sin(0) + 34

-8

-6

-4

-2

!" =

UV h1 TQH`BxiBQM

0

2% &

2

sin(+)

4

6

8

10

1 ./

U#V hJ TQH`BxiBQM

6B;m`2 jXe, AM +QHQ`, V M;H2@/2T2M/2Mi KB+`Q@+pBiv /BbT2`bBQM K2bm`2/ #v `2~2+iBQMb BM h1 TQ@ H`BxiBQMX #V M;H2@/2T2M/2Mi KB+`Q@+pBiv /BbT2`bBQM K2bm`2/ #v `2~2+iBQMb BM hJ TQH`BxiBQMX PM #Qi? bm#@6B;m`2b r?Bi2 /Qii2/ K`F2`b BM/B+i2 i?2 TQbBiBQM Q7 i?2 TQH`BiQM #`M+?2b K2@ bm`2/ #v M;H2 /2T2M/2Mi bT2+i`Qb+QTv- `2/ +m`p2b BM/B+i2 i?2 TQbBiBQM Q7 i?2 TQH`BiQM #`M+?2b +H+mHi2/ #v h@Ki`Bt K2i?Q/X *?`+i2`BxiBQM Q7 i?2 +pBiv rb T2`7Q`K2/ i `QQK i2KT2`@ im`2X

Figure 1 Rozenman et al. Figure 1 Rozenman et al. TM polarization jR

b b22M BM 6B; jXe- Qm` 2tT2`BK2MiH /i K2bm`2/ #v M;H2@`2bQHp2/ i`MbKBbbBQM bT2+i`Qb+QTv Bb BM ;`22K2Mi rBi? i?2 +H+mHiBQM Q7 i?2 i?2Q`2iB+H +m`p2b +H+mHi2/ #v h@Ki`Bt bBKmHiBQMX Pm` K2bm`2K2Mib +H2`Hv b?Qr i?i i?2 /BbT2`bBQM bTHBib iQ irQ TQH`BiQM #`M+?2b b 2tT2+i2/ 7Q`  bi`QM; +QmTHBM; +QM/BiBQM- r2 b22 /Bz2`2M+2 #2ir22M T E M/ T M TQH`BxiBQMb- b bm+? i?2 TQH`BiQMB+ #`M+?2b `2 H2bb /BbT2`bBp2 i T M TQH`BxiBQMX *H2`Hv- i?2b2 +m`p2b `2 BM ;QQ/ ;`22K2Mi rBi? i?2 /BbT2`bBQM K2bm`2/ #v M;H2@`2bQHp2/ bT2+i`Qb+QTv b r2HHX h?2 /vMKB+b Q7 TQH`BiQMb BM i?2 M2ti +?Ti2` rBHH #2 K2bm`2/ BM #Qi? T E M/ T M TQH`BxiBQM 7Q` i?2 HQr2` TQH`BiQM bii2bX h?2`27Q`2- r2 }ii2/ Qm` K2bm`K2Mib iQ i?2 TQH`BiQMB+ /BbT2`bBQM T`2/B+i2/ #v i?2 CvM2b *mKKBM;b KQ/2H UkXe8V M/ r2 +M 2ti`+i i?2 +QmTHBM; bi`2M;i? BM Qm` bKTH2 Bb, !Ω = 121meV X Ai +M #2 b22M 7`QK 6B; jXe@jXd i?i i?2 /BbT2`bBQM T`2/B+i2/ #v i?2 CvM2b@*mKKBM;b KQ/2H Bb BM ;`22K2Mi rBi? K2bm`2K2Mib #v M;H2@`2bQHp2/ i`MbKBbbBQM bT2+i`Qb+QTv- M;H2@`2bQHp2/ `2~2+iBQM bT2+i`Qb+QTv M/ h@Ki`Bt bBKmHiBQMbX

2.10

2.05

2.00

1.95

1.90 -10

Jaynes Cummings Simulation Transmission

2.05

![#$ ]

![#$ ]

2.10

Jaynes Cummings Simulation Transmission

2.00

1.95

-8

-6

-4

-2

&' =

0

2

4

6

8

1.90 -10

10

2* 1 sin(0) + 34

-8

-6

-4

-2

&' =

UV h1 TQH`BxiBQM

0

2

4

6

8

10

2* 1 sin(0) + 34

U#V hJ TQH`BxiBQM

6B;m`2 jXd, V q?Bi2 /Qii2/ K`F2`b BM/B+i2 i?2 TQbBiBQM Q7 i?2 TQH`BiQM #`M+?2b K2bm`2/ #v M;H2 /2T2M/2Mi i`MbKBbbBQM bT2+i`Qb+QTv- `2/ +m`p2b BM/B+i2 i?2 TQbBiBQM Q7 i?2 TQH`BiQM #`M+?2b +H+mHi2/ #v h@Ki`Bt K2i?Q/ U#Qi? i h1 TQH`BxiBQMVX h?2 #Hm2 +m`p2 Bb /BbT2`bBQM T`2/B+i2/ 7`QK /BbT2`bBQM `2HiBQM T`2/B+i2/ #v i?2 CvM2b@*mKKBM;b KQ/2H 7Q` i?2 HQr2` TQH`B@ iQM BM `2HiBQM UkXe8VX #V q?Bi2 /Qii2/ K`F2`b BM/B+i2 i?2 TQbBiBQM Q7 i?2 TQH`BiQM #`M+?2b K2bm`2/ #v M;H2 /2T2M/2Mi i`MbKBbbBQM bT2+i`Qb+QTv- `2/ +m`p2b BM/B+i2 i?2 TQbBiBQM Q7 i?2 TQH`BiQM #`M+?2b +H+mHi2/ #v h@Ki`Bt K2i?Q/ U#Qi? i hJ TQH`BxiBQMVX h?2 #Hm2 +m`p2 Bb /BbT2`bBQM T`2/B+i2/ 7`QK /BbT2`bBQM `2HiBQM T`2/B+i2/ #v i?2 CvM2b@*mKKBM;b KQ/2H 7Q` i?2 HQr2` TQH`BiQM BM `2HiBQM UkXe8VX

