Abstract

We consider the possibility of a complete real-time analysis of the polarization state of light using two types of polarization-holographic grating that decompose the light analyzed into orthogonal circular and orthogonal linear bases. It is shown that it is possible to determine the ellipticity, the direction of rotation, and the azimuth of the polarization ellipse of light by the measurement of the intensity of the diffraction orders by the obtained formulas. The possibility of creating gratings that give an orthogonal linear basis on actual polarization-sensitive materials is shown. A comparison of the experimental results with the theory is given.

© 2007 Optical Society of America

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References

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  1. Sh. Kakichashvili, "On polarization recording of holograms," Opt. Spectrosc. 33, 324-327 (1972).
  2. Sh. Kakichashvili, Polarization Holography (Nauka, 1989).
  3. B. Kilosanidze and Sh. Kakichashvili, "The recognition device on the basis of vectorial Fourier analysis of transparent objects of arbitrary type," J. Opt. Technol. 64, 67-69 (1997).
  4. I. Shatalin, V. Kakichashvili, and Sh. Kakichashvili, "Polarization hologram of 100% diffraction efficiency (polarization kinoform)," J. Tech. Phys. 13, 1051-1055 (1987).
  5. A. Mendez and J. M. C. Jonathan, "Anisotropic gratings recorded from two circularly polarized coherent waves," Opt. Commun. 47, 85-90 (1983).
    [CrossRef]
  6. T. Todorov, L. Nikolova, and N. Tomova, "Polarization holography: 2. Polarization holographic gratings in photoanisotropic materials with and without intrinsic birefringence," Appl. Opt. 23, 4588-4591 (1984).
    [CrossRef] [PubMed]
  7. Sh. Kakichashvili and I. Shatalin, "Polarization holographic gratings with high diffraction efficiency," J. Tech. Phys. 12, 277-280 (1986).
  8. G. Cipparrone, A. Mazzulla, and G. Russo, "Diffraction from holographic gratings in polymer-dispersed liquid crystals recorded by means of polarization light patterns," J. Opt. Soc. Am. B 18, 1821-1826 (2001).
    [CrossRef]
  9. F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Azopolymer holographic diffraction gratings: time dependent analyses of the diffraction efficiency, birefringence, and surface modulation induced by two linearly polarized interfering beams," Phys. Chem. 103, 6690-6699 (1999).
  10. L. Nikolova, T. Todorov, M. Ivanov, F. Andruzzi, S. Hvisted, and P. S. Ramanujam, "Polarization-holographic gratings in side-chain azobenze polyesters with linear and circular photoanisotropy," Appl. Opt. 35, 3835-3840 (1996).
    [CrossRef] [PubMed]
  11. Sh. Kakichashvili, "On the regularity in photoanisotropic phenomena," Opt. Spectrosc. 52, 317-322 (1982).
  12. Sh. Kakichashvili, "On the regularity in the phenomena of photoanisotropy and photogyrotropy," Opt. Spectrosc. 63, 911-917 (1987).
  13. S. J. Cloutier, "Polarization holography: orthogonal plane-polarized beam configuration with circular vectorial photoinduced anisotropy," J. Phys. D 38, 3371-3375 (2005).
    [CrossRef]
  14. G. Kakauridze and B. Kilosanidze, "Polarization-holographic gratings that form plane-polarized orders of diffraction," J. Opt. Technol. 73, 188-192 (2006).
    [CrossRef]
  15. R. C. Jones, "A new calculus for the treatment of optical systems," J. Opt. Soc. Am. 31, 488-493 (1941).
    [CrossRef]
  16. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).
  17. Sh. Kakichashvili, "The experimental investigation on a posteriori experiment in polarization holography," J. Tech. Phys. 19, 5-8 (1993).
  18. Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, "Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light," Opt. Spectrosc. 68, 1309-1312 (1990).
  19. I. Naydenova, L. Nikolova, T. Todorov, N. C. H. Holme, P. S. Ramanujam, and S. Hvilsted, "Diffraction from polarization holographic gratings with surface relief in side-chain azobenze polyester," J. Opt. Soc. Am. B 15, 1257-1265 (1998).
    [CrossRef]
  20. F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Inscription of holographic gratings using circularly polarized light: Influence of the optical setup on the birefringence and surface relief grating properties," Appl. Phys. B 74, 129-137 (2002).
    [CrossRef]
  21. G. Martinez-Ponce and C. Solano, "Polarization gratings with surface relief in dyed gelatin and their postdevelopment diffraction," Appl. Opt. 41, 2122-2128 (2002).
    [CrossRef] [PubMed]

