Optimisation des structures nanophotoniques pour le photovoltaïque

Texte intégral

(1)Optimisation des structures nanophotoniques pour le photovoltaïque Mamadou Aliou Barry. To cite this version: Mamadou Aliou Barry. Optimisation des structures nanophotoniques pour le photovoltaïque. Autre [cond-mat.other]. Université Clermont Auvergne, 2018. Français. �NNT : 2018CLFAC096�. �tel02389464�. HAL Id: tel-02389464 https://tel.archives-ouvertes.fr/tel-02389464 Submitted on 2 Dec 2019. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(10) %BOT VO EFVYJ¨NF DIBQJUSF KF NPOUSF RV‫۝‬JM FTU QPTTJCMF EF SFUSPVWFS MFT BSDIJUFDUVSFT OBUVSFMMFT M‫۝‬BJEF E‫۝‬BMHPSJUINFT E‫۝‬PQUJNJTBUJPO FU OPUBNNFOU M‫۝‬BJEF E‫۝‬BMHPSJUINFT ©WPMV UJPOOBJSFT RVJ TPOU EJSFDUFNFOU JOTQJS©T QBS M‫©۝‬WPMVUJPO FMMFNªNF +F QBTTF FO SFWVF MFT BM HPSJUINFT BEBQU©T BVY QSPCM¨NFT QIPUPOJRVFT BWFD VO HSBOE OPNCSF EF EFHS©T EF MJCFSU© DPOUJOVT QVJT KF NPOUSF RV‫۝‬JM FTU QPTTJCMF E‫۝‬PCUFOJS FTTFOUJFMMFNFOU UPVUFT MFT TUSVDUVSFT QIP UPOJRVFT FNCM©NBUJRVFT OBUVSFMMFT &O੗O EBOT VO USPJTJ¨NF DIBQJUSF K‫۝‬BQQMJRVF MB UFDIOJRVF BVY BOUJSF੘FUT QPVS MFT DFMMVMFT QIPUPWPMUB¯RVFT QPVS NPOUSFS RV‫۝‬PO QFVU VUJMJTFS DF॒F BQQSPDIF QPVS USPVWFS EF OPVWFMMFT TUSVDUVSFT S©HVMJ¨SFT +‫©۝‬UVEJF MB QIZTJRVF EF DFU BOUJSF੘FU US¨T DPOUSFJOUVJUJG FU KF DPNQBSF VOF S©BMJTBUJPO FYQ©SJNFOUBMF. .

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(16) kz =. √. √ k 2 − α2 FU EBOT MF DBT DPOUSBJSF FMMF T‫©۝‬DSJU kz = i α2 − k 2 POEFT ©WBOFTDFOUFT. TVJWBOU z %POD φ(z) QFVU ªUSF E©DPNQPT© EF MB NBOJ¨SF TVJWBOUF φ(z) = Aeikz z + Be−ikz z. . P¹ A FU B TPOU EFT DPOTUBOUFT RV‫۝‬JM GBVESB E©UFSNJOFS HS¢DF BVY DPOEJUJPOT BVY MJNJUFT "MPST PO E©EVJU RVF MFT DIBNQT T‫©۝‬DSJWFOU TPVT MB GPSNF TVJWBOUF φ(z) = (Aeikz z + Be−ikz z )ei(kx x−ωt). . %BOT MFT DPOEJUJPOT EF QBTTBHF EFT DPVDIFT E‫۝‬VOF DPVDIF VOF BVUSF DPVDIF BV OJWFBV EF MB QPMBSJTBUJPO T E JM Z B VOF DPOUJOVJU© EF Ey FU EF μ1 ∂z Ey FU QPVS MB QPMBSJTBUJPO T M JM Z B VOF DPOUJOVJU© EF Hy FU EF 1 ∂z Hy 0O QFVU S©TVNFS DF S©TVMUBUT TVS MB ੗HVSF -FT DIBNQT EBOT MB j¨NF DPVDIF DBSBDU©SJT©F QBS TB QFSN©BCJMJU© μj FU TB QFSNJ॒JWJU© j FU TJUV©F FOUSF zj FU zj+1 QFVWFOU TF QS©TFOUFS TPVT MB GPSNF TVJWBOUF ikz ,j(z−zj ) (A+ + Bj+ e−ikz ,j(z−zj ) ) ei(kx x−ω t) j e. . P¹ zj FTU MB QPTJUJPO EF MB MJNJUF TVQ©SJFVSF EF MB DPVDIF j D‫۝‬FTU EJSF MB DPPSEPOO©F EF M‫۝‬JOUFSGBDF FOUSF MF NJMJFV j − 1 FU MF NJMJFV j kz , j = μj j k 2 − α2 P¹ k = ωc = 2π λ FU P¹ MB SBDJOF DBSS©F FTU MF QSPMPOHFNFOU BOBMZUJRVF EF MB SBDJOF DBSS©F BV QMBO DPNQMFYF -FT + DPFਖ਼DJFOUT A+ j FU Bj TPOU DPOTJE©S©T DPNNF ©UBOU M‫۝‬POEF QMBOF E‫۝‬BNQMJUVEF ©HBMF 1 FU EF. DPOTUBOUF EF QSPQBHBUJPO α + &TTBZPOT EF DBMDVMFS MFT DPFਖ਼DJFOUT A+ j FU Bj QPVS QPVWPJS E©UFSNJOFS MF DPFਖ਼DJFOU EF. S©੘FYJPO r FU MF DPFਖ਼DJFOU EF USBOTNJTTJPO t 1PVS DFMB OPVT BMMPOT S©TPVESF VO TZTU¨NF. .