Figure JMC Rozenman et al.

jk

*?Ti2` 9 hBK2@_2bQHp2/ AK;BM; #v SmKT@S`Q#2 JB+`Qb+QTv 9XR AMi`Q/m+iBQM aBM+2 i?2 2`Hv /vb Q7 M2riQMBM K2+?MB+b- b+B2MiBbib r2`2 BMi2`2bi2/ BM K2bm`BM; i?2 KQiBQM Q7 #Q/B2b BM /Bz2`2Mi iBK2 M/ bTiBH b+H2bX >Qr2p2`- i?2 Mim`H Q#b2`piBQM i2+?MB[m2b r?B+? r2`2 mb2/ T`BQ` iQ i?2 kyi? +2Mim`v r2`2 KBMHv i?2 ?mKM 2v2 M/ i?2 ?mKM 2`X "v i?2 bi`i Q7 i?2 kyi? +2Mim`v- i?2 #BHBiv iQ Q#b2`p2 KQiBQM Q7 /vMKB+ T?vbB+H T`Q+2bb2b r2Mi #2vQM/ i?2 HBKBi Q7 Rb- r?B+? +Q``2bTQM/b iQ i?2 #HBMF Q7 M 2v2 Q` i?2 `2bTQMb2b Q7 i?2 2`X PM2 Q7 i?2 KQbi 7KQmb 2tT2`BK2Mib iQ K2bm`2 /vMKB+b #2vQM/ i?2 HBKBib Q7 ?mKM b2Mb2b 7Q` i?2 }`bi iBK2 rb iBK2@`2bQHpBM; Q7 MBKH M/ ?mKM HQ+QKQiBQM BM i?2 v2`b R33d@RNy9 #v JX 1/r2`/ (kj)- b r2HH b i?2 r2HH@FMQrM mHi` ?B;?@bT22/ T?QiQ;`T?v 2tT2`BK2Mib /QM2 #v >`QH/ 1/;2`iQM BM i?2 KB/ RN8yb (k9)X .m`BM; i?i iBK2- miBHBxBM; bMTb?Qi T?QiQ;`T?v+?`QMQT?QiQ;`T?v M/ bi`Q#Qb+QTv i2KTQ`H `2bQHmiBQMb /QrM iQ KB+`Qb2+QM/b #2+K2 pBH#H2X h?Qb2 2tT2`BK2Mib BMbTB`2/ b+B2MiBbib iQ mb2 mHi`7bi K2bm`BM; i2+?MB[m2b 7Q` i`+BM; /vMKB+ T`Q+2bb2b BM T?vbB+b M/ +?2KBbi`vX h`MbB2Mi #bQ`TiBQM bT2+i`Qb+QTv rb mb2/ iQ i`+F i?2 #bQ`#M+2 Q7 HB;?i i  +2`iBM T?QiQM 2M2`;v Q` BM  bT2+i`H `M;2 b  7mM+iBQM Q7 iBK2X h?2 2tTHQ`iBQM Q7 2p2` b?Q`i2` /vMKB+b BM KQH2+mH` `2+iBQMb ?/ #22M bi`QM;Hv +QmTH2/ iQ i?2 ;`/mH `2/m+iBQM Q7 Hb2` TmHb2 /m`iBQMb- }MHHv TT`Q+?BM; bm# 100f s TmHb2b (k8)X 1tT2`BK2Mib H2/ #v X >X w2rBH M/ :X _X 6H2KBM; - ?p2 T2`KBii2/ i?2 `2H iBK2 Q#b2`piBQM Q7 iQKB+ KQiBQM BMbB/2 KQH2+mH2b b r2HH b i?2 7Q`KiBQM M/ `mTim`2 Q7 +?2KB+H #QM/b (ke)X hQ/v- i?2 }2H/ BMpQHpBM; mHi`7bi QTiB+b Bb i`2K2M/QmbHv +iBp2- b Bi b2`p2b b  bQHB/ THi7Q`K 7Q` bim/vBM; mHi`7bi /vMKB+b Q7 KQH2+mH` M/ iQKB+ T?2MQK2M BM T?vbB+b- +?2KBbi`v- #BQHQ;v M/ 2p2M bi`QMQKv (kd- k3)X jj

lT iQ i?Bb /i2- T?vbB+H T`QT2`iB2b Q7 TQH`BiQMb- bm+? b HB72 iBK2b M/ 2KBbbBQM- r2`2 K2bm`2/ QMHv BM i?2 iBK2 /QKBMX aTiBH T`QT2`iB2b Q7 TQH`BiQMb r2`2 K2bm`2/ #v miBHBxBM; bi2/v@ bii2 i2+?MB[m2bX >Qr2p2`- iBK2 `2bQHp2/ bTiBH TQH`BiQMb /vMKB+b BM i?2 bm#@TB+Q iBK2 `2;BK2 `2KBMb mMFMQrMX SQH`BiQMb 2K2`;BM; BM Q`;MB+ Ki2`BHb M/ b2KB+QM/m+iQ`b ?p2 2ti`2K2Hv b?Q`i HB72@iBK2b Q7 Q`/2`b Q7 72r TB+Qb2+QM/b(kN)X h?2`27Q`2- i?2B` T?vbB+H T`QT2`iB2b- bm+? b 2M2`;v i`Mb72` T`Q+2bb2b M/ HB72iBK2b- +MMQi #2 K2bm`2/ #v Q`/BM`v +K2`b M/ mHi`7bi QTiB+b Bb miBHBx2/ 7Q` i?Bb Tm`TQb2X >2M+2- Qm` ;QH rb iQ miBHBx2 mHi`7bi iBK2 `2bQHp2/ TmKT T`Q#2 i2+?MB[m2b rBi? BK;BM; KB@ +`Qb+QTv- i?Bb HHQr2/ mb iQ K2bm`2 T?vbB+H T`QT2`iB2b BM i?2 bTiBH /QKBM rBi?  i2KTQ`H `2bQHmiBQM BM i?2 bm#@TB+Q `2;BK2X AM T`iB+mH`- bm+? bvbi2K HHQrb iQ K2bm`2 bTiBH /vMKB+b Q7 TQH`BiQMb BM Q`;MB+ +pBiB2b rBi? 100f s i2KTQ`H `2bQHmiBQM M/  bTiBH `2bQHmiBQM Q7 1µmX