2006

2005

S. J. Cloutier, "Polarization holography: orthogonal plane-polarized beam configuration with circular vectorial photoinduced anisotropy," J. Phys. D 38, 3371-3375 (2005).
[CrossRef]

2002

G. Martinez-Ponce and C. Solano, "Polarization gratings with surface relief in dyed gelatin and their postdevelopment diffraction," Appl. Opt. 41, 2122-2128 (2002).
[CrossRef] [PubMed]

F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Inscription of holographic gratings using circularly polarized light: Influence of the optical setup on the birefringence and surface relief grating properties," Appl. Phys. B 74, 129-137 (2002).
[CrossRef]

2001

1999

F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Azopolymer holographic diffraction gratings: time dependent analyses of the diffraction efficiency, birefringence, and surface modulation induced by two linearly polarized interfering beams," Phys. Chem. 103, 6690-6699 (1999).

1998

1997

B. Kilosanidze and Sh. Kakichashvili, "The recognition device on the basis of vectorial Fourier analysis of transparent objects of arbitrary type," J. Opt. Technol. 64, 67-69 (1997).

1996

1993

Sh. Kakichashvili, "The experimental investigation on a posteriori experiment in polarization holography," J. Tech. Phys. 19, 5-8 (1993).

1990

Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, "Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light," Opt. Spectrosc. 68, 1309-1312 (1990).

1987

I. Shatalin, V. Kakichashvili, and Sh. Kakichashvili, "Polarization hologram of 100% diffraction efficiency (polarization kinoform)," J. Tech. Phys. 13, 1051-1055 (1987).

Sh. Kakichashvili, "On the regularity in the phenomena of photoanisotropy and photogyrotropy," Opt. Spectrosc. 63, 911-917 (1987).

1986

Sh. Kakichashvili and I. Shatalin, "Polarization holographic gratings with high diffraction efficiency," J. Tech. Phys. 12, 277-280 (1986).

1984

1983

A. Mendez and J. M. C. Jonathan, "Anisotropic gratings recorded from two circularly polarized coherent waves," Opt. Commun. 47, 85-90 (1983).
[CrossRef]

1982

Sh. Kakichashvili, "On the regularity in photoanisotropic phenomena," Opt. Spectrosc. 52, 317-322 (1982).

1972

Sh. Kakichashvili, "On polarization recording of holograms," Opt. Spectrosc. 33, 324-327 (1972).

1941

Andruzzi, F.

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Buffeteau, T.

F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Inscription of holographic gratings using circularly polarized light: Influence of the optical setup on the birefringence and surface relief grating properties," Appl. Phys. B 74, 129-137 (2002).
[CrossRef]

F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Azopolymer holographic diffraction gratings: time dependent analyses of the diffraction efficiency, birefringence, and surface modulation induced by two linearly polarized interfering beams," Phys. Chem. 103, 6690-6699 (1999).

Cipparrone, G.

Cloutier, S. J.

S. J. Cloutier, "Polarization holography: orthogonal plane-polarized beam configuration with circular vectorial photoinduced anisotropy," J. Phys. D 38, 3371-3375 (2005).
[CrossRef]

Holme, N. C. H.

Hvilsted, S.

Hvisted, S.

Ivanov, M.

Jonathan, J. M. C.

A. Mendez and J. M. C. Jonathan, "Anisotropic gratings recorded from two circularly polarized coherent waves," Opt. Commun. 47, 85-90 (1983).
[CrossRef]

Jones, R. C.

Kakauridze, G.

Kakichashvili, Sh.

B. Kilosanidze and Sh. Kakichashvili, "The recognition device on the basis of vectorial Fourier analysis of transparent objects of arbitrary type," J. Opt. Technol. 64, 67-69 (1997).

Sh. Kakichashvili, "The experimental investigation on a posteriori experiment in polarization holography," J. Tech. Phys. 19, 5-8 (1993).

Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, "Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light," Opt. Spectrosc. 68, 1309-1312 (1990).

I. Shatalin, V. Kakichashvili, and Sh. Kakichashvili, "Polarization hologram of 100% diffraction efficiency (polarization kinoform)," J. Tech. Phys. 13, 1051-1055 (1987).

Sh. Kakichashvili, "On the regularity in the phenomena of photoanisotropy and photogyrotropy," Opt. Spectrosc. 63, 911-917 (1987).