(17) '࣒࣐ࣔ࣠ࣝ 4USVDUVSF NVMUJDPVDIFT DIBDVOF DBSBDU©SJT©F QBT TPO ©QBJTTFVS Zj+i − Zj TB QFSN©BCJMJU© μj FU TB QFSNJࡻJWJU© j . E‫©۝‬RVBUJPO QSPWFOBOU EFT SFMBUJPOT EF DPOUJOVJU© EFT EJ੖©SFOUT DIBNQT BV OJWFBV EFT JOUFS GBDFT $POTJE©SPOT MFT EJ੖©SFOUT NJMJFVY QPTT©EBOU QMVTJFVST DPVDIFT D‫۝‬FTU EJSF VO FNQJMF NFOU EF N DPVDIFT &O QPMBSJTBUJPO T M PO BVSB MF TZTU¨NF E‫©۝‬RVBUJPOT TVJWBOU ⎧ ⎪ ⎪ ⎨. − + + A− j + Bj = Aj+1 + Bj+1. ⎪ γj A− − B − = γj+1 A+ − B + ⎪ ⎩ j j j+1 j+1 j j+1. BWFD. ⎧ ⎪ + iγj (zj+1 −zj ) ⎨ A− j = Aj e ⎪ ⎩ B − = B + e−iγj (zj+1 −zj ) . j j. . . 1PVS MB QPMBSJTBUJPO T E OPVT SFNQMBDFSPOT MFT j QBS MFT μj NªNF TJ FO QSBUJRVF EBOT UPVT MFT DBMDVMT RVF OPVT BWPOT GBJU QBS MB TVJUF PO BWBJU UPVKPVST μj = 1. .

(18) &TTBZPOT EF S©TPVESF OVN©SJRVFNFOU DF TZTU¨NF E‫©۝‬RVBUJPO 1PVS DFMB OPVT BMMPOT DPOTJ E©SFS FO QSFNJFS MJFV RV‫۝‬BVDVOF POEF O‫۝‬FOUSF EBOT MB N − ime DPVDIF D‫۝‬FTU EJSF A+ N = 0 FU RVF M‫۝‬POEF QMBOF JODJEFOUF E‫۝‬BNQMJUVEF 1 QSPWJFOU EV IBVU EF MB TUSVDUVSF EPOD B1+ = 0 -F + = t FU MF DPFਖ਼DJFOU EF S©੘FYJPO FTU A+ DPFਖ਼DJFOU EF USBOTNJTTJPO t QFVU ªUSF BMPST BN 1 =r + %BOT DF DBT PO QFVU BMPST ©MJNJOFS MFT A+ j FU MFT Bj EV TZTU¨NF E‫©۝‬RVBUJPOT QPVS PCUFOJS. M‫۝‬FYQSFTTJPO EF r FU EF t 4J PO WFVU VOF TUBCJMJU© QBSGBJUF PO OF QFVU QBT MF GBJSF HS¢DF MB GPSDF CSVUF 0O OF QFVU QBT OPO QMVT VUJMJTFS MFT NBUSJDFT EF USBOTGFSU VTVFMMFT TJ PO WFVU RVF DFMB GPODUJPOOF EBOT UPVT MFT DBT &MMFT TPOU FO F੖FU JOTUBCMFT RVBOE PO B EFT ©WBOFTDFOUT $‫۝‬FTU QPVS §B RVF MFT NBUSJDFT 4 PV NBUSJDFT EF EJ੖VTJPO TPOU VUJMJT©FT .BUSJDFT EF EJॐVTJPO -F TZTU¨NF QFVU ªUSF ©DSJU EF MB NBOJ¨SF TVJWBOUF ⎤ − A ⎢ i ⎥ ⎦= ⎣ + Bi+1. ⎡. ⎡. γi i. γi ⎢ i. 1 i+1 ⎣ + γi+1. −. γi+1 i+1. 2 γii. ⎤⎡ ⎤ − i+1 B 2 γi+1 ⎥⎢ i ⎥ ⎦⎣ ⎦. γi+1 γi + − A i+1 i+1 i. . + &U QPVS GBJSF VOF MJBJTPO EFT EJ੖©SFOUT DPFਖ਼DJFOUT EFT POEFT NPOUBOUFT A+ j Bj BWFD MFT DP − Fਖ਼DJFOUT EFT POEFT EFTDFOEBOUFT A− j Bj PO QFVU S©©DSJSF MF TZTU¨NF DPNNF TVJU . ⎤ ⎡ ⎤ ⎤ ⎡ + + iγj hj 0 e A ⎥ ⎢ Bi ⎥ ⎢ i ⎥ ⎢ ⎦c⎣ ⎦ ⎣ ⎦=⎣ Bi− eiγj hj 0 A− i ⎡. . S. BWFD hj = zj+1 − zj -B NBUSJDF Sc FTU BQQFM© NBUSJDF EF TDB॒FSJOH NBUSJDF S PV NBUSJDF EF EJ੖VTJPO EF MB j¨NF DPVDIF 1PVS EPOOFS VOF NBUSJDF DPSSFTQPOEBOU M‫۝‬FNQJMFNFOU EFT TPVTTUSVDUVSFT JM O‫۝‬FTU QBT .

