金屬光柵在不同偏振下穿透機制之研究

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(1)Research on transmission mechanism of metallic gratings at different polarizations.

(2) Research on transmission mechanism of metallic gratings at different polarizations. Student. Wei-Lun Hung. Advisor. Dr. Shun-Tung Yen. A Thesis Submitted to Department of Electronics Engineering & Institute of Electronics College of Electrical Engineering and Computer Science National Chiao Tung University In Partial Fulfillment of the Requirements for the Degree of Master in Electronics Engineering June 2011 Hsinchu, Taiwan, Republic of China.

(3) P- (TM) S- (TE). Fabry-Perot. i.

(4) Research on transmission mechanism of metallic gratings at different polarizations Student. Wei-Lun Hung. Advisor. Dr. Shun-Tung Yen. Department of Electronic Engineering & Institute of Electronics National Chiao Tung University. Abstract We analyze transmission characteristics and near-field patterns of metallic gratings at different polarizations. We not only study the resonance transmission, but also focus on the transmission mechanism at Rayleigh wavelength where the standing wave is excited by incident wave. For P-polarization (TM), the standing wave causes surface charge redistribution, which results in null transmission. However, for S-polarization (TE), the constructive interference between incident wave and standing wave leads to high transmission. The calculation results are in good agreement with experiments. We show that the metallic gratings can be designed as optical filters for different polarizations by tuning the resonance wavelength of Fabry-Perot mode.. ii.

(5) MOSFET. Lab635. DC. iii.

(6) …………………………………………………... i. …………………………………………………... ii. ……………..………………………………………….. iii. …………..…………………………………………….. iv. ……...………………………………………………. vii ………………………………………………... 1 1.1. …………………………………………….. 1. 1.2. ………………………………………….. 3 …………………………………………… 4. 2.1. ………………………………………….. 4. 2.1.1. ………………………………………… 5. 1.. …………………………………………… 5. 2.. ………………………………… 7. 3.. ………………………………… 8. 2.1.2. ………………………………………... 14. 1.. ……………………………….. 14. 2.. ………………………………..…. 21 (1).. ………………..…………………. 21 iv.

(7) (2).. ……………………………..….. 24. (3).. ……………………...…….. 26 …………………………... 29. 3.1. P-. S-. …………………...……… 29. 3.1.1. ……………………….. 29. 3.1.2. ………………………..... 31. 3.2. P-. …………………………………..……… 32. 3.2.1. ………………..……....... 36. 3.2.2. …………………..…....... 40. 3.3. S-. ………………………………………..… 43. 3.3.1. …………………..…....... 43. 3.3.2. ……………………......... 46 ………………………………...…………….. 49. 4.1. …….…………………………..…………… 49 ………………………………...……..……… 52 ………………………………...……..…………... 54 ………………………………...……..……………….. 56. v.

(8) 1.1. 1 [1]. 1.2. 2 [2] ( ). 2.1. ( ). ( ). S-. ( ). ߝଵ. ( ) ߝ௠௘௧௔௟. 4. P-. ߝଷ. ( ). ߝ௦௟௜௧. (a) TM(2-25) (b) 26. 2.2 TE(2-32). 3.1. ax. 3.2. 3.3. ax=0.15Lx L. ax a z. 30. (a)TM (b)TE. 31. 0.15Lx 0.01Lx P-. 32. 3.4. 33 vi.

(9) 3.5. P-. kx0. 34. ax=0.15Lx. (a) L=0.15Lx (b) L=0.25Lx. (c)L=0.35Lx (d)L=0.45Lx. 3.6. ax=0.15Lx L=0.15Lx. 3.7. λ=1.012Lx (b) L=0.45Lx λ=1.28Lx. ax=0.15Lx L=0.45Lx. 3.8. (a). (a). 35. P-. (a) L=0.15Lx (b). 36. λ=Lx. 37. P-. ax=0.15Lx z=0. L=0.01Lx. (b). λ=Lx. P-. +1. -1 λ. 3.9. (a) (b) (c). 3.10 λ=Lx (a). 38. 1/4. 0. ax=0.15Lx. L=0.01Lx P-. 1/4. (b). vii. 39 0.

(10) 3.11 (a)λ=0.9 1 1.1 Lx. (b) λ=1. Ez. 40. 1.1 Lx Lx=24 µm. 3.12 P-. L=0.2 µm. ax=6 8 10 µm. 41. Si 11.2. 3.13 Lx=24 µm L=0.2 µm ax=6 µm P-. (a) λ=Lx 41. (b) λ=ඥεଷ Lx. 3.14 Lx=24 µm L=0.2 µm ax=6 µm P-. 42 (0th). (total). 3.15 S-. (a). L=0.01Lx. 43. ax=0.2~0.8 Lx (b) L=0.6Lx ax=0.8Lx λ=1.2Lx. 3.16 (a). |Ey| ax=0.8Lx. z=0. 3.17. (b). ax=0.8Lx. L=0.01Lx λ=Lx. S-. L=0.01Lx S-. (Ey). viii. λ=Lx. 44 +1 -1. λ=Lx 45.

(11) λ<Lx. 3.18 λ>ඥεଷ Lx. Lx<λ<ඥεଷ Lx. 3.19 S-. 46. Lx=24 µm L=0.2 µm. ax=18 20 22 µm. 47. Si 11.2. 3.20 Lx=24 µm L=0.2 µm ax=22 µm S-. (a) λ=Lx 48. (b) λ=ඥεଷ Lx. 4.1. 4.2. 49. (a) P-. Lx=24 µm ax=0.05Lx L=0.02Lx (b) S-. Lx=24 µm. ax=0.374Lx L=0.267Lx. 11.9. 4-2. ix. 50.

