ìÒëwñåÇ©ÇÁÇÃòaé¸îg.pdf
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- えみ かむら
- 5 years ago
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1 (SFG L 2 2. (1/m'/m/2 SFG /m' 3 m/2 4 m'/m 5 m' z 1 6 m m'/m z SFG 9 1/m' 9 m/2 9 m'/m 10 m' z 1 11 m m'/m z SFG 13 1/m' SFG 13 m/2 SFG 17 m'/m SFG 21 m' SFG 25 m SFG (1/m'/m/m"/2 SFG /m' 38 m''/2 38 m'/m 39 m/m'' 41 m' z 1 42 m m'/m z 2 43 m" m/m" z SFG 45 1/m' 45 m''/2 46 m'/m 47 m/m'' 48 m' z SFG - 1
2 m m'/m z 2 50 m" m/m" z r 1m, s = n 1 cosθ 1 n m cosθ m n 1 cosθ 1 + n m cosθ m, 1m,s = r 1m, p = n 1 cosθ m n m cosθ 1 n 1 cosθ m + n m cosθ 1, 1m, p = 2n 1 cosθ 1 n 1 cosθ 1 + n m cosθ m 2n 1 cosθ 1 n 1 cosθ m + n m cosθ 1 r 1m,x = -r m1,x = r 1m,p, r 1m,y = -r m1,y = r 1m,s, r 1m,z = -r m1,z = -r 1m,p r 2m,x = -r m2,x = r 2m,p, r 2m,y = -r m2,y = r 2m,s, r 2m,z = -r m2,z = -r 2m,p 1m,x = (cosθ m /cosθ 1 1m,p, 1m,y = 1m,s, 1m,z = (sinθ m /sinθ 1 1m,p m1,x = (cosθ 1 /cosθ m m1,p, m1,y = m1,s, m1,z = (sinθ 1 /sinθ m m1,p 2m,x = (cosθ m /cosθ 2 2m,p, 2m,y = 2m,s, 2m,z = (sinθ m /sinθ 2 2m,p m2,x = (cosθ 2 /cosθ m m2,p, m2,y = m2,s, m2,z = (sinθ 2 /sinθ m m2,p 1m,α m1,α = 1 + r 1m,α r m1,α = 1 - r 1m,α 2, 2m,α m2,α = 1 + r 2m,α r m2,α = 1 - r 2m,α 2, (α = x, y, z L L SFG SFG E SF E SF, α = β L αβ P β SF Snell SFG (- (+ L m s p x y z 4πiω SF /c 4πiω SF 2 /c 2 (- (+ -z +z L L i/j,s(p, α m' I j α (α = x, y, z s p (- (+ -, + 2 SFG - 2
3 m m' SFG L L - 1/m,p,x = cosθ m,sf /(n 1,SF cosθ m,sf + n m,sf cosθ 1,SF L - 1/m,s,y = 1/(n 1,SF cosθ 1,SF + n m,sf cosθ m,sf L - 1/m,p,z = (n m /n m' sinθ m',sf /(n 1,SF cosθ m,sf + n m,sf cosθ 1,SF = (n m /n m' 2 sinθ m,sf /(n 1,SF cosθ m,sf + n m,sf cosθ 1,SF L + 1/m,p,x = cosθ 1,SF /(n 1,SF cosθ m,sf + n m,sf cosθ 1,SF L + 1/m,s,y = 1/(n 1,SF cosθ 1,SF + n m,sf cosθ m,sf L + 1/m,p,z = -(n 1 /n m' sinθ m',sf /(n 1,SF cosθ m,sf + n m,sf cosθ 1,SF = -(n 1 /n m' 2 sinθ 1,SF /(n 1,SF cosθ m,sf + n m,sf cosθ 1,SF m m'' SFG L L - 2/m,p,x = cosθ 2,SF /(n 2,SF cosθ m,sf + n m,sf cosθ 2,SF L - 2/m,s,y = 1/(n 2,SF cosθ 2,SF + n m,sf cosθ m,sf L - 2/m,p,z = (n 2 /n m" sinθ m",sf /(n 2,SF cosθ m,sf + n m,sf cosθ 2,SF = (n 2 /n m" 2 sinθ 2,SF /(n 2,SF cosθ m,sf + n m,sf cosθ 2,SF L + 2/m,p,x = cosθ m,sf /(n 2,SF cosθ m,sf + n m,sf cosθ 2,SF L + 2/m,s,y = 1/(n 2,SF cosθ 2,SF + n m,sf cosθ m,sf L + 2/m,p,z = -(n m /n m" sinθ m",sf /(n 2,SF cosθ m,sf + n m,sf cosθ 2,SF = -(n m /n m" 2 sinθ m,sf /(n 2,SF cosθ m,sf + n m,sf cosθ 2,SF SFG L L - m/m,p,x = L + m/m,p,x = cosθ m,sf /(2n m,sf cosθ m,sf L - m/m,s,y = L + m/m,s,y = 1/(2n m,sf cosθ m,sf L - m/m,p,z = -L + m/m,p,z = sinθ m,sf /(2n m,sf cosθ m,sf SFG SFG 2. (1/m'/m/2 SFG 2.1. SFG m'/m m/m" (SFG 4 (SFG 4 1/m' 1 (a: E + (by reflecion and ransmission sources and E - (for n = 0 source E vis,α (0 E ir,β (0 = E 0 vis,αe 0 ir,β (1 [(1 + e2iβ m ', vish m' + ( + e2 iβ m',vish m' r m2,vis,α e 2iβ m, vish m 1 e 2iβ m',vis h m' + ( r m2,vis,α e 2iβ m, vis h m 2 SFG - 3
4 (1 [(1+ e2iβ m',ir h m' + ( + e2iβ m ', irh m' r m2,ir,β e2iβ m, irh m e 2iβ m ', ir h m' + ( + r 1 m',ir,β exp[2ni(h m anθ m,sf + h m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis (2.1 1/m' m' (a: E + and E - (by reflecion sources E vis,α (0 + E ir,β (0 + = E 0 vis,αe 0 ir,β [(1+ e2 iβ m',vish m' + ( + e 2iβ m ', vish m' r m2,vis,α e2 iβ m,vish m + ( 1m',ir,β [(1 + e2iβ m',irh m' + ( + e 2 iβ m',irh m ' r m2,ir,β e2 iβ m,irh m + ( exp[2ni(h m anθ m,sf + h m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis (2.2 m/2 2 (a: E + source E vis,α (h m' + h + m E ir,β (h m' + h + m = E 0 vis,α E 0 ir,β m'm,vis,α m2,vis,α e i( β m', vis h m' +β m, vis h m + ( 1m',ir,β m'm,ir,β m2,ir,β e i(β m',ir h m' +β m,ir h m + ( exp[2ni(h m anθ m,sf + h m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis (2.3 (b: E - sources (for n > 0, by reflecion E vis,α (h m' + h + m E ir,β (h m' + h + m = E 0 vis,α E 0 ir,β m'm,vis,α m2,vis,α e i( β m', vis h m' +β m, vis h m + ( 1m',ir,β m'm,ir,β m2,ir,β e i(β m',ir h m' +β m,ir h m + ( exp[i(2n + 1(h m anθ m,sf + h m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis (2.4 m/2 m (a: E + (by reflecion and E - sources E vis,α (h m' + h m E ir,β (h m' + h m = E 0 vis,α E 0 ir,β m'm,vis,α (1 + r m2,vis,α e i( β m ', vis h m' +β m,vis h m + ( 2 SFG - 4
5 1 m',ir,β m'm,ir,β (1 + r m2,ir,β e i( β m',ir h m ' +β m, ir h m + ( exp[i(2n + 1(h m anθ m,sf + h m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis (2.5 m'/m m' (a: E + and E - (by reflecion sources E vis,α (h m' E ir,β (h m' = E 0 vis,αe 0 ir,β e iβ m ', vis h m ' (1+ r (1+ m2,vis,α e2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( exp[ih m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis exp[i(2n + 1(h m anθ m,sf + h m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis (2.6 (b: E + (by reflecion and E - sources E vis,α (h m' E ir,β (h m' = E 0 vis,αe 0 ir,β e iβ m ', vis h m ' (1+ r (1+ m2,vis,α e2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( exp[ih m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis exp[2ni(h m anθ m,sf + h m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis (2.7 m'/m m (a: E + and E - (by reflecion sources E vis,α (h + m' E ir,β (h + m' = E 0 vis,αe 0 ir,β m'm,vis,α e iβ m',vis h m' (1 + r m2,vis,α e 2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( exp[ih m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis exp[2ni(h m anθ m,sf + h m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis (2.8 (b: E + (by reflecion and E - sources 2 SFG - 5
6 E vis,α (h + m' E ir,β (h + m' = E 0 vis,αe 0 ir,β m'm,vis,α e iβ m',vis h m' (1 + r m2,vis,α e 2 iβ m,vis h m + ( 1 m',ir,β m'm,ir,β e iβ m',ir h m ' (1+ r m2,ir,β e 2iβ m, ir h m + ( exp[ih m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis exp[2ni(h m anθ m,sf + h m' anθ m',sf ( k m,ir sinθ m,ir k m,vis sinθ m,vis (2.9 m' z 1 [A (m' n : E + sources E vis,α (z 1 = E 0 vis,α 1 e 2iβ m',vis h m' + ( r m2,vis,α e 2iβ m, vis h m {(1+ r m2,vis,α e 2 iβ m,vish m exp[iz 1 k m',vis cosθ m',vis (1 + anθ m',sf anθ m',vis +( + r m2,vis,α e 2 iβ m,vish m e 2iβ m ', vish m ' exp[iz 1 k m',vis cosθ m',vis ( + anθ m',sf anθ m',vis exp[ i(2n + 2(h m anθ m,sf + h m' anθ m',sf k m,vis sinθ m,vis (2.10a 1 m',ir,β E ir,β (z 1 = E 0 ir,β + ( {(1+ r m2,ir,β e 2iβ m, irh m exp[iz 1 k m',ir cosθ m',ir (1 + anθ m',sf anθ m',ir +( + r m2,ir,β e 2iβ m,irh m e 2iβ m ', irh m' exp[iz 1 k m',ir cosθ m',ir ( + anθ m',sf anθ m',ir exp[ i(2n + 2(h m anθ m,sf + h m' anθ m',sf k m,vis sinθ m,vis (2.10b E vis,α (z 1 E ir,β (z 1 = E 0 vis,αe 0 ir,β 1 m',vis,α + ( 1 m',ir,β + ( {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m exp[iz 1 (k m',vis cosθ m',vis (1+ anθ m',sf anθ m',vis + k m',ir cosθ m',ir (1 + anθ m',sf anθ m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' exp[iz 1 (k m',vis cosθ m',vis (1+ anθ m',sf anθ m',vis + k m',ir cosθ m',ir (+ anθ m',sf anθ m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' exp[iz 1 (k m',vis cosθ m',vis ( + anθ m',sf anθ m',vis + k m',ir cosθ m',ir (1+ anθ m',sf anθ m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' exp[iz 1 (k m',vis cosθ m',vis ( + anθ m',sf anθ m',vis + k m',ir cosθ m',ir ( + anθ m',sf anθ m',ir 2 SFG - 6