(19) O©DFTTBJSF EF MFT NVMUJQMJFS FOUSF FMMF QMVUPU EF MFT DPNCJOFS TFMPO MF TDI©NB RVF OPVT BMMPOT E©DSJSF DJ EFTTPVT $F॒F PQ©SBUJPO FTU BQQFM©F DBTDBEBHF 4J OPVT BWPOT. ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎢A⎥ ⎢L11 L12 ⎥ ⎢ C ⎥ ⎦⎣ ⎦ ⎣ ⎦=⎣ D L21 L22 B ⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎢D⎥ ⎢P11 P12 ⎥ ⎢B ⎥ ⎣ ⎦=⎣ ⎦⎣ ⎦ E F P21 P22. FU. . . &O GBJTBOU VO DBTDBEBHF PO PCUJFOU VOF SFMBUJPO EF HFOSF ⎡ ⎤ ⎡ L12 P11 L21 ⎢A⎥ ⎢L11 + 1−L11 P22 ⎣ ⎦=⎣ P21 L21 E 1−L22 P11. ⎤⎡ ⎤ ⎥ ⎢C ⎥ ⎦⎣ ⎦. 21 L22 P12 F P22 + P1−L 22 P11 L12 P12 1−L11 P22. . 1PVS SFMJFS MFT DPFਖ਼DJFOUT Aj FU Bj KVTRV‫۝‬ MB QSFNJ¨SF DPVDIF PO DPOUJOVF EF DBTDBEFS MFT NBUSJDFT S ⎡. ⎤. + ⎢A1 ⎥. ⎣. ⎤⎡. ⎡. ⎤. S12 ⎥ ⎢B1+ ⎥. ⎢S11 ⎦=⎣ ⎦⎣ ⎦ Bj S21 S22 Aj. . &U BVY DPFਖ਼DJFOUT Aj FU Bj EF MB EFSOJ¨SF DPVDIF PO B ⎡. ⎤. ⎡. ⎤⎡. ⎤. U12 ⎥ ⎢Bj+ ⎥. ⎢ Aj ⎥ ⎢U11 ⎣ ⎦=⎣ ⎦⎣ ⎦ − BN U21 U22 A− N. . "QS¨T BWPJS E©UFSNJO© MB NBUSJDF S FU MB NBUSJDF U OPVT QPVWPOT ©DSJSF Aj FU Bj FO DPOTJ E©SBOU RVF M‫۝‬BNQMJUVEF EF M‫۝‬POEF JODJEFOUF FTU ©HBMF 1 FU RVF EBOT MB EFSOJ¨SF DPVDIF JM O‫۝‬Z B. .

(20) RV‫۝‬VOF TFVMF POEF RVJ TPSU EF MB TUSVDUVSF "MPST PO B ⎡. ⎤. ⎤⎡. ⎡ U12 ⎢ 1−U11 S22. ⎢Aj ⎥ ⎣ ⎦=⎣ S22 U12 B 1−S22 U11. ⎤. − U11 S21 1−U11 P22 ⎥ ⎢AN ⎥ S21 1−S22 U11. ⎦⎣. B1+. ⎦.. . &O DIBRVF QPJOU EF MB TUSVDUVSF OPVT QPVWPOT DPOOB®USF M‫۝‬BNQMJUVEF EV DIBNQ DS©F QBS M‫۝‬POEF JODJEFOUF USBWFST MFT DPFਖ਼DJFOUT Aj FU Bj 1BS DPOT©RVFOU MF DPFਖ਼DJFOU EF S©੘FYJPO EF MB TUSVDUVSF FTU MF DPFਖ਼DJFOU EF MB QSFNJ¨SF MJHOF FU EF MB QSFNJ¨SF EF MB DPMPOOF EF MB NBUSJDF 0O QFVU BMPST M‫©۝‬UVEJFS FO GBJTBOU WBSJFS MB MPOHVFVS E‫۝‬POEF PV M‫۝‬BOHMF E‫۝‬JODJEFODF 6O QSFNJFS FYFNQMF FTU NPOUS© TVS MB ੗HVSF PV PO WPJU MF DPFਖ਼DJFOU EF S©੘FYJPO TVS VOF TJNQMF JOUFSGBDF FOUSF EFVY EJ©MFDUSJRVFT-F QS©NJFS JOEJDF FTU n1 = 1 FU MF TFDPOE FTU n2 = 1, 5 0O WPJU DMBJSFNFOU RVF MF DPFਖ਼DJFOU EF S©੘FYJPO E©QFOE EF MB QPMBSJTBUJPO EF MB MVNJ¨SF JODJEFOUF %BOT MF DBT EF MB QPMBSJTBUJPO 5. PO WPJU US¨T OF॒FNFOU RVF MF DPFਖ਼DJFOU EF S©੘FYJPO T‫۝‬BOOVMF QPVS VO BOHMF QBSUJDVMJFS BQQFM© BOHMF EF #SFXTUFS -PSTRV‫۝‬VOF POEF QMBOF FTU S©੘©DIJF M‫۝‬JODJEFODF EF #SFXTUFS BMPST M‫۝‬POEF S©੘©DIJF FTU QBSGBJUFNFOU QPMBSJT©F FU TPO DIBNQ ©MFDUSJRVF FTU QBSBMM¨MF M‫۝‬JOUFSGBDF QVJTRVF TFVMF MB QPMBSJTBUJPO 5& FTU S©੘©DIJF. . .PPTI FU MB QSPQBHBUJPO EF GBJTDFBVY. "V E©QBSU K‫۝‬BJ EPOD VUJMJT© MFT NBUSJDFT 4 EJSFDUFNFOU QVJT .PPTI QPVS MFT DBMDVMT QMVT ©WPMV©T DPNNF MB QSPQBHBUJPO EF GBJTDFBVY EBOT MFT TUSVDUVSFT QVJTRVF D‫۝‬FTU TVS DF NªNF QSJODJQF RVF .PPTI FTU CBT© "WFD M‫۝‬FOTFNCMF EF QSPHSBNNFT FO GBJU RVJ DPOTUJUVF .PPTI PO QFVU QBS FYFNQMF ©UVEJFS MB QSPQBHBUJPO EFT GBJTDFBVY EBOT MFT TUSVDUVSFT -F QSJODJQF FTU EF EJWJTFS MF GBJTDFBV JODJEFOU FO VOF TVQFSQPTJUJPO E‫۝‬POEFT QMBOFT QSPHSFTTJWFT NPOPDISPNBUJRVFT IPNPHÖFT &OTVJUF DFMB DPOTJTUF S©TPVESF OPUBNNFOU MFT ©RVBUJPOT EF .BYXFMM QPVS DIBDVOF EF DFT POEFT QMBOFT. .