(12) 1.1 (Christiaan Huygens). (Augustin-Jean Fresnel). 1.1[1]. (. ). (Gustav Robert Kirchhoff) 1.2[1, 2]. (opaque). (Green's theorem). 1.1. [1] 1.

(13) 1.2. [2]. [3-7] Ebbesen. (FDTD)[9] (Waveguide mode). [8]. (RCWA)[10] (Modal expansion)[11]. [12-24] 2.

(14) 1.2. [12-17, 20, 23, 24]. (Rayleigh wavelength) [25-31] Fabry-Perot [18, 21, 22]. Fabry-Perot. 3.

(15) 2.1 2.1 S-. 2.1. ( ). P-. (. ). ( (. (. ) . (. ). ( ). . ). ) . 4. ( ). S(. ). P.

(16) 2.1.1 1. ( ) ( ) [32]. S-. P-. 0 1   ik x , g x v E(S ,)g ( x ) = −1 e  Lx   0     1   1  ik x (v ) EP,g ( x ) = 0  e x ,g  Lx  k  − x,g   k (v)   z,g 

(17) ,. 2-1a. 2-1b. ,. k x,g = (v). kz,g. ω c. Sinθ +. 2 n gπ. 2-2a. Lx. ω  =  ε v  − k x2, g , v = 1, 3 c . . 2. . 2-2b. g=1,2,3…N N. zˆ × H H FS , g ( x ) ≜. 1 Lx.  0  ik x ,g x  −1 e  . 5. 2-3a.

(18) FP , g ( x ) ≜. 1 Lx.  1  ik x ,g x  0 e  . 2-3b. E(S ,)g , ( x ) = FS , g ( x ). 2-4a. E(P ,)g , ( x ) = FP , g ( x ). 2-4b. v. v. zˆ × H. (v) S , g ,. ( x) = −. ck z(,vg). ωZ 0 εv. zˆ × H (Pv,)g , ( x ) = −. Z0. FS , g ( x ). 2-4c. FP , g ( x ). 2-4d. . ( ). E(1) ( x, z ) =. E(3) ( x, z ) =. ∑. zˆ × H(1) ( x, z ). ∑. zˆ × H(3) ( x, z ). ∑. σ =S ,P g. (. ik z( 3) ,g ( z − L ). (. (. ik z( 3) ,g ( z − L). ∑ zˆ × Hσ(3),g , ( x ) aσ(3),g e. σ =S ,P g. 6. ik z(1) ,g z. + bσ(3), g e. ik z(1) ,g z. ∑ zˆ × Hσ(1),g , ( x ) aσ(1),g e. σ =S ,P g. =. (. ∑ Eσ(1),g , ( x ) aσ(1),g e. ∑ Eσ(3),g , ( x ) aσ(3),g e. σ = S ,P g. =. ∑. ( ). − bσ(1), g e. + bσ(1), g e. − ik z(1) ,g z. − ik z( 3) ,g ( z − L ). − ik z(1) ,g z. − bσ(3), g e. ). 2-5a. 2-5b. ). − ik z( 3) ,g ( z − L). ). 2-6a. ). 2-6b.

(19) 2. ( ). ( ) (Parallel-plate waveguide). TE. TM. [33]. 0     − L a     x x   niπ  x − (2)    ETE x = ( ) 2  2   ,i ,  Sin    a a   x  x    . 2-7a.  Lx − a x      π x − n   2  j  2    Cos  (2) ETM , j , ( x ) =  a x ax         0  . 2-7b. i=1,2,3…I j=1,2,3…J. I . TE. zˆ × H. ( x) = −. TE TM. TM . zˆ × H. 1/√2 (2) TE ,i ,. J. k z( ,i) 2. Z0. ω. (2) ETE ,i , ( x ). c. 7. 2-8a.

(20) ω zˆ × H. (2) TM , j ,. ε slit. (2) ( x ) = − c ( 2) ETM , j , ( x ) Z 0k z , j. 2-8b. ,.  2 k z( ,k) =  ε slit . ω.  nkπ  −    c   ax  2. 2. 2-9. ( ). E(2) ( x, z ) (2)  (2) = ∑ ETE ,i , ( x ) aTE ,i e  i. ik z( ,2i ) z. (2)  (2) + ∑ ETM , j , ( x ) aTM , j e  j. (2) + bTE ,i e. ik z( 2, j) z. ik z( 2,i ) ( L − z ). (2) + bTM , je.  . 2-10a. ik z( ,2j) ( L − z ).  . ik z( 2,i ) ( L − z ).  . zˆ × H(2) ( x, z ) (2)  (2) = ∑ zˆ × HTE ,i , ( x ) aTE ,i e  i. + ∑ zˆ × H j. (2) TM , j ,. ik z( ,2i ) z. (2) − bTE ,i e. 2-10b. ik z , j z ik z , j ( L − z )  (2) (2) − e b e ( x )  aTM TM , j ,j  (2). (2). 3.. [34]. ( ) TM. TM. TE r=. 2-1 TM. 8. !

(21). !. "#. .