7 exp[ i(2n + 2(h m anθ m,sf + h m' anθ m',sf (k m,vis sinθ m,vis + k m,ir sinθ m,ir (2.11 [B n (m' : E - sources E vis,α (z 1 = E 0 vis,α 1 e 2iβ m',vis h m' + ( r m2,vis,α e 2iβ m, vis h m {(1+ r m2,vis,α e 2 iβ m,vish m exp[iz 1 k m',vis cosθ m',vis (1 anθ m',sf anθ m',vis +( + r m2,vis,α e 2 iβ m,vish m e 2iβ m ', vish m ' exp[iz 1 k m',vis cosθ m',vis ( anθ m',sf anθ m',vis exp[ i2n(h m anθ m,sf + h m' anθ m',sf k m,vis sinθ m,vis (2.12a 1 m',ir,β E ir,β (z 1 = E 0 ir,β + ( {(1+ r m2,ir,β e 2iβ m, irh m exp[iz 1 k m',ir cosθ m',ir (1 anθ m',sf anθ m',ir +( + r m2,ir,β e 2iβ m,irh m e 2iβ m ', irh m' exp[iz 1 k m',ir cosθ m',ir ( anθ m',sf anθ m',ir exp[ i2n(h m anθ m,sf + h m' anθ m',sf k m,vis sinθ m,vis (2.12b E vis,α (z 1 E ir,β (z 1 = E 0 vis,αe 0 ir,β 1 m',vis,α + ( 1 m',ir,β + ( {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m exp[iz 1 (k m',vis cosθ m',vis (1 anθ m',sf anθ m',vis + k m',ir cosθ m',ir (1 anθ m',sf anθ m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' exp[iz 1 (k m',vis cosθ m',vis (1 anθ m',sf anθ m',vis + k m',ir cosθ m',ir ( anθ m',sf anθ m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' exp[iz 1 (k m',vis cosθ m',vis ( anθ m',sf anθ m',vis + k m',ir cosθ m',ir (1 anθ m',sf anθ m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' exp[iz 1 (k m',vis cosθ m',vis ( anθ m',sf anθ m',vis + k m',ir cosθ m',ir ( anθ m',sf anθ m',ir exp[ i2n(h m anθ m,sf + h m' anθ m',sf (k m,vis sinθ m,vis + k m,ir sinθ m,ir (2.13 m m'/m z 2 [A (m n : E + sources E vis,α (h m + z 2 = E 0 1 m',vis,α m'm,vis,α e iβ m', vis h m' vis,α 1+ r 1 m',vis,α e 2iβ m', vis h m' + ( e 2iβ m', vis h m' r m2,vis,α e2iβ m,vis h m {exp[iz 2 k m,vis cosθ m,vis (1+ anθ m,sf anθ m,vis +r m2,vis,α e 2 iβ m,vish m exp[iz 2 k m,vis cosθ m,vis (+ anθ m,sf anθ m,vis 2 SFG - 7
8 exp[ i(2n + 2(h m anθ m,sf + h m' anθ m',sf k m,vis sinθ m,vis (2.14a E ir,β (h m + z 2 = E 0 1m',ir,β m'm,ir,β e iβ m', ir h m' ir,β 1 e 2 iβ m',ir h m ' + ( e 2 iβ m',ir h m ' r m2,ir,β e2iβ m,ir h m {exp[iz 2 k m,ir cosθ m,ir (1 + anθ m,sf anθ m,ir +r m2,ir,β e 2iβ m,ir h m exp[iz 2 k m,ir cosθ m,ir (+ anθ m,sf anθ m,ir exp[ i(2n + 2(h m anθ m,sf + h m' anθ m',sf k m,ir sinθ m,ir (2.14b E vis,α (h m + z 2 E ir,β (h m + z 2 = E 0 vis,α E 0 ir,β 1 m',vis,α m'm,vis,α e iβ m ', vis h m' + ( 1m',ir,β m'm,ir,β e iβ m',ir h m ' + ( {exp[iz 2 (k m,vis cosθ m,vis (1+ anθ m,sf anθ m,vis + k m,ir cosθ m,ir (1 + anθ m,sf anθ m,ir +r m2,ir,β e 2iβ m,ir h m {exp[iz 2 (k m,vis cosθ m,vis (1+ anθ m,sf anθ m,vis + k m,ir cosθ m,ir (+ anθ m,sf anθ m,ir +r m2,vis,α e 2 iβ m,vish m {exp[iz 2 (k m,vis cosθ m,vis ( + anθ m,sf anθ m,vis + k m,ir cosθ m,ir (1+ anθ m,sf anθ m,ir +r m2,vis,α r m2,ir,β e 2i(β m,ir +β m, vis h m {exp[iz 2 (k m,vis cosθ m,vis ( + anθ m,sf anθ m,vis + k m,ir cosθ m,ir ( + anθ m,sf anθ m,ir exp[ i(2n + 2(h m anθ m,sf + h m' anθ m',sf (k m,vis sinθ m,vis + k m,ir sinθ m,ir (2.15 [B (m n : E - sources E vis,α (h m + z 2 = E 0 1 m',vis,α m'm,vis,α e iβ m', vis h m' vis,α 1+ r 1 m',vis,α e 2iβ m', vis h m' + ( e 2iβ m', vis h m' r m2,vis,α e2iβ m,vis h m {exp[iz 2 k m,vis cosθ m,vis (1 anθ m,sf anθ m,vis +r m2,vis,α e 2 iβ m,vish m exp[iz 2 k m,vis cosθ m,vis ( anθ m,sf anθ m,vis exp[ i2n(h m anθ m,sf + h m' anθ m',sf k m,vis sinθ m,vis (2.16a E ir,β (h m + z 2 = E 0 1m',ir,β m'm,ir,β e iβ m', ir h m' ir,β 1 e 2 iβ m',ir h m ' + ( e 2 iβ m',ir h m ' r m2,ir,β e2iβ m,ir h m {exp[iz 2 k m,ir cosθ m,ir (1 anθ m,sf anθ m,ir +r m2,ir,β e 2iβ m,ir h m exp[iz 2 k m,ir cosθ m,ir ( anθ m,sf anθ m,ir exp[ i2n(h m anθ m,sf + h m' anθ m',sf k m,ir sinθ m,ir (2.16b 2 SFG - 8
9 E vis,α (h m + z 2 E ir,β (h m + z 2 = E 0 vis,α E 0 ir,β 1 m',vis,α m'm,vis,α e iβ m ', vis h m' + ( 1m',ir,β m'm,ir,β e iβ m',ir h m ' + ( {exp[iz 2 (k m,vis cosθ m,vis (1 anθ m,sf anθ m,vis + k m,ir cosθ m,ir (1 anθ m,sf anθ m,ir +r m2,ir,β e 2iβ m,ir h m {exp[iz 2 (k m,vis cosθ m,vis (1 anθ m,sf anθ m,vis + k m,ir cosθ m,ir ( anθ m,sf anθ m,ir +r m2,vis,α e 2 iβ m,vish m {exp[iz 2 (k m,vis cosθ m,vis ( anθ m,sf anθ m,vis + k m,ir cosθ m,ir (1 anθ m,sf anθ m,ir +r m2,vis,α r m2,ir,β e 2i(β m,ir +β m, vis h m {exp[iz 2 (k m,vis cosθ m,vis ( anθ m,sf anθ m,vis + k m,ir cosθ m,ir ( anθ m,sf anθ m,ir exp[ i2n(h m anθ m,sf + h m' anθ m',sf (k m,vis sinθ m,vis + k m,ir sinθ m,ir ( SFG SFG vis ir 1/m' 1 (a: E + (by reflecion and ransmission sources and E - (for n = 0 source P * a (0 = χ aαβ E 0 vis,αe 0 ir,β (1 [(1 + e2iβ m ', vish m' + ( + e2 iβ m',vish m' r m2,vis,α e 2iβ m, vish m 1 e 2iβ m',vis h m' + ( r m2,vis,α e 2iβ m, vis h m (1 [(1+ e2iβ m',ir h m' + ( + e2iβ m ', irh m' r m2,ir,β e2iβ m, irh m e 2iβ m ', ir h m' + ( + r 1 m',ir,β (2.18 1/m' m' (a: E + and E - (by reflecion sources P * a (0 + = χ aαβ E 0 vis,α E 0 ir,β [(1+ e2 iβ m',vish m' + ( + e 2iβ m ', vish m' r m2,vis,α e2 iβ m,vish m + ( 1m',ir,β [(1 + e2iβ m',irh m' + ( + e 2 iβ m',irh m ' r m2,ir,β e2 iβ m,irh m + ( (2.19 m/2 2 2 SFG - 9
10 (a: E + source P * a (h m' + h + m = χ aαβ E 0 vis,αe 0 ir,β m'm,vis,α m2,vis,α e i( β m', vis h m' +β m, vis h m + ( 1m',ir,β m'm,ir,β m2,ir,β e i(β m',ir h m' +β m,ir h m + ( e 2iβ m ', ir h m' r m2,ir,β e2iβ m, ir h (2.20 m (b: E - sources (for n > 0, by reflecion P * a (h m' + h + m = χ aαβ E 0 vis,αe 0 ir,β m'm,vis,α m2,vis,α e i( β m', vis h m' +β m, vis h m + ( 1m',ir,β m'm,ir,β m2,ir,β e i(β m',ir h m' +β m,ir h m + ( e 2iβ m ', ir h m' r m2,ir,β e2iβ m, ir h (2.21 m m/2 m (a: E + (by reflecion and E - sources P * a (h m' + h m = χ aαβ E 0 vis,α E 0 ir,β m'm,vis,α (1 + r m2,vis,α e i( β m ', vis h m' +β m,vis h m + ( 1 m',ir,β m'm,ir,β (1 + r m2,ir,β e i( β m',ir h m ' +β m, ir h m + ( e 2iβ m ', ir h m' r m2,ir,β e2iβ m, ir h (2.22 m m'/m m' (a: E + and E - (by reflecion sources P * a (h m = χ aαβ E 0 vis,α E 0 ir,β e iβ m ', vis h m ' (1+ r (1+ m2,vis,α e2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ (1+ r m2,ir,β e2iβ m,ir h m + ( (2.23 (b: E + (by reflecion and E - sources P a * (h m = χ aαβ E 0 vis,α E 0 ir, β α, β 2 SFG - 10
