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G(ω) = G0+Pn

k=1

akiω

iω+bk

G(ω) = G0+G∞(iωτ)β

1+(iωτ )β

G(ω) = G0h1 + Pkαk−ω2+2iξkωkω

−ω2+2iξkωkω+ω2

ki

G(ω) = G0h1 + Pn

k=1 ∆kω2+iωΩk

ω2+Ω2

ki

G(ω) = G0h1 + η1−e−st0

st0i

G(ω) = G0h1 + η1+2(st0/π)2−e−st0

1+2(st0/π)2i

G(ω) = G0h1 + η eω2/4µn1−erf iω

2√µoi

µ

Es

|E(ω)|=ESsµ2+ω2(1 + )2

µ2+ω2

φ

φE(ω)= tan−1µω

µ2+ω2(1 + )

|E(ω)| → ESµ→ ∞ |E(ω)| → ES(1 + )µ→0∀ω > 0

|E(ω)| → ESω→0|E(ω)| → ES(1 + )ω→ ∞ ∀µ > 0

φE(ω)→0µ→ ∞ φE(ω)→0µ→0∀ω > 0

φE(ω)→0ω→0φE(ω)→0ω→ ∞ ∀µ > 0

µ→ ∞ ω→0

µ→0ω→ ∞

l1l2l3α β γ Es

E1eq =t3

L

n

X

j=1

m

P

i=1

(l1ij cos αij −l2ij cos βij)

m

P

i=1

l2

1ijl2

2ij (l1ij +l2ij) (cos αij sin βij −sin αij cos βij )2

Esij((l1ij cos αij −l2ij cos βij )2)

E2eq =Lt3

n

P

j=1

m

P

i=1

(l1ij cos αij −l2ij cos βij)

m

P

i=1

Esij l2

3ij cos2γij l3ij +l1ij l2ij

l1ij +l2ij +l2

1ij l2

2ij (l1ij +l2ij ) cos2αij cos2βij

(l1ij cos αij −l2ij cos βij )2−1

ν12eq =−1

L

n

X

j=1

m

P

i=1

(l1ij cos αij −l2ij cos βij)

m

P

i=1

(cos αij sin βij −sin αij cos βij)

cos αij cos βij

ν21eq =−L

n

P

j=1

m

P

i=1

(l1ij cos αij −l2ij cos βij)

m

P

i=1

l2

1ijl2

2ij (l1ij +l2ij) cos αij cos βij (cos αij sin βij −sin αij cos βij )

(l1ij cos αij −l2ij cos βij)2l2

3ij cos2γij l3ij +l1ij l2ij

l1ij +l2ij +l2

1ij l2

2ij (l1ij +l2ij ) cos2αij cos2βij

(l1ij cos αij −l2ij cos βij )2

G12eq =Lt3

n

P

j=1

m

P

i=1

(l1ij cos αij −l2ij cos βij)

m

P

i=1

Esij l2

3ij sin2γij l3ij +l1ij l2ij

l1ij +l2ij −1

Esij

t

L i j

i= 1,2,3, ..., m j = 1,2,3, ..., n

m n

ij

ith jth

Es

Esij Esij 1 + ij

iω

µij + iω

E1v(ω) = t3

L

n

X

j=1

m

P

i=1

(l1ij cos αij −l2ij cos βij)

m

P

i=1

l2

1ijl2

2ij (l1ij +l2ij) (cos αij sin βij −sin αij cos βij )2

Esij 1 + ij

iω

µij + iω((l1ij cos αij −l2ij cos βij)2)

E2v(ω) = Lt3

n

P

j=1

m

P

i=1

(l1ij cos αij −l2ij cos βij)

m

P

i=1

Esij 1 + ij

iω

µij + iωl2

3ij cos2γij l3ij +l1ij l2ij

l1ij +l2ij +l2

1ij l2

2ij (l1ij +l2ij ) cos2αij cos2βij

(l1ij cos αij −l2ij cos βij )2−1

G12v(ω) = Lt3

n

P

j=1

m

P

i=1

(l1ij cos αij −l2ij cos βij)