(22) Ex = − Ez =.  ∂H y  i ε ( x ) k0  ∂z . 2-11a.  ∂H y  i ε ( x ) k0  ∂x . Hy=. 2-11b. i  ∂E z ∂E x  −   k 0  ∂x ∂z . 2-11c. = $/%. ε'. rLx rLx  ε , x − ≤ ≤ metal  2 2 ε ( x) =  rLx r  ε slit , ≤ x ≤  1 −  Lx 2  2  x. z. 2-12. "# ', ( = )' (. Λ. ∂2Z ( z ) = −Λ 2 Z ( z ) 2 ∂z (. 2-13 2-11. 2-13 !'+,Λ(. ! ', ( = -' !'+,Λ(. 2-13. ∂X ( x )  = −iε ( x ) k0V ( x )  ∂x   2   ∂V ( x ) = −ik  1 − Λ X ( x) 0 2   ∂x  ε ( x ) k0 . 9. 2-14.

(23) 2-14.  ∂2 X ( x) = − ( ε metal k0 2 − Λ 2 ) X ( x )  2 ∂x  2  ∂ V ( x) = − ε k 2 − Λ2 V ( x) ( metal 0 )  ∂x 2 . = / 0 − Λ0. 2-15.  rLx   −iε metal k0  rLx  rLx        rLx  V −  Sin  β  x +   X ( x ) = X  − 2  Cos  β  x + 2   + β 2       2         V ( x ) = V  − rLx  Cos  β  x + rLx   + −i β X  − rLx  Sin  β  x + rLx              2   ε metal k0  2  2    2     .   rLx  −iε metal k0  rLx   rLx  V −  Sin ( β rLx )  X  2  = X  − 2  Cos ( β rLx ) + β     2      V  rLx  = V  − rLx  Cos ( β rL ) + −i β X  − rLx  Sin ( β rL ) x x     2  ε metal k0  2   2 . 2-16. 2-15. 2-16. 2-17. 2-17.   rLx     X  2    Cos ( β rLx )     =   rLx    −i β  V  2    ε k Sin ( β rLx )    metal 0  . −iε metal k0. rL   Sin ( β rLx )   X  − x   β 2        rLx   Cos ( β rLx )  V −   2  . 2-18. α = / 0 − Λ0   r    X   1 −  Lx     2     r     V   1 −  Lx     2    iε k     rL   Cos α (1 − r ) Lx  − slit 0 Sin α (1 − r ) Lx    X  x    α  2   =  − iα Sin α (1 − r ) L     rLx   Cos α (1 − r ) Lx  x   ε k V    slit 0   2  . 10. 2-19.

(24) 2-18. 2-19 (Bloch theorem) 2-18. 2-19.   r     rLx    X   1 −  Lx    X  − 2  2       =ΞΞ   1 2   r      rLx    V   1 −  Lx   V − 2   2        . iε slit k0   − − ⋅ − Cos 1 1 r L Sin r L α α     ( ) ( ) x x       α  Ξ1 =   − iα Sin α (1 − r ) L   Cos α (1 − r ) Lx  x   ε k   slit 0 .   Cos ( β rLx ) Ξ2 =   −i β  ε k Sin ( β rLx )  metal 0. 2-21a. −iε metal k0.  Sin ( β rLx )  β   Cos ( β rLx )  .   r     rLx    X   1 −  Lx    X − 2  2      ik L Sin θ  =e 0 x     r      rLx    V   1 −  Lx   V − 2   2        . 2-20. 2-20. 2-21b. 2-22. 2-22. ik0 Lx Sinθ. e  Ξ1Ξ 2 −   0 .   rLx   X −  0     2   =0   eik0 Lx Sinθ     rLx   V − 2     . 11. 2-23.

(25) (non-trivial solution).   eik0 Lx Sinθ Det  M −    0.    = 0 eik0 Lx Sinθ   0. TM. 2-24. (eigenvalue equation). Cos ( k0 Lx Sinθ ) − Cos α (1 − r ) Lx  Cos ( β rLx )  1  ε β αε +  slit + metal  Sin α (1 − r ) Lx  Sin ( β rLx ) = 0 2  αε metal ε slit β . Λ. 2-25. TM. 2-25. y. ( ) 2 ( 2 ) iΛl z ( 2 ) iΛl ( L − z )  H y( ) ( x, z ) = ∑ X TM , l ( x )  aTM + bTM , le , le . 2-26. l. X TM , l ( x ) =  rLx  −iε metal k0 rL  rL rL     V0,TM Sin  β  x + x  , − x ≤ x ≤ x Cos  β  x + 2  + 2  2 2 β        U Cos α  x − rLx  − i ε slit k0 V Sin α  x − rLx  , rLx ≤ x ≤  1 − r  L     x    1,TM 2  2  2 α 1,TM    2  . V0,TM. eik0Lx Sinθ − M 1 = M2. U1,TM = Cos ( β rLx ) +. 2-27. 2-28a. −iε metal k0. V1,TM = V0,TM Cos ( β rLx ) +. β. V0,TM Sin ( β rLx ). −i β Sin ( β rLx ) ε metal k0. 2-28b. 2-28c. M 1 = Cos α (1 − r ) Lx  Cos ( β rLx ) −. ε slit β Sin α (1 − r ) Lx  Sin ( β rLx ) αε metal 12. 2-28d.