j9

9Xk S`BM+BTH2b Q7 mHi`7bi SmKT@S`Q#2 JB+`Qb+QTv SmKT@T`Q#2 K2bm`2K2Mib `2 ;2M2`HHv mb2/ BM Q`/2` iQ bim/v mHi`@7bi /vMKB+H T`Q+2bb2b7QHHQrBM; i?2 T2`im`#iBQM Q7 i?2 T?vbB+H bvbi2K 7`QK Bib 2[mBHB#`BmK bii2X h?Bb Bb ++QKTHBb?2/ #v 2t+BiBM; i?2 bvbi2K #v  b?Q`i TmKT TmHb2- r?B+? KQ/B}2b i?2 QTiB+H T`QT2`iB2b Q7 i?2 bKTH2X h?2 T`Q#2 TmHb2 i?2M K2bm`2b i?2 bKTH2 M/ i?2 KQ/B}+iBQMb BM i?2 QTiB+H T`QT2`iB2b +M #2 2t?B#Bi2/ BM i?2 bT2+i`H +?M;2 Q7 i?2 T`Q#2 TmHb2X h?2 T`Q#2 TmHb2 Bb +?`+i2`Bx2/ #v Bib BMi2MbBivbT2+i`mK- T?b2 M/ TQH`BxiBQMX "v +QKT`BM; i?2 KQ/B}+iBQMb BM i?2b2 QTiB+H T`QT2`iB2b r2 `2 #H2 2ti`+i T?vbB+H M/ +?2KB+H T`QT2`iB2b Q7 i?2 bKTH2X b b22M BM 6B; 9XR- BM Qm` b2imT- i?2 TmKT TmHb2 T2`im`#b i?2 bKTH2 i  ;Bp2M iBK2 t = 0X h?2M i?2 T`Q#2 TmHb2- r?B+? Bb /2Hv2/ rBi? `2bT2+i iQ i?2 TmKT TmHb2 #v mbBM;  /2Hv bi;2- Bb `2~2+i2/ 7`QK i?2 T2`im`#2/ bKTH2 iQ  /2i2+iQ`X  }t2/ /2Hv ∆t Bb +?Qb2M M/ i?2 2tT2`BK2Mi Bb `2T2i2/ b2p2`H iBK2b 7Q` /Bz2`2Mi iBK2 /2Hvb, ∆t1 , ∆t2 , ∆t3 , ... X h?2 r?QH2 T`Q+2bb ;Bp2b mb i?2 `2~2+i2/ bT2+i`mK Q7 i?2 2t+Bi2/ bKTH2 i /Bz2`2Mi iBK2 /2HvbX h?Bb Bb mbmHHv `272``2/ iQ b i?2 iBK2@`2bQHp2/ `2~2+iBQM i2+?MB[m2X AM Qm` 2tT2`BK2Mib r2 rMi iQ T`Q#2 bKTH2b BM r?B+? 2Bi?2` 2t+BiQMb Q` TQH`BiQMb `2 2t+Bi2/X aBM+2 i?2 #bQ`TiBQM BM bm+? bKTH2b /2T2M/b QM i?2 2t+Bi2/ TQTmHiBQM Q7 BibǶ KQH2+mH` 2t+BiQMbBi /2+`2b2b i?2 T`Q##BHBiv iQ #bQ`# T?QiQMbX h?mb- r2 rBHH b22 p`BiBQMb BM i?2 `2~2+i2/ T`Q#2 bB;MHX h?2 `2~2+i2/ bB;MH Bb /2}M2/ #v,

Runpumped =

IRunpumped I0

Rpumped =

IRpumped I0

U9XRV

q?2`2 IR Bb i?2 BMi2MbBiv Q7 i?2 `2~2+i2/ T`Q#2 TmHb2 rBi? Q` rBi?Qmi i?2 TmKT M/ I0 Bb i?2 BMi2MbBiv Q7 i?2 BM+B/2Mi T`Q#2 TmHb2X .BpBM; i?2b2 `2HiBQMb M/ /2}MBM; ∆R b ∆R = Rpumped − Runpumped r2 ;2i i?i i?2 `2HiBp2 +?M;2 BM `2~2+iBQM Bb, pumped/unpumped

∆R Ipumped = −1 R Iunpumped

U9XkV

AM Q`/2` iQ K2bm`2 #Qi? Ipumped M/ Iun−pumped - i?2 TmKT TmHb2b `2 T2`BQ/B+HHv #HQ+F2/ M/ mM#HQ+F2/ #v M QTiB+H +?QTT2`X