(21) 0.25. 0.7. 0.6 0.2. Coecient de réexion. 0.5. 0.15 0.4. 0.3. 0.1. 0.2 0.05 0.1. 0. 0 0. 20. 40. 60. 80. 0. 20. 40. 60. 80. Angle en degré (°). Angle en degré (°). '࣒࣐ࣔ࣠ࣝ .PEVMF BV DBSS© EV DPFख़JDJFOU EF S©GMFYJPO FO GPODUJPO EF MًBOHMF EًJODJEFODF QPVS VOF QPMBSJTB UJPO -B GJHVSF HBVDIF SFQS©TFOUF MF DPFख़JDJFOU EF S©GMFYJUJPO FO QPMBSJTBUJPO 5& FU DFMMF EF MB ESPJUF NPOUSF MB MF DPFख़JDJFOU EF MB S©GMFYJPO FO QPMBSJTBUJPO 5.. &O੗O MB S©QPOTF EF MB TUSVDUVSF DIBRVF POEF QMBOF FTU QSJTF FO DPNQUF QPVS H©O©SFS VOF DBSUF EV DIBNQ ©MFDUSJRVF PV NBHO©UJRVF EBOT UPVUF MB TUSVDUVSF ©DMBJS©F QBS MF GBJTDFBV FU BJOTJ WJTVBMJTFS MB QSPQBHBUJPO EF DF EFSOJFS -B ੗HVSF NPOUSF DF RVJ BSSJWF VO GBJTDFBV BSSJWBOU TVS VOF JOUFSGBDF FOUSF EFVY EJ©MFD USJRVFT M‫۝‬JODJEFODF EF #SFXTUFS FO QPMBSJTBUJPO 5. 0O WPJU DMBJSFNFOU RV‫۝‬JM O‫۝‬Z B QSBUJRVF NFOU QBT EF S©੘FYJPO FU RVF M‫۝‬JOU©HSBMJU© EF MB MVNJ¨SF FTU USBOTNJTF EBOT MF TFDPOE NJMJFV $F TFSBJU US¨T JOU©SFTTBOU EF QPVWPJS GBJSF DF HFOSF EF DIPTFT JODJEFODF OPSNBMF OPVT WFSSPOT QMVT MPJO RVF MFT BOUJSF੘FUT GPOU FYBDUFNFOU DFMB &OTVJUF BWFD MF QSPHSBNNF .PPTI PO QFVU TJNVMFS MF GBJTDFBV EF MB S©GSBDUJPO EF MB MVNJ¨SF WFOBOU EF M‫۝‬BJS TVS VO NJMJFV E‫۝‬JOEJDF 1.5 FO QPMBSJTBUJPO T E 0O WPJU MF SBZPO JODJEFOU MF QMVT JOUFOTF MF SBZPO USBOTNJT FU MF SBZPO S©੘©DIJ 'JHVSF . -‫۝‬BWBOUBHF EF .PPTI D‫۝‬FTU RV‫۝‬JM FTU GBDJMF VUJMJTFS NªNF EBOT EFT DBT VO QFV DPNQMJRV©T RVJ VUJMJTFOU ©OPSN©NFOU EF DPVDIFT DPNNF MFT NJSPJST EF #SBHH 'JHVSF . .

(22) '࣒࣐ࣔ࣠ࣝ 3©TVMUBU EًVOF TJNVMBUJPO ©MFDUSPNBHO©UJRVF S©BMJT©F BWFD MF QSPHSBNNF .PPTI FO QPMBSJTBUJPO T M NPOUSBOU VO GBJTDFBV S©GSBDU© MًJODJEFODF EF #SFXTUFS QBS VO EJPQUSF FOUSF EFVY NJMJFVY EًJOEJDF n1 = 1 FU n2 = 1.5. '࣒࣐ࣔ࣠ࣝ 3©TVMUBU EًVOF TJNVMBUJPO ©MFDUSPNBHO©UJRVF S©BMJT©F BWFD MF QSPHSBNNF .PPTI FO QPMBSJTBUJPO T E NPOUSBOU VO GBJTDFBV FOUSF EFVY NJMJFVY EًJOEJDF n1 = 1 FU n2 = 1.5. .

