φ(t)

∼

∼

TE0

φ(z)

φ(z)

φ(z)

φ(z)

η(λ)

G(z,λ)

λ

φ(z)

η(λ)

η(λ) =

tCIGS∫

0

G(z,λ)φ(z)dz

tCIGS

η(λ) φ(z)

0 ≤ z < zSCR

ϕ(z) = 1

zSCR ≤ z ≤ zMo

ϕ(z) =

(1

Leff[ z−zMo

Leff]− SMo

D [ z−zMoLeff

])

1Leff

[ zMo−zSCRLeff

] + SMoD [ zMo−zSCR

Leff]

zMo zSCR

Leff

SMo

φ(z)

φ(z)

(η(λ))

b

bnoiseless

bmeas

bnoiseless

bmeas b± η η

bnoiseless

b b

bmeas

µm

µm

J

J − 1

Uj Vj xj

n = n + ik

xj−1

⎛

⎜⎝Uj−1

Vj−1

⎞

⎟⎠ = Mj

⎛

⎜⎝Uj

Vj

⎞

⎟⎠

Mj

Mj =

⎛

⎜⎝Φj

−iγj

Φj

−iγj Φj Φj

⎞

⎟⎠

Φj = kαj(xj − xj−1)

α = n θ = (n2 − β2)1/2

β = n θ.

γ

α/z0 Ez −Hy Hx Hz = Ey = Ex = 0αz0/n2 Hz Ey −Ex Ez = Hy = Hx = 0

γ, U, V,W

M =J∏

j=1

Mj =

⎛

⎜⎝m11 m12

m21 m22

⎞

⎟⎠

χM(β) = γcm11 + γcγsm12 +m21 + γsm22 = 0

β

P3HT : PCBM

λ

P3HT : PCBM

P3HT : PCBM

P3HT : PCBM

TM0

TM0

TM0

TM0

nTop nBot = = 0

= 100

TM0 TE0

P3HT : PCBMnTop nBot kTop kBot nTop kTop

TE0 TM0

P3HT : PCBMtglass tIT0

tTop tBot tAl

TM0

TE0 TE0

P3HT TM0

TE0

( = 100

TM0 TE0

( = 100 )

(| |2) TE0 TM0

P3HT : PCBM

= = 3.5 = 3.5

= 1.8, = 1.8 = 1.8 ktop kbot

| |2

(| |2)

= = 3.5 TE0

TM0

TE0

TE0

TM0

TM0

(| |2) λ =500

P3HT : PCBM= = 3.5 = 3.5

= 1.8, = 1.8 nTop

kTop kBot TE0

TM0

| |2

TM0

= 1.8, = 1.8 = 1.8

TE0

TM0

TiO2(n = 2.6) V2O5(n = 2.3)

= 100

TM0 TE0

T iO2

P3HT : PCBM V2O5 nTop nBot kTop kBot TE0

TM0

P3HT : PCBMtglass tIT0

tTop tBot tAu

TiO2 V2O5

β = 1.85 β = 1.67

β = 1.84 β = 1.70

TiO2 V2O5

TEM

TMM

TECal

TMCal

TE0

Cu(In,Ga)Se2

φ(z)

φ(z)

φ(z)

φ(z)

η(λ)

φ(z)

φ(z)

G(z,λ)

λ

φ(z) η(λ)

η(λ) =

tCIGS∫

0

G(z,λ)φ(z)dz

tCIGS

G(z,λ) = 0 z < 0 z > tCIGS G(z,λ)

G(z,λ)

G(z,λ)

η(λ)

φ(z)

0 ≤ z < zSCR

ϕ(z) = 1

zSCR ≤ z ≤ zMo

ϕ(z) =

(1

Leff[ z−zMo

Leff]− SMo

D [ z−zMoLeff

])

1Leff

[ zMo−zSCRLeff

] + SMoD [ zMo−zSCR

Leff]

zMo zSCR

Leff

SMo

φ(z) η(λ)

G(z,λ)

φ(z)

zm0 = 2300nm zSCR = 350nm Leff = 900nm SMo/D = 4× 103cm−1

φ G(z,λ)

