Abstract

The scatterometric and electromagnetic signatures of a pattern are computed with the perturbation method combined with the Fourier modal method in order to reduce computational time. From an electromagnetic point of view, the grating is characterized by its scattering matrix, which allows the computation of the reflection and transmission coefficients. A slight variation of profile parameters or electrical ones provides a small fluctuation of the scattering matrix; consequently, an analytical expression of the local behavior of its eigenvectors and eigenvalues can be obtained by using a perturbation method.

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References

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  1. J. R. McNeil, “Applications of optical scatterometry to microelectronics materials processing,” in Proceedings of the IEEE Lasers and Electro-Optics Society Annual Meeting (LEOS), (IEEE, 1990), pp. 628–628.
    [CrossRef]
  2. S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, and J. R. McNeil, “Scatterometry measurement of sub-0.1 μm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
    [CrossRef]
  3. P. C. Logofatu, D. Apostol, V. Damian, V. Nascov, F. Garoi, A. Timcu, and I. Iordache, “Scatterometry, an optical metrology technique for lithography,” in Proceedings of the International Semiconductor Conference, CAS, 2004 (IEEE, 2004), pp. 517–520.
  4. R. M. Al-Assaad and D. M. Byrne, “Error analysis in inverse scatterometry. I. Modeling,” J. Opt. Soc. Am. A 24, 326–338(2007).
    [CrossRef]
  5. K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am. 68, 1206–1210 (1978).
    [CrossRef]
  6. P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
    [CrossRef]
  7. G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996).
    [CrossRef]
  8. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
    [CrossRef]
  9. S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
    [CrossRef]
  10. M. G. Moharam and T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392(1982).
    [CrossRef]
  11. K. Edee, J. P. Plumey, G. Granet, and J. Hazart, “Perturbation method for the rigorous coupled wave analysis of grating diffraction,” Opt. Express 18, 26274–26284 (2010).
    [CrossRef] [PubMed]
  12. I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
    [CrossRef]
  13. I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
    [CrossRef]
  14. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Mécanique Quantique, T2 (Hermann, 1973), pp. 1083–1095.

2010 (1)

2007 (1)

1998 (1)

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, and J. R. McNeil, “Scatterometry measurement of sub-0.1 μm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

1996 (3)

1982 (1)

1981 (2)

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

1978 (1)

1975 (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

Adams, J. L.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Al-Assaad, R. M.

Andrewartha, J. R.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Apostol, D.

P. C. Logofatu, D. Apostol, V. Damian, V. Nascov, F. Garoi, A. Timcu, and I. Iordache, “Scatterometry, an optical metrology technique for lithography,” in Proceedings of the International Semiconductor Conference, CAS, 2004 (IEEE, 2004), pp. 517–520.

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

Botten, I. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Byrne, D. M.

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, B. Diu, and F. Laloë, Mécanique Quantique, T2 (Hermann, 1973), pp. 1083–1095.

Coulombe, S. A.

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, and J. R. McNeil, “Scatterometry measurement of sub-0.1 μm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

Craig, M. S.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Damian, V.

P. C. Logofatu, D. Apostol, V. Damian, V. Nascov, F. Garoi, A. Timcu, and I. Iordache, “Scatterometry, an optical metrology technique for lithography,” in Proceedings of the International Semiconductor Conference, CAS, 2004 (IEEE, 2004), pp. 517–520.

Diu, B.

C. Cohen-Tannoudji, B. Diu, and F. Laloë, Mécanique Quantique, T2 (Hermann, 1973), pp. 1083–1095.

Edee, K.

Garoi, F.

P. C. Logofatu, D. Apostol, V. Damian, V. Nascov, F. Garoi, A. Timcu, and I. Iordache, “Scatterometry, an optical metrology technique for lithography,” in Proceedings of the International Semiconductor Conference, CAS, 2004 (IEEE, 2004), pp. 517–520.

Gaylord, T. K.

Granet, G.

