Chapitre 15 :Propagation des ondes électromagnétiques
Transcription
Chapitre 15 :Propagation des ondes électromagnétiques
T his work is licensed under a Creative Commons “Attribution-ShareAlike 4.0 International” license. !" ∇⋅ =$ ∇∧ = $ ∇⋅ % =− ∂ # = µ $ε $ ∇∧ ∂ !" &' ∇ * − µ $ε $ ∂ ∂ * * ( !" & * ∂ − µ $ε $ * = $ ∂ = $ ∇* = # + ( ∇* = ∇* , - ) ε $ µ$ ∇* ∇* ) .- - . . - . .- . . − + 0 / . + # . # 1 # . = + . − + − . + ' = 2. . - 2 ∂ ∂ − = × = ∂ ∂ 2 2 ∂ ∂ = × = ∂ ∂ ∇ = 4 ∂ 3 ∂ = # 2 − ∂ ∂ ∇ ∇= − ∂ ∂ Ismaël Bouya http://melusine.eu.org/syracuse/immae/ # * 4 # • 5 % − ( !" & ) ∂ ∂ =− ∂ ∂ ∧ = + . ∧ ∧ 4 . . = =$ − 5 = 4 % • !" &' ∧ ∂ = ∂ ∧ 3 * ∂ ∂ 1 ) 3 .6 # 7 3 .% # • • !3 = - • # • # 1 1! 3 8 = ε$ * - • - 9 * + * *µ$ = ε$ * * + * *µ $ * = ε$ * = * µ$ ( π= ∧ µ$ • 9 π= = = * µ$ # 3 : ; - τ = π * = ε$ ∧ * - < 6 1 .- 4 ' • - = . • 2 - =+ ( 3 < 1 :π . ⋅ −ω 3 3 ω 8 * 2 . ω ! = 3 < ) . ⋅ −ω 3 + . ω . = 3 . • ∂ ↔−ω ∇↔ ∂ * 4 # < • !" ⋅ =$ !" &> ⋅ !" &' ! !" &' =$ ( !" & ! ) ∧ =+ω ∧ =− • 6 %# !" &> %# !" &' ! ω * 3 3 3 + 0 < . ? @ . • + %# = !" &' ω ( ∧ @ ∧ 1 ρ =$ ω ∧ # =− ⋅ !" & ) ω * =$ − * ω =− ω * 8 * # A • 5 = ω* * ! 1 . ) 3 = 5 5 B A = $ $ −ϕ - − $ −ϕ −ϕ $ −ϕ $ $ • - ( =+ . −ω 3 ) $ .ω3 − $ .ω3 − .ω3 − $ $ +ϕ +ϕ − $ .ω3 − $ +ϕ +ϕ 8 ϕ = ϕ −ϕ - ) 1C 7 # ? 3 1 $ = $ $ .ω3 − .ω3 − + ϕ # • ϕ =$ # 5 5 ? .π3 1! 4 + # @ 3 = = $ $ .ω3 − .ω3 − 3 3 : • # 7 3 + 7 # 6 ! • ! ! ϕ= # ? π 8π * * . ! $ = $ = $ 7 $ - = $ −ϕ $ $ = D $ −3 575 $ $ = $ 3 $ = 3 =−3 6 B ! B 3 6 B B B ω3 − ω3 /* /* : % 1 ! ) . 1 1 @7 • ( # = ε$ * < * + * *µ$ > = ε$ + . * + = ε$ * F = ε$. * @ 7 * $ + * $ # # B 3 • # 9 <π >= • 3 ( 9 - × + . ∧ F = * *µ$ # <π > = = < > F µ$ ! + !" ⋅ ∧ ρ ε $ε =+ ω = ⋅ ∧ %GH =$ = µ $ µ . − ωε $ε -A ρ B µ ε ! 3 , . • ⋅ ∧ =$ =+ω # !" ⋅ =$ ∧ = − ωµ $ µ ε $ε #( .ρ =$ B . E • • + 3 * * H = ω *ε $ µ $ ω* = ω *ε $ µ $ε µ = ε µ • 1 * # I ε @7 ε µ = + ! 7 # µ .ω * * − ∇* = − = ω* * − ∂* − ∂* = ! * # =ε µ . ) = D+ 3 D D A ! # % . DD≥ $ 3 * # =± ω 5 ω = ω Dω = * * # ! .. −ω = − DDω . D ω −ω 3 D ω 4 ω* . D+ 3 D D . # 1 ϕ = . D+ 3 D D A =+ - 3 * - • H - # ! 13 % ϕ 1 ! 1 # # B B 3% B # % B B B 3 5 − /δ # # δ= D Dω 3 B D 5 4 D≠ $ 4 D= $ 575 4 D≠ $ DD = $ DD ≠ $ D D 575 575 ∈ ∈ DD ≠ $ D 575 ∈ ! ! . K 3 #( # 3 !" ρ ε $ε =+ ω ⋅ = ∧ , ⋅ ∧ ρ B =$ = µ $ µ . − ωε $ε 3 • . B − ωρ + • % • = τ * − ωτ ρ ⋅ ρ =$ ⋅ =$ ⋅ 575 ω =ω = ( ) # ρ = ε $ε ⋅ 4 ⋅ !" &> ρ ε $ε # D σ$ = − ωτ σ= ; ω #- =σ3 ⋅ ρ= ⋅ =$ ω ρ σ σ ω 575 ρ − ε $ε σ ρ =$ ω ω ρ ≠$ ε $ε = σ =$ 1 = < 7 ⋅ 3 =$ ? D #( ω . σ . ε $ε B 1 J B 3 = σ3 - = µ$ µ .