j8

6B;m`2 9XR,  ivTB+H b+?2K2 Q7  TmKTĜT`Q#2 2tT2`BK2Mi,  TmKT TmHb2 T2`im`#b i?2 bKTH2 i t = 0- i?2 T`Q#2 TmHb2 ;Q2b i`Qm;?  /2Hv bi;2- `2~2+i2/ 7`QK i?2 bKTH2 M/ i?2M K2bm`2/ #v i?2 /2i2+iQ` UIpumped M/ Iun−pumped `2 K2bm`2/VX AM Qm` 2tT2`BK2Mib- r2 rMi iQ K2bm`2 ?Qr +QM}M2/ 2t+BiiBQMb Q7 TQH`BiQMb bT`2/ iQr`/b i?2 bKTH2X h?2`27Q`2- r2 mb2  r?Bi2 T`Q#2 #2K r?B+? +Qp2`b i?2 r?QH2 `2;BQM Q7 BMi2`2bi U_PAV M/ i?2 TmKT Bb 7Q+mb2/ iQ i?2 +2Mi2` Q7 Qm` _PAX AM Qi?2` rQ`/b- i?2 /BK2i2` Q7 i?2 TmKT Bb Km+? bKHH2` i?M i?2 /BK2i2` Q7 i?2 T`Q#2 (Dpump < Dprobe )- r?B+? Bb BM +QMi`bi iQ i`/BiBQMH TmKT T`Q#2 i2+?MB[m2bX JQ`2Qp2`- r2 mb2 M BK;BM; H2Mb iQ K2bm`2 bTiBH p`BiBQMb BM Qm` bKTH2- BM +QMi`bi iQ bBM;H2 TQBMi /2i2+iBQM r?2`2 i?2 r?QH2 `2 Bb p2`;2/X Ai Bb BKTQ`iMi iQ MQi2 i?i BM M B/2H bvbi2K r2 rQmH/ rMi iQ b2i i?2 TmKT /BK2i2` iQ #2 b bKHH b TQbbB#H2X >Qr2p2`- Qm` 2tT2`BK2MiH bvbi2K Bb HBKBi2/ #v i?2 ##2 /Bz`+iBQM HBKBiX hQ /Bz2`2MiBi2 #2ir22M TmKT2/ M/ mMTmKT2/ BK;2b i?2 `2T2iBiBQM `i2 Q7 i?2 /2i2+iQ` ?b iQ #2 B/2MiB+H iQ i?2 QM2 Q7 i?2 T`Q#2X Pm` i2KTQ`H `2bQHmiBQM Bb MQi HBKBi2/ iQ Qm` /2i2+iQ` #mi iQ i?2 TmHb2 r?B+? ?b  TmHb2 H2M;i? Q7 ∼ 100f sX AM i?2Q`v- Qm` i2KTQ`H `2bQHmiBQM +QmH/ HbQ #2 HBKBi2/ #v /2Hv bi;2 KBMBKH bi2TX >Qr2p2`- Qm` /2Hv bi;2 ?b  KBMBKH bi2T Q7 1µm r?B+? ;Bp2b  i2KTQ`H `2bQHmiBQM Q7 3.37f sX

je

9Xj h?2 2tT2`BK2MiH b2imT  bF2i+? Q7 i?2 2tT2`BK2MiH b2imT Bb K2MiBQM2/ BM 6B; 9XkX q2 mb2  TmHb2/ Hb2` KTHB}2` bvbi2K UaTBi}`2 +2- #v aT2+i`@S?vbB+bV QT2`i2/ i  `2T2iBiBQM `i2 Q7 500HzX S`i Q7 i?2 #2K Bb mb2/ ;2M2`i2 M 80f s TmKT TmHb2- BM Q`/2` iQ ;2M2`i2  bBM;H2 rp2H2M;i? TmKT TmHb2 r2 mb2/ M miQKi2/ QTiB+H T`K2i`B+ KTHB}2` UhPSa S`BK2V- r?B+? Bb imM2/ iQ 520nmX h?2 TmKT #2K Bb Tbb2/ i?`Qm;? M QTiB+H +?QTT2` bvbi2K Uh?Q`H#b J*kyyyV - r?B+? Bb bvM+?`QMBx2/ rBi? i?2 bK2 i`B;;2` +?MM2H 7`QK i?2 T`Q#2 #2KX aBM+2 i?2 QTiB+H +?QTT2` Bb bvM+?`QMBx2/ rBi? i?2 TmKT #2K- Bi #HQ+Fb 2p2`v b2+QM/ TmKT TmHb2X b  `2bmHi- i?2 `2T2iBiBQM `i2 Bb /2+`2b2/ 7`QK 500hz iQ 250hzX AM Q`/2` iQ ;2M2`i2  #`Q/ bT2+i`H #M/rB/i? T`Q#2 TmHb2 r2 `2bQ`i2/ iQ bmT2`@+QMiBMmmK ;2M@ 2`iBQM i2+?MB[m2X amT2`@+QMiBMmmK ;2M2`iBQM Ua*:V Bb  T`Q+2bb r?2`2 Hb2` TmHb2b rBi? M``Qr bT2+i`H #M/rB/i?- bm+? b Qm`b- `2 +QMp2`i2/ iQ TmHb2b rBi? p2`v #`Q/ bT2+i`H #M/rB/i?X AM Qm` +b2 r2 TH+2 M /Dmbi#H2 B`Bb M/ LX. iQ /Dmbi i?2 rB/i? M/ i?2 BMi2MbBiv Q7 i?2 7Q+mb2/ #2K- i?2 TmHb2 Bb i?2M 7Q+mb2/ BMiQ  bTT?B`2 +`vbiH 7Q` bmT2`@+QMiBMmmK ;2M2`iBQMX h?2 ;2M@ 2`i2/ T`Q#2 TmHb2  bT2+i`mK r?B+? bT`2/b 7`QK 450nm iQ 1000nm M/  /m`iBQM Q7 150f sr?B+? Bb  ivTB+H pHm2 7Q` mbBM; aTT?B`2 THi2 7Q` ;2M2`iBM; +QMiBMmQmb r?Bi2 HB;?i (jy)X S`BQ` iQ i?i- i?2 T`Q#2 TmHb2 Tbb2b i?`Qm;?  /2/B+i2/ +QKTmi2` +QMi`QHH2/ /2Hv bi;2 UL2rTQ`i AGa GBM2` ai;2- k8ymm- JAJ 1µm- .* JQiQ`- aJ*RyyV iQ +QMi`QH i?2 iBK2 /2Hv ∆t #2ir22M i?2 T`Q#2 M/ i?2 TmKT TmHb2bX h?2 a*: T`Q#2 TmHb2 Tbb2b i?`Qm;? M +?`QKiB+ H2Mb UL1 = 50.8mmV iQ ;2M2`i2  +QHHBKi2/ #2KX h?2 #2K Tbb2b i?`Qm;?  b?Q`i Tbb }Hi2` UaS6- λ < 700nmV iQ }Hi2` i?2 Q`B;BMH 800nm #2K- i?2M Bi Tbb2b i?`Qm;?  HQM; Tbb }Hi2` UGS6- λ > 580nmV iQ +`2i2  #`Q/#M/ bT2+i`mK r?B+? T`Q#2b i?2 HQr2` TQH`BiQM bii2 UλTLPM = 617 ± 10nm-λTLPE = 605 ± 10nmVX AM Q`/2` iQ 7Q+mb i?2 #2K QM i?2 bKTH2 r2 mb2 MQi?2` H2Mb UL2 = 125mmV- i?2M i?2 `2~2+i2/ #2K Bb BK;2/ #v  +K2` H2Mb ULBFFQ` 50mm -f /1.2V rBi? K;MB}+iBQM Q7 8yX h?2 LBFQM +K2` H2Mb Bb miBHBx2/ BM Qm` bvbi2K 7Q` BK;BM; M/ K;MB}+iBQM Q7 i?2 KQ/B}+iBQMb Q7 i?2 T`Q#2 TmHb2 7`QK i?2 bKTH2 iQ i?2 b*JPaX h?2 b*JPa +K2` UM/Q` wvHV Bb HbQ bvM+?`QMBx2/ rBi? i?2 bK2 i`B;;2` b i?2 +?QTT2`- r?B+? HHQrb iQ K2bm`2 TmKT2/ M/ mMTmKT2/ BK;2b Q7 i?2 T`Q#2 bB;MHX hQ bvM+?`QMBx2 i?2 +K2` rBi? i?2 T`Q#2 i`B;;2`  /2/B+i2/ 2H2+i`QMB+ TmHb2 /2Hv2` rb #mBHi #v i?2 TTHB2/ 2H2+i`QMB+b /2T`iK2Mi Q7 i?2 b+?QQH b+?QQH Q7 T?vbB+bX S`BQ` iQ i?2 b*JPa +K2` #M/@Tbb }Hi2` Bb TH+2/ U"S6V rBi? i`MbKBbbBQM bT2+i`mK i λ = 655 ± 20nmX h?2 }Hi2` Bb iBHi2/ iQ /Dmbi i?2 rp2H2M;i? iQ i?i /2bB`2/ `2;BQM Q7 i?2 HQr2` TQH`BiQM bii2 rp2H2M;i?, λtilt = 615 ± 20nmX hQ i2bi M/ +QM}`K i?2 `2~2+i2/ T`Q#2 #2K Bb BM/22/ BM i?2 /2bB`2/ bT2+i`H /QKBM-  #2K bTHBii2` Bb TH+2/ T`BQ` iQ i?2 b*JPa M/ `2~2+ib i?2 bB;MH iQ  bT2+i`QK2i2`X W h?2 BMi2MbBiv Q7 i?2 TmKT #2K r?2M 7Q+mb2/ QM i?2 bKTH2 rb b2i iQ 86 cm 2 M/ i?2 BMi2MbBiv

