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! ! !& !6 ( '-( ! 10−2 100 ]−1 % " 6"# *! "( "0 " 01& "5 "- α "!! "# - ! '54! !'!" " ! "( !!4 !"#4 ' !# "( " " ."(! 2.2! !& " "1( G(ω)M "( 22!& ! " 6 !& *& !5 0'-IBAKNα(ω) = α0 G(ω)./- -! 01& "5 6"# ."( !"#( ; " 5 ( ! "!"( "! ( ,& !!"# "# (! !# 5 '"-(6"# "! ! 41 ( '"-( ! 0" .! !! ! !# !* ! ! ! !# !5*5; ! !-41* - !! 0"' 26 G(ω)"$ ( =!G ! ' " !& ! * & . *(1 & ! ' "!! "(" 65* !5* 65* * %5; !'55 !5 !- ( "( " !& .!5* * & n1 n2 < '; ' *( - " - !6Mn = n1 + n2 = ][^_`.AKO," ' "! ! - " - !6 * n2 ! (dn21(0)(0)(инд)(инд)n2 + w12 n1 − w21 n2 + w12 n1 .= − w21 +AKABdtτ0% & - ! ' # 5& -" !! !! * - !6 !( ' -! ! (! !#4 6 (0)1/τ0 ) 0'5'"-!"#& " 6 (! !#4 w21 ) %!& -"!-! ' "4 * ( ' -! 0'5'"-!"# -.(0)!6 ( (! !#4 w12 e !- ' (0)(0)E2 − E1 kT w21 w12 ) 9!& -!!5& -"5 0 ""565 * 1 ↔ 2< !"(( AKAB n1 = n − n2 ( -! B12 = B21 '.(ин)5( w21 AIA "-dn214B122B12(0)=−+ρ n2 + w12 +ρ n,AKAAdtτπ Δω0π Δω01τ=1τ0(0)IA(0)AKAI+ w12 + w21 .% ! ! ! ; "( ! ' AKAA ! " .! τ ,"( 1( ' 0 -!!# -! ! 41 .!- ' *& # E2 !"# 5 -! 0'5'"-!"#5 6 5 ! "#.0# '! ' "(!# !!(0)# , " 5 " w12 = 0 =! " ."# '(! !# 5* " '"#!! ";# 1!* ' #% !65* "(* dn2 / d t = 0 5 " "- ' AKAAn2 =(2B12 τ /πcΔω0 ) I(1 + 4B12 τ /πcΔω0 ) In,AKAK I = cρ 3 "! !# ! " ! !# ' '"-( % ! ! ! '"-( ! I = 0 ! ( n2 = 0 n1 == n ! -! n2 − n1 = −n < 5 & ! ! ! I → ∞ " ! * & 54! (M n2 = n1 = n/2n2 − n1 = 0 < *! " 51 * 1 ↔ 2 ' 5'"-D # AKAK '"(! ! 04 *! !MIs =π c Δω04B12 τ,AKA 414 5 " ! ! 51( 8"5 AI AI AIII '"(4! ('!# ! !# 51( Is - '.

"1(MIs =ω2στAKA,-! ! "( 2'- ( !"4 5 " !&"-5,& !!"# AK " ! Z = n2 − n1 ."(41& "- ' "( " "1( 1#4!;& AKAK : AKA ! 05!# !" Z=Z01 + I/Is,AKA Z0 '-! !! !414 ' !# " !& ! ! !(0); "( ! I = 0 % (! 5; " w12 = 0"- Z0 = −n,- .L- / 5)().L-6- 1 +N "! ' AKA -"#( ' !# " !& !"- ! ! 0"-( E!5& ;!0 '('! ( "-& Is ! !# 0"-( !! '-(I = Is -"#( ' !# " !& ! < I Is22! 51( 0-#%"- Is ! "( 2'- !"M "(*5 0"-( ' - "1( σ ! . !# '"-( I '4 6* ω ! "- σ I/ω !'- & ! ! 6 "1( ! !# "-( # ! ! ! !! ! ".6 " ! * ( 1/τ ! I ∼ Is ) 51 !! ( '!5D # 0* -!# -! '" 5; " "( ;5* "& 5141* ( 6" "-! ! 0"-( 7 ; !0! !"#"'=22! 51( ! 4 "# !& "! 7.51 #;! 22!5& 226! "1( !.5* ' 5* "141* ! ( * ! 0' !" !( -! - ! 05! -# "'5 7 51! 226! "( !5* ! -! - ! 05.! -# "!"#5 7 51 ("(! ( !& "& !#4 !.( 6"# -! ! !# '"-( "'5* .! 76 !* ( 51 ' ' 5* * ! 5'!# 4 " !& *7 51 " !& & ' * .! 2!"#5& *! % !- & ! !' @ : +0! : @ -!" ( "& & )5 "# ' #; "1( "- ! ! 0."-( 5 5 '" 0 " ? %" 1 IB.* *.

