UniTest 2008-

535 22.343 47 - --,-, 2007 . : ; -- , . . 47. 1.0[] : / . . ,. . ,. . . ..(2 ). - :,2008. ( : 94-2007 /. .. . ). 1 ..(DVD). .- :IntelPentium() 1 ;512 ;2 - ;DVD ;MicrosoftWindows2000 SP 4 / XP SP 2 /Vista(32) ;AdobeReader 7.0(- pdf). ISBN 978-5-7638-1273-2 () ISBN 978-5-7638-1452-1 ( ) .0320802571 06.12.2008 . () - - ,, ,,- . , . - . - -.. -, , . 140400.68 140000 , . , 2008 - . . :--; . - . , , - . . 01.10.2008 2 : , 660041, , . , 79 . -3- . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 5 5 1 1. . , , . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 6 6 2 2. . - - . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 1 11 1 3 3. . . .. .. .. .. .. .. .. .. .. .. .. . 1 15 5 4 4. . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 2 21 1 5 5. . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 2 27 7 6 6. . . .. .. .. .. .. .. .. . 3 32 2 7 7. . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 3 37 7 8 8. . . .. .. .. .. .. .. .. .. .. .. . 4 43 3 9 9. . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 4 49 9 1 10 0. . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 5 54 4 1 11 1. . - - . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 5 59 9 1 12 2. . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 6 65 5 1 13 3. . - - . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 7 76 6 1 14 4. . . .. .. .. .. .. .. .. .. . 8 82 2 1 15 5. . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 8 88 8 1 16 6. . . .. .. .. .. .. .. .. .. . 9 93 3 1 17 7. . . .. .. .. .. . 9 97 7 . -4- . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 1 10 03 3 . -5- 60- ,,-, , , - . , . . .., , -,- . - -,-, , . ;- , --,.--;, .,- ;,- . - ; ,, .- -,, ,- . . -6- 1 1. . , , ,. -.- . ,.,, .,, , ()-(,). . ,,. , - , .- -, . , - -.-()-.- , , - . () ,.- -.,-, ( ). , - , , -. , . . . 1925., ______________________ . 1. , . -7- . 60- ,-,- -,, . , ,-.-, ,,- , , -, , - . -. - .,,, -P E = ,..-, . : , aE , - . aE , ~ /2, ,e.~108,~108109 /.-0,110/-.- 106107 /. - . ,--,,-.- . . . . . - 1925 . - 1. , . -8- ( 1,5 %) .--,-.- -,- .--,, (). , . . ,, .- , -.,-, - . - -. , -. -,. 1 2, 1 2 ,, 1 2 2 1 + = h h ( ( )1 2 2 11 2 = = h ).- 1 2 (- 1 2 = ).- . . .- 1. , . -9- , , -. ,.. .- . , -().- , , . ..,-, , , , -. , -,-.; , -,. - . ,,, , . 1962 ., -1965. , . -. -. ,(-). -, ., - - , 1. , . -10- ,, , . .-,,,-, , -. . ,- .-,-.-,- . . . -11- 2 2. . - - ..-. . , . . . . - . - - , - 1961 . , - , . 