Nanjing University IN Surface plasmon polariton (SPP) From Maxwell's Eqs,we can get the wave equation V2E +keE =0, Considering the waveguide modes in x direction,then 82E, +(k6e-B2)E,=0. 02H,+(e-B門H,=0 82 1 Hy =i- aEy Ex=-i- 1H u08z e088z H2= E:= B ωUo ωeoe For TE mode For TM mode Dielectrie Superlattice Laboratory Nat.Lab.Microstructures Dr.Tao Li taoli@nju.edu.cn
Nanjing University From Maxwell From Maxwell s ’ Eqs, we can get the wave equation Considering the waveguide modes in x direction, then For TE mode For TM mode Dielectric Superlattice Laboratory Nat. Lab. Microstructures Dr. Tao Li taoli@nju.edu.cn
Nanjing University Surface plasmon polariton (SPP) For TE case Ey(z)=A2eBe-k2: 1 Hs(z)=-iA2-kzeiBxe-ka: ωo Z>0 62 Dielectric H2(z)=A2 B nse ks po 81 Ey()=AleiBxekz Metal Hx()=iA I koisx oh Z<0 w H2(z)=A1- B eiBxchs o According to the continuity of H,and sE.at the interface A1(k1+k2)=0. A2=A1=0, No mode for TE wave Dielectrie Superlattice Laboratory Nat.Lab.Microstructures Dr.Tao Li taoli@nju.edu.cn
Nanjing University For TE case ε2 Z>0 ε1 Z<0 According to the continuity of Hy and εEz at the interface No mode for TE wave Dielectric Superlattice Laboratory Nat. Lab. Microstructures Dr. Tao Li taoli@nju.edu.cn
Nanjing University Surface plasmon polariton (SPP) For TM case Hy(z)=A2elBxe-k2i E,(2)iAk we082 Z>0 82 Dielectric E,()=-A1 B eiBx e-k2z WE0E2 81 Hy(z)=AlelBxehz Metal Ex()=-iA1-Ikreseh: Z<0 08u6j E:()=-A1- B eiBx chi e081 According to the continuity ofH and sE at the interface k2 =- 82 → k好=B2-k行ε1 8182 k1 k号=B2-行ε2 B=ko 81+E2 Dielectrie Superlatice Laboratory A surface wave! Nat.Lab.Microstructures Dr.Tao Li taoli@nju.edu.cn
Nanjing University For TM case Z>0 ε2 Z<0 ε1 According to the continuity of H According to the continuity of H and εE at the interface y and εEz at the interface A surface wave! Dielectric Superlattice Laboratory Nat. Lab. Microstructures Dr. Tao Li taoli@nju.edu.cn A surface wave!
Nanjing University Surface plasmon polariton (SPP) Bulk Plasmon Light The God close a door with a window open! WsP when k-→o Forbidden band 2 8m(0)=1- 2 =-ed 0 0 001 002 94 @sp Dielectrie Superlattice Laboratory Nat.Lab.Microstructures Dr.Tao Li taoli@nju.edu.cn
Nanjing University Bulk Plasmon Light The God close a door with a window open! ωP Forbidden band Forbidden band 2 w en h p k ω ω → ∞ SP Surface Plasmon Forbidden band 2 ( 1 ) p p m d ω ε ω ε ω ω ω = − = − = 1 sp d ω ε = + Dielectric Superlattice Laboratory Nat. Lab. Microstructures Dr. Tao Li taoli@nju.edu.cn
Nanjing University Surface plasmon polariton (SPP) SPP:ksp>kuight Bulk Plasmon Light ko=kg+k+k2 Forbidden band k=0,for TM mode and k,>ko SPP So,k2<0,k.is an Im 001 02 9 SPP is also an evanescent wave Dielectrie Superlattice Laboratory Nat.Lab.Microstructures Dr.Tao Li taoli@nju.edu.cn
Nanjing University S k k Bulk Plasmon Light PP: kspp>klight 2 222 0 0 xyz kkkk k for TM mode = + + SPP Forbidden band 0 0, y x k for TM mode and k k = > SPP 0 2 , 0, Im x z z So k k is an < SPP is also an evanescent wave Dielectric Superlattice Laboratory Nat. Lab. Microstructures Dr. Tao Li taoli@nju.edu.cn