m

P

i=1

Esij 1 + ij

iω

µij + iωl2

3ij sin2γij l3ij +l1ij l2ij

l1ij +l2ij −1

L=n(h+lsin θ)l1ij =l2ij =l3ij =l αij =θ βij = 180◦−θ γij = 90◦

i j

E1v=κ1t

l3cos θ

(h

l+ sin θ) sin2θ

E2v=κ2t

l3(h

l+ sin θ)

cos3θ

G12v=κ2t

l3h

l+ sin θ

h

l2(1 + 2h

l) cos θ

κ1κ2

κ1=m

n

n

X

j=1

1

m

P

i=1

1

Esij 1 + ij

iω

µij + iω

κ2=n

m

1

n

P

j=1

1

m

P

i=1

Esij 1 + ij

iω

µij + iω

κ1κ2

ω→0

Esij =Es

µij =µ ij = i = 1,2,3, ..., m j = 1,2,3, ..., n κ1

κ2Es

Esij =Esµij =µ ij = i = 1,2,3, ..., m j = 1,2,3, ..., n

E1v=ES1 + iω

µ+ iωζ1

E2v=ES1 + iω

µ+ iωζ2

G12v=ES1 + iω

µ+ iωζ3

ζi(i= 1,2,3)

ζ1=t3

L

n

X

j=1

m

P

i=1

(l1ij cos αij −l2ij cos βij)

m

P

i=1

l2

1ijl2

2ij (l1ij +l2ij) (cos αij sin βij −sin αij cos βij )2

(l1ij cos αij −l2ij cos βij)2

ζ2=Lt3

n

P

j=1

m

P

i=1

(l1ij cos αij −l2ij cos βij)

m

P

i=1 l2

3ij cos2γij l3ij +l1ij l2ij

l1ij +l2ij +l2

1ij l2

2ij (l1ij +l2ij ) cos2αij cos2βij

(l1ij cos αij −l2ij cos βij )2−1

ζ3=Lt3

n

P

j=1

m

P

i=1

(l1ij cos αij −l2ij cos βij)

m

P

i=1 l2

3ij sin2γij l3ij +l1ij l2ij

l1ij +l2ij −1

|E1v|=Esζ1sµ2+ω2(1 + )2

µ2+ω2

|E2v|=Esζ2sµ2+ω2(1 + )2

µ2+ω2

|G12v|=Esζ3sµ2+ω2(1 + )2

µ2+ω2

φ

φE1v=φE2v=φG12v= tan−1µω

µ2+ω2(1 + )

ω→0

L=n(h+lsin θ)l1ij =l2ij =l3ij =l αij =θ βij = 180◦−θ γij = 90◦i j

µ→0µ→ ∞ ω→0ω→ ∞

|E1v| → ESζ1µ→ ∞ |E1v| → ES(1 + )ζ1µ→0∀ω > 0

|E1v| → ESζ1ω→0|E1v| → ES(1 + )ζ1ω→ ∞ ∀µ > 0

|E2v| → ESζ2µ→ ∞ |E2v| → ES(1 + )ζ2µ→0∀ω > 0

|E2v| → ESζ2ω→0|E2v| → ES(1 + )ζ2ω→ ∞ ∀µ > 0

|G12v| → ESζ3µ→ ∞ |G12v| → ES(1 + )ζ3µ→0∀ω > 0

|G12v| → ESζ3ω→0|G12v| → ES(1 + )ζ3ω→ ∞ ∀µ > 0

φE1v, φE2v, φG12v→0µ→ ∞

φE1v, φE2v, φG12v→0µ→0∀ω > 0

φE1v, φE2v, φG12v→0ω→0

φE1v, φE2v, φG12v→0ω→ ∞ ∀µ > 0

L=n(h+lsin θ)l1ij =l2ij =l3ij =l

αij =θ βij = 180◦−θ γij = 90◦i j

Esij =Esµij =µ ij =

i= 1,2,3, ..., m j = 1,2,3, ..., n

E1v=Es1 + iω

µ+ iωt

l3cos θ

(h

l+ sin θ) sin2θ

E2v=Es1 + iω

µ+ iωt

l3(h

l+ sin θ)

cos3θ

G12v=Es1 + iω

µ+ iωt

l3h

l+ sin θ

h

l2(1 + 2h

l) cos θ

|E1v|=Essµ2+ω2(1 + )2

µ2+ω2t

l3cos θ

(h

l+ sin θ) sin2θ

|E2v|=Essµ2+ω2(1 + )2

µ2+ω2t

l3(h

l+ sin θ)

cos3θ

|G12v|=Essµ2+ω2(1 + )2

µ2+ω2t

l3h

l+ sin θ

h

l2(1 + 2h

l) cos θ

φ

φE1v=φE2v=φG12v= tan−1µω

µ2+ω2(1 + )