jd

W Q7 i?2 T`Q#2 #2K i i?2 THM2 Q7 i?2 bKTH2 rb K2bm`2/ iQ #2 0.16 cm 2 7i2` bT2+i`H }Hi2`BM; (580 − 700nm)- r?B+? Bb Km+? bKHH2` i?i i?2 TmKT BMi2MbBivX

6Q` 2+? iBK2 /2Hv- r2 K2bm`2  b2`B2b Q7 k8y TmKT2/ M/ k8y mMTmKT2/ T`Q#2 bB;MHbX 1+? TB` Q7 7`K2b Bb /BpB/2/ QM2 #v MQi?2` iQ Q#iBM  bBM;H2 7`K2 Q7 i`MbB2Mi `2~2+iBQM ∆R X AM i?Bb R rv r2 ;2i  b2[m2M+2 Q7 TmKT2/ M/ mMTmKT2/ BK;2b M/ i?2M r2 /BpB/2 2+? BK;2 QM2 #v MQi?2` M/ p2`;2 Qp2` i?2 r?QH2 b2`B2b Q7 k8y TB`b iQ `2/m+2 MQBb2X q?BH2 i`vBM; iQ Q#b2`p2 bTiBH /vMKB+b 7Q` i?2 }`bi iBK2- r2 2M+QmMi2`2/ b2p2`H /B{+mHiB2bX PM2 Q7 i?2K rb i?2 /2bi`m+iBQM Q7 i?2 bKTH2 7i2`  b?Q`i iBK2 Q7 30 − 60sec- r?B+? ;p2 mb i?2 BM#BHBiv iQ K2bm`2 M2Bi?2` i?2 /vMKB+b MQ` i?2 HB72 iBK2b Q7 TQH`BiQMb BM Qm` bvbi2KX h?mb- r2 mb2/  #2K bTHBii2` M/ /Bb+Qp2`2/ #v 2tT2`BK2Mi i?i bi`QM; +QmTHBM; /BbTT2`2/ +QKTH2i2Hv BM i?2 bT2+i`H `2;BK2 7i2` R KBMmi2X JQ`2Qp2`- r2 /Bb+Qp2`2/ #v +QBM+B/2M+2 i?i r?2M i?2 T`Q#2 bT2+i`mK Bb HBKBi2/ iQ λ > 580nm- i?2 Qp2`HH /K;2 BM i?2 bKTH2 Bb b2p2`2Hv `2/m+2/ M/ bi`QM; +QmTHBM; Bb Q#b2`p2/ 7Q` HQM; T2`BQ/b Q7 iBK2 UivTB+HHv 60 − 90 KBMmi2bVX h?Bb 2tT2`BK2Mi i2+?2b mb i?i 2t+BiBM; i?2 mTT2` TQH`BiQM bii2 #v i?2 T`Q#2 TmHb2 /2bi`Qvb i?2 KQH2+mH2b BM Bi- r?BH2 i?2 i?2Q`v #2?BM/ i?Bb T?2MQK2M `2KBMb mM+H2`X h?Bb bim/v ?b ;Bp2M mb bi#H2 +QM/BiBQMb iQ T`Q+22/ rBi? i?2 K2bm`2K2Mi Q7 bTiBH /vMKB+bX