11 1m', vis,α e iβ m ', vish m ' (1+ (1+ r m2, vis,α e 2iβ m, vish m 1+ r 1m', vis,α e 2iβ h m ', vis m' + (r m'm, vis,α e 2iβ h m ', vis m' r m2,vis,α e 2iβ h m,vis m 1m', ir, β e iβ h m',ir m ' (1+ r m'm, ir,β (1+ r m2,ir,β e 2iβ h m, ir m ( r 1m', ir,β r m'm, ir,β e 2iβ h m',ir m ' + ( e 2iβ h m ', ir m ' r m2, ir, β e 2iβ h m,ir m m'/m m (a: E + and E - (by reflecion sources P * a (h + m = χ aαβ E 0 vis,αe 0 ir,β m'm,vis,α e iβ m',vis h m' (1 + r m2,vis,α e 2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ (1+ r m2,ir,β e2iβ m,ir h m + ( (2.25 (b: E + (by reflecion and E - sources P * a (h + m = χ aαβ E 0 vis,αe 0 ir,β m'm,vis,α e iβ m',vis h m' (1 + r m2,vis,α e 2 iβ m,vis h m + ( 1 m',ir,β m'm,ir,β e iβ m',ir h m ' (1+ r m2,ir,β e 2iβ m, ir h m + ( (2.26 m' z 1 [A n (m' : E + sources P * a (z 1 = χ aαβ E 0 vis,α E 0 ir,β 1 m',vis,α + ( 1 m',ir,β + ( {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m exp[iz 1 (k m',vis cosθ m',vis (1+ anθ m',sf anθ m',vis + k m',ir cosθ m',ir (1 + anθ m',sf anθ m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' exp[iz 1 (k m',vis cosθ m',vis (1+ anθ m',sf anθ m',vis + k m',ir cosθ m',ir (+ anθ m',sf anθ m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' exp[iz 1 (k m',vis cosθ m',vis ( + anθ m',sf anθ m',vis + k m',ir cosθ m',ir (1+ anθ m',sf anθ m',ir 2 SFG - 11
12 +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' exp[iz 1 (k m',vis cosθ m',vis ( + anθ m',sf anθ m',vis + k m',ir cosθ m',ir ( + anθ m',sf anθ m',ir (2.27 [B n (m' : E - sources P * a (z 1 = χ aαβ E 0 vis,α E 0 ir,β 1 m',vis,α + ( 1 m',ir,β + ( {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m exp[iz 1 (k m',vis cosθ m',vis (1 anθ m',sf anθ m',vis + k m',ir cosθ m',ir (1 anθ m',sf anθ m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' exp[iz 1 (k m',vis cosθ m',vis (1 anθ m',sf anθ m',vis + k m',ir cosθ m',ir ( anθ m',sf anθ m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' exp[iz 1 (k m',vis cosθ m',vis ( anθ m',sf anθ m',vis + k m',ir cosθ m',ir (1 anθ m',sf anθ m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' exp[iz 1 (k m',vis cosθ m',vis ( anθ m',sf anθ m',vis + k m',ir cosθ m',ir ( anθ m',sf anθ m',ir (2.28 m m'/m z 2 [A n (m : E + sources P * a (z 2 = χ aαβ E 0 vis,α E 0 ir,β 1 m',vis,α m'm,vis,α e iβ m ', vis h m' + ( 1m',ir,β m'm,ir,β e iβ m',ir h m ' + ( {exp[iz 2 (k m,vis cosθ m,vis (1+ anθ m,sf anθ m,vis + k m,ir cosθ m,ir (1 + anθ m,sf anθ m,ir +r m2,ir,β e 2iβ m,ir h m {exp[iz 2 (k m,vis cosθ m,vis (1+ anθ m,sf anθ m,vis + k m,ir cosθ m,ir (+ anθ m,sf anθ m,ir +r m2,vis,α e 2 iβ m,vish m {exp[iz 2 (k m,vis cosθ m,vis ( + anθ m,sf anθ m,vis + k m,ir cosθ m,ir (1+ anθ m,sf anθ m,ir 2 SFG - 12
13 +r m2,vis,α r m2,ir,β e 2i(β m,ir +β m, vis h m {exp[iz 2 (k m,vis cosθ m,vis ( + anθ m,sf anθ m,vis + k m,ir cosθ m,ir ( + anθ m,sf anθ m,ir (2.29 [B n (m : E - sources P * a (z 2 = χ aαβ E 0 vis,α E 0 ir,β 1 m',vis,α m'm,vis,α e iβ m ', vis h m' + ( 1m',ir,β m'm,ir,β e iβ m',ir h m ' + ( {exp[iz 2 (k m,vis cosθ m,vis (1 anθ m,sf anθ m,vis + k m,ir cosθ m,ir (1 anθ m,sf anθ m,ir +r m2,ir,β e 2iβ m,ir h m {exp[iz 2 (k m,vis cosθ m,vis (1 anθ m,sf anθ m,vis + k m,ir cosθ m,ir ( anθ m,sf anθ m,ir +r m2,vis,α e 2 iβ m,vish m {exp[iz 2 (k m,vis cosθ m,vis ( anθ m,sf anθ m,vis + k m,ir cosθ m,ir (1 anθ m,sf anθ m,ir +r m2,vis,α r m2,ir,β e 2i(β m,ir +β m, vis h m {exp[iz 2 (k m,vis cosθ m,vis ( anθ m,sf anθ m,vis + k m,ir cosθ m,ir ( anθ m,sf anθ m,ir ( SFG (SFG 1/m' 1 SFG (a: E - (0 - + r 1m' E + (0 - (SFG (2.1 L + m'/m'p(z 1 1m' L + 1/1P(z 1 = 0 a 0 * = a a 0 = 1 E (0 ne = {L /1 + L + 1/1[r 1m' + 1m' m'1 (r m'm + r m2 b 2 a 2 1+ r 1 m' r m'm a 2 + (r m'm + r 1 m' a 2 r m2 b 2 P * (z 1 = 0 = (L/1 + r 1 m' L + 1/1(1 + r m'm r m2 b 2 + (r 1m' L /1 + L + 1/1(r m'm + r m2 b 2 a r 1 m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 1 = 0 (L /1,px + r 1m',p L + 1/1,px = (r 1m',p L /1,px + L + 1/1,px = L /m',px (L /1,sy + r 1m',s L + 1/1,sy = (r 1m',s L /1,sy + L + 1/1,sy = L /m',sy (L /1,pz + r 1m',p L + 1/1,pz = (r 1 m',p L /1,pz + L + 1/1,pz = L /m',pz (n m" = n 1 2 SFG - 13
14 E (0 ne = (1+ r m'mr m2 b 2 ± (r m'm + r m2 b 2 a r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 L /m'p * (z 1 = 0 (upper sign for x and y, lower sign for z (2.18 E (0 ne,p = E 0 vis,α E 0 ir,β (1 [(1 + e2iβ m ', vish m' + ( + e2 iβ m',vish m' r m2,vis,α e 2iβ m, vish m 1 e 2iβ m',vis h m' + ( r m2,vis,α e 2iβ m, vis h m (1 [(1+ e2iβ m',ir h m' + ( + e2iβ m ', irh m' r m2,ir,β e2iβ m, irh m e 2iβ m ', ir h m' + ( + r 1 m',ir,β (1 + r m'm,sf,p r m2,sf,p e 2iβ β m,sf h m + (r m'm,sf,p + r m2,sf,p e 2iβ m,sf h m [ e2iβ m', SF h m' 1+ r 1 m,,sf,p r m'm,sf,p e 2 iβ m',sf h m' + (r m'm,sf,p + r 1m',SF,p e 2iβ m', SF h m' r m2,sf,p e2iβ m, SF h L/m',px χ m xαβ (1 + r m'm,sf,p r m2,sf,p e 2iβ β m, SF h m (r m'm,sf,p + r m2,sf,p e 2iβ m, SF h m + e2iβ m',sf h m' 1 + r 1m,,SF,p r m'm,sf,p e 2iβ m ', SF h m' + (r m'm,sf,p + r 1m',SF,p e 2 iβ m',sf h m ' r m2,sf,p e2 iβ m,sf h L/m',pz χ m zαβ (n m" = n 1 E (0 ne,s = E 0 vis,αe 0 ir,β (1 [(1 + e2iβ m ', vish m' + ( + e2 iβ m',vish m' r m2,vis,α e 2iβ m, vish m 1 e 2iβ m',vis h m' + ( r m2,vis,α e 2iβ m, vis h m (2.31a (1 [(1+ e2iβ m',ir h m' + ( + e2iβ m ', irh m' r m2,ir,β e2iβ m, irh m e 2iβ m ', ir h m' + ( + r 1 m',ir,β (1 + r m'm,sf,s r m2,sf,s e 2iβ m,sf h m + (r + r m'm,sf,s m2,sf,s e2iβ m, SF h m e2 iβ m',sf h m' 1+ r 1 m,,sf,s r m'm,sf,s e 2 iβ m',sf h m' + (r m'm,sf,s + r 1m',SF,s e 2iβ m', SF h m' r m2,sf,s e2 iβ m,sf h L/m',sy χ m yαβ (2.31b (b: E + (0 - (2.2 L + m'/m'p(z 1 1m' L + 1/1P(z 1 = 0 a 0 * = a a 0 = 1 E + 2(h m + ne = 1m' m2 m'm ab 1+ r 1m' r m'm a 2 + (r m'm + r 1 m' a 2 r m2 b 2 L + 1/1P * (z 1 = 0 1m',p L + 1/1,px = L + 1/m',px, 1m',s L + 1/1,sy = L + 1/m',sy, 1m',p L + 1/1,pz = L + 1/m',pz (n m" = n 1 2 SFG - 14
15 E + 2(h m + ne = m'm m2 ab 1+ r 1m' r m'm a 2 + (r m'm + r 1 m' a 2 r m2 b 2 L + 1/m'P * (z 1 = 0 (2.18 E + 2(h + m ne,p = E 0 vis,α E 0 ir,β (1 [(1 + e2iβ m ', vish m' + ( + e2 iβ m',vish m' r m2,vis,α e 2iβ m, vish m 1 e 2iβ m',vis h m' + ( r m2,vis,α e 2iβ m, vis h m (1 [(1+ e2iβ m',ir h m' + ( + e2iβ m ', irh m' r m2,ir,β e2iβ m, irh m e 2iβ m ', ir h m' + ( + r 1 m',ir,β 1m',SF,p m2,sf,p e i(β β m, SF h m +β m',sf h m ' (L + 1/m',px χ xαβ + L + 1/m',pz χ zαβ 1+ r 1 m,,sf,p r m'm,sf,p e 2 iβ m',sf h m' + (r m'm,sf,p + r 1m',SF,p e 2iβ m', SF h m' r m2,sf,p e2iβ m, SF h m (n m" =n 1 (2.32a E + 2(h + m ne,s = E 0 vis,αe 0 ir,β (1 [(1 + e2iβ m ', vish m' + ( + e2 iβ m',vish m' r m2,vis,α e 2iβ m, vish m 1 e 2iβ m',vis h m' + ( r m2,vis,α e 2iβ m, vis h m (1 [(1+ e2iβ m',ir h m' + ( + e2iβ m ', irh m' r m2,ir,β e2iβ m, irh m e 2iβ m ', ir h m' + ( + r 1 m',ir,β 1 m',sf,s m2,sf,s e i(β β m, SF h m +β m ', SF h m' L + 1/m',syχ yαβ 1+ r 1 m,,sf,s r m'm,sf,s e 2 iβ m',sf h m' + (r m'm,sf,s + r 1m',SF,s e 2iβ m', SF h m' r m2,sf,s e2 iβ m,sf h m (2.32b 1/m' m' SFG (a: (2.1 (2.3 z 1 = 0 a 0 * = a a 0 = 1 E (0 ne = m'1[(r m'm + r m2 b 2 a 2 L + m'/m' + (1 + r m'm r m2 b 2 L m'/m' 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 1 = 0 1m',p L + m'/m',px = 1m',p L m'/m',px = L /m',px, 1m',s L + m'/m',sy = 1m',s L m'/m',sy = L /m',sy, 1m',p L + m'/m',pz = m',p L m'/m',pz = L /m',pz (n m" = n m' 2 SFG - 15