'" ("( "' 7"&5& *! 6 . "1( ! 0"#;& ! ! '"" %" !! "&( ! @- 5 # ; !.5 !! ! 0" 1 0" 0!5& 5 " " '.( "' 0 ";* 0 '! ! 5 & !. !, * 5 !" 55& D # !-.!# !"4 755& 3 ! 0!5 !0"#"41& ( !- '! 0"#; ".6 % !"# 3 ! "# 5& ,"!"# ! "#. ! "# '"-!# ( @ '5!# *! ! ."# 5 "!"# !# !5* τи !"# " -! ' ( * & !( " 65 6 " !#4 0-# τи τ < ! *(! ( ! !# "5* 2.6& *& !& !5 '& !41&"#5' 5 "!!5 " % '"#!! 0"44! ( 6"."(6 G0 5 " 6!& ! 05!# 1 !"6"5& ( * ! 5* 22! !5* 5 ' # !".!# ( 0!& "# 3 ! "# "!"# !# ! !# ".- ( " "# #; " 6 τи τ % !&!6 "! !# 22! 51( "! ! 0."-(F = I(t) d t.AKAIIIKτи!" AKA ! "#4 ' 0"-( "-& .!& ' ( & !( "# τи %"- F '(! ( ,"(* !5& !! - !"-! ( ! "! ! ! ! ! ! I) 0"-( '(& %!!* !5&!!< "- "# !! 22! 51( !5 " -! ! F "#&; ! n2 *! ! !-! !5 0;5 ( A # I # A - 0!( " 6( ' ( & !( "# τи !- . *!%( - ! ! 51( "-Fs = Is τ = ω/2σ,AKAN414 -5& 5 " "! ! 51( ; " -"# " n2 = 0 "& 226"# .

( AKAAdn21II1+n2 +=−n,dtτIs2τ Is"- -! 6 & !( "# " ! " I Is "( n2 " !( 2"M1n2 (F ) = n [1 − exp (−F /Fs )].2AKAO/! 4 "! -! (Z = Z0 exp (−F /Fs )AKIB" !#4 51! ( ! Z → 0) F Fs .AKIAI,- .L- / 5)().L-9- ,(K/"' =.% !& "! 6"#4 "-( "# 0"#;* '-.& 1 ! " "' '"-( "#'4! ( !5 "!" =! '"(! !"!# 64 '"-( 5 -.! 0*& "(6 ! "(< " 5*& 1 ! "'. "!"& "! .(!# 22! 51( %5; 05" "- 2" AKA'541( '(! ( -"#( ( ! !.

! " ? -! !& ' ! '".-( "# z 226! ' 5* !# β "&5 226! "( α0 ' 5! ( dIdz= −βI +α0 I1 + I/Is.β! ! 05!# & ' AKII " "!# dI/dz = 0 ?!!.! " Iвх < Im ! " "! ( 70! " Iвх > Im ! "0"(! ( /05- !"(! ! "-& α0 /β 1 -! 5 0 " "!# 9 Im = (α0 /β)Is G ! !# - !5 "-< " " I Is ! !5 0' 0"4!.( 6"#5& ! 5*& ! ! "& "!"(MI(L) = Iвх exp [(α0 − β)L].AKIK% ! ! ! !# β = 0) "# 51 I Is ) 6"#5& ! (! ( "&5MI(L) = Iвх + α0 LIs .=! '-! -! ! ! ! !# 15& 5141& " .! "4 5 "!5 - ! "!"( 4 0"(! 01& !< "- !# !6( 1 ! (! ( % "- "5* -5* '-& !;( β/α0 1 I IsI(L) =α0βIs [1 − exp (−βL)] + Iвх exp (−βL).AKI AKI< 0"#;* "* βL 1) *& " '!*! 5*& !.! "# '-(AKII=! ;!# ( <"-41 ( ! ! 6.! ! 6 ' !# &! 5*4 !. !# I(L) ' ! ! *& Iвх '"-5* '-(*! α0 , β, I '& " "!"( L / ! ; 01 "* 0' % ! ! ! ! -.! " ( ;(< !! -! " α0 /β < 1 ! !# '".-( ! 05! "( ! "5 '! L "#" AKII '( dI/dz < 0 ?"!"# " 2.26! "( " 0"#;* !(* " "!" '!*!% 0! "- α0 /β > 1 ! !# " 5* ' !.!- " "!"( !! '-(α0I(z)|z→∞ = Im =− 1 Is ,IImax =α0βIs .AKI/! 4 "! !! 5& 5 -! "'.