(26) ik0 ε slit β Cos ( β rLx ) Sin α (1 − r ) Lx   M2 = −   αβ  +αε metal Cos α (1 − r ) Lx  Sin ( β rLx )   . 2-28e. TE. E y(. 2). ( x, z ) = ∑ X TE , l ( x ) aTE( 2), l eiΛ z + bTE(2), l eiΛ ( L− z )  l. l. 2-29. l. X TE , l ( x )  rLx  k0 rLx  rLx rLx     Cos  β  x + 2  + i β V0,TE Sin  β  x + 2  , − 2 ≤ x ≤ 2        = U Cos α  x − rLx  + i k0 V Sin α  x − rLx  , rLx ≤ x ≤ 1 − r  L 1,TE     x      1,TE 2  α 2  2  2    . V0,TE. eik0 Lx Sinθ − ψ 1 = ψ2. 2-30. 2-31a. k  rL  U1,TE = X  x  = Cos ( β rLx ) + i 0 V0,TE Sin ( β rLx ) β  2 . 2-31b. β  rL  V1,TE = V  x  = V0,TE ⋅ Cos ( β rLx ) + i ⋅ Sin ( β rLx ) k0  2 . 2-31c. ψ 1 = Cos α (1 − r ) Lx  Cos ( β rLx ). β − Sin α (1 − r ) Lx  Sin ( β rLx ) α ik0  β Cos ( β rLx ) Sin α (1 − r ) Lx   ψ2 =   αβ +αCos α (1 − r ) Lx  Sin ( β rLx )   . 2-31d. 2-31e. TE Cos ( k0 Lx Sinθ ) − Cos α (1 − r ) Lx  Cos ( β rLx ). 1 β α + ⋅  +  ⋅ Sin α (1 − r ) Lx  Sin ( β rLx ) = 0 2 α β . 13. 2-32.

(27) 2.1.2. (unit cell). (Hermitian operator). (matching boundary condition). 1. 2-5a 2-5b. ∑ ∑ Eσ ( x ) ( aσ σ = S ,P g. (1) , g ,. (1) ,g. (. 2-10a. (. ik z( ,2i ) L. (2) (2) (2) + ∑ ETM , j , ( x ) aTM , j + bTM , j e j. 2-10b. + bσ(1), g ). (2) (2) (2) = ∑ ETE ,i , ( x ) aTE ,i + bTE ,i e i. 2-6a 2-6b. ) ik z( ,2j) L. 14. 2-33a. ).

(28) ∑ ∑ Eσ ( x ) ( aσ σ = S ,P g. (3) , g ,. (3) ,g. (. (2) (2) = ∑ ETE ,i , ( x ) aTE ,i e i. + bσ(3), g ). ik z( ,2i ) L. (. (2) (2) + ∑ ETM , j , ( x ) aTM , j e j. ik z( ,2j) L. zˆ × Hσ ( x ) ( aσ ∑ ∑ σ =S ,P g. (1) , g ,. (1) ,g. (. 2-33b. (2) + bTM ,j. ik z( ,2i ) L. (. (2) (2) (2) + ∑ zˆ × HTM , j , ( x ) aTM , j − bTM , j e j. zˆ × Hσ ( x ) ( aσ ∑ ∑ σ =S ,P g. (3) , g ,. (3) ,g. (. (2) (2) = ∑ zˆ × HTE ,i , ( x ) aTE ,i e i. (. ). 2-33c. ik z( ,2j) L. ). − bσ(3), g ). ik z( ,2i ) L. (2) (2) + ∑ zˆ × HTM , j , ( x ) aTM , j e j. ). − bσ(1), g ). (2) (2) (2) = ∑ zˆ × HTE ,i , ( x ) aTE ,i − bTE ,i e i. ). (2) + bTE ,i. (2) − bTE ,i. ik z( ,2j) L. ). 2-33d. (2) − bTM ,j. ) . (. 0. ~. 2-33a. 4 0. ). 2-33b. aS(1), g + bS(1), g. (. (2)  Lx +2 ax (2)  (2) * (2) ik z ,i L = ∑  ∫Lx − ax ETE ,i , ( x ) FS , g ( x ) dx  aTE ,i + bTE ,i e i  2 . (. ).  Lx +2 ax (2)  (2) * ik z( 2, j) L (2) + ∑  ∫Lx − ax ETM , j , ( x ) FS , g ( x ) dx  aTM + b e ,j TM , j j  2 . 15. 2-34a. ).

(29) a P(1), g + bP(1), g. (. ( 2)  Lx +2 ax (2)  (2) * (2) ik z ,i L = ∑  ∫Lx − ax ETE ,i , ( x ) FP , g ( x ) dx  aTE + b e TE ,i ,i i  2 . ). (.  Lx +2 ax (2)  (2) * ik z( ,2j) L (2) + ∑  ∫Lx −ax ETM , j , ( x ) FP , g ( x ) dx  aTM , j + bTM , j e j  2  2-33c. 2-34b. ). 2-33d. aS(3), g + bS(3), g. (.  Lx +2 ax (2)  (2) ikz( ,2i ) L * (2) = ∑  ∫Lx − ax ETE ,i , ( x ) FS , g ( x ) dx  aTE + bTE ,i e ,i i  2 . ). (.  Lx +2 ax (2)  (2) ikz( ,2j) L * (2) + ∑  ∫Lx − ax ETM , j , ( x ) FS , g ( x ) dx  aTM + bTM , je ,j j  2  aP(3), g + bP(3), g. (.  Lx +2 ax (2)  (2) ikz( 2,i ) L * (2) = ∑  ∫Lx − ax ETE ,i , ( x ) FP , g ( x ) dx  aTE + bTE ,i e ,i i  2 . (. 2-34c. ). ).  Lx +2 ax (2)  (2) ikz( 2, j) L * (2) + ∑  ∫Lx − ax ETM , j , ( x ) FP , g ( x ) dx  aTM , j e + bTM ,j j  2 . 2-34d. ). 2-34. A(1) + B (1) = M E ( A(2) + DB ( 2) ). 2-35a. A(3) + B (3) = M E ( DA(2) + B ( 2) ). 2-35b. 5. 6. A(1) = ( aS(1),1 , ..., aS(1), N , aP(1),1 , ..., aP(1), N ). T. (2) (2) ( 2) (2) A( 2) = ( aTE ,1 , ..., aTE , I , aTM ,1 , ..., aTM , J ). A(3) = ( aS(3),1 , ..., aS(3), N , aP(3),1 , ..., aP(3), N ). T. 16. 2-36a T. 2-36b 2-36c.