16 E (0 ne = m'1[(1 + r m'm r m2 b 2 ± (r m'm + r m2 b 2 a 2 1+ r 1m' r m'm a 2 + (r m'm + r 1 m' a 2 r m2 b 2 L /m'p * (z 1 = 0 (upper sign for x and y, lower sign for z (2.19 E (0 ne,p = E 0 vis,α E 0 ir,β [(1+ e2 iβ m',vish m' + ( + e 2iβ m ', vish m' r m2,vis,α e2 iβ m,vish m + ( 1m',ir,β [(1 + e2iβ m',irh m' + ( + e 2 iβ m',irh m ' r m2,ir,β e2 iβ m,irh m + ( (1 + r m'm,sf,p r m2,sf,p e 2iβ β m,sf h m + (r m'm,sf,p + r m2,sf,p e 2iβ m,sf h m [ e2iβ m', SF h m' 1+ r 1 m,,sf,p r m'm,sf,p e 2 iβ m',sf h m' + (r m'm,sf,p + r 1m',SF,p e 2iβ m', SF h m' r m2,sf,p e2iβ m, SF h L/m',px χ m xαβ (1 + r m'm,sf,p r m2,sf,p e 2iβ β m, SF h m (r m'm,sf,p + r m2,sf,p e 2iβ m, SF h m + e2iβ m',sf h m' 1 + r 1m,,SF,p r m'm,sf,p e 2iβ m ', SF h m' + (r m'm,sf,p + r 1m',SF,p e 2 iβ m',sf h m ' r m2,sf,p e2 iβ m,sf h L/m',pz χ m zαβ (n m" = n m' E (0 ne,s = E 0 vis,αe 0 ir,β [(1+ e2 iβ m',vish m' + ( + e 2iβ m ', vish m' r m2,vis,α e2 iβ m,vish m + ( (2.33a 1m',ir,β [(1 + e2iβ m',irh m' + ( + e 2 iβ m',irh m ' r m2,ir,β e2 iβ m,irh m + ( (1 + r m'm,sf,s r m2,sf,s e 2iβ m,sf h m + (r + r m'm,sf,s m2,sf,s e2iβ m, SF h m e2 iβ m',sf h m' 1+ r 1 m,,sf,s r m'm,sf,s e 2 iβ m',sf h m' + (r m'm,sf,s + r 1m',SF,s e 2iβ m', SF h m' r m2,sf,s e2 iβ m,sf h L/m',sy χ m yαβ (2.33b (b: (2.2 (2.4 z 1 = 0 a 0 * = a a 0 = 1 E + 2(h m' + h m + ne = m2ab[ m'm L + m'/m' + r m'1 m'm L m'/m' 1+ r 1m' r m'm a 2 + (r m'm + r 1 m' a 2 r m2 b 2 P * (z 1 = 0 m'm,p L + m'/m',px = m'm,p L m'/m',px = L + m'/m,px, m'm,s L + m'/m',sy = m'm,s L m'/m',sy = L + m'/ m,sy, m'm,p L + m'/m',pz = m'm,p L m'/m',pz = L + m'/m,pz (n m" = n m' 2 SFG - 16
17 E + 2(h m' + h m + ne = m2 ab(1± r m'1 1+ r 1m' r m'm a 2 + (r m'm + r 1 m' a 2 r m2 b 2 L m' /mp * (z 1 = 0 (upper sign for x and y, lower sign for z (2.19 E + 2(h m' + h + m ne,p = E 0 vis,α E 0 ir,β [(1+ e2 iβ m',vish m' + ( + e 2iβ m ', vish m' r m2,vis,α e2 iβ m,vish m + ( 1m',ir,β [(1 + e2iβ m',irh m' + ( + e 2 iβ m',irh m ' r m2,ir,β e2 iβ m,irh m + ( ei( β βm, h SF m +β m ', SF h m' [(1+ r m'1,sf,p L + m'/m,px χ xαβ + (1 r m'1,sf,p L + m'/m,pz χ zαβ 1 + r 1m,,SF,p r m'm,sf,p e 2iβ m', SF h m' + (r m'm,sf,p + r 1 m',sf,p e 2iβ m ', SF h m' r m2,sf,p e2iβ m,sf h (n m m" = n m' (2.34a E + 2(h m' + h + m ne,s = E 0 vis,αe 0 ir,β [(1+ e2 iβ m',vish m' + ( + e 2iβ m ', vish m' r m2,vis,α e2 iβ m,vish m + ( 1m',ir,β [(1 + e2iβ m',irh m' + ( + e 2 iβ m',irh m ' r m2,ir,β e2 iβ m,irh m + ( e i( β β m,sf h m +β m',sf h m ' (1+ r m'1,sf,s L + m'/m,syχ yαβ 1+ r 1 m,,sf,p r m'm,sf,p e 2 iβ m',sf h m' + (r m'm,sf,p + r 1m',SF,p e 2iβ m', SF h m' r m2,sf,p e2iβ m, SF h m (2.34b m/2 2 SFG (a: E - (h + m (2.7 z 2 = h m b 0 * = 1 b 0 = b E (0 ne = 2m m'1 b 2 (r m'm + r 1 m' a 2 L 2/2 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 2 = h m + 2m,p L 2/2,px = L m/2,px, 2m,s L 2/2,sy = L m/2,sy, 2m,p L 2/2,pz = L m/2,pz (n m" = n 2 2 SFG - 17
18 E (0 ne = m'1 b 2 (r m'm + r 1m' a 2 L m/2 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 2 = h m + (2.20 E,p (0 ne = E 0 vis,α E 0 ir,β m'm,vis,α m2,vis,α e i( β m', vis h m' +β m, vis h m + ( 1m',ir,β m'm,ir,β m2,ir,β e i(β m',ir h m' +β m,ir h m + ( 2m,SF,p m'1,sf,p e2iβ m,sfh m (r m'm,sf,p + r 1m',SF,p e 2 iβ m',sfh m' [L m/2,px χ xαβ + L m/2,pz χ zαβ 1 + r 1 m',sf,p r m'm,sf,p e 2 iβ m',sf h m' + (r m'm,sf,p + r 1m',SF,p e 2iβ m', SF h m' r m2,sf,p e2iβ m, SF h m (n m" = n 2 (2.35a E,s (0 ne = E 0 vis,αe 0 ir,β m'm,vis,α m2,vis,α e i( β m', vis h m' +β m, vis h m + ( 1m',ir,β m'm,ir,β m2,ir,β e i(β m',ir h m' +β m,ir h m + ( 2m,SF,s m'1,sf,s (r m'm,sf,s + r 1m',SF,s e 2iβ m ', SF h m' e2iβ m,sf h m L m/2,sy χ yαβ 1+ r 1 m',sf,p r m'm,sf,p e 2 iβ m',sf h m' + (r m'm,sf,p + r 1m',SF,p e 2iβ m', SF h m' r m2,sf,p e2iβ m, SF h m (2.35b (b: E + (z 2 = h + m + r 2m E - (z 2 = h + m (2.8 L - m/mp(z 2 1m' L - 2/2P(z 2 = h + m (2.8 z 2 = h m b 0 * = 1 b 0 = b E + 2(h m' + h m + ne ={L + 2/2 + L 2/2[r 2 m 2m m2 b 2 (r m'm + r 1 m' a 2 1+ r 1 m' r m'm a 2 + (r m'm + r 1 m' a 2 r m2 b 2 P * (z 2 = h m + = (1+ r 1m'r m'm a 2 (L + 2/2 + r 2m L 2/2 + (r m'm + r 1m' a 2 b 2 (r m2 L + 2/2 + L 2/2 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 2 = h m + (L + 2/2,px + r 2m,p L 2/2,px = (r m2,p L + 2/2,px + L 2/2,px = L + 2/m,px (L + 2/2,sy + r 2 m,s L 2/2,sy = (r m2,s L + 2/2,sy + L 2/2,sy = L + 2/m,sy (L + 2/2,pz + r 2m,p L 2/2,pz = (r m2,p L + 2/2,pz + L 2/2,pz = L + 2/m,pz (n m" = n 2 2 SFG - 18
19 E + 2(h m' + h m + ne = (1+ r 1 m'r m'm a 2 ± (r m'm + r 1 m' a 2 b 2 1+ r 1m' r m'm a 2 + (r m'm + r 1 m' a 2 r m2 b 2 L + 2/mP * (z 2 = h m + (upper sign for x and y, lower sign for z (2.20 E + 2,p (h m' + h + m ne = E 0 vis,α E 0 ir,β m'm,vis,α m2,vis,α e i( β m', vis h m' +β m, vis h m + ( 1m',ir,β m'm,ir,β m2,ir,β e i(β m',ir h m' +β m,ir h m + ( { [(1+ r 1 m',sf,p r m'm,sf,p e2 iβ m',sfh m ' + (r m'm,sf,p + r 1m',SF,p e2 iβ m',sfh m ' e2iβ m, SFh m L 2/m,px χ xαβ 1+ r 1 m',sf,p r m'm,sf,p e 2 iβ m',sf h m ' + (r m'm,sf,p + r 1m',SF,p e 2iβ m',sf h m' r m2,sf,p e 2iβ m, SF h m + [(1+ r 1 m',sf,p r m'm,sf,p e2 iβ m',sfh m ' (r m'm,sf,p + r 1 m',sf,p e2iβ m ', SFh m' e2iβ m,sfh m L 2/m,pz χ zαβ 1 + r 1m',SF,p r m'm,sf,p e 2iβ m', SF h m' + (r m'm,sf,p + r 1 m',sf,p e 2iβ m ', SF h m' r m2,sf,p e2iβ m,sf h m (n m" = n 2 E + 2,s (h m' + h + m ne = E 0 vis,αe 0 ir,β m'm,vis,α m2,vis,α e i( β m', vis h m' +β m, vis h m + ( (2.36a 1m',ir,β m'm,ir,β m2,ir,β e i(β m',ir h m' +β m,ir h m + ( [(1 + r 1m',SF,s r m'm,sf,s e2iβ m ', SFh m' + (r m'm,sf,s + r 1m',SF,s e2iβ m ', SFh m' e2iβ m,sfh m L 2/m,syχ yαβ 1 + r 1m',SF,s r m'm,sf,s e 2iβ m', SF h m' + (r m'm,sf,s + r 1m',SF,s e 2iβ m ', SF h m' r m2,sf,s e2iβ m, SF h m (2.36b m/2 m SFG (a: (2.5 (2.7 z 2 = h m b 0 * = 1 b 0 = b E (0 ne = ab mm' (r m2 L + m/m + L m/m 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 2 = h m mm',p L + m/m,px = mm',p L m/m,px = L m'/m,px, mm',s L + m/m,sy = mm',s L m/m,sy = L m'/m,sy, mm',p L + m/m,pz = mm',p L m/m,pz = L m'/m,px (n m" = n m 2 SFG - 19