j3

6B;m`2 9Xk,  a+?2KiB+ /B;`K Q7 i?2 QTiB+H b2imTX h?2 TmKT TmHb2 Tbb2b i?`Qm;? M QTiB+H +?QTT2` iQ +`2i2 TmHb2b 7Q` TmKT2/ M/ mMTmKT2/ K2bm`K2Mib M/ 7Q+mb2/ QM i?2 bKTH2 #v i?BM H2MbX  /2Hv bi;2 Bb TH+2/ BM i?2 QTiB+H Ti? Q7 i?2 T`Q#2 #2K iQ +QMi`QH i?2 iBK2 /2Hv #2ir22M i?2 T`Q#2 M/ i?2 TmKT TmHb2b U∆tVX h?2 bmT2`@+QMiBMmmK Ua*:V T`Q#2 #2K Bb ;2M2`i2/ #v TH+BM;  bTT?B`2 +`vbiH M/ M Dmbi#H2 B`Bb rBi? M LX.X h?2 T`Q#2 #2K Tbb2b i?`Qm;? b?Q`i Tbb λSP F < 700nm M/ HQM; Tbb λLP F > 580nm }Hi2`b UaS6-GS6V iQ +`2i2  #M/ Tbb bT2+i`mK r?B+? Bb 7Q+mb2/ QM i?2 bKTH2 #v i?BM H2Mb M/ i?2M #2BM; `2~2+i2/ 7`QK BiX h?2 `2~2+i2/ T`Q#2 #2K Bb K;MB}2/ #v 8y #v  LBFQM H2Mb #v r?B+? r2 HbQ BK;2 i?2 T`Q#2 #2K iQ  b*JPa +K2` THM2-  #M/ Tbb }Hi2` 595nm < λ < 635nm U".6V Bb TH+2/ iQ }Hi2` i?2 TmKT TmHb2X AM //BiBQM-  #2K bTHBii2` U"aV Bb //2/ BM i?2 QTiB+H Ti? #2ir22M i?2 LBFQM BK;BM; H2Mb M/ i?2 b*JPa iQ T2`7Q`K bT2+i`Qb+QTB+ K2bm`2K2MibX

jN

9X9 _2bmHib 6B`bi- r2 i2bi2/ Qm` bvbi2K QM  `272`2M+2 bKTH2 Q7 Q`;MB+ KQH2+mH2b Uh."*V /QT2/ BM TQHvK2` USoV QM  ;Hbb bm#bi`i2X h?2 bKTH2 rb 7#`B+i2/ ++Q`/BM; iQ +?Ti2` UjXRXRV rBi? QMHv  bBM;H2 KB``Q`- BM bm+? i?2`2 Bb MQ +pBivX q2 `272` iQ i?Bb bKTH2 b #`2 KQH2+mH2b- b i?2v `2 MQi +QmTH2/ iQ HB;?iX

*+,

($)

(%)

(")

'()

-()

(&)

6()

9()

6B;m`2 9Xj, AK;2b Q7 KQH2+mH` +HQm/ i /Bz2`2Mi iBK2 /2Hvb K2bm`2/ #v mHi`7bi TmKT@T`Q#2 KB+`Qb+QTvX V i 0ps #V i 3ps +V i 6ps /V i 9ps aBM+2 r2 2t+Bi2 #`2 2t+BiQMb- r?B+? ?p2  i`MbTQ`i `M; Q7 72r MMQK2i2`b QMHv- r2 /Q MQi 2tT2+i iQ Q#b2`p2 bTiBH /vMKB+b BM bm+? bKTH2bX AM/22/- Qm` `2bmHib UT`2b2Mi2/ BM 6B; 9XjV BM/B+i2 i?i  +HQm/ Q7 KQH2+mH` 2t+BiQMb /Q2b MQi 2tTM/ BM i?2 KB+`QM b+H2X h?2 bB;MH /2+vb Qp2` iBK2 M/  HB72 iBK2 Q7 72r TB+Qb2+QM/b Bb Q#b2`p2/- b Bi Bb r2HH FMQrM 7Q` h."* KQH2+mH2bX Pm` 7Q+mb2/ TmKT #2K QM i?2 bKTH2 vB2H/b  `2bmHib Q7 2−3µm 7Q+mbBM; rB/i?X 6m`i?2` MHvbBb Q7 i?2 /i T`2b2Mi2/ BM 6B; 9Xj +M #2 /QM2 #v 2ti`+iBM; i?2 +`Qbb@b2+iBQM Q7 i?2 2t+BiQMB+ +HQm/ #v  bTiBH bmK Q7 i?2 KQH2+mH` +HQm/ BM i?2 p2`iB+H tBbX

9y

0.25 0

Temporal Kinetics 1

Δ' ⁄' [Normalized]

Δ' ⁄' [)*+$,-./01]

Molecular Cloud vs Displacement – Cross Section 1 0ps 3ps 0.75 6ps 9ps 0.5

Bare Molecules

0.75

0.5

0.25

-0.25 0

2

4

6

8

10

12

14

![#$]

-1

1

3 5 7 delay [ps]

9

11

(b)

(a)

6B;m`2 9X9, V LQ`KHBx2/ +`Qbb b2+iBQM BM i?2 p2`iB+H tBb Q7 BK;2b 7`QK 6B; 9XjX #V h2KTQ`H FBM2iB+b Q7 #`2 KQH2+mH2b- 2ti`+i2/ 7`QK 6B; 9XjX P#pBQmbHv- r2 b22 7`QK 6B; 9X9 UV i?i i?2 2t+BiQMB+ +HQm/ /Q2b MQi 2tTM/- Bi Bb HbQ BKTQ`iMi iQ K2MiBQM i?i r2 T`2b2Mi MQ`KHBx2/ /iX 6B; 9X9 U#V T`2b2Mib i?2 i2KTQ`H FBM2iB+bX Ai +M #2 b22M i?i i?2 #`2@2t+BiQM HB72iBK2 Bb TT`QtBK2MiHv 2ps- b rb Q#b2`p2/ T`2pBQmbHv #v Qi?2` 2tT2`BK2MibX L2ti- r2 +QM/m+i2/  b2`B2b Q7 2tT2`BK2Mib iQ K2bm`2 bTiBH TQH`BiQMb /vMKB+b BM KB+`Q@ +pBiv bKTH2bX b Bi rb K2MiBQM2/ BM i?2 T`2pBQmb +?Ti2`- TQH`BiQM /BbT2`bBQM Bb TQH`BxiBQM /2T2M/2MiX h?2`27Q`2- r2 bim/v TQH`BiQM /vMKB+b BM #Qi? T M M/ T E TQH`BxiBQMbX