(30) ( = (b. B (1) = bS(1),1 , ..., bS(1), N , bP(1),1 , ..., b(1) P,N. B (2). (2) TE ,1. (. ). T. (2) (2) (2) , ..., bTE , I , bTM ,1 , ..., bTM , J ). B (3) = bS(3),1 , ..., bS(3), N , bP(3),1 , ..., b(3) P,N 78. 2-36d T. ). T. 2-36e 2-36f. 9.  [ M 11 ]g ,i ME =   [ M 21 ] g ,i   [ DTE ]i ,i ' D=  0J ×I  0;×=. [ M 12 ]g , j   [ M 22 ]g , j    [ DTM ] j , j ' . 0I ×J. >×?. 2-38 0=×;. [ M 11 ]g ,i = ∫. 2-37. Lx + a x 2 Lx − a x 2. ?×>. :. (2) ETE ,i , ( x ) FS , g ( x ) dx *. 2-39a. [ M 12 ]g , j = ∫. Lx + a x 2 Lx − a x 2. (2) ETM , j , ( x ) FS , g ( x ) dx. 2-39b. [ M 21 ]g ,i = ∫. Lx + a x 2 Lx − a x 2. (2) ETE ,i , ( x ) FP , g ( x ) dx. 2-39c. [ M 22 ]g , j = ∫. [ DTE ]i,i ' = e. Lx + a x 2 Lx − a x 2. *. *. (2) ETM , j , ( x ) FP , g ( x ) dx *. ik z( ,2i ) L. [ DTM ] j , j ' = e. δ ii '. 2-39d 2-40a. ik z( ,2j) L. δ jj '. 2-40b. 17.

(31) ck z(2) ,i. ω. (. (2) (2) aTE ,i − bTE ,i ⋅ e. ik z( 2,i ) L. ). ck z(1), g  Lx +2 a x  (1) * (2) (1) =∑  ∫Lx − ax FS , g ( x ) ETE ,i , ( x ) dx  ( aS , g − bS , g ) ω  2 g  +∑. ck. g. (. ωε slit ck z(2) ,j. 1 (1) z,g.  Lx +2 a x  (1) * (2) (1) E F x x dx ( ) ( )  ∫Lx − a x P , g  ( aP , g − bP , g ) TE ,i ,  2 . (2) (2) aTM , j − bTM , j e. ik z( ,2j) L. ). ck z(1), g  Lx +2 a x  (1) * (2) (1) =∑ F x E x dx ( ) ( )  ∫Lx − a x S , g  ( aS , g − bS , g ) TM , j , ω  2 g  +∑. ck. g. ck z(2) ,i. ω. (. 1 (1) z,g. (2) aTE ,i e. +∑ g. ωε slit ck. (2) z, j. ck. (. ik z( ,2i ) L. (2) − bTE ,i. ). ik z( ,2j) L. (2) − bTM ,j. ). Lx + a x ck z(3)  (3) * ,g  (2) (3) 2 =∑ F x E x dx ( ) ( )  ∫Lx − a x S , g  ( aS , g − bS , g ) TM , j , ω  2 g . +∑ g. ck. 2-41c.  Lx +2 a x  (3) * (2) (3) F E x x dx ( ) ( )  ∫Lx − a x P , g  ( aP , g − bP , g ) TE ,i ,  2 . (2) aTM , je. 3 (3) z,g. 2-41b.  Lx +2 ax  (1) * (2) (1) F E x x dx ( ) ( )  ∫Lx −a x P , g  ( aP , g − bP , g ) TM , j ,  2 . Lx + a x ck z(3)  (3) * ,g  (2) (3) 2 =∑  ∫Lx − ax FS , g ( x ) ETE ,i , ( x ) dx  ( aS , g − bS , g ) ω  2 g . 3 (3) z,g. 2-41a. 2-41c.  Lx +2 ax  (3) * (2) (3) F E x x dx ( ) ( )  ∫Lx −a x P , g  ( aP , g − bP , g ) TM , j ,  2  2-41. Y (2) ( A( 2) − DB (2) ) = M H Y (1) ( A(1) − B (1) ). 2-42a. Y ( 2) ( DA( 2) − B ( 2) ) = M H Y (3) ( A(3) − B (3) ). 2-42b. 18.

(32) ε (v) . ε0. ck z( ,vk). YS   k ,k ' = ω δ kk '. 2-43a. YP( v )  = ωεvv δ kk '   k ,k ' ck ( ) z ,k. 2-43b. @ . Y. (v ).  YS( v )    k ,k ' =  0  .   YP( v )     k ,k ' . 0. 2-44. 7A.  [ M 11 ] † g ,i MH =  [M ] †  12 g ,i. [ M 21 ]g , j† . [ M 22 ]g , j. †.   . 2-45. 2-35. 2-42.  A(2)   (2)  B   YH(2) + M H YH(1) M E =  ( M H YH(3) M − YH(2) ) D . 2-46. ( M HYH(1) M E − YH(2) ) D   2 M HYH(1) A(1)   (3) (3)  M H YH(3) M E + YH(2)   2 M H YH B  −1. A(3) = M E ( DA(2) + B (2) ) − B (3). 2-47a. B (1) = M E ( A(2) + DB (2) ) − A(1). 2-47b. 5. 5 19. 2-46. ( ).