(23) '࣒࣐ࣔ࣠ࣝ 1SPQBHBUJPO EًVO GBJTDFBV EBOT VO NJSPJS EF #SBHH FO JODJEFODF OPSNBMF. . .©UIPEFT NPEBMFT. -FT N©UIPEFT NPEBMFT EF 'PVSJFS POU ©U© JOWFOU©FT BV NJMJFV EFT BOO©FT QBS .PIBSBN FU (BZMPS NBJT FMMFT ©UBJFOU JOTUBCMFT FO QPMBSJTBUJPO T M $‫۝‬FTU N EF TDJMJDJVN JOE©QFOEBN NFOU 1IJMJQQF -BMBOOF FU (©SBSE (SBOFU RVJ POU USPVW© DPNNFOU MB SFOESF QMVT TUBCMF DF RVJ B PVWFSU MB WPJF ©OPSN©NFOU E‫۝‬VUJMJTBUJPOT EF DFT N©UIPEFT RVJ POU M‫۝‬BWBOUBHF E‫۝‬ªUSF M©H¨SFT NªNF TJ FMMFT OF QSFOOFOU FO DPNQUF RVF EFT H©PN©USJFT RVJ QFVWFOU TF E©DPVQFS FO DPVDIFT Q©SJPEJRVFT -F QSJODJQF EFT DFT N©UIPEFT FTU EF E©DPNQPTFS MB TUSVDUVSFT FO DPVDIFT JOWBSJBOUFT TVJ WBOU z 1PVS DIBDVOF EF DFT DPVDIFT PO DBMDVMF MFT NPEFT RVJ QFVWFOU T‫۝‬Z QSPQBHFS FU MFVS DPOTUBOUF EF QSPQBHBUJPO WFSUJDBMF $FMB SFTTFNCMF CFBVDPVQ MB N©UIPEF EF S©TPMVUJPO EBOT MFT NJMJFVY MBNFMMBJSFT TBVG RVF TJ PO DIPJTJU EF DPOTJE©SFS NPEFT JM Z B DPFਖ਼DJFOUT QPVS MFT NPEFT NPOUBOUT FU QPVS MFT NPEFT EFTDFOEBOUT &OTVJUF PO ©DSJU MFT DPOEJUJPOT BVY MJNJUFT FOUSF MFT DPVDIFT S©TFBVY PV MFT DPVDIFT IP. .

(24) NPHÖFT $F TPOU MFT NªNFT DPOEJUJPOT EF DPOUJOVJU© RVF QPVS MFT NJMJFVY MBNFMMBJSFT NBJT PO PCUJFOU BMPST EFT NBUSJDFT EF EJ੖VTJPO QPVS DIBRVF JOUFSGBDF RVJ TPOU QMVT HSBOEFT UPVKPVST BWFD OPUSF FYFNQMF EFT NPEFT MB NBUSJDF E‫۝‬JOUFSGBDF FTU VOF NBUSJDF DBSS©F EF DÚ© 0O QFVU BVTTJ GBDJMFNFOU ©DSJSF EFT NBUSJDFT EF DPVDIFT EF MB NªNF UBJMMF FU H©O©SBMJTFS MF DBTDBEBHF QPVS QPVWPJS BTTPDJFS MFT NBUSJDFT 4 QPVS MFT JOUFSGBDFT FU MFT DPVDIFT FYBDUFNFOU EF MB NªNF NBOJ¨SF RV‫۝‬PO BTTPDJF MFT NBUSJDFT 4 QPVS MFT NJMJFVY MBNFMMBJSFT. . 4USVDUVSFT QIPUPOJRVFT. .ªNF TJ MFT PSEJOBUFVST FU MFT N©UIPEFT EF GBCSJDBUJPO QFSNF॒FOU BVKPVSE‫۝‬IVJ E‫۝‬FOWJTBHFS EFT TUSVDUVSFT UPVKPVST QMVT DPNQMJRV©FT MFT PCKFUT QIPUPOJRVFT MFT QMVT JNQPSUBOUT FU MFT QMVT VUJMJT©T FU DPNQSJT TPOU EFT NVMUJDPVDIFT DPNNF MB DPVDIF BOUJSF੘FU PV MFT NJSPJST EF #SBHH PV FODPSF MFT DFMMVMFT QIPUPWPMUB¯RVFT 0O QFVU QBSGBJUFNFOU MFT TJNVMFS BWFD MFT UFDIOJRVFT EF NBUSJDFT 4 FU .PPTI FU BJOTJ NJFVY DPNQSFOESF MFVS DPNQPSUFNFOU. . $PVDIF BOUJSF॒FU. -B DPVDIF BOUJSF੘FU FOUSF EFVY NJMJFVY E‫۝‬JOEJDFT n1 FU n2 FTU VOF DPVDIF E‫۝‬JOEJDF JO √ λ0 P¹ λ0 UFSN©EJBJSF n = n1 n2 FU E‫©۝‬QBJTTFVS PQUJRVF λ0 /4 TPJU VOF ©QBJTTFVS S©FMMF EF 4n FTU MB MPOHVFVS E‫۝‬POEF EF USBWBJM 0O QFVU NPOUSFS RVF EBOT DFT DPOEJUJPOT VOF S©TPOBODF TQFDUSBMFNFOU US¨T MBSHF QFSNFU E‫۝‬PCUFOJS VO DPFਖ਼DJFOU EF USBOTNJTTJPO EF फ़BOE JM O‫۝‬FTU QBT QPTTJCMF EF GBJSF VO NJMJFV E‫۝‬JOEJDF FYBDUFNFOU n PO QFVU BV NPJOT DPOTFSWFS MB CPOOF ©QBJTTFVS PQUJRVF $FT EJ੖©SFOUT DPNQPSUFNFOUT TPOU JMMVTUS©T ੗HVSF *M FTU JOU©SFTTBOU EF SFHBSEFS DF RVJ TF QBTTF RVBOE PO GBJU WBSJFS M‫©۝‬QBJTTFVS EF MB DPVDIF BOUJSF੘FU WPJSF ੗HVSF 4J FMMF OF WBSJF RVF US¨T QFV D‫۝‬FTU KVTUF MB S©TPOBODF RVJ TF E©QMBDF .BJT TJ PO MB EPVCMF EBOT DF DBT PO PCUJFOU MB QMBDF VOF BOUJS©TPOBODF FU MB DPVDIF DS©F VO DPFਖ਼DJFOU EF S©੘FYJPO FODPSF QMVT ©MFW© 4J PO USJQMF DF॒F ©QBJTTFVS PO SFUSPVWF VOF DPVDIF .