"!" 01&"5 ! !# 5* '"-( "(! ( - -.! ! !#4 51( 226! "& "( .226! !# ) "# '- ! ! '"-( !(41 ( "!"4 !"! ( ! -!! '"-!# -5& !' "5 ! 1 ! " 51( "1! ( ' -! ' 5* !# ! !' @" '-& "1& ! 1.4 ! ! ! '"-( "#&; !.( "# "!"(7 ! 0 !(!"# ! 1 -" B.* 0!"  ) <* G !( !64 "# 51( I/Is 1 '" '"-( AKII 15 dIdz= −βI + α0 Is .AKIC " ! !# !! "# '-( ! dI/ d z = 09 ' "- !! '"#!! AKI%5; ;" -# 0 " 55* " '- .*( "# 5* " -' 5141 ( "41 ""141 ' 5 5 !"(( - !# ! "&&! "! ; '"( /!! ";# -! "( ."# '"-( !* !- "# 5 " ".(* "# 51( " 2"Fmax =α0βFs ,AKIN0( AKI D # Fs 3 "! !# 51( AKANI,- .L- / 5)()"* ;!! !& "! 6 '"-( !* "-(* ' .! ( ! ( ( ." !& "#'! ( "( ! "( "!!5*"0& "'. "!"( / !5 "!!5"0( !- ' '4! ( "'.! <.'- "!"( !! ! -!05 "-!# ( !#"( "!!& "5 !41& * =! "-" !# ( * 2'5* - !!5* 01 .! !5* 5* *! ! * '"-(+'5.!5 "5 05!# !- '"-( '4.1 ( ! ! 5*(1 ' ; .! ! ,"( "'& 6 "( 6 01 0*.

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b -! "( !- * "!! !# " 70* * '! ' .

0"#; "5 "5G;41& ; 05" "  ) <*5 !5& AON "" "( "#'( !& "! ! '55& !.5!5& '! !(1& ' * '" 015* !- .L-P- 1/ *"C /I "5* !( L λ ! < 1 ! & !&;& 26 !5!5& '! !# !2.! 80 : < '"# ! ! 1! ( "41& "! ' ' 6,& !!"# ! *& !- & "!"# '.! AKA !"(41& 0& !2! 80 : <LÇ1Ç2Âûõîäíîåèçëó÷åíèåÀêòèâíàÿñðåäà2 :0) + /1 T 1,0 +B /1 T ,+- +B T ,-B L T - +'"5& "41 1 ! %*& " ! "'" !2! F "5& " 5*! -' - !-'- '" <'( " "! 5;;* ' !2.! " !5* " 3 0 -!5* !&! "-!# 226! - !& !5 1 ! "(*!- '"-( " "5 λMG=(1 − R)2 K1 − 2RK cos (4πL/λ) + R2 K 2.AKIOD # K 3 226! "( 5 '" '! 01& "5 ' * K = exp (αL) R 3 226!!( 1 ! ' '" !2! % ' ! " cos (4πL/λ) = 1 "-G=(1 − R)2 K(1 − RK)2.AKKB<- -! !241* "-& ! 5!;* ! 6* '! ! ;;* "414 ' !"# " RK < 1 < K → R−1226! "( G 01! ( 0 - !# =! '-! -!'! 6(IN,- .L- / 5)().L-<- "(/ /*!", ! .2@3:!/- -! "RK = 1,"α = αкр =1L ln1RAKKA !# !- " "(41 '0( C5 " "# !M ! ' * "5 05!# . 5 " ' !! *D! -! " '0( ! "-!# .! !( ' '( ! ! '"-( *( '! % " !# R1 R2 3 2.26!5 !( '" D1 D2 AKA L 3 !- (" '! G ! " !!( !& -! ( '" D2 " "0# !& 5 < -! -"#5&! ! !# '"-( I0 <&( '! " ".-! ! !# '-( I0 eαL α 3 226! "( < "!( ! '" D1 ! !# "5 !! R1 I0 eαL <&(!& ' -' '! !'; # ! '" D2 " 0! !#! !# I1 = R1 R2 I0 e2αL 9 0' ' 6" ! .

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