(33) 2-47. ( ). 6 S-. (Poynting vector). P-. TS ,m =. Re ck. ∑ Re. (1) z ,n. ω. n. a. ck z(3) ,m. (1) 2 S ,n. ∑ Re n. g=1. ck z(1),n. ω. + ∑ Re. a. ωε 3 ck z(3) ,m. (1) 2 S ,n. a P(3),m. ωε1 ck z(1),n. 2-48a. a. (1) 2 P ,n B ( 3) = 0. 2. + ∑ Re n. = 0 FG,. 2. n. Re TP ,m =. ω. aS(3),m. ωε1 ck z(1),n. 2-48b. a. (1) 2 P ,n B ( 3) = 0. 2-2a

(34) , = $/% D,E. FH,. S P. S-. P-. aS(1,)n = δ n1 (1). a P ,n =. ck z(1),n. ω ε1. 2-49a. δ n1. 2-49b. S x z. y. P . c ,J /$√. x. 20.

(35) 2.. S-. P-. ( ) "

(36). TE. !#. TE. TE TM ". !

(37). TM. P-. TM. "#. !. S-. S P ( ). TE TM. (2-25. 2-32) ( ). P-. TM. TE. (1). P. ( ). ( ) !

(38). 2-26. "#. 1 ik x ,n x (1) e aP ,n + bP(1),n ) ( Lx. ∑ n. (. = ∑ X TM , l ( x ) aTM , l + bTM , l e l. (2). (2). iΛ l L. 1 ik x ,n x (3) e aP ,n + bP(3),n ) ( Lx. ∑ n. (. = ∑ X TM , l ( x ) aTM , l e l. (2). iΛ l L. ( ). (2). + bTM , l. ). 2-50a. ). 2-50b. 21.

(39) ∑ n. =. 1. ε2 ( x). ∑ n. =. 1 ik x ,n x (1) (1) e k z ,n ( a P ,n − bP(1),n ) Lx. ∑X. TM , l. l. (2). iΛ l L. 2-50c. ). (3) 1 ik x ,n x k z ,n (3) e a P ,n − bP(3),n ) ( ε3 Lx. 1. ε2. ( x ) Λ l ( aTM , l − bTM , l e (2). X ∑ x ( ). 2-50d. ( 2 ) iΛ h (2) − bTM ( x ) Λ l ( aTM , le ,l ) l. TM , l. l. ( ). (. . /. a. (1) P ,m. +b.  1 = ∑  L l  x. a. (3) P ,m. +b.  1 = ∑  L l  x. (a. − bP(1),m ). k z(1),m. ε1. (1) P ,m. (3) P ,m. (1) P ,m.  Λ = ∑ l  L l  x k z(3) ,m. ε3. (a. (3) P ,m.  r 1−  Lx  2 rL − x 2. ∫. K ,L

(40) ).  r  1−  Lx  2 rL − x 2. X TM , l ( x ) e.  r 1−  Lx  2 rL − x 2. X TM , l ( x ) e. ∫. ∫. X TM , l ( x ). ε2 ( x). e. ik x , m x. e. ik x , m x. ik x , m x.  (2) ( 2 ) iΛl L dx  aTM , l + bTM , l e  . ). 2-51a.  ( 2 ) iΛ L ( 2) l + bTM dx  aTM , le ,l  . ). 2-51b. ik x , m x. (. (.  (2) ( 2 ) iΛ l L dx  aTM , l − bTM , l e  . (. ). 2-51c. − bP(3),m ).  Λ = ∑ l  L l  x.  r 1−  Lx  2 rL − x 2. ∫. X TM , l ( x ). ε2 ( x).  ( 2 ) iΛ L (2) l dx  aTM − bTM , le ,l  . (. 22. ). 2-51d.

(41) N. Aσ( v ) = ( aσ( v,1) , ..., aσ( v, )N ). 2-52a. Bσ( v ) = ( bσ( v,1) , ..., bσ( v, N) ). 2-52b. T. σ. S. T. P. [ χ ]m,l. 1 = Lx. [Ω]m,l. Λ = l Lx.  r  1−  Lx  2 rL − x 2. ∫.  r  1−  Lx  2 rL − x 2. ∫. X TM , l ( x ) e. X TM , l ( x ). ε2 ( x). e. [ K ]m,l = eiΛ Lδ ml Y. . =. k z( ,vm). εv. dx. ik x ,m x. dx. 2-53a. 2-53b 2-53c. l. (v ) H m ,l. ik x ,m x. δ ml. 2-53d. 2-37 (2) (2) AP(1) + BP(1) = χ ( ATM + KBTM ). 2-54a. (2) ( 2) AP(3) + BP(3) = χ ( KATM + BTM ). 2-54b. ( 2) (2) YH( ) ( AP(1) − BP(1) ) = Ω ( ATM − KBTM ). 2-54c. ( 2) (2) YH( ) ( AP(3) − BP(3) ) = Ω ( KATM − BTM ). 2-54d. 1. 3. 2-54. 23.