(25) Reflexion 0.16. 0.14. Reflexion. 0.12. 0.1. 0.08. 0.06. 0.04 400. 500. 600 Wavelength. 700. 800. '࣒࣐ࣔ࣠ࣝ -B DPVSCF FO CMFV NPOUSF MF DPFख़JDJFOU EF S©GMFYJPO QPVS VOF JOUFSGBDF FOUSF EFVY NJMJFVY EًJOEJDFT FU -B DPVSCF FO SPVHF FTU MF DPFख़JDJFOU √ EF S©GMFYJPO QPVS VOF JOUFSGBDF FOUSF EFVY NJMJFV EًJOEJDFT BWFD VOF DPVDIF BOUJSFGMFU EPOU MًJOEJDF FTU 1.5 &O WFSU PO B VO JOEJDF BWFD VOF ©QBJTTFVS λ/4 ∗ 1.1 FOGJO MB DPVSCF FO OPJS NPOUSF RVًFO DIBOHFBOU Mً©QBJTTFVS PO DIBOHF MB MPOHVFVS EًPOEF EF S©TPOBODF. BOUJSF੘FU Fਖ਼DBDF NBJT MB MBSHFVS EF MB S©TPOBODF B EJNJOV© QBS SBQQPSU MB DPVDIF MB QMVT ੗OF $‫۝‬FTU QPVS DF॒F SBJTPO RVF MB DPVDIF λ/4 FTU S©FMMFNFOU MF NFJMMFVS BOUJSF੘FU QPTTJCMF FMMF GPODUJPOOF TVS VO MBSHF TQFDUSF. . .JSPJST EF #SBHH. -F NJSPJS EF #SBHH PV %#3 %JTUSJCVUFE #SBHH 3F੘FDUPS FTU VOF TVQFSQPTJUJPO EF DPVDIFT QMBOFT USBOTQBSFOUFT E‫۝‬JOEJDF EF S©GSBDUJPO ©MFW© FU CBT E‫©۝‬QBJTTFVS. λ0 4n . P¹ λ0 FTU MB MPOHVFVS. E‫۝‬POEF EF USBWBJM FU n M‫۝‬JOEJDF PQUJRVF EF DIBRVF DPVDIF -‫۝‬IJTUPJSF EFT NJSPJST EJ©MFDUSJRVFT FTU DPNQMJRV©F 0O MFT BQQFMMF NJSPJST EF #SBHH QBS S©G©SFODFT BVY USBWBVY EF 8JMMJBN -BXSFODF #SBHH MBVS©BU EV QSJY /PCFM EF QIZTJRVF EF TVS MB S©੘FYJPO EFT SBZPOT 9 QBS MFT DPVDIFT BUPNJRVFT NBJT DF O‫۝‬FTU QBT QSPQSFNFOU QBSMFS #SBHH RVJ B JOWFOU© MF NJSPJS EJ©MFDUSJRVF (S¢DF BVY JOUFSG©SFODFT DPOTUSVDUJWFT FO S©੘FYJPO FU EFTUSVDUJWFT FO USBOTNJTTJPO MF NJ. .