σ − ωε $ε σ3 εD = ε + = − ωµ $ µ ε $ε D ∧ - ε $ω ? B ρ =$ . " ) • 5 # M 3 =− = H # 5 . . # B ( 2 2 = 1 = ! > M7 .* H # % ν2 3 # *J3 $ O3N 5 2 $: N ) $ ( • 575 # - 9 − *8 ) 2 *3 $ GM D H 1 2 = λ= # - ν $$P 1 = 3 $−E B 3 4 . ⋅ −ω 3 ρε µ ε =µ = ) D 575 # B 3 , • 5 5 5 5 ' # ! C H H #. - 4 !" = . + ∧ # #- ( 4 Q L 11 1B 3 ( 1 3 # . $− : ( # )1B # ∧ 1 3 3 = 11 ? 3 ∧ << B • - << 7 != 1 = ρ. ) ρ. . ) 5 ( ) . D 575 5 - 3 1 . +ρ 2 . ρ << λ 1 = - ( = . ! − ω3 = - # . +ρ = - ( $ ! . . ⋅ − ω3 =− − 3 ω ρ2 ρ << λ 3*π ω λ2 3*π << ω # ( ) @ 1 3 • - ? = + = 3 ω << 3 1! # B ( B) & Q $ = # 1 B × .− 3 + . B ≈− 3 # ≈ % × 3 ≈− B 3 # # # * 3 ω #- # σ= ! σ∈ < # > = + .σ ⋅ F = $ * # >=< ⋅ ) 3 σ= τ = . − ωτ * τ → +∞ 5 * ω ⋅ !" &> − ωρ + 5 5 % ρ ω− * 3 ωε $ =$ - ρ .ω * − ω * = $ 5 4 ω =ω ω* = ω = * ε$ ρ =$3 ρ ≠$ • - ρ ε$ ⋅ =$ ωρ = σ3 3 ⋅ = σ B 11 4 ω ≠ω = =σ #- • 5 τ . − ωτ * * ε$ = EJ 4H ρ ε$ * ω 3 #- ω ≠ω . - • 4 + !" &' !" & = µ $ .σ − ωε $ ∧ ∧ * = − ωε $ µ $ − − ω* ω* * * = ω* ω* ω* − * ω = ωµ $ε $ ω =$ = ω ∧ ( ) = − ωε $ µ $ ∧ ω ⋅ 3 − 4 - ρ =$ R = ω * µ $ε $ − ω* ω* ω* −ω* * • # ω − ∂* ∇ = * − * * ∂ 1 ω >ω * - * # • - . &> ∈ 9 φ = ω ω3 = + . ω* −ω* 3 = − ω % 9 - = # = ω* ω* 7 3 ω + . 11 B ω ω * - # φ = * D 575 # = − # # ω* ω* # 3 < 3 ω ω % N ω >> ω # 7 S T3 * 1 ω <ω 3 • ω* −ω* = - − /δ = = δ − ω3 $ - • = +∞ φ ω =ω 3 ρ ≠$ 9B 4 ρ =$ #( 4 ρ ≠$ =$ B 3 ≠$ * ⋅ 3 − = $3 # = ωµ $ε $ ω = − B # ω* ω* D U ) # !" & * ρ 3 − ε$ ω 575 ) =$ −ωρ ε$ * . '+ 1! • 4 ω >ω 5 0 %# 5 =$ • 4 ω <ω 5 5 5 4 4 H #( ( + 1! >> δ 2δ # 1 3 # π +π = π # π = $3 π = −π 1! 3 1 ? ( 3 # 3 8 > • 4 ω 1 1 ! 3 B ) 11 . • 7 ( # #( 1 6 ) N 5 (&G ( B 7 . 5 - 1B #( B # B # B # ω B .ω ∝ 1 ω ω 1 6 1 11 .7 7 1 " ) # 0 ) # 7 # ! ) . ? ! ? # 3 : * ) ) 5 5 5 # 7 3 # # 7 # 3 + H ! ) ! A ) # 3 # 3 , 1 0 * 11 B@ # B 8 0 ( • # B • 7 # 3 ( .# 7 # ! : % • 1! ∆ α ∆D 3 • - ! # D 575 1 =< π > • H 5 θ = =η 5 3 8 .ω3 + ϕ 3 .ω3 + ϕ * =η 8 α . ∆D * $ $ * $ α ∆ * = ! θ3 ∆ .ω3 + ϕ8 * $ θ α3 ∆D H = ε$ 3 < - = ε$ 3 <η : = ε$ η: * $ * * $ ∧ µ$ .ω3 + ϕ8 α< # B # < > .π = * * 4 7 * * * $ . .ω3 + ϕ8 * * θ .ω3 + ϕ8 ( # θ >= α> * θ> ) * * * * $ 1 θ # .< # * * * $ θ >= = ε$ η : : ? * : $ * * $ α $ .- $ # : = ε$ η < % * * $ B .ω3 + ϕ8 1 * θ> < • 'B - ( 1 1 % 3 E - 1 . % M1 7 1 # σ // >> σ ⊥ 3 • < ⊥ // ⊥ % @ $= ⋅ $// >> $⊥ = σ3 * 3 B B ⊥ 3