(42) ( 2)  ATM   (2)   BTM . (Ω.  Ω −1YH(1) χ + I =  Ω −1Y ( 3) χ − I K H . (. ). ). . 5H. (Identity matrix) 2-55. ( ). 2-54a 2-48b. S-. ( Π )m ,l Ω. ( ). Λ = l Lx.  r  1−  Lx  2 rL − x 2. ∫. Π. 2-55. YH(1) χ − I K   2Ω −1Y (1) A(1)  H P   3 ( ) − 1 (3) 3 Ω −1YH( ) χ + I   2Ω YH BP   −1. "

(43). 2-29. X TM , l ( x ). ε2 ( x). e. ik x ,m x. !#. . 6H. 2-54b 2-49b. P-. 2-56. dx. S-. (overlap integral). (2). ( ). TE. TM. (2-25. 2-32) α β 24.

(44) 1043. 100i Cos(100i) Λ 20. 0 2-25. 2-32. (Drude model) 8.47x1028 (m-3). (conductivity). 5.69x107 (s/m) 2.2. 2. (initial guess). 25.

(45) 2.2. (a). (3).. TM(2-25) (b). TE(2-32). (overlap integral) (Ω χ. Π). χ. 1 Lx.  r  1−  Lx  2 rL − x 2. ∫. 1 = Lx 1 + Lx 1 + Lx 1 + Lx. X TM , l ( x ) e. ik x ,m x. dx. rLx 2 rLx − 2. rL   ik x   Cos  β  x + x   e x ,m dx 2   . rLx 2 rL − x 2.  −iε metal k0 rLx    ik x ,m x   V Sin x + dx β  0,TM   e   2 β     . ∫ ∫. ∫.  r  1−  Lx  2 rLx 2.  rLx    ik x ,m x   dx U1,TM Cos α  x −   e 2      . ∫.  r  1−  Lx  2 rLx 2.  ik0 rLx    ik x ,m x   dx  − V1,TM Sin α  x −   e 2 α     . 26. 2-57.

(46) 1 Lx =. ie. rLx 2 rL − x 2. ∫. rL   ik x   Cos  β  x + x   e x ,m dx 2   . 1 − irLx k x ,m 2.  −eirLx k x ,m k x ,m + k x ,mCos ( β rLx ) + i β Sin ( β rLx )    2 2 Lx ( k x ,m − β ). ) (. (. ) . − i ( β + k x , m ) rLx  ei ( β − k x ,m )rLx − 1 e −1 e  = −  2i Lx  ( β − k x ,m ) ( β + k x ,m )  1 irLx k x ,m 2. 2-58.  . 1 ± (1 − 2 r )   Exp i ( s − k x ,m ) Lx  −1 2 1 ±   S (s) = 2i Lx ( s − k x ,m ). 2-59a. 1 ± (1 − 2 r )   Exp  −i ( s + k x ,m ) Lx  −1 2 1 ±   T (s) = 2i Lx ( s + k x ,m ). 2-59b. 1. Σ1 = e 2. Σ2 = e. irLx k x ,m.  −  k0ε metal − − S ( β ) + T − ( β )) (  ( S ( β ) − T ( β ) ) − V0,TM β  . 1 − irLx k x , m 2. k0V1,TM +   + + S (α ) + T + (α ) )  ( U1,TM ( S (α ) − T (α ) ) − α  . 2-60a. 2-60b. P-. [ χ ]m,l. 1 = Lx. [Ω]m,l. Λ = l Lx.  r 1−  Lx  2 rL − x 2. ∫.  r  1−  Lx  2 rL − x 2. ∫. Σ. X TM , l ( x ) e X TM , l ( x ). ε2 ( x). ik x , m x. e. dx = Σ1 + Σ 2. 2-61a.  Σ  dx = Λ l  1 + Σ 2   ε metal . 2-61b. ik x ,m x. Σ0 27.

(47) S-. 28.

(48) [35]. PP-. 3.1 P-. S-. S-. S-. P-. S-. 3.1.1. k0 = k z 2 + k ⊥ 2. 3-1. . kT kT. k kT. z. 29.

(49) (TEM mode). 3.1. ax. ax az. TE TM. 3.1 (Parallel-plate waveguide). TE. (Rectangular waveguide). 30.

(50) P-. S-. TE TM P-. S-. TM TE. 3.1.2. P-. TM. TM. S-. 3.2. TEM. TE. (a)TM. (b)TE. 31. 3.2(a). 3.2(b). TEM.

(51) PS-. PP-. 3.2 PP-. 3.3. ax=0.15Lx. L=0.15Lx. 0.9 1.1. 3.3 ax=0.15Lx. L. 0.15Lx. 32. 0.01Lx. P-.

(52) (Fano resonance)[36, 37]. 3.4. (state) (discrete). (dispersion relation). 3.4. (surface plasmon polaritons) (spoof surface plasmon). 33.

(53) (n) ωSPP ( k x,0 ) = c. U VW V. ( ). 1. ε dielectric. k x ,0 +. 2π n Lx. 3-2. ( ). 1. 3.5 Pkx0 ax=0.15Lx (a) L=0.15Lx (b) L=0.25Lx (c)L=0.35Lx (d)L=0.45Lx . ωGHH. 3.5(a). 3.5(b)(c)(d) Fabry-Perot. 34.

(54) P-. 3.6(a) ax=0.15Lx L=0.15Lx 3.6(b) ax=0.15Lx. L=0.45Lx. 3.6(a). 3.6 (b) L=0.45Lx. ax=0.15Lx λ=1.28Lx P-. (a) L=0.15Lx. λ=1.012Lx. 3.7. ω p2 ε (ω ) = 1 − ω (ω + iγ ) 3.7. ωp. 9 eV. 3-3. γ 0.1 0.01 0.001 eV( 35. ωp.