(26) 0.04. Reflexion. 0.03. 0.02. 0.01. 0 300. 400. 500. 600. 700. 800. 900. Wavelength. '࣒࣐ࣔ࣠ࣝ $PFख़JDJFOU EF S©GMFYJPO FO GPODUJPO EF Mً©QBJTTFVS EF MB DPVDIF BOUJSFGMFU -B DPVSCF CMFV JOEJRVF MB S©GMFYJPO MPSTRVF Mً©QBJTTFVS EF MB DPVDIF FTU λ/40O WPJU RVًFMMF NPOUSF MB NFJMMFVS BOUJSFGMFU -B DPVSCF SPVHF FTU MB DPVDIF EPOU Mً©QBJTTFVS FTU λ/2 %BOT DF DBT MF DPFख़JDJFOU EF S©GMFYJPO FTU QMVT ©MFW© MB MPOHVFVS EًPOEF 600nm PO B VOF BOUJS©TPOBODF &OGJO MB DPVSCF OPJSF NPOUSF MB S©GMFYJPO EF MB MVNJ¨SF MPSTRVF Mً©QBJTTFVS EF MB DPVDIF BOUJSFGMFU FTU 3 ∗ λ/4 "WFD DFࡻF ©QBJTTFVS PO PCUJFOU WSBJNFOU VO BOUJSFGMFU P¹ MB S©TPOBODF FTU QMVT ©USPJUF NBJT BV NªNF FOESPJU RVF QPVS VOF ©QBJTTFVS λ/2. SPJS EF #SBHH QFSNFU EF S©੘©DIJS MB MVNJ¨SF CJFO QMVT Fਖ਼DBDFNFOU RV‫۝‬VO N©UBM -F DPFਖ਼DJFOU EF S©੘FYJPO FTU E‫۝‬BVUBOU QMVT ©MFW© RVF MF OPNCSF EF DPVDIFT FTU ©MFW© -FT NJSPJST EF #SBHH TPOU QSJODJQBMFNFOU VUJMJT©T QPVS MB GBCSJDBUJPO EFT DBWJU©T EFT MBTFST FU EJPEFT MBTFST -FVS GPSUF S©੘FDUJWJU© QFSNFU EF S©BMJTFS EFT DBWJU©T PQUJRVFT GPSU DPFਖ਼DJFOU EF RVBMJU© BTTVSBOU BJOTJ VO CPO DPO੗OFNFOU EFT QIPUPOT -F DIBOHFNFOU E‫۝‬BOHMF E‫۝‬JODJEFODF B UFOEBODF E©DBMFS MF TQFDUSF FO S©੘FYJPO EV NJSPJS WPJS ੗HVSF 6O NJSPJS EF #SBHH QPTTËF EPOD EFT QSPQSJ©U©T GPSD©NFOU TFOTJCMFT M‫۝‬BOHMF E‫۝‬JODJEFODF -FT NJSPJST EF #SBHH TPOU FO S©BMJU© VO FYFNQMF EF TUSVDUVSF QIPUPOJRVF Q©SJPEJRVF RV‫۝‬PO BQQFMMF DSJTUBVY QIPUPOJRVFT KVTUFNFOU DBVTF EF MFVS S©HVMBSJU© -FT DSJTUBVY QIPUPOJRVFT POU ©U© US¨T ©UVEJ©T EBOT MFT BOO©FT KVTUFNFOU BWFD MFT UFDIOJRVFT OVN©SJRVFT ©WPRV©FT DJ EFTTVT -FT N©UIPEFT NPEBMFT EF 'PVSJFS QBS FYFNQMF POU ©U© US¨T VUJMJT©FT EBOT DF DPOUFYUF .

(27) Reflexion 1. 0.8. Reflexion. 0.6. 0.4. 0.2. 0 300. 400. 500. 600. 700. 800. Wavelength. '࣒࣐ࣔ࣠ࣝ 4QFDUSF EF S©GMFYJPO EF MB MVNJ¨SF QPVS EJWFST BOHMFT EًJODJEFODF 0deg = 0 QPVS MB DPVSCF SPVHF 0deg = 30 QPVS MB DPVSCF KBVOF FU 0deg = 45 QPVS MB DPVSCF WFSUF 0O DPOTUBUF RVF MF TQFDUSF TF E©QMBDF EF MB ESPJUF WFST MB HBVDIF EPOD WFST MFT QMVT DPVSUFT MPOHVFVST EًPOEFT BV GVS FU NFTVSF RVF MًBOHMF EًJODJ EFODF BVHNFOUF "V QBTTBHF MًBOHMF EF S©GMFYJPO BVHNFOUF BWFD MًBOHMF EًJODJEFODF DPNNF QPVS VOF JOUFSGBDF TJNQMF. -FT NJSPJST EF #SBHH POU VOF MBSHFVS TQFDUSBMF VUJMF CJFO E©੗OJF FU SFMBUJWFNFOU ©USPJUF $F RVJ MB E©੗OJU D‫۝‬FTU MF DPOUSBTUF E‫۝‬JOEJDF 1MVT DFMVJDJ FTU HSBOE QMVT MB CBOEF JOUFSEJUF FTU MBSHF -B ੗HVSF NPOUSF TVS RVFMRVFT DBT MFT NPEJ੗DBUJPOT EV TQFDUSF RVBOE PO NPEJ੗F MFT JOEJDFT EFT EJ੖©SFOUFT DPVDIFT FO DPOTFSWBOU MFVS ©QBJTTFVS PQUJRVF EF λ0 /4. . .JSPJST EJ©MFDUSJRVFT HSBEJFOU. $PNNF JMMVTUS© BV QBSBHSBQIF QS©D©EFOU MFT NJSPJST EF #SBHH POU VOF MBSHFVS TQFDUSBMF VUJMF CJFO E©੗OJF FU SFMBUJWFNFOU ©USPJUF 0O QFVU WPVMPJS QPVS EFT BQQMJDBUJPOT BTTF[ QS©DJTFT DPNNF MB NJTF FO GPSNF EF QVMTF EF MBTFST GFNUPTFDPOEF BWPJS EFT NJSPJST EJ©MFDUSJRVFT P੖SBOU VO NFJMMFVS DPOUS´MF VOF CBOEF QBTTBOUF QMVT MBSHF PV E‫۝‬BVUSFT QSPQSJ©U©T QMVT FYP UJRVFT %BOT DF DBT VO DFSUBJO UZQF EF TUSVDUVSF QFVU ªUSF FOWJTBH© $F TPOU EFT NJSPJST EJ©MFD .