2.1. -, =6943,. , , -., -(), 2 22 , ( 2 ) = = =3471,5.- , -,, . . 2.1. , - . , ; , 100 %. , . . -() - 2 2. - . -12- 96%., 50%.-., -,-. , 1 2 s = , 1 2( ,sn m n m = ). -,-. . ( ) , - , -,-. , .-, , -.- ., ,-,. , . (1962) -.-,-13451 .- ,,- -, , - . - , . 2. - . -13- . 2.2. ,-, . ,-, , . .-,- , ( ) . , . () (). . --,.-, . , ---., . -,.-, . -,,-,,, . . , - -, , . .,-0 2. - . -14- -. : - ,,40- , , -. . 2.1. 2.1 - , -, , - , -, , .-, . -. - - , , , , - . , -, -.--. .-. -. , , , - , - . , -, -. --.-. .--.-.--. - . , -- , () , () . - . . -15- 3 3. . . . .-..- . . . --.- 1 1, , 0, 0H ErotE rotH divD divHc t c t = = = = , ,, , , ,.(3.1) 4 D E P = +, , ,, (3.2) P,-. 2 22 2 2 21 4 E ProtrotEc t c t + = , ,,,(3.3) 2 22 2 2 21 4 E PEc t c t = , ,,.(3.4) (3.1),(3.2)- ; . (3.1)(3.4) ,. ,-. , , . - = (), (3.5) . . . ,- 3. . -16- -,, aE E . - -. (3.5) -.- , - (1) (2) 2 (3) 3 (4) 4( ) ......... P P E E E E E = = + + + +(3.6) . -()- . (1) , (2) , (3) ,(4) - . , (1) -, (2) , (3) . . - . (3.1)(3.6)--. 0cos( ) E E t kz = =( )( ) ( )012i t kz i t kzE e e + . (3.7) (3.6) , . (2) 2 2 (2) 20 01cos ( ) (1 cos(2 2 ))2P E t kz E t kz = = + (3.8) -:-- (2) 2012cP E = - (2) 22 01cos 22P E t = Z. (3.6)-.,(3.7) (3.6),,,-.- , , 3. . -17- . (1) 2 (3) 3P E E = + .(3.9) n -24 D E P E n E = + = = , 1 4 n P E = + . (3.10) (3.9)(3.10) , (3) 2002n n En = + ,(3.11) (1)01 4 n = + .(3.12) I . I = 2/8, 0 2n n n = + , (3.13) n0 ; ; 2(3)2016nn c = .(3.14) (3.13),-. ,,,-,,-,,..n2, ,-., n2 = 31016 2/. , (3.13), , , .-, (), , 3. . -18- (3.13) . ,-(3.6),.. . , . . , -,. , P P P = +, , ,.(3.15) (3.15)(3.3),(3.4),- 2 2 22 2 2 2 2 21 4 4 P P ErotrotEc t c t c t + + = , , ,,,3.16) 2 2 22 2 2 2 2 21 4 4 P P EEc t c t c t = , , ,,. (3.17) (3.16)(3.17) , -(,- . .). . -zv . ;,- v 2 . (3.8). -2 ().- z., , ; -, . z- ;z=0(.3.1,). z, 2 , ( ) ; ( )( ) v c n k k n c = = = . - 3. . -19- z' ( ) 2 2 z t kz = . (3.18) z,-z',(z')K(zz'). (2 )(2 ) K n c = v(2)== /(2) 2 . )) . 3.1 , z , - z', ( ) 2 2 ( ) 2 z t kz K z z t Kz kz = = + (2). (3.19) 2 k K k = , - . , - z , , - z' z' = 0 z' = z: 0 0(2 ) cos ( ') ' cos (2 ') 'z zE A z dz A t Kz kz dz = = + ,(3.20) , z, k . (3.20) 2(2 ) sin cos(2 )2 2A k kzE t Kzk = + . (3.21) (3.21) z: 2(2 ) sin2A kzAk = .(3.22) 3. . -20- . 3.1, z (2 ) Ak , (3.22),. .-() k = 0 , , K = 2k a n() = n(2).(3.23) ,,. . . - , , -, , . -, , . ., ,,(3.23),-. - . .(3.22) (2 ) A z k = 0 0 k . (3.22) , -( k =0)- Z, :(2 ) A= Az. - ( 0 k ) - Z. 4 Z k = . (3.24) l = /k/.(3.25) - . l . , , , -.--., . . -21- 4 4. . -.;-.