(55) γ. 8 10 eV. ωp. 0.01 eV. γ 0.02 eV). 10.8 eV. 3.7(a). 3.7(b) Fabry-Perot. 3.7. ax=0.15Lx. (a) L=0.15Lx (b) L=0.45Lx. 3.2.1 P-. 36. P-.

(56) 3.3 ax=0.15Lx. 3.8 (a) λ=Lx P-. L. ax=0.15Lx. 0.15Lx. λ=Lx. L=0.01Lx +1. 0.01Lx. z=0. (b). -1. λ=Lx . ,Y. 2-2(b). . ,Y. 2-2(b). 3.8(b) !

(57). P+1 -1. Y Z1. z. !. "#. . ,Y +x -x. 37.

(58) (K . K . ) !. !. 3.8(a). λ 1/4. 3.9 (b). (c). (a) 0. 3.9 0 0.5λ. λ. 0.25λ 90. i. 38. 0.75λ Re[E × H* ].

(59) 3.10. !. , +1 -1 45. 45. +1 -1 , 3.8. 3.10 λ=Lx. ax=0.15Lx (b). L=0.01Lx. P-. (a). 1/4. 0. ! 3.11(a) ,. z. (induce). λ=0.9 1 1.1 Lx , (dipole). 39.

(60) λ=Lx. z. ,. 3.11(b). λ=1.1Lx. λ=Lx. 3.11 (a)λ=0.9. 1 1.1 Lx. (b) λ=1. Ez. 1.1 Lx. 3.2.2 3.12 24 µm. 0.9~10 THz. 11.2. 40. 11.9.

(61) 3.12 P-. Lx=24 µm L=0.2 µm. 3.13 Lx=24 µm L=0.2 µm. ax=6 µm. ax=6. P-. 8. 10 µm. Si 11.2. (a) λ=Lx (b) λ=/ε Lx. 2-2(b) ( ). ( ) λ=Lx. ( ). 41.

(62) ( ). λ=/ε Lx. λ=Lx λ=/ε Lx. 3.10(a) ( ) 3.13(b). ( ) ( ) x. +1. -1. / ε[. λ=. P-. 0. Lx. ( ) +2 -2. 3.14 Lx=24 µm L=0.2 µm ax=6 µm P(0th). (total). 3.14 (0th). 42. (total).

(63) 3.3 S3.3.1. 3.15 SL=0.6Lx. (a). L=0.01Lx λ=1.2Lx. ax=0.8Lx. 3.1.2. ax=0.2~0.8 Lx (b) |Ey|. S3.15(a). L=0.01Lx S-. Fabry-Perot. 3.15(b). Ey. Fabry-Perot 3.15(a) 43. λ=Lx.

(64) 3.16 (a) λ=Lx S-. ax=0.8Lx. L=0.01Lx +1. λ=Lx. z=0. (b). -1. λ=Lx. PSax=0.8Lx. 3.16 "

(65). L=0.01Lx. λ=Lx +1. !# !# 0 +1. !#. -1. " -1. 3.16(a) !# 3.16(a). +1 -1. 0. 1 (Evanescence wave). 44.

(66) λ=Lx. PS(Lorentzian function). 3.17. ax=0.8Lx. 3.17 . 0. λ=Lx. L=0.01Lx S-. z. 45. x. (Ey).

(67) 3.3.2. λ<Lx. 3.18. 3.18. Lx<λ</ε Lx. 2-2(b) λ<Lx. ( ). Lx<λ</ε Lx λ>/ε Lx. ( ) ( ). λ>/ε Lx. ( ) ( ) ( ). ( ). 3.19. P-. 11.2 λ=Lx. λ=Lx. λ=/ε Lx. 3.20(a). ( ). ( ). ( ). 46.

(68) λ=/ε Lx. 3.20(b). ( ). ( ) ( ). 1. 1 3.4. ( )+2 -2. 3.19 S-. Lx=24 µm L=0.2 µm. 47. ax=18. 20. 22 µm. Si 11.2.

(69) 3.20 Lx=24 µm L=0.2 µm. ax=22 µm S-. 48. (a) λ=Lx (b) λ=/ε Lx.

(70) 4.1 P-. S-. Fabry-Perot. PTEM. P-. S-. TEM. Fabry-Perot. S2ax>λ λ>Lx. Fabry-Perot. S-. ax>(Lx/2) 3.15(b) S-. 4.1. 4.1. 49.

(71) 2π   mπ   nπ   = +  ε slit λ   L   a x   2. P-. 2. n. 0.  λ =  P - polarized : n = 0 → L x    S - polarized : n = 1 → λ =  Lx   . 2. 4-1 S-. 1. 2 ε slit L m Lx 2 ε slit 2.  1   1    +   L / Lx   a x / Lx . 4-2 2. 4.2. 4.2 (a) PL=0.267Lx. Lx=24 µm ax=0.05Lx L=0.02Lx (b) S11.9. Lx=24 µm. εslit=11.9 50. Lx=24 µm ax=0.374Lx 4-2. λ=1.5Lx.

(72) 4.2. 4-2. P-. S-. ( ). ( ). 2k z L + 2φ = 2nπ. 4-3. (. ). (. ). 4-2. 51.

(73) ( ). P-. PP-. SS-. 1. 1. 52. S-.

(74) Fabry-Perot P-. 53. S-.

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