η(λ) λ

x1 Leff

x2 SMo/D

x1 x2

J(x1, x2) =∑

λ

⎡

⎣tCIGS∫

0

G(z,λ)ϕ(z, x1, x2)dz − η(λ)

⎤

⎦2

Leff SMo/D 2(F (x1, x2))

x1 x2

x1 = 890nm x2 = 4.1× 103cm−1

xj = xj − α∂

∂xjJ(x1, x2) for j = 1 and j = 2

x1 = 899.980nm x2 = 3.997× 103cm−1

Leff

SMo/D 2(J(x1, x2))

φ(z) zm0 = 2300nm

zSCR = 350nm Leff = 920nm

SMo/D = 4.3× 103cm−1

φ(z)

G(z,λ)

φ(z) Cu(In,Ga)Se2

φ(z)

(η(λ))

φ(z)

G(z,λ) G(z,λ)

G(z,λ)

η(λ)

λi, i = 1, ...N ηi = η(λi)

φ(z)

φj (tj−1, tj) t0 = 0

ηi =N∑

j=1

Gijφj i = 1, . . . , N

Gij =

∫ ti

tj−1

G(z, λi)dz

G ∈ RN×N

G = UΣV T =N∑

i=1

uiσivTi

∑∈ RN×N

∑= diag(σ1, . . . , σn), σ1 ≥ σ2 ≥ · · · ≥ σn ≥ 0

U ∈ RN×N V ∈ RN×N

U = (u1, . . . , uN), V = (v1, . . . , vN)

φ

φ = G−1η =N∑

i=1

uTi η

σivi

φ uTi η

σi

uTi η σi

φk

φk =k∑

i=1

uTi η

σivi

uTi η

σi

G(z,λ)

φ(z) 0 < z < tCIGS tCIGS

φ(z) φ(z) = 1 0 < z < zSCR

zSCR

φ(z) = exp[−(z − zSCR)/L]

φ G(z,λ)

η(λ)

λ

uTi η uT

i η/σi

φ(z)

φ

G−1

η(λ)

φ

φ

G

b

bnoiseless

bmeas bnoiseless

bmeas

b± η η

bnoiseless

b

b

bmeas

f(s) =

b∫

a

K(s, t)φ(t)dt

K(s, t) φ(t)

Ax = b

A

aij = ωjK(si, tj)

xj = φ(tj)

bi = f(si)

⎫⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎭i, j = 1, ..., n

xλ

x

{∥Ax− b∥22 + λ2 ∥x∥22

}

∥Ax− b∥22∥x∥22 ∥v∥2

v ∥v∥2 =√∑n

i=1 |vi|2

λ2

xλ =n∑

i=1

φ[λ]i

uTi b

σivi

ϕ[λ]i

ϕ[λ]i =

σ2i

σ2i + λ2

≈

⎧⎪⎨

⎪⎩

1 σi ≥ λ

σ2i /λ

2 σi ≤ λ

λ

δ1

λ > 0

∥b− bexact∥2 ≤ δ ≤ δ1

λ = λ(δ) δ ε > 0

δ(ε) ≤ δ1 bδ ∈ U

∥bexact − bδ∥ ≤ δ(ε)

∥xexact − xλ∥ ≤ ε

δ1 λ

δ

b = bexact + ε

λ

λ

∥Axλ − b∥

vdp∥e∥2 vdp

∥Axλ − b∥2 = vdp∥ε∥2

λ

b± η η

∥Axλ − b∥2bexact

∥Axλ − b∥2

Pk

Pk

main

main

main

main

Pk

φ(t)

K(s, t)

φ(t)

f(s)

f(s) =

π/2∫

−π/2

K(s, t)φ(t)dt

K(s, t) = ( (s) + (t))2(

(π( (s) + (t)))

π( (s) + (t))

)2

−π/2 ≤ s, t ≤ π/2

t

φ(t) = 2 (−6(t− 0.8)2) + (−2(t+ 0.5)2)

b

A

t

K

φ(t)