--. . - . ,- -.,, ,-. . -. ;. .-,.,- . -(),(-),- . ; 10161014 . -,-()-.10131011. ;- 1010 . -,()-.,- -.(,,--). 10 - . ; . -, 4. . -22- ,.- . -( ).,,- . (1)( )ikP E =, ,i 3(1)1( 1, 2, 3)i ik kkP E k == =, (4.1) ik . ; : (1)11(1) (1)22(1)330 0( ) 0 00 0ik = .(4.2) ,-,(1) (1) (1) (1)11 22 33 = = = (4.2) (1). P E =, , , 11 22 33 = ,( z). , ., (1) (1) (1)11 22 33 ,-(,).- . - . - .-()---,- , . (4.1) : (1)31( )i ki kkP E E== . (4.3) ,- 4. . -23- . (1) () : 3 3 3(1) (1) (2) (3)1 1 1( )ik jk ikj j ikjm j mj j mE E E E = = == + + , (4.4) (1) (2) (3); ;ik ikj ikjm (2-);- ( 3- ) -(4-)., (4.4) . : (1) (1) 11 12 (1) 21 221; 10 10 ; 10 10ik ikj ikjm B (/)2. (4.4) , 109(/),,(4.4) . (4.4) (4.3), : (1) (2) (3)i i i jk k ikj j k ikjm k j mk j k k j mP P P E E E E E E = + = + + .(4.5) - - . , , (2)ikj . ,- . , (2)122- , (2)223 z. : +, +, z+z. (2)ikj ( -).- (2)ikj . , (2)ikj = (2)ikj, , (2)ikj= 0. ,,, .--;-.- - (1) (3)i i i jk k ikjm k j mk k j mP P P E E E E = + = + . (4.6) 4. . -24- ,, ,,-,, ,, . , . 4.1 () . . . . , -. -- . 32 20 . . . . -,-., . , . - , . . .- , -: 3 1 2 = . , . -,: (2)1 2 3( , )ikj . -: (2)1 2( )ikj , (2)ikj , ., (2)ikj ,93=27. (2)1 2 3( , )ikj - : 4. . -25- (2) (2)ikj ijk . (4.7) (4.7) (2)ikj 18. ; . , : (2) (2) (2) (2) (2) (2)123 132 213 131 312 321; = = = = . (4.8) (4.7) (2)ijk (i,j,k, ) ( i, l, i = 1, 2, 3; l = 1, 2, ..., 6). (4.3). (2) (2)P DF =, , 6( )( )1 i i il llP P d F== = (4.9) 1(2)13 15 16 11 12 14 2(2)21 22 23 24 25 26 3(2)431 32 34 33 35 3656xyzFP d d d d d d Fd d d d d d FPFd d d d d dPFF = = .(4.10) 1 11 2 22 3 33 4 23 5 13 31 6 12 21; ; ; ; ;i i i i i i i i i i i i i id d d d d d = = = = = = = = . F :1 2 3 4 5 6; ; ; ; ;x x y y z z y z z y x z z x x y y xF E E F E E F E E F E E E E F E E E E F E E E E + + + . (4.10), - 1414360 0 0 0 00 0 0 0 00 0 0 0 0dDdd = .(4.11) , - : 4. . -26- [ ](2) (2)1 2 1 2 1( ) ( )ikj ikj + = + .(4.12) , ,. (4.12)-. 1 2 = = (4.12) : (2) (2)(2 ) (2 )ikj kij = .(4.13) , , (2)ikj -. . : (2) (2) (2) (2) (2) (2)ikj kij jki ijk kji jik = = = = = .(4.14) ,- . . -27- 5 5. . .-.. . . . , , -,-. , . -,-,- -.,- , . ,, (3.16),(3.17),3.,-,-: 2 22 2 2 24P EEc t c t = , ,,.(5.1) , - . , , . . / = / = 0; ,z. : 1 12 23 3( )1 1( )2 2( )3 3( , ) ( ) ,( , ) ( ) ,( , ) ( ) .i t k zi t k zi t k zE z t A z eE z t A z eE z t A z e===(5.2) 1,23;( )iA z i . , , -., i--z,. , () . 5. . -28- (5.1) , (5.2) (5.1)z-(..,( ), ( ) k n nc = = ). z, -((5.1)0). i . - (5.1) , 1 2 3, , , . 