20 E (0 ne = ab(1 ± r m2 L m'/m 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 2 = h m (upper sign for x and y componens, lower sign for z componen (2.23 E,p (0 ne = E 0 vis,α E 0 ir,β e iβ m ', vis h m ' (1+ r (1+ m2,vis,α e2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( ei( β m',sfh m' +β m, SFh m [(1 + r m2,sf,p L m'/m,px χ xαβ + (1 r m2,sf,p L m'/m,pz χ zαβ 1+ r 1 m',sf,p r m'm,sf,p e 2 iβ m',sf h m' + (r m'm,sf,p + r 1m',SF,p e 2iβ m', SF h m' r m2,sf,p e2iβ m, SF h m (n m" = n m (2.37a E,s (0 ne = E 0 vis,αe 0 ir,β e iβ m ', vis h m ' (1+ r (1+ m2,vis,α e2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( e i( β m ', SF h m' +β m,sf h m (1+ r m2,sf,s L m'/m,syχ yαβ 1+ r 1 m',sf,s r m'm,sf,s e 2 iβ m',sf h m' + (r m'm,sf,s + r 1m',SF,s e 2iβ m', SF h m' r m2,sf,s e2 iβ m,sf h m (2.37b (b: (2.6 (2.8 z 2 = h m b 0 * = 1 b 0 = b E + 2(h m' + h m + ne = (1 + r 1m'r m'm a 2 L + m/m (r m'm + r 1 m' a 2 b 2 L m/m 1 + r 1 m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 2 = h m m2,p L + m/m,px = m2,p L m/m,px = L + m/2,px, m2,s L + m/m,sy = m2,s L m/m,sy = L + m/2,sy, m2,p L + m/m,pz = m2,p L m/m,pz = L + m/2,pz (n m" = n m 2 SFG - 20
21 E + 2(h m' + h m + ne = [(1 + r 1m'r m'm a 2 m (r m'm + r 1m' a 2 b 2 L + m/2 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 2 = h m (upper sign for x and y componens, lower sign for z componen (2.23 E + 2,p (h m' + h + m ne = E 0 vis,α E 0 ir,β e iβ m ', vis h m ' (1+ r (1+ m2,vis,α e2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( { [(1+ r 1 m',sf,p r m'm,sf,p e2 iβ m',sfh m ' (r m'm,sf,p + r 1m',SF,p e2iβ m ', SFh m' e2iβ m,sfh m L + m/2,px χ xαβ 1+ r 1 m',sf,p r m'm,sf,p e 2 iβ m',sf h m ' + (r m'm,sf,p + r 1m',SF,p e 2iβ m',sf h m' r m2,sf,p e 2iβ m, SF h m + [(1+ r 1 m',sf,p r m'm,sf,p e2 iβ m',sfh m ' + (r m'm,sf,p + r 1m',SF,p e2 iβ m',sfh m' e 2iβ m, SFh m L + m/2,pz χ zαβ 1+ r 1m',SF,p r m'm,sf,p e 2 iβ m',sf h m ' + (r m'm,sf,p + r 1m',SF,p e 2iβ m',sf h m' r m2,sf,p e 2iβ m, SF h m (n m" = n m E + 2,s (h m' + h + m ne = E 0 vis,αe 0 ir,β e iβ m ', vis h m ' (1+ r (1+ m2,vis,α e2 iβ m,vis h m + ( (2.38a 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( [(1 + r 1m',SF,s r m'm,sf,s e2iβ m ', SFh m' (r m'm,sf,s + r 1 m',sf,s e2 iβ m',sfh m' e 2iβ m, SFh m L + m/2,syχ yαβ 1 + r 1m',SF,s r m'm,sf,s e 2iβ m', SF h m' + (r m'm,sf,s + r 1m',SF,s e 2iβ m ', SF h m' r m2,sf,s e2iβ m, SF h m (2.38b m'/m m' SFG (a: (2.1 (2.3 z 1 = h m' a 0 * = 1 a 0 = a E (0 ne = a m'1[(r m'm + r m2 b 2 L + m'/ m' + (1+ r mm ' r m2 b 2 L m'/m' 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 1 = h m' m'1,p L + m'/m',px = m'1,p L m'/m',px = L /m',px, m'1,s L + m'/m',sy = m'1,s L m'/m',sy = L /m',sy, m'1,p L + m'/m',pz = m'1,p L m'/m',pz = L /m',px (n m" = n m' 2 SFG - 21
22 E (0 ne = a[(1 + r mm'r m2 b 2 ± (r m'm + r m2 b 2 L /m' 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 1 = h m' = a(1 ± r mm' (1± r m2 b 2 L /m' 1+ r 1 m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 1 = h m' (upper sign for x and y componens, lower sign for z componen (2.23 E,p (0 ne = E 0 vis,α E 0 ir,β e iβ m ', vis h m ' (1+ r (1+ m2,vis,α e2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( e iβ m', SF h m' { [(1+ r (1 + r mm',sf,p m2,sf,p e2iβ m,sf h m L/m',px χ xαβ 1 + r 1m',SF,p r m'm,sf,p e 2iβ m ', SF h m' + (r m'm,sf,p + r 1m',SF,p e 2iβ m',sf h m ' r m2,sf,p e2 iβ m,sf h m e iβ m',sf h m' + [(1 r (1 r mm',sf,p m2,sf,p e2 iβ m,sf h m L/m',pz χ zαβ 1 + r 1m',SF,p r m'm,sf,p e 2iβ m ', SF h m' + (r m'm,sf,p + r 1m',SF,p e 2 iβ m',sf h m ' r m2,sf,p e2 iβ m,sf h (n m m" = n m' (2.39a E,s (0 ne = E 0 vis,αe 0 ir,β e iβ m ', vis h m ' (1+ r (1+ m2,vis,α e2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( e iβ m ', SF h m' (1+ r mm',sf,s (1+ r m2,sf,s e 2iβ m,sf h m L/m',syχ yαβ 1+ r 1 m',sf,s r m'm,sf,s e 2 iβ m',sf h m' + (r m'm,sf,s + r 1m',SF,s e 2iβ m', SF h m' r m2,sf,p e2iβ m, SF h m (2.39b (b: (2.2 (2.4 z 1 = h m' a 0 * = 1 a 0 = a E + 2(h m' + h + m ne = m2 m'm b(l + m'/ m' + r m'1 a 2 L m'/m' 1+ r 1m' r m'm a 2 + (r m'm + r 1 m' a 2 r m2 b 2 P * (z 1 = h m' m'm,p L + m'/m',px = m'm,p L m'/m',px = L + m'/m,px, m'm,s L + m'/m',sy = m'm,s L m'/m',sy = L + m'/ m,sy, 2 SFG - 22
23 m'm,p L + m'/m',pz = m'm,p L m'/m',pz = L + m'/m,pz (n m" = n m' E + 2(h m' + h + m ne = m2 b(1 ± r m'1 a 2 L + m'/ m 1+ r 1m' r m'm a 2 + (r m'm + r 1 m' a 2 r m2 b 2 P * (z 1 = h m' (upper sign for x and y componens, lower sign for z componen (2.23 E + 2,p (h m' + h + m ne = E 0 vis,α E 0 ir,β e iβ m ', vis h m ' (1+ r (1+ m2,vis,α e2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( m2,sf,p eiβ m', SFh m' [(1+ r m'1,sf,p e2iβ m ', SFh m' L+ m'/ m,px χ xαβ + (1 r m'1,sf,p e 2 iβ m',sfh m' L + m'/m,zxχ zαβ 1+ r 1m',SF,p r m'm,sf,p e 2iβ m',sf h m ' + (r m'm,sf,p + r 1m',SF,p e 2 iβ m',sf h m' r m2,sf,p e 2iβ m, SF h m (n m" = n m' E + 2,s (h m' + h + m ne = E 0 vis,αe 0 ir,β e iβ m ', vis h m ' (1+ r (1+ m2,vis,α e2 iβ m,vis h m + ( (2.40a 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( m2,sf,s e iβ m ', SF h m' (1 + r m'1,sf,s e 2iβ m ', SF h m' L+ m'/ m,syχ yαβ 1+ r 1 m',sf,s r m'm,sf,s e 2 iβ m',sf h m' + (r m'm,sf,s + r 1m',SF,s e 2iβ m', SF h m' r m2,sf,s e2 iβ m,sf h m (2.40b m'/m m SFG (a: (2.5 (2.7 z 2 = 0 b 0 * = b b 0 = 1 E (0 ne = a m'1 m'm (r m2 b 2 L + m'/m' + L m'/m' 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 1 = h m' mm',p L + m/m,px = mm',p L m/m,px = L m'/m,px, mm',s L + m/m,sy = mm',s L m/m,sy = L m'/m,sy, mm',p L + m/m,pa = mm',p L m/m,pa = L m'/m,pa (n m" = n m 2 SFG - 23
24 E (0 ne = a m'1 (1± r m2 b 2 L m'/ m 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 1 = h m' (upper sign for x and y componens, lower sign for z componen (2.25 E,p (0 ne = E 0 vis,α E 0 ir,β m'm,vis,α e iβ m',vis h m' (1 + r m2,vis,α e 2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( m'1,sf,p eiβ m', SFh m' [(1+ r m2,sf,p e2iβ m, SFh m L m'/m,px χ xαβ + (1 r m2,sf,p e 2iβ m,sfh m L m'/ m,pz χ zαβ 1+ r 1 m',sf,p r m'm,sf,p e 2 iβ m',sf h m ' + (r m'm,sf,p + r 1m',SF,p e 2iβ m', SF h m' r m2,sf,p e 2iβ m, SF h m (n m" = n m E,s (0 ne = E 0 vis,αe 0 ir,β m'm,vis,α e iβ m',vis h m' (1 + r m2,vis,α e 2 iβ m,vis h m + ( (2.41a 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( m'1,sf,s e iβ m',sf h m' (1+ r m2,sf,s e 2iβ m,sf h m L m'/m,syχ yαβ 1+ r 1 m',sf,s r m'm,sf,s e 2 iβ m',sf h m' + (r m'm,sf,s + r 1m',SF,s e 2iβ m', SF h m' r m2,sf,s e2 iβ m,sf h m (2.41b (b: (2.6 (2.8 z 2 = 0 b 0 * = b b 0 = 1 E + 2(h m' + h m + ne = m2b[(1+ r 1m' r m'm a 2 L + m/m (r m'm + r 1 m' a 2 L m/m 1 + r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 2 = 0 m2,p L + m/m,px = m2,p L m/m,px = L + m/2,px, m2,s L + m/m,sy = m2,s L m/m,sy = L + m/2,sy, m2,p L + m/m,pz = m2,p L m/m,pz = L + m/2,pz (n m" = n m E + 2 (h m' + h m + ne = b[(1+ r 1m' r m'm a 2 m (r m'm + r 1m' a 2 L + m/2 1+ r 1m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 2 = 0 2 SFG - 24