Guizal, B.

Hazart, J.

Iordache, I.

P. C. Logofatu, D. Apostol, V. Damian, V. Nascov, F. Garoi, A. Timcu, and I. Iordache, “Scatterometry, an optical metrology technique for lithography,” in Proceedings of the International Semiconductor Conference, CAS, 2004 (IEEE, 2004), pp. 517–520.

Knop, K.

Lalanne, P.

Laloë, F.

C. Cohen-Tannoudji, B. Diu, and F. Laloë, Mécanique Quantique, T2 (Hermann, 1973), pp. 1083–1095.

Li, L.

Logofatu, P. C.

P. C. Logofatu, D. Apostol, V. Damian, V. Nascov, F. Garoi, A. Timcu, and I. Iordache, “Scatterometry, an optical metrology technique for lithography,” in Proceedings of the International Semiconductor Conference, CAS, 2004 (IEEE, 2004), pp. 517–520.

McNeil, J. R.

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, and J. R. McNeil, “Scatterometry measurement of sub-0.1 μm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

J. R. McNeil, “Applications of optical scatterometry to microelectronics materials processing,” in Proceedings of the IEEE Lasers and Electro-Optics Society Annual Meeting (LEOS), (IEEE, 1990), pp. 628–628.
[CrossRef]

McPhedran, R. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Minhas, B. K.

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, and J. R. McNeil, “Scatterometry measurement of sub-0.1 μm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Naqvi, S. S. H.

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, and J. R. McNeil, “Scatterometry measurement of sub-0.1 μm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

Nascov, V.

P. C. Logofatu, D. Apostol, V. Damian, V. Nascov, F. Garoi, A. Timcu, and I. Iordache, “Scatterometry, an optical metrology technique for lithography,” in Proceedings of the International Semiconductor Conference, CAS, 2004 (IEEE, 2004), pp. 517–520.

Peng, S. T.

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

Plumey, J. P.

Raymond, C. J.

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, and J. R. McNeil, “Scatterometry measurement of sub-0.1 μm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

Tamir, T.

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

Timcu, A.

P. C. Logofatu, D. Apostol, V. Damian, V. Nascov, F. Garoi, A. Timcu, and I. Iordache, “Scatterometry, an optical metrology technique for lithography,” in Proceedings of the International Semiconductor Conference, CAS, 2004 (IEEE, 2004), pp. 517–520.

IEEE Trans. Microwave Theory Tech. (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123–133 (1975).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Vac. Sci. Technol. B (1)

S. A. Coulombe, B. K. Minhas, C. J. Raymond, S. S. H. Naqvi, and J. R. McNeil, “Scatterometry measurement of sub-0.1 μm linewidth gratings,” J. Vac. Sci. Technol. B 16, 80–87 (1998).
[CrossRef]

Opt. Acta (2)

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Opt. Express (1)

Other (3)

J. R. McNeil, “Applications of optical scatterometry to microelectronics materials processing,” in Proceedings of the IEEE Lasers and Electro-Optics Society Annual Meeting (LEOS), (IEEE, 1990), pp. 628–628.
[CrossRef]

C. Cohen-Tannoudji, B. Diu, and F. Laloë, Mécanique Quantique, T2 (Hermann, 1973), pp. 1083–1095.

P. C. Logofatu, D. Apostol, V. Damian, V. Nascov, F. Garoi, A. Timcu, and I. Iordache, “Scatterometry, an optical metrology technique for lithography,” in Proceedings of the International Semiconductor Conference, CAS, 2004 (IEEE, 2004), pp. 517–520.

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Figures (21)

Fig. 1
Fig. 1

Grating configuration: two periods are depicted.

Fig. 2
Fig. 2

Staircase approximation: the grating is replaced by a stack of lamellar gratings.

Fig. 3
Fig. 3

Comparison between ρ and ρ for different values of R 1 and λ = 240 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 4 , R 2 = 20 nm , CD = 100 nm , α = 88 ° , θ = 70 ° , d = 200 nm .