ω→0µ→0µ→ ∞ ω→0ω→ ∞

|E1v| → ESt

l3cos θ

(h

l+ sin θ) sin2θµ→ ∞

|E1v| → ES(1 + )t

l3cos θ

(h

l+ sin θ) sin2θµ→0∀ω > 0

|E1v| → ESt

l3cos θ

(h

l+ sin θ) sin2θω→0

|E1v| → ES(1 + )t

l3cos θ

(h

l+ sin θ) sin2θω→ ∞ ∀µ > 0

|E2v| → ESt

l3(h

l+ sin θ)

cos3θµ→ ∞

|E2v| → ES(1 + )t

l3(h

l+ sin θ)

cos3θµ→0∀ω > 0

|E2v| → ESt

l3(h

l+ sin θ)

cos3θω→0

|E2v| → ES(1 + )t

l3(h

l+ sin θ)

cos3θω→ ∞ ∀µ > 0

|G12v| → ESt

l3h

l+ sin θ

h

l2(1 + 2h

l) cos θµ→ ∞

|G12v| → ES(1 + )t

l3h

l+ sin θ

h

l2(1 + 2h

l) cos θµ→0∀ω > 0

|G12v| → ESt

l3h

l+ sin θ

h

l2(1 + 2h

l) cos θω→0

|G12v| → ES(1 + )t

l3h

l+ sin θ

h

l2(1 + 2h

l) cos θω→ ∞ ∀µ > 0

φE1v, φE2v, φG12v→0µ→ ∞

φE1v, φE2v, φG12v→0µ→0∀ω > 0

φE1v, φE2v, φG12v→0ω→0

φE1v, φE2v, φG12v→0ω→ ∞ ∀µ > 0

θ= 30◦

E1v=E2v= 2.3ES1 + iω

µ+ iωt

l3

θ= 30◦

G12v= 0.57ES1 + iω

µ+ iωt

l3

bybz

σ2

H

λiψi(y2, z2) = Za1

−a1Za2

−a2

ΓH(y1, z1;y2, z2)ψi(y1, z1)dy1dz1

−a16y6a1−a26z6a2

ψi(y2, z2) = ψ(y)

i(y2)ψ(z)

i(z2)

λi(y2, z2) = λ(y)

i(y2)λ(z)

i(z2)

λ(y)

iψ(y)

i(y1) = Za1

−a1

e(−|y1−y2|/by)ψ(y)

i(y2)dy2

ψi(ζ) = cos(ωiζ)

qa+sin(2ωia)

2ωi

λi=2σ2

Hb

ω2

i+b2i

ψi(ζ) = sin(ω∗

iζ)

qa−sin(2ω∗

ia)

2ωi∗

λ∗

i=2σ2

Hb

ω∗2

i+b2i

b= 1/by1/bza=a1a2ζ ωiωi∗

b−ωitan(ωia)=0 ωi+btan(ωia)=0

θ= 30◦h

l= 1 θ= 30◦h

l= 1.5

θ= 45◦h

l= 1 θ= 45◦h

l= 1.5

E1

θ= 30◦h

l= 1 θ= 30◦h

l= 1.5

θ= 45◦h

l= 1 θ= 45◦h

l= 1.5

E2

θ= 30◦h

l= 1 θ= 30◦h

l= 1.5

θ= 45◦h

l= 1 θ= 45◦h

l= 1.5

ν12

θ= 30◦h

l= 1 θ= 30◦h

l= 1.5

θ= 45◦h

l= 1 θ= 45◦h

l= 1.5

ν21

E1

E2

G12

θ= 30◦h/l = 1 r= 0 r= 2 r= 4 r= 6

θ= 30◦h/l = 1 r= 6

E1

r= 3 r= 6

E2

r= 3 r= 6

G12

r= 3 r= 6

r= 3

r= 6

E1

r= 3 r= 6

E2

r= 3 r= 6

G12

r= 3 r= 6

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