J2bm`2K2Mib rBi? hJ TQH`BxiBQM SQH`BiQM KB+`Q@+pBiv bKTH2b r2`2 TH+2/ M/ K2bm`2/ BM i?2 bK2 rv b #`2 KQH2+mH2bX h?2 `2bmHib 7Q` 0 − 7ps M/ T M TQH`BxiBQM `2 b?QrM BM 6B; 9X8 #2HQrX LQi2 i?i Qm` bKTH2b `2 7#`B+i2/ iQ #2 i `2bQMM+2 i 45◦ - bm+? i?i r2 K2bm`2 TQH`BiQMb r?B+? `2 2t+iHv ?H7 T?QiQMB+ M/ ?H7 2t+BiQMB+X

9R

(%) *"+,)./0

(')

(()

())

!"#

2"#

7"#

5"#

6B;m`2 9X8, AK;2b Q7 TQH`BiQM +HQm/ i /Bz2`2Mi iBK2 /2Hvb K2bm`2/ #v mHi`7bi TmKT@T`Q#2 KB+`Qb+QTv i T M TQH`BxiBQMX V i 0ps #V i 2ps +V i 5ps /V i 7psX h?2 r?Bi2 ``Qr b?Qrb i?2 T`QD2+iBQM Q7 i?2 T`Q#2 TmHb2 QM i?2 bKTH2 THM2X "v HQQFBM; i i?2 BK;2b BM 6B; 9X8 Bi Bb +H2`Hv b22M i?i i?2 TQH`BiQM +HQm/ Bb 2tTM/BM; rBi? iBK2 Qp2` b2p2`H KB+`QMbX h?Bb Bb i?2 }`bi /B`2+i Q#b2`piBQM Q7 KQiBQM /vMKB+b Q7 TQH`BiQM BM Q`;MB+ KB+`Q@+pBiB2bX h?2 `2bmHib +H2`Hv b?Qr i?i Qm` QTiB+H b2imT Bb +T#H2 Q7 /2i2+iBM; i?2 /vMKB+b Q7 TQH`BiQMb BM i?2 TB+Q@KB+`Q `2;BK2X q2 b22 M 2M?M+2K2Mi BM i`MbTQ`i `M;2 BM Q`;MB+ Ki2`BHb #v j Q`/2`b Q7 K;MBim/2 /m2 iQ i?2 +QmTHBM; i?2K iQ HB;?i U+QKT`2/ rBi? #`2 KQH2+mH2bVX Polariton Cloud vs displacement – Cross section 7

1 0ps 2ps 5ps 7ps

0.75

6 5

0.5

4[#$]

Δ' ⁄ ' [)*+$,-./01]

Polariton Cloud Width

0.25

4 3 2

0

5 ≈ 0.4 − 0.9

1 0

2

4

6

8

10

12

![#$]

0

2

4

6

#$ 23

8

10

delay[23]

(a)

(b)

6B;m`2 9Xe, V LQ`KHBx2/ +`Qbb b2+iBQM BM i?2 p2`iB+H tBb Q7 BK;2b 7`QK 6B; 9X8 #V SQH`BiQM rB/i? p2`bmb iBK2 /2Hv

9k

;BM- QM2 +M b22 7`QK 6B; 9Xe i?2 2tTMbBQM Q7 i?2 TQH`BiQM +HQm/X h?2 2tTMbBQM Q++m`b iQ i?2 H27i bB/2- r?B+? Bb  `2bmHi Q7 i?2 7+i r2 T`Q#2 i?2 bKTH2 i 45◦ M/ Q#b2`p2 bm+? TQH`BiQMb r?B+? ?p2 i?2 +Q``2bTQM/BM; KQK2MimK k∥ X AM //BiBQM iQ i?i- BM 6B; 9Xe r2 THQi i?2 rB/i? Q7 i?2 TQH`BiQM +HQm/ 2ti`+i2/ 7`QK 6B; 9X8 M/ bim/v i?2 rB/i? Q7 i?2 +HQm/ Qp2` iBK2 b b?QrM BM 6B; 9Xe U#VX PM2 +M b22 i?i i?2 2tTMbBQM Q7 i?2 TQH`BiQM +HQm/ Bb TT`QtBKi2Hv HBM2` rBi?  2tTMbBQM p2HQ+Biv Q7 v = 0.4 µm X bbmKBM; i?i i?2 ps TQH`BiQM +HQm/ Bb /Bz`+iBQM HBKBi2/ #v i?2 bTQi Q7 i?2 TmKT M/ rb BMBiBHHv i D(0) ∼ 200nmi?2 2tTMbBQM p2HQ+Biv b?QmH/ #2 v = 0.9 µm X h?2`27Q`2 r2 bii2 i?i i?2 pHm2 Bb 2biBKi2/ iQ ps µm #2 0.4 < v < 0.9 ps X 6`QK i?2 /BbT2`bBQM `2HiBQM U6B; jXe U#VV r2 +M +H+mHi2 i?2 2tT2+i2/ vg r?B+? Bb vg = 25.2 µm i 45◦ X >Qr2p2`- Qm` K2bm`2K2Mi ;Bp2b M 2tTMbBQM p2HQ+Biv r?B+? Bb k ps Q`/2`b Q7 K;MBim/2 bKHH2`X h?2 bHQr 2tTMbBQM +QmH/ #2 2Bi?2` /m2 iQ  MQM2@#HHBbiB+ i`MbTQ`i K2+?MBbK BM Qm` bvbi2K Q` TQH`BiQM@TQH`BiQM BMi2`+iBQMb- r?B+? `2 M2;H2+i2/ BM C* KQ/2H- #v r?B+? r2 2ti`+i i?2 ;`QmT p2HQ+BivX