Fig. 4
Fig. 4

Comparison between ρ and ρ for different values of R 1 and λ = 400 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 4 , R 2 = 20 nm , CD = 100 nm , α = 88 ° , θ = 70 ° , d = 200 nm .

Fig. 5
Fig. 5

Comparison between ρ and ρ for different values of R 1 and λ = 600 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 4 , R 2 = 20 nm , CD = 100 nm , α = 88 ° , θ = 70 ° , d = 200 nm .

Fig. 6
Fig. 6

ζ ( R 1 ) for different values of the wavelength λ = 240 nm , λ = 400 nm , λ = 600 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 4 , R 2 = 20 nm , CD = 100 nm , α = 88 ° , θ = 70 ° , d = 200 nm .

Fig. 7
Fig. 7

Comparison between ρ and ρ for different values of the CD and λ = 240 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 4 , R 1 = 20 nm , R 2 = 20 nm , α = 88 ° , θ = 70 ° , d = 200 nm .

Fig. 8
Fig. 8

Comparison between ρ and ρ for different values of the CD and λ = 400 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 4 , R 1 = 20 nm , R 2 = 20 nm , α = 88 ° , θ = 70 ° , d = 200 nm .

Fig. 9
Fig. 9

Comparison between ρ and ρ for different values of the CD and λ = 600 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 4 , R 1 = 20 nm , R 2 = 20 nm , α = 88 ° , θ = 70 ° , d = 200 nm .

Fig. 10
Fig. 10

ζ ( CD ) for different values of the wavelength λ = 240 nm , λ = 400 nm , λ = 600 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 4 , R 1 = 20 nm , R 2 = 20 nm , α = 88 ° , θ = 70 ° , d = 200 nm .

Fig. 11
Fig. 11

ζ ( CD ) for different values of the wavelength λ = 240 nm , λ = 400 nm , λ = 600 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 10 , R 1 = 20 nm , R 2 = 20 nm , α = 88 ° , θ = 70 ° , d = 200 nm .

Fig. 12
Fig. 12

Comparison between ρ and ρ for different values of α and λ = 240 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 10 , R 1 = 20 nm , R 2 = 20 nm , CD = 100 nm , θ = 70 ° , d = 200 nm .

Fig. 13
Fig. 13

Comparison between ρ and ρ for different values of α and λ = 400 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 10 , R 1 = 20 nm , R 2 = 20 nm , CD = 100 nm , θ = 70 ° , d = 200 nm .

Fig. 14
Fig. 14

Comparison between ρ and ρ for different values of α and λ = 600 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 10 , R 1 = 20 nm , R 2 = 20 nm , CD = 100 nm , θ = 70 ° , d = 200 nm .

Fig. 15
Fig. 15

ζ ( α ) for different values of the wavelength λ = 240 nm , λ = 400 nm , λ = 600 nm . Numerical parameters: M = 20 , N c = 1500 , n p = 10 , R 1 = 20 nm , R 2 = 20 nm , CD = 100 nm , θ = 70 ° , d = 200 nm .

Fig. 16
Fig. 16

Comparison between ρ and ρ for different values of λ, ( λ [ 235 , 245 ] nm ). Numerical parameters: M = 20 , N c = 1500 , α = 88 ° , n p = 6 , R 1 = 20 nm , R 2 = 20 nm , C D = 100 nm , θ = 0 ° , d = 200 nm .

Fig. 17
Fig. 17

Comparison between ρ and ρ for different values of λ, ( λ [ 235 , 245 ] nm ). Numerical parameters: M = 20 , N c = 1500 , α = 88 ° , n p = 6 , R 1 = 20 nm , R 2 = 20 nm , CD = 100 nm , θ = 5 ° , d = 200 nm .