Sh. Kakichashvili and I. Shatalin, "Polarization holographic gratings with high diffraction efficiency," J. Tech. Phys. 12, 277-280 (1986).

Sh. Kakichashvili, "On the regularity in photoanisotropic phenomena," Opt. Spectrosc. 52, 317-322 (1982).

Sh. Kakichashvili, "On polarization recording of holograms," Opt. Spectrosc. 33, 324-327 (1972).

Sh. Kakichashvili, Polarization Holography (Nauka, 1989).

Kakichashvili, V.

I. Shatalin, V. Kakichashvili, and Sh. Kakichashvili, "Polarization hologram of 100% diffraction efficiency (polarization kinoform)," J. Tech. Phys. 13, 1051-1055 (1987).

Kilosanidze, B.

G. Kakauridze and B. Kilosanidze, "Polarization-holographic gratings that form plane-polarized orders of diffraction," J. Opt. Technol. 73, 188-192 (2006).
[CrossRef]

B. Kilosanidze and Sh. Kakichashvili, "The recognition device on the basis of vectorial Fourier analysis of transparent objects of arbitrary type," J. Opt. Technol. 64, 67-69 (1997).

Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, "Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light," Opt. Spectrosc. 68, 1309-1312 (1990).

Lagugne-Labarthet, F.

F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Inscription of holographic gratings using circularly polarized light: Influence of the optical setup on the birefringence and surface relief grating properties," Appl. Phys. B 74, 129-137 (2002).
[CrossRef]

F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Azopolymer holographic diffraction gratings: time dependent analyses of the diffraction efficiency, birefringence, and surface modulation induced by two linearly polarized interfering beams," Phys. Chem. 103, 6690-6699 (1999).

Martinez-Ponce, G.

Mazzulla, A.

Mendez, A.

A. Mendez and J. M. C. Jonathan, "Anisotropic gratings recorded from two circularly polarized coherent waves," Opt. Commun. 47, 85-90 (1983).
[CrossRef]

Naydenova, I.

Nikolova, L.

Ramanujam, P. S.

Russo, G.

Shatalin, I.

I. Shatalin, V. Kakichashvili, and Sh. Kakichashvili, "Polarization hologram of 100% diffraction efficiency (polarization kinoform)," J. Tech. Phys. 13, 1051-1055 (1987).

Sh. Kakichashvili and I. Shatalin, "Polarization holographic gratings with high diffraction efficiency," J. Tech. Phys. 12, 277-280 (1986).

Shaverdova, V.

Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, "Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light," Opt. Spectrosc. 68, 1309-1312 (1990).

Solano, C.

Sourisseau, C.

F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Inscription of holographic gratings using circularly polarized light: Influence of the optical setup on the birefringence and surface relief grating properties," Appl. Phys. B 74, 129-137 (2002).
[CrossRef]

F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Azopolymer holographic diffraction gratings: time dependent analyses of the diffraction efficiency, birefringence, and surface modulation induced by two linearly polarized interfering beams," Phys. Chem. 103, 6690-6699 (1999).

Todorov, T.

Tomova, N.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Appl. Opt.

Appl. Phys. B

F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Inscription of holographic gratings using circularly polarized light: Influence of the optical setup on the birefringence and surface relief grating properties," Appl. Phys. B 74, 129-137 (2002).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Opt. Technol.

B. Kilosanidze and Sh. Kakichashvili, "The recognition device on the basis of vectorial Fourier analysis of transparent objects of arbitrary type," J. Opt. Technol. 64, 67-69 (1997).

G. Kakauridze and B. Kilosanidze, "Polarization-holographic gratings that form plane-polarized orders of diffraction," J. Opt. Technol. 73, 188-192 (2006).
[CrossRef]

J. Phys. D

S. J. Cloutier, "Polarization holography: orthogonal plane-polarized beam configuration with circular vectorial photoinduced anisotropy," J. Phys. D 38, 3371-3375 (2005).
[CrossRef]

J. Tech. Phys.

Sh. Kakichashvili, "The experimental investigation on a posteriori experiment in polarization holography," J. Tech. Phys. 19, 5-8 (1993).

I. Shatalin, V. Kakichashvili, and Sh. Kakichashvili, "Polarization hologram of 100% diffraction efficiency (polarization kinoform)," J. Tech. Phys. 13, 1051-1055 (1987).