∥Ax− b∥2∥Ax− b∥2

∥Ax− b∥2

b− 0.1 < b < b+ 0.2

b− 2 < b < b+ 1

b− 0.1 < b < b+ 0.2

b− 2 < b < b+ 1

b−0.1 < b < b+0.2b− 2 < b < b+ 1

Cu(In1−x Gax Se2

µm

µm

ith

k

xi∫

0

[v2(x)−N2i ]

12dx = (i− 1)π + φ0 + φt, i = 1, 2, 3...

n(xi) = Ni

v(x) =

⎧⎪⎨

⎪⎩

n(x) (TE)

n(x)[1 + n(x)n(x)−2n2(x)k2n4(x) ] (TM)

⎫⎪⎬

⎪⎭

Ni = βi/k ith

βi k = 2π/λ

xi ith

x0 N0

φ0 φi ≡ φt = cons t

x0 xi

x0

φ0 φt

n(xi) = Ni

Ni xi

φ0 =−1

{r0

[N2

i − n2glass

N20 −N2

i

] 12}

r0 = 1 r0 = (N0/nglass)2

xi =

(i− 1)π + φ0(Ni) + φt −i−1∑j=1

k{xj

[(N2

avg,j −N2i )

1/2 − (N2avg,j+1 −N2

i )1/2

]}

k(N2avg,i −N2

i )1/2

, i = 1, 2, 3

Navg,i = (Ni +Ni−1)/2

5

µm

µm

µm µm µm

µm

µm

nPA 1.93 0.13(x/tPA)2

tPA

tIM

∆RMS

µm µm µm

π/4

tIM tPA

∆RMS ∆RMS

∆RMS

tIMtPA nPA

1.93 0.13(x/tPA)2 λ

tIMµm µm µm tPA µm tIM tPA µm nPA

tIM tPA µmtIM µm tPA λ

tIM µm nIM tPA µm

tIM µm tPA µm

tIM tPA

µm

∆RMS

∆RMS

µm

∆RMS ∆RMS

∆RMS

nPA

nIM

nIM nPA

µm

µm

∆RMS

∆RMS

µm

µm

µm

µm tIM

µm 5

µm

tPA µm µm

tPA

tIM

µm

vP3HT

vPCBM nP3HT nPCBM

vP3HTnP3HT −Ni

nP3HT + 2Ni+ vPCBM

nPCBM −Ni

nPCBM + 2Ni= 0, i = 1, 2, 3...

vP3HT + vPCBM = 1

µm

µmtIM µm

π/4

π/4

(Ni, xi)

π/4

n(x) = 1.93−0.13(x/tPA)2

(tpA, tIM )

tIM = 5µm tpA = 1µm

tIM = 10µm tpA = 1µm

µmtpA = 500nm µm

φi

tpA = 500nm

n(x) = 1.93 − 0.13(x/tPA)2 (tPA, tIM )

tIM = 5µmtPA = 0.5µm

φi

tPA = 500nm

φi

xi φi

π/4

µm

φi

φi

φi

φi =−1

{r0Pa+ [ (ξ1) + (ξ1)] +

1/31 [ ′

i(ξ1) +′i(ξ1)]

r0Pa+ [ (ξ1)− (ξ1)] +1/31 [ ′

i(ξ1)− ′i(ξ1)]

}

φi =π

4+ −1

[Pa+Ai(ξ2)−D1/3

2 A′(ξ2)i

Pa+Bi(ξ2)−D1/32 B

′(ξ2)i

]

r0 = 1 r0 = n2(a−)/n2(a+)

P 2 = k2(N2i − n2(x))

Pa+ = P (x = a+)

Pa− = P (x = a−)

D1 = k2[N2i − n2(x = a−)]/(a− xi)

D2 = k2[n2(x = a−)−N2i ]/(a− xi)

ξ1 = ξ(x = a−) = P 2a−D

−2/31

ξ2 = ξ(x = a+) = P 2a+D

−2/32

φi

φi = π/4 xi

xi Ni

φi

φi x′i

xi

x,i : δ = |x,

i − xi|

xi

a = xi=f + (xi=f − xi=f−1)/2

xi = f

φi = π/4

φi

µm tPA = 500nm

φi π/4

µm tPA

φi

π/4

π/4

π/4