Fig. 18
Fig. 18

ζ ( λ ) , ( λ [ 235 , 245 ] nm ) for different values of the angle of incidence θ = 0 ° , θ = 5 ° . Numerical parameters: M = 20 , N c = 1500 , n p = 6 , R 1 = 20 nm , R 2 = 20 nm , CD = 100 nm , d = 200 nm .

Fig. 19
Fig. 19

Comparison between ρ and ρ for different values of λ, ( λ [ 580 , 620 ] nm ). Numerical parameters: M = 20 , N c = 1500 , α = 88 ° , n p = 6 , R 1 = 20 nm , R 2 = 20 nm , CD = 100 nm , θ = 0 ° , d = 200 nm .

Fig. 20
Fig. 20

Comparison between ρ and ρ for different values of λ, ( λ [ 580 , 620 ] nm ). Numerical parameters: M = 20 , N c = 1500 , α = 88 ° , n p = 6 , R 1 = 20 nm , R 2 = 20 nm , CD = 100 nm , θ = 70 ° , d = 200 nm .

Fig. 21
Fig. 21

ζ ( λ ) , ( λ [ 580 , 620 ] nm ) for different values of the angle of incidence θ = 0 ° , θ = 70 ° . Numerical parameters: M = 20 , N c = 1500 , n p = 6 , R 1 = 20 nm , R 2 = 20 nm , CD = 100 nm , d = 200 nm .

Equations (35)