Sh. Kakichashvili and I. Shatalin, "Polarization holographic gratings with high diffraction efficiency," J. Tech. Phys. 12, 277-280 (1986).

Opt. Commun.

A. Mendez and J. M. C. Jonathan, "Anisotropic gratings recorded from two circularly polarized coherent waves," Opt. Commun. 47, 85-90 (1983).
[CrossRef]

Opt. Spectrosc.

Sh. Kakichashvili, "On polarization recording of holograms," Opt. Spectrosc. 33, 324-327 (1972).

Sh. Kakichashvili, "On the regularity in photoanisotropic phenomena," Opt. Spectrosc. 52, 317-322 (1982).

Sh. Kakichashvili, "On the regularity in the phenomena of photoanisotropy and photogyrotropy," Opt. Spectrosc. 63, 911-917 (1987).

Sh. Kakichashvili, B. Kilosanidze, and V. Shaverdova, "Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light," Opt. Spectrosc. 68, 1309-1312 (1990).

Phys. Chem.

F. Lagugne-Labarthet, T. Buffeteau, and C. Sourisseau, "Azopolymer holographic diffraction gratings: time dependent analyses of the diffraction efficiency, birefringence, and surface modulation induced by two linearly polarized interfering beams," Phys. Chem. 103, 6690-6699 (1999).

Other

Sh. Kakichashvili, Polarization Holography (Nauka, 1989).

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

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Figures (3)

Fig. 1
Fig. 1

Parameters of polarization ellipse.

Fig. 2
Fig. 2

Intensities of diffraction orders + 1 and 1 versus the azimuth of linear polarization of an incident wave for different types of gratings: (1) L , (2) L H , and (3) L V .

Fig. 3
Fig. 3

Schematic of the set for analysis of polarized light: (1) polarization-holographic element, (2) photodetectors, and (3) the measuring device.

Tables (2)

Tables Icon

Table 1 Intensities of the Orders of Diffraction from Gratings C , L H , and L V for Different Polarization States of Incident Light

Tables Icon

Table 2 Values of the Parameters of Polarization Ellipse

Equations (231)