J2bm`2K2Mib rBi? h1 TQH`BxiBQM L2ti- r2 `2T2i2/ i?2 K2bm`2K2Mib rBi?  T E TQH`Bx2/ T`Q#2- `2bmHib 7Q` 0 − 10ps `2 b?QrM BM 6B; 9Xd #2HQrX q2 `2KBM/ ;BM i?i Qm` bKTH2b `2 7#`B+i2/ iQ #2 2t+iHv ?H7 T?QiQMB+ ?H7 2t+BiQMB+ i 45◦ 7Q` hJ TQH`BxiBQMX h?2`27Q`2- ++Q`/BM; iQ `2HiBQMb UkXek-kXejV- BM i?2b2 b2`B2b Q7 K2bm`2K2Mib r2 T`Q#2 TQH`BiQMb r?B+? `2 70W 2t+BiQMB+ M/ 30W T?QiQMB+X

(%) +",-*' ./0

!"#

(()

())

(*)

1"#

4"#

(')

7"#

10"#

6B;m`2 9Xd, AK;2b Q7 TQH`BiQM +HQm/ i /Bz2`2Mi iBK2 /2Hvb K2bm`2/ #v mHi`7bi TmKT@T`Q#2 KB+`Qb+QTvX V i 0ps #V i 1ps +V i 4ps /V i 7ps 2V i 10ps "v HQQFBM; i i?2 BK;2b BM 6B; 9Xd r2 b22 ;BM i?i i?2 TQH`BiQM +HQm/ Bb 2tTM/BM;X HbQ r2 b22 i?i i?2 2tTMbBQM Bb bHB;?iHv /Bz2`2Mi 7Q` T E TQH`BxiBQMX q2 2ti`+i i?2 +`Qbb@b2+iBQM 7Q` K2bm`2K2Mib /QM2 i T E TQH`BxiBQM b r2 /B/ 7Q` T M TQH`@ BxiBQMX

9j

6

0.75

5

0.5

4

2[#$]

Δ' ⁄ ' [)*+$,-./01]

Polariton Cloud Width

Polariton Cloud vs displacement – Cross section 1

0.25

3 2

0 -0.25 0

3 ≈ 0.2 − 0.5

1 2

4

6 8 ![#$]

10

12

14

(a)

0

2

4 6 10-,=[;QT}2H/ 2i HX h?2Q`v Q7 i?2 +QMi`B#miBQM Q7 2t+BiQMb iQ i?2 +QKTH2t /B2H2+iB+ +QMbiMi Q7 +`vbiHbX S?vbX _2pX G2iiX- RRkU8V- RN83X (ky) aX ai2M?QHK 2i HX ZmMimK i?2Q`v Q7 2H2+i`QK;M2iB+ }2H/b BMi2`+iBM; rBi? iQKb M/ KQH2+mH2bX S?vbB+b _2TQ`ib *- eURV- RNdjX (kR) >X .2M; 2i HX 1t+BiQM@TQH`BiQM #Qb2@2BMbi2BM +QM/2MbiBQMX _2pB2rb P7 JQ/2`M S?vbB+b3kUR93NV- kyRyX (kk) GX *X a?2M M/ CX X EQM;X TTHB2/ 1H2+i`QK;M2iBbKX *2M;;2 G2`MBM;- RNN8X (kj) JX 1/r2`/ 2i HX MBKH HQ+QKQiBQM , M 2H2+i`Q@T?QiQ;`T?B+ BMp2biB;iBQM Q7 +QMb2+miBp2 T?b2b Q7 MBKH KQp2K2MibX S?BH/2HT?B , S`BMi2/ #v CX"X GBTTBM+Qii +QKTMv- j9UkV- R33dX (k9) >X 1X 1/;2`iQM M/ CX _X EBHHBMX 6Hb?5, a22BM; i?2 mMb22M #v mHi` ?B;?@bT22/ T?QiQ;`T?vX *XhX "`M7Q`/ *Q- RN89X (k8) :X ai2BMK2v2` 2i HX  `2pB2r Q7 mHi`7bi QTiB+b M/ QTiQ2H2+i`QMB+bX CQm`MH Q7 QTiB+b , Tm`2 M/ TTHB2/ QTiB+b- 8- kyyjX (ke) X>X w2rBHX 62KiQ+?2KBbi`v @ iQKB+@b+H2 /vMKB+b Q7 i?2 +?2KB+H #QM/ mbBM; mHi`7bi Hb2`bX qQ`H/ a+B2MiB}+ Sm#HBb?BM; *Q- kyyyX (kd) X q2BM2`X lHi`7bi PTiB+bX qBH2v b2`B2b BM Tm`2 M/ TTHB2/ QTiB+b- kyyNX (k3) SX: E`vmFQp 2i HX 62KiQb2+QM/ Hb2`b 7Q` bi`QT?vbB+bX S?vbB+b @ lbT2F?B- 83U3V- kyR8X (kN) hX a+?r`ix 2i HX SQH`BiQM /vMKB+b mM/2` bi`QM; HB;?i@KQH2+mH2 +QmTHBM;X *?2KS?vb*?2KR9URV- kyRjX (jy) _X "2`2`X lHi`7bi i`MbB2Mi #bQ`TiBQM bT2+i`Qb+QTv, T`BM+BTH2b M/ TTHB+iBQM iQ T?QiQ@ bvMi?2iB+ bvbi2KbX S?QiQbvMi? _2b- kyyNX 93

(jR) .X X wBib2p 2i HX .BzmbBp2 T`QT;iBQM Q7 2t+BiQM@TQH`BiQMb i?`Qm;? i?BM +`vbiH bH#bX a+B2MiB}+ _2TQ`ib- 8- kyR8X

9N