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ν j ( x ) = { ν , x [ 0 , l j ] , 1 , otherwise . .
L F ( x , y ) = 1 k 2 y 2 F ( x , y ) .
TE L = 1 k 2 x 2 + ν 2 ( x ) ,
TM L = 1 k 2 ν 2 ( x ) x 1 ν 2 ( x ) x + ν 2 ( x ) .
F ( x , y ) = X ( x ) Y ( y ) .
L X ( x ) = r 2 X ( x ) ,
F ( x , y ) = m = 1 m = 2 N + 1 ( A m e i k r m y + B m e i k r m y ) X m ( x ) .
Im ( r m ) < 0 or r m > 0 if     r m is     real .
X m ( x ) = n = n = X m n e n ( x ) ,
B 1 A 2 = S 11 S 12 S 21 S 22 A 1 B 2 .
B 1 = S 11 A 1 , A 2 = S 21 A 1 .
S ( a ) ψ p ( a ) = λ p ( a ) ψ p ( a ) .
S ( b ) S ( a ) = P = ( b a ) P ˜ ,
S ( b ) ψ p ( b ) = λ p ( b ) ψ p ( b ) ,
λ p ( b ) = n ( b a ) n λ p ( n ) , ψ p ( b ) = n ( b a ) n ψ p ( n ) .
[ S ( a ) + ( b a ) P ˜ ] n ( b a ) n ψ p ( n ) = m , n ( b a ) m + n λ p ( m ) ψ p ( n ) .
S ( a ) ψ p ( 0 ) = λ p ( 0 ) ψ p ( 0 ) ,
S ( a ) ψ p ( 1 ) + P ˜ ψ p ( 0 ) = λ p ( 0 ) ψ p ( 1 ) + λ p ( 1 ) ψ p ( 0 ) ,
S ( a ) ψ p ( 2 ) + P ˜ ψ p ( 1 ) = λ p ( 0 ) ψ p ( 2 ) + λ p ( 1 ) ψ p ( 1 ) + λ p ( 2 ) ψ p ( 0 ) .
ψ p , ψ p = 1 , ψ p ( 0 ) , ψ p real ,
ψ p ( 0 ) , ψ p ( 0 ) = 1 ,
ψ p ( 0 ) , ψ p ( 1 ) = ψ p ( 1 ) , ψ p ( 0 ) = 0 ,
ψ p ( 0 ) , ψ p ( 2 ) = ψ p ( 2 ) , ψ p ( 0 ) = 1 2 ψ p ( 1 ) , ψ p ( 1 ) ,
λ p ( b ) = λ p ( 0 ) + ( b a ) ψ p ( 0 ) , P ˜ ψ p ( 0 ) + o ( ( b a ) 2 ) ,
ψ p ( b ) = ψ p ( 0 ) + ( b a ) q p ψ q ( 0 ) , P ˜ ψ p ( 0 ) λ p ( 0 ) λ q ( 0 ) ψ q ( 0 ) + o ( ( b a ) 2 ) .
λ p ( b ) = λ p ( 0 ) + ( b a ) ψ p ( 0 ) , P ˜ ψ p ( 0 ) + ( b a ) 2 q p ψ q ( 0 ) , P ˜ ψ p ( 0 ) ψ p ( 0 ) , P ˜ ψ q ( 0 ) λ p ( 0 ) λ q ( 0 ) + o ( ( b a ) 3 ) ,
ψ p ( b ) = ψ p ( 0 ) + ( b a ) q p ψ q ( 0 ) , P ˜ ψ p ( 0 ) λ p ( 0 ) λ q ( 0 ) ψ q ( 0 ) + ( b a ) 2 q p l p ψ l ( 0 ) , P ˜ ψ p ( 0 ) ψ q ( 0 ) , P ˜ ψ l ( 0 ) ( λ p ( 0 ) λ l ( 0 ) ) ( λ p ( 0 ) λ q ( 0 ) ) ψ q ( 0 ) ( b a ) 2 q p ψ p ( 0 ) , P ˜ ψ p ( 0 ) ψ q ( 0 ) , P ˜ ψ p ( 0 ) ( λ p ( 0 ) λ q ( 0 ) ) 2 ψ q ( 0 ) ( b a ) 2 1 2 q p ψ p ( 0 ) , P ˜ ψ q ( 0 ) ψ q ( 0 ) , P ˜ ψ p ( 0 ) ( λ p ( 0 ) λ q ( 0 ) ) 2 ψ q ( 0 ) + o ( ( b a ) 3 ) .
λ p ( c ) = λ p ( 0 ) + c a η ψ p ( 0 ) , P ψ p ( 0 ) + ( c a η ) 2 q p ψ q ( 0 ) , P ψ p ( 0 ) ψ p ( 0 ) , P ψ q ( 0 ) λ p ( 0 ) λ q ( 0 ) + o ( η 3 ) ,
ψ p ( c ) = ψ p ( 0 ) + c a η q p ψ q ( 0 ) , P ψ p ( 0 ) λ p ( 0 ) λ q ( 0 ) ψ q ( 0 ) + ( c a η ) 2 q p l p ψ l ( 0 ) , P ψ p ( 0 ) ψ q ( 0 ) , P ψ l ( 0 ) ( λ p ( 0 ) λ l ( 0 ) ) ( λ p ( 0 ) λ q ( 0 ) ) ψ q ( 0 ) ( c - a η ) 2 q p ψ p ( 0 ) , P ψ p ( 0 ) ψ q ( 0 ) , P ψ p ( 0 ) ( λ p ( 0 ) λ q ( 0 ) ) 2 ψ q ( 0 ) ( c a η ) 2 1 2 q p ψ p ( 0 ) , P ψ q ( 0 ) ψ q ( 0 ) , P ψ p ( 0 ) ( λ p ( 0 ) λ q ( 0 ) ) 2 ψ q ( 0 ) + o ( η 3 ) .
S ( c ) = [ ψ ( c ) ] [ λ ( c ) ] [ ψ ( c ) ] 1 ,
I s = sin 2 ψ sin Δ , I c = sin 2 ψ cos Δ ,
ρ = r TE r TM = tan ψ e i Δ .
ζ ( ξ p ) = Int [ log 10 | 1 ρ ( ξ p ) ρ ( ξ p ) | ] ,
e n ( x ) = e i 2 π x sin θ / λ e i 2 π n x / d .
e ˜ n ( x ) = e i 2 π x sin θ / ( λ + η ) e i 2 π n x / d ,

Metrics