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ψ = ( ψ x exp i a x ψ y exp i a y ) exp i ω t , ξ = ( ξ x exp i b x ξ y exp i b y ) exp i ( ω t + δ ) ,
ψ ^ x = ψ x exp i a x
ψ ^ y = ψ y exp i a y
ξ ^ x = ξ x exp i b x
ξ ^ y = ξ y exp i b y
E Σ = ( ψ x exp i a x + ξ x exp i b x exp i δ ψ y exp i a y + ξ y exp i b y exp i δ ) exp i ω t .
Re ( E Σ ) = p cos ω t + q sin ω t ,
p = ( ψ x cos a x + ξ x cos ( b x + δ ) ψ y cos a y + ξ y cos ( b y + δ ) ) ,
q = ( ψ x sin a x + ξ x sin ( b x + δ ) ψ y sin a y + ξ y sin ( b y + δ ) ) .
I 1 , 2 = E 1 , 2 E 1 , 2 * = 1 2 [ ( p x 2 + p y 2 ) + ( q x 2 + q y 2 ) ] ± 1 2 [ ( p x 2 p y 2 ) + ( q x 2 q y 2 ) ] 2 + 4 ( p x p y + q x q y ) 2 ,
sin 2 θ = 2 ( p x p y + q x q y ) [ ( p x 2 p y 2 ) + ( q x 2 q y 2 ) ] 2 + 4 ( p x p y + q x q y ) 2 ,
cos 2 θ = ( p x 2 p y 2 ) + ( q x 2 q y 2 ) [ ( p x 2 p y 2 ) + ( q x 2 q y 2 ) ] 2 + 4 ( p x p y + q x q y ) 2 ,
I 1
I 2
E 1
E 2
E 1, 2 *
E 1, 2
E E *
s ^
v ^ L
v ^ G
n ^ 1 2 = n ^ 0 2 + s ^ ( I 1 + I 2 ) + [ v ^ L ( I 1 I 2 ) ] 2 + [ v ^ G ( I + I ) ] 2 ,
n ^ 2 2 = n ^ 0 2 + s ^ ( I 1 + I 2 ) [ v ^ L ( I 1 I 2 ) ] 2 + [ v ^ G ( I + I ) ] 2 ,
n ^ 1
n ^ 2
n ^ 0
n ^ = n i n τ
s ^
v ^ L
v ^ G
I 1 + I 2
I 1 I 2
I + I
M exp ( 2 i κ d n ^ 0 ) exp [ i κ d s ^ 2 n ^ 0 ( I 1 + I 2 ) ] [ m 11 m 12 m 21 m 22 ] ,
m 11 , 22 = 1 cos θ [ i κ d v ^ L 2 n ^ 0 ( I 1 I 2 ) ] ,
m 12 , 21 = sin 2 θ [ i κ d v ^ L 2 n ^ 0 ( I 1 I 2 ) ] κ d v ^ G 2 n ^ 0 ( I + I ) .
κ = 2 π / λ ,
M = M 0 + M 1 + M + 1 ,
M 0 exp ( 2 i κ d n ^ 0 ) [ 1 0 0 1 ] ,
M 1 i κ d 2 n ^ 0 exp ( 2 i κ d n ^ 0 ) exp ( i δ ) [ ( s ^ + v ^ L ) ψ ^ x * ξ ^ x + ( s ^ v ^ L ) ψ ^ y * ξ ^ y ( v ^ L + v ^ G ) ψ ^ x * ξ ^ y + ( v ^ L v ^ G ) ψ ^ y * ξ ^ x ( v ^ L v ^ G ) ψ ^ x * ξ ^ y + ( v ^ L + v ^ G ) ψ ^ y * ξ ^ x ( s ^ v ^ L ) ψ ^ x * ξ ^ x + ( s ^ + v ^ L ) ψ ^ y * ξ y ]
M + 1 i κ d 2 n ^ 0 exp ( 2 i κ d n ^ 0 ) exp ( i δ ) [ ( s ^ + v ^ L ) ψ ^ x ξ ^ x * + ( s ^ v ^ L ) ψ ^ y ξ ^ y * ( v ^ L + v ^ G ) ψ ^ y ξ ^ x * + ( v ^ L v ^ G ) ψ ^ x ξ ^ y * ( v ^ L v ^ G ) ψ ^ y ξ ^ x * + ( v ^ L + v ^ G ) ψ ^ x ξ ^ y * ( s ^ v ^ L ) ψ ^ x ξ ^ x * + ( s ^ + v ^ L ) ψ ^ y ξ ^ y * ] .
M 0
M 1
M + 1
1
+ 1
M 0
M 1
M + 1
ψ x = ψ
ψ y = 0
a y a x = 0
ξ x = 0
ξ y = ψ
b y b x = 0
s ^ = v ^ L
v ^ L = v ^ G
M 1
M + 1
M 1 i κ d v ^ L n ^ 0 2 ψ 2 exp ( 2 i κ d n ^ 0 ) exp ( i δ ) exp ( i a x ) × exp ( i b y ) [ 0 0 1 0 ] ,
M + 1 i κ d v ^ L n ^ 0 2 ψ 2 exp ( 2 i κ d n ^ 0 ) exp ( i δ ) exp ( i a x ) × exp ( i b y ) [ 0 1 0 0 ] .
( cos α sin α )
+ 1
cos α ( 0 1 )
sin α ( 1 0 )
I 1 cos 2 α
I + 1 sin 2 α
( 1 0 )
( 0 1 )
( 0 1 )
( 1 0 )
1 2 ( 1 ± i )
( 0 1 )
( 1 0 )
( E x exp i φ x E y exp i φ y ) ,
E x exp i φ x ( 0 1 )