25 b(1 m r = m'm (1 m r 1m' a 2 L + m/2 1+ r 1 m' r m'm a 2 + (r m'm + r 1m' a 2 r m2 b 2 P * (z 2 = 0 (upper sign for x and y componens, lower sign for z componen (2.25 E + 2,p (h m' + h + m ne = E 0 vis,α E 0 ir,β m'm,vis,α e iβ m',vis h m' (1 + r m2,vis,α e 2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( e iβ m,sf h m { (1 r (1 r m'm,sf,p 1m',SF,p e2iβ m',sf h m' L + m/2,px χ xαβ 1 + r 1m',SF,p r m'm,sf,p e 2iβ m ', SF h m' + (r m'm,sf,p + r 1m',SF,p e 2iβ m',sf h m ' r m2,sf,p e2 iβ m,sf h m e iβ m, SF h m + (1+ r (1+ r m'm,sf,p 1 m',sf,p e2iβ m ', SF h m' L+ m/2,pz χ zαβ 1 + r 1m',SF,p r m'm,sf,p e 2iβ m ', SF h m' + (r m'm,sf,p + r 1m',SF,p e 2 iβ m',sf h m ' r m2,sf,p e2 iβ m,sf h (n m m" = n m (2.42a E + 2,s (h m' + h + m ne = E 0 vis,αe 0 ir,β m'm,vis,α e iβ m',vis h m' (1 + r m2,vis,α e 2 iβ m,vis h m + ( 1 m',ir,β e iβ m',ir h m ' (1+ r (1+ m2,ir,β e2iβ m,ir h m + ( e iβ m,sf h m (1 r m'm,sf,s (1 r 1m',SF,s e2 iβ m',sf h m ' L+ m/2',sy χ yαβ 1+ r 1 m',sf,s r m'm,sf,s e 2 iβ m',sf h m' + (r m'm,sf,s + r 1m',SF,s e 2iβ m', SF h m' r m2,sf,s e2 iβ m,sf h m (2.42b m' SFG ( 2.1 ~ (2.4 a 0 = e ik m' z 1 /cosθ m', a 0 * = e iβ m' h m ' /cosθ m' e ik m ' z 1 /cosθ m' (2.10 ~ (2.17 (2.27 ~ (2.30 h/cosθ z/cosθ β h β z a 0 = e iβ m ' z 1, a 0* = e iβ m' h m ' e iβ m ' z 1 2 SFG - 25
26 P * a = χ aαβ E 0 vis,αe 0 ir,β 1 m',vis,α + ( 1 m',ir,β + ( (a: E + sources (2.1 (2.27 E (0 = m'1 e 2iβ m' h m ' (r m'm + r m2 e 2 iβ m h m L+ * m'/m'p a αβ {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m exp[iz 1 ( β m',sf + β m',vis + β m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' exp[iz 1 ( β m',sf + β m',vis β m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' exp[iz 1 ( β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' exp[iz 1 ( β m',sf β m',vis β m',ir E - sources (2.3 (2.28 E (0 = m'1 (1 + r mm' r m2 e 2iβ m h m L * m'/ m'p a αβ {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m exp[iz 1 (β m',sf + β m',vis + β m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' exp[iz 1 (β m',sf + β m',vis β m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' exp[iz 1 (β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' exp[iz 1 (β m',sf β m',vis β m',ir E + SFG z 1 0 h m' z 1 = 0 h m' E - z 1 h m' 0 z 1 = h m' 0 SFG m'1,p L + m'/m',px = L - 1/m',px, m'1,s L + m'/m',sy = L - 1/m',sy, m'1,p L + m'/m',pz = -L - 1/m',pz (n m" = n m' m'1,p L - m'/m',px = L - 1/m',px, m'1,s L - m'/m',sy = L - 1/m',sy, m'1,p L - m'/m',pz = L - 1/m',pz (n m" = n m' 2 SFG - 26
27 E (0 ne = L /m'p a * αβ i δ {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m [(1+ r mm',sf r m2,sf e 2iβ m,sfh m ei( β m ', SF+β m',vis +β m',ir h m' β m',sf + β m',vis + β m',ir ±(r m'm,sf + r m2,sf e 2 iβ m,sfh m e 2iβ m ', SFh m' e i( β m ', SF+β m',vis+β m',ir h m' β m',sf β m',vis β m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' [(1+ r mm',sf r m2,sf e 2iβ m,sfh m ei( β m ', SF+β m',vis β m', ir h m' β m',sf + β m',vis β m',ir ±(r m'm,sf + r m2,sf e 2 iβ m,sfh m e 2iβ m ', SFh m' e i( β m ', SF+β m',vis β m', ir h m' β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' [(1+ r mm',sf r m2,sf e 2iβ m,sfh m ei( β m ', SF β m ', vis+β m', ir h m' β m',sf β m',vis + β m',ir ±(r m'm,sf + r m2,sf e 2 iβ m,sfh m e 2iβ m ', SFh m' e i( β m ', SF β m ', vis+β m', ir h m' β m',sf + β m',vis β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' [(1+ r mm',sf r m2,sf e 2iβ m,sfh m ei( β m ', SF β m ', vis β m',ir h m' β m',sf β m',vis β m',ir ±(r m'm,sf + r m2,sf e 2 iβ m,sfh m e 2iβ m ', SFh m' ei( β m', SF β m', vis β m ', ir h m' β m',sf + β m',vis + β m',ir (upper sign for x and y componens, lower sign for z componen E (0 p = E 0 vis,α E 0 ir,β αβ i δ 1 m',vis,α + ( 1 m',ir,β + ( {{(1+ r m2,vis,α e 2iβ m, vish m (1+ r m2,ir,β e 2iβ m, irh m [(1+ r mm',sf,p r m2,sf,p e 2iβ m,sfh m ei(β m',sf +β m ', vis+β m',ir h m' β m',sf + β m',vis + β m',ir +(r m'm,sf,p + r m2,sf,p e 2iβ m, SFh m e 2 iβ m',sfh m' e i( β m',sf +β m ', vis+β m', ir h m' β m',sf β m',vis β m',ir 2 SFG - 27
28 +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' [(1+ r mm',sf,p r m2,sf,p e 2iβ m,sfh m ei(β m',sf +β m ', vis β m ', ir h m' β m',sf + β m',vis β m',ir +(r m'm,sf,p + r m2,sf,p e 2iβ m, SFh m e 2 iβ m',sfh m' e i( β m',sf +β m ', vis β m',ir h m' β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' [(1+ r mm',sf,p r m2,sf,p e 2iβ m,sfh m ei(β m',sf β m',vis +β m ', ir h m' β m',sf β m',vis + β m',ir +(r m'm,sf,p + r m2,sf,p e 2iβ m, SFh m e 2 iβ m',sfh m' e i( β m',sf β m',vis+β m',ir h m' β m',sf + β m',vis β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' [(1+ r mm',sf,p r m2,sf,p e 2iβ m,sfh m ei(β m',sf β m',vis β m',ir h m' β m',sf β m',vis β m',ir +(r m'm,sf,p + r m2,sf,p e 2iβ m, SFh m e 2 iβ m',sfh m' e i( β m',sf β m',vis β m', ir h m' L /m',px χ β m',sf + β m',vis + β xαβ m',ir +{(1 + r m2,vis,α e 2iβ m, vish m (1 + r m2,ir,β e 2 iβ m,irh m +[(1 + r mm',sf,p r m2,sf,p e 2iβ m, SFh m ei( β m', SF+β m',vis +β m ', ir h m' β m',sf + β m',vis + β m',ir (r m'm,sf,p + r m2,sf,p e 2 iβ m,sfh m e 2iβ m ', SFh m' e i( β m ', SF+β m',vis+β m',ir h m' β m',sf β m',vis β m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' +[(1 + r mm',sf,p r m2,sf,p e 2iβ m, SFh m ei( β m', SF+β m',vis β m',ir h m' β m',sf + β m',vis β m',ir (r m'm,sf,p + r m2,sf,p e 2 iβ m,sfh m e 2iβ m ', SFh m' e i( β m ', SF+β m',vis β m', ir h m' β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' +[(1 + r mm',sf,p r m2,sf,p e 2iβ m, SFh m ei( β m', SF β m ', vis+β m',ir h m' β m',sf β m',vis + β m',ir (r m'm,sf,p + r m2,sf,p e 2 iβ m,sfh m e 2iβ m ', SFh m' e i( β m ', SF β m ', vis+β m', ir h m' β m',sf + β m',vis β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' +[(1 + r mm',sf,p r m2,sf,p e 2iβ m, SFh m ei( β m', SF β m ', vis β m ', ir h m' β m',sf β m',vis β m',ir (r m'm,sf,p + r m2,sf,p e 2 iβ m,sfh m e 2iβ m ', SFh m' e i( β m ', SF β m ', vis β m',ir h m' β m',sf + β m',vis + β m',ir L /m',pz χ zαβ (n m" = n m' (2.43a 2 SFG - 28
29 E (0 s = E 0 vis,αe 0 ir,β αβ i δ 1 m',vis,α + ( 1 m',ir,β + ( {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m [(1+ r mm',sf,s r m2,sf,s e 2iβ m,sfh m ei(β m',sf +β m ', vis+β m',ir h m' β m',sf + β m',vis + β m',ir +(r m'm,sf,s + r m2,sf,s e 2iβ m, SFh m e 2 iβ m',sfh m' e i( β m',sf +β m ', vis+β m', ir h m' β m',sf β m',vis β m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' [(1+ r mm',sf,s r m2,sf,s e 2iβ m,sfh m ei(β m',sf +β m ', vis β m ', ir h m' β m',sf + β m',vis β m',ir +(r m'm,sf,s + r m2,sf,s e 2iβ m, SFh m e 2 iβ m',sfh m' e i( β m',sf +β m ', vis β m',ir h m' β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' [(1+ r mm',sf,s r m2,sf,s e 2iβ m,sfh m ei(β m',sf β m',vis +β m ', ir h m' β m',sf β m',vis + β m',ir +(r m'm,sf,s + r m2,sf,s e 2iβ m, SFh m e 2 iβ m',sfh m' e i( β m',sf β m',vis+β m',ir h m' β m',sf + β m',vis β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' [(1+ r mm',sf,s r m2,sf,s e 2iβ m,sfh m ei(β m',sf β m',vis β m',ir h m' β m',sf β m',vis β m',ir +(r m'm,sf,s + r m2,sf,s e 2iβ m, SFh m e 2 iβ m',sfh m' e i( β m',sf β m',vis β m', ir h m' β m',sf + β m',vis + β m',ir L /m',syχ yαβ (2.43b (b: E + sources (2.2 (2.27 E + 2(h m' + h + m = m2 e iβ m' h m' m'm L + * m'/m'p a αβ {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m exp[iz 1 ( β m',sf + β m',vis + β m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' exp[iz 1 ( β m',sf + β m',vis β m',ir 2 SFG - 29