(28) Reflexion 1. 0.8. Reflexion. 0.6. 0.4. 0.2. 0 300. 400. 500. 600. 700. 800. Wavelength. '࣒࣐ࣔ࣠ࣝ 7BSJBUJPO EF MB MBSHFVS EV TQFDUSF EF MB MVNJ¨SF FO GPODUJPO EV DPOUSBTUF EًJOEJDFT%BOT DFࡻF DPVSCF JM FTU DMBJS RVF MB MBSHFVS EF MB CBOEF JOUFSEJUF BVHNFOUF FO GPODUJPO EF MًBVHNFOUBUJPO EV DPOUSBTUF EًJOEJDF-ًJOEJDF PQUJRVF EF MB QSFNJ¨SF DPVDIF FTU n1 = 1.4-B DPVSCF JOEJRV©F FO CMFV MًJOEJDF FTU 1.87 -B MBSHFVS TQFDUSBMF EF DFࡻF DPVSCF FTU WJTJCMFNFOU JOG©SJFVS DFMMF JOEJRV©F FO SPVHF EPOU MF TFDPOE JOEJDF FTU 2 &O GJO MB DPVSCF USBD©F FO OPJSF B VOF MBSHFVS TQFDUSBMF QMVT HSBOEF RVF MFT EFVY BVUSFT DPVSCF EV GBJU RVF TPO TFDPOE JOEJDF B VOF WBMFVS TVQ©SJFVS DFMMF EF EFVY BVUSFT DPVSCFT ©HBMF 2.12. USJRVFT EPOU MFT QBSBNÜSFT H©PN©USJRVFT DIBOHFSBJFOU HSBEVFMMFNFOU 0O QFVU GBDJMFNFOU DPNQSFOESF QPVSRVPJ D‫۝‬FTU JOU©SFTTBOU EBOT MF DBT P¹ PO WFVU ©MBSHJS MB CBOEF JOUFSEJUF FO FNQJMBOU EFT NJSPJST EF #SBHH TVDDFTTJGT PO ©MBSHJU MB CBOEF JOUFSEJUF EF MB TUSVDUVSF NªNF MFT EJ੖©SFOUFT MPOHVFVST E‫۝‬POEF OF TFSPOU QBT S©੘©DIJFT BV NªNF OJWFBV EBOT MB TUSVDUVSF %F OPNCSFVY EJTQPTJUJGT FYJTUFOU VUJMJTBOU DF QSJODJQF FU QSPQPTBOU EFT TUSVDUVSFT MFOUFNFOU WBSJBCMFT EJUFT ۡDIJSQFEۡ FO BOHMBJT 6O FYFNQMF FTU NPOUS© ੗HVSF QSPWFOBOUF E‫۝‬VO BSUJDMF US¨T DJU© EF MB DPNNVOBVU© EFT MBTFST GFNUPTFDPOEF $F RVF NPOUSFOU MFT BSUJDMFT DPODFSOBOU DFT NJSPJST EJ©MFDUSJRVFT QBSUJDVMJFST D‫۝‬FTU RV‫۝‬JMT POU VOF HSBOEF ੘FYJCJMJU© "V EFM E‫۝‬ªUSF S©੘©DIJTTBOU PO QFVU MFT VUJMJTFS FO DPOUS´MBOU MFVS EJTQFSTJPO %JTQPTFS EF N©UIPEFT QFSNF॒BOU EF DS©FS EFT NJSPJST EJ©MFDUSJRVFT BWFD EFT GPODUJPOT NPEVMBCMFT QPVSSBJU EPOD BWPJS VO HSBOE JOU©SªU QSBUJRVF. .

(29) '࣒࣐ࣔ࣠ࣝ 'JHVSF UJS©F EF NPOUSBOU VO NJSPJS EJ©MFDUSJRVF HSBEJFOU VUJMJT© QPVS MFT MBTFST GFNUPTFDPOEF. . $FMMVMFT QIPUPWPMUB¯RVFT. -FT DFMMVMFT QIPUPWPMUB¯RVFT QFVWFOU ªUSF DPOTJE©S©FT DPNNF EFT TUSVDUVSFT MBNFMMBJSFT FO QSFNJ¨SF BQQSPYJNBUJPO &O S©BMJU© DFSUBJOFT QS©TFOUFOU VOF SVHPTJU© RVJ GBWPSJTF M‫۝‬BCTPSQUJPO EF MB MVNJ¨SF NBJT VOF NPE©MJTBUJPO EF MB DFMMVMF DPNNF VOF TUSVDUVSF NVMUJDPVDIF EPOOF E©K EF US¨T CPOT S©TVMUBUT -F QSJODJQF FTU EF GBJSF FO TPSUF RVF MB MVNJ¨SF TPJU BCTPSC©F EBOT VOF DPVDIF EJUF BDUJWF DPOTUJUV©F E‫۝‬VO NBU©SJBV TFNJDPOEVDUFVS %BOT DF॒F DPVDIF EFT QBJSFT ©MFDUSPOUSPV TPOU BMPST H©O©S©FT $PNNF MF TFNJDPOEVDUFVS FTU EPQ© EF NBOJ¨SF EJ੖©SFOUF TVJWBOU MB QSPGPO EFVS PO B EFT FOESPJUT EPQ©T / FU EFT FOESPJUT EPQ©T 1 $FMB DPOEVJU VOF T©QBSBUJPO EFT ©MFDUSPOT FU EFT USPVT FU M‫۝‬BQQBSJUJPO E‫۝‬VOF UFOTJPO BVY CPSOFT EV NBU©SJBV TFNJDPOEVDUFVS *M GBVU FOTVJUF QPVWPJS DPMMFDUFS DFT QPSUFVST EF DIBSHF -‫۝‬BSSJ¨SF EF M‫©۝‬MFDUSPEF FTU FO H©O©SBM. .

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