1 2 3 + = . (5.3) (5.3)-,-, .,, 1 2( ) + h , -, 3 h . (4.5) : [ ][ ][ ]3 2 3 23 1 3 11 2 1 2( ) ( ) (2) (2)1 3 2( ) ( ) (2) (2)2 3 1( ) ( ) (2) (2)3 2 1( ) ,( ) ,( ) .i t k k zi t k k zi t k k zP A A eP A A eP A Ae + +=== (5.4) (2) - (4.14). (5.1)(5.4)-i.-. ,, . .-. (5.1) , - , , - 1 , 5. . -29- [ ]1 11 13 2 3 22 2( ) 2 2 1 1 11 1 1 1 2 22( ) 2 11 1 22 (2)( ) ( ) 2 (2) 13 2 3 2 2( ) ( )( ) 2 ,( ) ,( )( ) .i t k zi t k zi t k k zE A z A zk A z ik k ez z zEA z etPA A ez = = = (5.5) . , 22( ) ( ) k n nc = = , , , - 22dA d Akdz dz> ,(5.5)- , (5.1), - (5.3), (5.5) : 3 2 13 2 13 2 12( ) (2) 1 13 2 212( ) (2) 2 23 1 222( ) (2) 3 31 2 232,2,2.i k k ki k k ki k k kdAi A A edz k cdAi A A edz k cdAi A A edz k c = = = (5.6) ., .,- , ( , - : 3 2 1k k k k = (5.7) , -- : , ; - . ,. (5.6). , , , , -.- 5. . -30- . ,, 1 2 3 + = .-, 1 2 , (5.6) 2(2) 3 31 2 232,i kzdAi A A edz k c = (5.8) 2(2) 33 1 2 23 02Li kA i A A ek c = , L , 2(2) 33 1 2 232( 1)i kLA i A A ek c k = .(5.9) (5.8),(5.9) .(5.6), . . (5.6) , 1 2, -.,-.0 k = , (5.6) (2) 1 13 212 ,n c dAi A Adz= (5.10) (2) 2 23 122n c dAi A Adz= , (5.11) (2) 3 31 232 ,n c dAi A Adz= (5.12) ,(5.10)(5.11)- (5.12), 3 3 3 1 1 1 2 2 21 2 3( ) ( ) ( ) n c d A A n c d A A n c d A Adz dz dz = = .(5.13) , 28cnS AA= (5.14) 5. . -31- (5.13), , 3 1 21 2 3 = = . (5.13) - , , .,, -,, , -.(-,: 1 2 3 + = ) ,-, . - 1 3 2 = - , 3 1 , 2 . , , , . ,-, 3 1 2, , 1 2 3 . 2 , - : () 3 - 2 . 2 , . 1 . 2 -; .-,, , 2 . , -. , 8. ,, , - . . -32- 6 6. . . - . . . () ,-,, ,-., .- . , -- . 1 2 = , : 1 32 = . (5.8) 2(2) 2 3 31 232i kzdAi A edz k c = . (6.1) 3( 0) 0 A z = = z (6.1) 2(2) 2 33 1 232( 1)i kzA i A ek c k = .(6.2) (5.14) 23A , 222(2) 2 2 3 33 1 232 sin8cn xS A zk c x = ,(6.3) 2 x kz = . (6.3) , - : 1.0 k 2sin xx . (6.2) (3.22), - , 3.1. 2.k =0 (z=L).,,- , . 6. . -33- 3. - . ,,- k =0. , , -,-.-,- . ., .---();-. , , -.-(-),,-.-, . (ordinary);- . (traordinary) ; - -. ; -. .6.1 , : -,.-,,-one;-.o- (V0=/). -,.- . ne < o -,ne>o,.- , ,, .ne- 2 2 2 2( ) ( ) 1z o x en n n n + = . 6. . -34- (. . 6.1) . 6.1. 2 2 2 2 2 2( ) cos ) ( ) sin ) 1e eo en n n n + = (6.4) 2 2 2 20 0( ) ( ) coseo e en n n n n n = . (6.5) (6.5),,- , 2 2 2 2 20 0 0( ) ( ) ( ) cosee e o ev c n c n n n n n = = .(6.6) . -:-.. 6.2--(-) ( ).,-, , : no ne ne( ) ne no ) ) . 6.2 6. . -35- ( ) (2 )eon n = .(6.7) (6.7)-, ,.- ., .- . .(). , - . -. , , , ; --,,--.-, , (--).---,-- (. 6.1). 6.1 -- -- , , -,., , : - -, - -. . , , . ,k n c = .- . --.--- = +2 1.