E y exp i φ y ( 1 0 )
I 1 E x 2
I + 1 E y 2
s ^ = v ^ L
v ^ L = v ^ G
v ^ G
s ^
v ^ L
v ^ G = 0
s ^ v ^ L
M 1 i κ d v ^ L 2 n ^ 0 2 ψ 2 exp ( 2 i κ d n ^ 0 ) exp ( ± i δ ) exp ( i a x ) × exp ( ± i b y ) [ 0 1 1 0 ] .
v ^ L = v ^ G
( cos α sin α )
( sin α cos α )
1 2 ( 1 ± i )
( E x exp i φ x E y exp i φ y ) ,
i 2 ( 1 i )
( E y exp i φ y E x exp i φ x )
M 2 1 2 ( κ d v ^ L 2 n ^ 0 ) ψ 2 exp ( 2 i κ d n ^ 0 ) exp ( ± 2 i δ ) exp ( 2 i a x ) × exp ( ± 2 i b x ) [ 1 0 0 1 ] .
ψ x = ψ
ψ y = 0
a y a x = 0
ξ x = ψ
ξ y = 0
b y b x = 0
s ^
v ^ L
v ^ G
( M 1 ) H i κ d n ^ 0 ψ 2 exp ( 2 i κ d n ^ 0 ) exp ( ± i δ ) exp ( i a x ) × exp ( ± i b x ) [ s ^ + v ^ L 0 0 s ^ v ^ L ] ,
v ^ G
s ^ v ^ L
( M 1 ) H i κ d v ^ L n ^ 0 ψ 2 exp ( 2 i κ d n ^ 0 ) exp ( ± i δ ) exp ( i a x ) × exp ( ± i b x ) [ 1 0 0 0 ] .
· 0 π 4 π 2 3 π 4 π 5 π 4 3 π 2 7 π 4 2 π .
ψ x = 0
ψ y = ψ
a y a x = 0
ξ x = 0
ξ y = ψ
b y b x = 0
M 1
( M 1 ) V i κ d v ^ L n ^ 0 ψ 2 exp ( 2 i κ d n ^ 0 ) exp ( ± i δ ) exp ( i a y ) × exp ( ± i b y ) [ s ^ v ^ L 0 0 s ^ + v ^ L ] ,
s ^ v ^ L
( M 1 ) V i κ d v ^ L n ^ 0 ψ 2 exp ( 2 i κ d n ^ 0 ) exp ( ± i δ ) exp ( i a y ) × exp ( ± i b y ) [ 0 0 0 1 ] .
0 π 4 π 2 3 π 4 π 5 π 4 3 π 2 7 π 4 2 π .
( sin α cos α )
cos α ( 1 0 )
sin α ( 0 1 )
cos 2 α
sin 2 α
( E x exp i φ x E y exp i φ y )
E x exp i φ x ( 1 0 )
E y exp i φ y ( 0 1 )
[ cos α sin α sin α cos α ] ( E x exp i φ x E y exp i φ y ) = E x exp ( i φ x ) × ( cos α + i ε sin α sin α + i ε cos α ) ,
[ cos α sin α sin α cos α ]
ε = E y / E x
0 ε 1
ϕ y φ x = π / 2
ε = I 1 , C I + 1 , C I 1 , C + I + 1 , C , 0 ε 1 ,
I 1 , C
I + 1 , C
( I 1 , C / I + 1 , C ) > 1
( I 1 , C / I + 1 , C ) < 1
( L H )
Φ ± 1 , H E x exp ( i φ x ) ( cos α + i ε sin α ) ( 1 0 ) .
I 1 , H = I + 1 , H E x 2 ( cos 2 α + ε 2 sin 2 α ) .
( L V )
Φ 1 , V E x exp i φ x ( sin α + i ε cos α ) ( 0 1 ) ,
I 1 , V = I + 1 , V E x 2 ( sin 2 α + ε 2 cos 2 α ) .
α = arctan I V ε 2 k I H k I H ε 2 I V ,
k = η H / η V
L H
L V
I 1 , C
I + 1 , C
I + 1 , V
I + 1 , H
I 1 , V
I 1 , H
L H
L V
L
L H
L V
( s ^ = v ^ L , v ^ L = v ^ G )
v ^ G
s ^
v ^ L
s ^ = v ^ L
s ^ = 0.047 + i 0.002
v ^ L = 0.047 + i 0.007
λ = 488   nm
12   mm
30   mW / cm 2
D = 1.3
( 488   nm )
λ = 632.8   nm
8% 55%
1 5 J / cm 2
L
L H
L V
520 1200   nm
1 8   min
3 ° 5 °
10 15   μm
L
L H
L V
L V
L H
L V
s ^ = v ^ L
( λ = 632.8   nm )
C 65 %
L H 18 %
L V 24 %
12 mm
( λ = 632.8   nm )
L H
L V
I 1 , C
I + 1 , C
I 1 , H
I + 1 , H
I 1 , V
I + 1 , V
I 0
I 1 , C
I + 1 , C
I 1 , H
I 1 , V
I + 1 , H
I + 1 , V
L H
L V
L H
L V
L H
L V
( 1 0 )
( 2 + i 3 i )
( 3 i 2 i + 1 )
( i 2 + 3 i )
( 2 3 i i )
( 1 3 )
( 1 i )
( 1 + 2 i 3 )
( 2 + i 3 i )
( 3 ( 1 + i ) 1 i )
+ 1
1
L
L H
L V

Metrics