30 +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' exp[iz 1 ( β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' exp[iz 1 ( β m',sf β m',vis β m',ir E - sources (2.4 (2.28 E + 2(h m' + h + m = m2 e iβ m' h m' r m'1 m'm L * m'/m'p a αβ {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m exp[iz 1 (β m',sf + β m',vis + β m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' exp[iz 1 (β m',sf + β m',vis β m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' exp[iz 1 (β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' exp[iz 1 (β m',sf β m',vis β m',ir E + SFG z 1 0 h m' z 1 = 0 h m' E - SFG z 1 h m' 0 z 1 = h m' 0 m'm,p L + m'/m',px = L + m'/m,px, m'm,s L + m'/m',sy = L + m'/m,sy, m'm,p L + m'/m',pz = L + m'/m,pz (n m" = n m' m'm,p L - m'/m',px = L + m'/m,px, m'm,s L - m'/m',sy = L + m'/m,sy, m'm,p L - m'/m',pz = -L + m'/m,pz (n m" = n m' E + 2(h m' + h + m = m2 e i( β m' h m' +β m h m L + * i m'/mp a δ αβ {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m [ ei( β m',sf +β m', vis+β m',ir h m ' β m',sf β m',vis β m',ir ± r m'1 e i( βm ', SF+βm',vis+βm',ir hm ' β m',sf + β m',vis + β m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' [ ei( β m',sf +β m', vis β m ', ir h m' β m',sf β m',vis + β m',ir ± r m'1 e i( β m',sf +βm ', vis β m',ir hm ' β m',sf + β m',vis β m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' [ ei( β m',sf β m',vis +β m ', ir h m' β m',sf + β m',vis β m',ir ± r m'1 e i( β m',sf β m',vis+βm',ir hm ' β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' 2 SFG - 30
31 [ ei( β m',sf β m',vis β m',ir h m ' β m',sf + β m',vis + β m',ir ± r m'1 e i( βm ', SF βm ', vis β m',ir hm ' β m',sf β m',vis β m',ir (upper sign for x and y componens, lower sign for z componen E + 2 p (h m' + h + m = E 0 vis,α E 0 ir,β m2 e i( β m ' h m' +β m h m i δ αβ 1 m',vis,α + ( 1 m',ir,β + ( {{(1+ r m2,vis,α e 2iβ m, vish m (1+ r m2,ir,β e 2iβ m, irh m [ ei( β m',sf +β m', vis+β m',ir h m ' β m',sf β m',vis β m',ir + r m'1,sf,p e i( β m',sf +βm ', vis+βm', ir hm' β m',sf + β m',vis + β m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' [ ei( β m',sf +β m', vis β m ', ir h m' β m',sf β m',vis + β m',ir + r m'1,sf,p e i( βm ', SF+βm',vis βm', ir hm' β m',sf + β m',vis β m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' [ ei( β m',sf β m',vis +β m ', ir h m' β m',sf + β m',vis β m',ir + r m'1,sf,p e i( βm ', SF βm ', vis+βm', ir hm' β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' [ ei( β m',sf β m',vis β m',ir h m ' β m',sf + β m',vis + β m',ir + r m'1,sf,p e i( β m',sf β m',vis βm', ir hm' β m',sf β m',vis β m',ir L + m'/m,px χ xαβ +{(1 + r m2,vis,α e 2iβ m, vish m (1 + r m2,ir,β e 2 iβ m,irh m [ ei( β m',sf +β m', vis+β m',ir h m ' β m',sf β m',vis β m',ir r m'1,sf,p e i( βm ', SF+βm',vis+βm',ir hm' β m',sf + β m',vis + β m',ir +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' [ ei( β m',sf +β m', vis β m ', ir h m' β m',sf β m',vis + β m',ir r m'1,sf,p e i( β m',sf +βm ', vis β m',ir hm' β m',sf + β m',vis β m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' [ ei( β m',sf β m',vis +β m ', ir h m' β m',sf + β m',vis β m',ir r m'1,sf,p e i( β m',sf β m',vis+βm',ir hm' β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' 2 SFG - 31
32 [ ei( β m',sf β m',vis β m',ir h m ' β m',sf + β m',vis + β m',ir r m'1,sf,p e i( βm ', SF βm ', vis β m',ir hm' β m',sf β m',vis β m',ir L + m'/m,pz χ zαβ (n m" = n m' (2.44a E + 2s (h m' + h m + = E 0 vis,αe 0 ir,β m2 e i( β m' h m' +β m h m αβ 1 m',vis,α + ( 1 m',ir,β + ( {(1+ r m2,vis,α e 2 iβ m,vish m (1+ r m2,ir,β e 2iβ m, irh m [ ei( β m',sf +β m', vis+β m',ir h m ' β m',sf β m',vis β m',ir + r m'1,sf,s e i( βm ', SF+βm',vis+βm',ir hm' β m',sf + β m',vis + β m',ir i δ +(1 + r m'm,vis,α r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2iβ m ', irh m' [ ei( β m',sf +β m', vis β m ', ir h m' β m',sf β m',vis + β m',ir + r m'1,sf,s e i( β m',sf +βm ', vis β m',ir hm' β m',sf + β m',vis β m',ir +( + r m2,vis,α e 2 iβ m,vish m (1 + r m2,ir,β e 2iβ m, irh m e 2iβ m ', vish m ' [ ei( β m',sf β m',vis +β m ', ir h m' β m',sf + β m',vis β m',ir + r m'1,sf,s e i( β m',sf β m',vis+βm',ir hm' β m',sf β m',vis + β m',ir +( + r m2,vis,α e 2 iβ m,vish m ( + r m2,ir,β e 2iβ m, irh m e 2i(β m',vis +β m ', ir h m' [ ei( β m',sf β m',vis β m',ir h m ' β m',sf + β m',vis + β m',ir + r m'1,sf,s e i( βm ', SF βm ', vis β m',ir hm' β m',sf β m',vis β m',ir L + m'/m,syχ yαβ (2.44b m SFG (2.5 ~ (2.8 b 0 = e ik m z 2 /cosθ m, P * a = χ aαβ E 0 vis,αe 0 ir,β b 0* = e iβ m h m /cosθ m e ik m z 2 /cosθ m 1 m',vis,α m'm,vis,α e iβ m ', vis h m' + ( 1m',ir,β m'm,ir,β e iβ m',ir h m ' + ( (a: E + sources (2.5 ( SFG - 32
33 E (0 = m'1 mm' r m2 e iβ m ' h m' e 2iβ m h m L+ * m/mp a αβ {exp[iz 2 ( β m,sf + β m,vis + β m,ir + r m2,ir,β e 2iβ m, irh m exp[iz 2 ( β m,sf + β m,vis β m,ir +r m2,vis,α e 2 iβ m,vish m exp[iz 2 ( β m,sf β m,vis + β m,ir +r m2,vis,α r m2,ir,β e 2i(β m,ir +β m, vis h m exp[iz 2 ( β m,sf β m,vis β m,ir E - sources (2.7 (2.30 E (0 = m'1 mm' e iβ m' h m' L * m/mp a αβ {exp[iz 2 (β m,sf + β m,vis + β m,ir + r m2,ir,β e 2iβ m, irh m exp[iz 2 (β m,sf + β m,vis β m,ir +r m2,vis,α e 2 iβ m,vish m exp[iz 2 (β m,sf β m,vis + β m,ir +r m2,vis,α r m2,ir,β e 2i(β m,ir +β m, vis h m exp[iz 2 (β m,sf β m,vis β m,ir E + SFG z 2 0 h m z 2 = 0 h m E - SFG z 2 h m 0 z 2 = h m 0 mm', p L + m/m,px = L - m'/m,px, mm',s L + m/m,sy = L - m'/m,sy, mm',p L + m/m'pz = -L - m'/m,pz (n m" = n m mm', p L - m/m,px = L - m'/m,px, mm',s L - m/m,sy = L - m'/m,sy, mm',p L - m/m'pz = L - m'/m,pz (n m" = n m E (0 = m'1 e iβ m' h m' L * i m'/ mp a δ αβ {[ ei( β m, SF+β m,vis +β m, ir h m β m,sf + β m,vis + β m,ir ± r m2 e 2 iβ m,sfh m e i( βm, SF+βm,vis +βm, ir hm β m,sf β m,vis β m,ir +r m2,ir,β e 2iβ m,ir h m [ ei( β m, SF+β m,vis β m, ir h m β m,sf + β m,vis β m,ir ± r m2 e 2iβ m,sfh m e i( βm,sf +βm, vis β m,ir hm β m,sf β m,vis + β m,ir +r m2,vis,α e 2 iβ m,vish m [ ei( β m,sf β m, vis+β m,ir h m β m,sf β m,vis + β m,ir ± r m2 e 2iβ m, SFh m e i( βm, SF βm, vis+βm, ir hm β m,sf + β m,vis β m,ir +r m2,vis,α r m2,ir,β e 2i(β m,vis +β m, ir h m [ ei( β m, SF β m, vis β m, ir h m β m,sf β m,vis β m,ir ± r m2 e 2 iβ m,sfh m e i( βm, SF βm, vis wβm, ir hm β m,sf + β m,vis + β m,ir (upper sign for x and y componens, lower sign for z componen E (0 p = E 0 vis,α E 0 ir,β m'1,sf,p e i( β m ', SF+β m',vis +β m',ir h m' i αβ δ 2 SFG - 33