(6.8) I|1|=|2|,() 6. . -36- (6.8) : 21 = . (6.9) , 022 ( ) (2 )en nc c = . (6.10) (6.5), -: ( ) ( )2 2 2 2(2 )cos ( ) (2 ) (2 ) (2 )( )oc o e o eonn n n nn = . (6.11) .- ( ) (2 )o en n . (6.12) = 90, 90-. -,. -- -, , : ( ) ( )2 2 2 2 2 2 2 2( ) ( ) 2 (2 ) (2 )( )( ) ( ) ( ) cos (2 ) (2 ) (2 ) coso e o eoo o e c o o e cn n n nnn n n n n n + = .(6.13) cosc ,(6.11) . ,-. 1. . , . 2. 90- . . 3.:- (2) . . . -37- 7 7. . . -.. .-. . j (5.6), ,(jAk) ( ) , - . -,(.6),,-,- .- ( ) ( ) exp ( )j j jA z a z i z = ,(7.1) ( ) ( )j ja z z - . (5.6), : ( )2 (2) 22j j jk c =(7.2) j- , 3 1 2k k k k = . (5.7): 11 3 222 3 133 1 2exp( ),exp( ),exp( ).dAi A A i kzdzdAi A A i kzdzdAi A A i kzdz= = = (7.3) (-- , 1 2( ) ( ), A z A z = 3 2( ) ( ) A z A z )- (7.3) 7. . -38- * 11 1 22 22 1( )( ) ( ) exp( ),( )( )exp( ).dA zi A z A z i kzdzdA zi A z i kzdz= = (7.4) Aj(z) aj(z) j(z), 1 11 1 1 2 1 22 2 22 2 1 1 2exp[ (2 )],exp[ (2 )],da dia i a a i kzdz dzda dia i a i kzdz dz + = + + = + (7.4) 21-2+kz = , -, , exp(i) = cos() isin() 1 11 1 1 22 2 22 2 1(cos sin ),(cos sin ).da dia i a a idz dzda dia i a idz dz+ = + = + , 2d1/dz2/dz=d/dzkz, 1,2,- : ( )11 1 22 22 121 2 2 1 2sin 0,sin 0,2 cos 0.daa adzdaadzdk a a adz+ = = + = (7.5) , -,,,, . - -, . .-(5.7) 3 1 20 k k k k = = d/dz = = 2d1/dz-d2/dz (7.5) : 7. . -39- ( )11 1 22 22 121 2 2 1 2sin 0,sin 0,2 cos 0.daa adzdaadzda a adz+ = = + = (7.6) . .(7.6) 1, 2-, ( )2 22 1 1 2( ) ( ) 0 a z a zz + =.(7.7) , z , , . 21U , 2 22 1 1 2( ) ( ) a z a z + =21U (7.8) 21U ( z = 0): 2 22 1 1 2(0) (0) a a + =21U . (7.9) (7.6) -1 2,.- , , 1, 2 2 21 221 22( )sin ,3 cos .daU adzd Uadz a= = (7.10) . (7.10), z,,: . 21U 22 1(0) a -cos ., ,2 = ,cos =0,0 d dz = . z, , ,,- 7. . -40- (7.10). , . , (7.10) 2 = : 2 2 21 2( )daU adz = ,(7.11) : 2 22 1 2( ) z da U a = , ,2(z),-2(0)=0,- 1( ) ( ); ( ) th e e e e th ch = + + = : 2 1( ) ( ) a z Uth Uz = .(7.12) 1 1 1 2(0) U a = , (7.12) ( ) 2 1 2 1 1 2 1( ) (0) (0) a z a th a z = . (7.13) (7.8), 1(z): ( )111 2 1(0)( )(0)aa zch a z = .(7.14) .7.1. 1(z) 2(z), ( )( ) 1 2 10 z . 7.1. (7.13),(7.14),-.-1 0.5 12 ( )(0) a z =11( )(aa21( )(0)aa 7. . -41- ( )11 2 1(0) L a = ,(7.15) , ., . 2 = const. ,,-, ,..L, (7.15). (7.10),,L,- , . . . . . (7.10)-(k=0)..-c1(pumpmode),a2(secondharmonic)(phase)z(.7.2L,m=0.03 ( )11 2 1(0) z a = ), . 7.2. (z=0), (0), =/2. ( )11 2 1(0) z a = ,-7.1,(7.13), (7.14). ( )11 2 1(0) z L a = 2 -1.. 1 2 , - , = /2. 7. . -42- . 7.2 . l k = .(3.25) ( )11 2 1(0) L a = ..7.3- 2(z) : 1) ,3) ,4) ,5) 2) . l L l L l L l L ~=