34 1 m',vis,α m'm,vis,α + ( 1 m',ir,β m'm,ir,β + ( {{[ ei( β m, SF+β m,vis+β m,ir h m β m,sf + β m,vis + β m,ir + r m2,sf,p e 2iβ m, SFh m e i( β m,sf +βm, vis+βm,ir hm β m,sf β m,vis β m,ir +r m2,ir,β e 2iβ m,ir h m [ ei( β m, SF+β m,vis β m, ir h m β m,sf + β m,vis β m,ir + r m2,sf,p e 2iβ m, SFh m e i( βm, SF+βm,vis β m, ir hm β m,sf β m,vis + β m,ir +r m2,vis,α e 2 iβ m,vish m [ ei( β m,sf β m, vis+β m,ir h m β m,sf β m,vis + β m,ir + r m2,sf,p e 2iβ m,sfh m e i( βm,sf β m,vis+βm,ir hm β m,sf + β m,vis β m,ir +r m2,vis,α r m2,ir,β e 2i(β m,vis +β m, ir h m [ ei( β m, SF β m, vis β m,ir h m + r β m,sf β m,vis β m2,sf,p e 2iβ m,sfh m e i( β m,sf β m,vis wβ m, ir hm L m'/m,px χ m,ir β m,sf + β m,vis + β xαβ m,ir {{[ ei( β m, SF+β m,vis+β m,ir h m β m,sf + β m,vis + β m,ir r m2,sf,p e 2iβ m,sfh m e i( βm, SF+βm,vis +βm, ir hm β m,sf β m,vis β m,ir +r m2,ir,β e 2iβ m,ir h m [ ei( β m, SF+β m,vis β m, ir h m β m,sf + β m,vis β m,ir r m2,sf,p e 2iβ m,sfh m e i( β m,sf +βm, vis βm,ir hm β m,sf β m,vis + β m,ir +r m2,vis,α e 2 iβ m,vish m [ ei( β m,sf β m, vis+β m,ir h m β m,sf β m,vis + β m,ir r m2,sf,p e 2iβ m, SFh m e i( βm, SF βm, vis+βm, ir hm β m,sf + β m,vis β m,ir +r m2,vis,α r m2,ir,β e 2i(β m,vis +β m, ir h m [ ei( β m, SF β m, vis β m,ir h m β m,sf β m,vis β m,ir r m2,sf,p e 2iβ m, SFh m e i( βm, SF βm, vis wβm,ir hm β m,sf + β m,vis + β m,ir L m'/m,pz χ zαβ (n m" = n m (2.45a E (0 s = E 0 vis,αe 0 ir,β m'1,sf,s e i( β m ', SF+β m',vis +β m',ir h m' i αβ δ 1 m',vis,α m'm,vis,α + ( 1 m',ir,β m'm,ir,β + ( {[ ei( β m, SF+β m,vis +β m, ir h m β m,sf + β m,vis + β m,ir + r m2,sf,s e 2 iβ m,sfh m e i( βm,sf +βm,vis +βm, ir hm β m,sf β m,vis β m,ir +r m2,ir,β e 2iβ m,ir h m [ ei( β m, SF+β m,vis β m, ir h m β m,sf + β m,vis β m,ir + r m2,sf,s e 2iβ m,sfh m e i( β m,sf +βm, vis βm,ir hm β m,sf β m,vis + β m,ir +r m2,vis,α e 2 iβ m,vish m [ ei( β m,sf β m, vis+β m,ir h m β m,sf β m,vis + β m,ir + r m2,sf,s e 2iβ m, SFh m e i( βm, SF βm, vis+βm, ir hm β m,sf + β m,vis β m,ir +r m2,vis,α r m2,ir,β e 2i(β m,vis +β m, ir h m [ ei( β m, SF β m, vis β m,ir h m β m,sf β m,vis β m,ir + r m2,sf,s e 2iβ m, SFh m e i( βm, SF βm, vis wβm,ir hm β m,sf + β m,vis + β m,ir L m'/m,syχ yαβ (2.45b 2 SFG - 34
封面(JP)
4881 Murietta Street. hino,. 9.11.2 Printed in Taiwan MS-01-R1-JP IR MOTOR STG S series MS series MMS series S series S-series 4 1 S-PM-4/ 2 2 8 2 2 S-P-X2/4 8 2 8 00 14 2 S-P-X2/4/ 8 2 10 1490 01 02 S
さくらの個別指導 ( さくら教育研究所 ) A a 1 a 2 a 3 a n {a n } a 1 a n n n 1 n n 0 a n = 1 n 1 n n O n {a n } n a n α {a n } α {a
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SFGÇÃÉXÉyÉNÉgÉãå`.pdf
SFG 1 SFG SFG I SFG (ω) χ SFG (ω). SFG χ χ SFG (ω) = χ NR e iϕ +. ω ω + iγ SFG φ = ±π/, χ φ = ±π 3 χ SFG χ SFG = χ NR + χ (ω ω ) + Γ + χ NR χ (ω ω ) (ω ω ) + Γ cosϕ χ NR χ Γ (ω ω ) + Γ sinϕ. 3 (θ) 180
6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P
6 x x 6.1 t P P = P t P = I P P P 1 0 1 0,, 0 1 0 1 cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ x θ x θ P x P x, P ) = t P x)p ) = t x t P P ) = t x = x, ) 6.1) x = Figure 6.1 Px = x, P=, θ = θ P
4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P = 90, = ( ) = X
4 4. 4.. 5 5 0 A P P P X X X X +45 45 0 45 60 70 X 60 X 0 P P 4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P 0 0 + 60 = 90, 0 + 60 = 750 0 + 60 ( ) = 0 90 750 0 90 0
> > <., vs. > x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D > 0 x (2) D = 0 x (3
13 2 13.0 2 ( ) ( ) 2 13.1 ( ) ax 2 + bx + c > 0 ( a, b, c ) ( ) 275 > > 2 2 13.3 x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D >
4 R f(x)dx = f(z) f(z) R f(z) = lim R f(x) p(x) q(x) f(x) = p(x) q(x) = [ q(x) [ p(x) + p(x) [ q(x) dx =πi Res(z ) + Res(z )+ + Res(z n ) Res(z k ) k
f(x) f(z) z = x + i f(z). x f(x) + R f(x)dx = lim f(x)dx. R + f(x)dx = = lim R f(x)dx + f(x)dx f(x)dx + lim R R f(x)dx Im z R Re z.: +R. R f(z) = R f(x)dx + f(z) 3 4 R f(x)dx = f(z) f(z) R f(z) = lim R
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85 4 86 Copright c 005 Kumanekosha 4.1 ( ) ( t ) t, t 4.1.1 t Step! (Step 1) (, 0) (Step ) ±V t (, t) I Check! P P V t π 54 t = 0 + V (, t) π θ : = θ : π ) θ = π ± sin ± cos t = 0 (, 0) = sin π V + t +V
#A A A F, F d F P + F P = d P F, F y P F F x A.1 ( α, 0), (α, 0) α > 0) (x, y) (x + α) 2 + y 2, (x α) 2 + y 2 d (x + α)2 + y 2 + (x α) 2 + y 2 =
#A A A. F, F d F P + F P = d P F, F P F F A. α, 0, α, 0 α > 0, + α +, α + d + α + + α + = d d F, F 0 < α < d + α + = d α + + α + = d d α + + α + d α + = d 4 4d α + = d 4 8d + 6 http://mth.cs.kitmi-it.c.jp/
1 3 1.1.......................... 3 1............................... 3 1.3....................... 5 1.4.......................... 6 1.5........................ 7 8.1......................... 8..............................
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![( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e](/thumbs/98/136160482.jpg "( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e")
( ) Note 3 19 12 13 8 8.1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R, µ R, τ R (1a) L ( ) ) * 3) W Z 1/2 ( - )
春期講座 ~ 極限 1 1, 1 2, 1 3, 1 4,, 1 n, n n {a n } n a n α {a n } α {a n } α lim n an = α n a n α α {a n } {a n } {a n } 1. a n = 2 n {a n } 2, 4, 8, 16,
春期講座 ~ 極限 1 1, 1 2, 1 3, 1 4,, 1 n, n n {a n } n a n α {a n } α {a n } α lim an = α n a n α α {a n } {a n } {a n } 1. a n = 2 n {a n } 2, 4, 8, 16, 32, n a n {a n } {a n } 2. a n = 10n + 1 {a n } lim an
SO(3) 49 u = Ru (6.9), i u iv i = i u iv i (C ) π π : G Hom(V, V ) : g D(g). π : R 3 V : i 1. : u u = u 1 u 2 u 3 (6.10) 6.2 i R α (1) = 0 cos α
SO(3) 48 6 SO(3) t 6.1 u, v u = u 1 1 + u 2 2 + u 3 3 = u 1 e 1 + u 2 e 2 + u 3 e 3, v = v 1 1 + v 2 2 + v 3 3 = v 1 e 1 + v 2 e 2 + v 3 e 3 (6.1) i (e i ) e i e j = i j = δ ij (6.2) ( u, v ) = u v = ij
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51 5 5.1 5.1.1 P r P z θ P P P z e r e, z ) r, θ, ) 5.1 z r e θ,, z r, θ, = r sin θ cos = r sin θ sin 5.1) e θ e z = r cos θ r, θ, 5.1: 0 r
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第3章
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知能科学：ニューラルネットワーク
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知能科学：ニューラルネットワーク
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高等学校学習指導要領解説 数学編
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