Abstract

We investigated theoretically the interference of two counterpropagating polarized light beams in optically anisotropic media whose optical axis is in the film plane and is gradually rotated around the thickness direction. Results indicated that pure polarization modulation without intensity variation is obtained in the inhomogeneous media when the total angle of the rotation is much smaller than the total retardation. Reflective anisotropic gratings recorded by the polarization modulation were formulated as the perturbation of the dielectric tensor, and diffraction properties were studied using coupled-wave analysis (CWA) and a numerical method. By assuming that the period of the intrinsic distribution is substantially larger than that of the induced one, we demonstrated that CWA estimates the diffraction efficiency and the polarization state of the diffracted light with high accuracy.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Nikolova and T. Todorov, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579–588 (1984).
    [CrossRef]
  2. T. Huang and K. H. Wagner, “Holographic diffraction in photoanisotropic organic materials,” J. Opt. Soc. Am. A 10, 306–315 (1993).
    [CrossRef]
  3. L. Nikolova, T. Todorov, M. Ivanov, F. Andruzzi, S. Hvilsted, and P. S. Ramanujam, “Polarization holographic gratings in side-chain azobenzene polyesters with linear and circular photoanisotropy,” Appl. Opt. 35, 3835–3840 (1996).
    [CrossRef]
  4. R. Birabassov and T. V. Galstian, “Analysis of the recording and reconstruction of the polarization state of light,” J. Opt. Soc. Am. B 18, 1423–1427 (2001).
    [CrossRef]
  5. W. Zhang, S. Bian, S. I. Kim, and M. G. Kuzyk, “High-efficiency holographic volume index gratings in DR1-dye-doped poly(methyl methacrylate),” Opt. Lett. 27, 1105–1107 (2002).
    [CrossRef]
  6. F. L. Labarthet, T. Buffeteau, and C. Sourisseau, “Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on birefringence and surface relief grating properties,” Appl. Phys. B 74, 129–137 (2002).
    [CrossRef]
  7. F. Ciuchi, A. Mazzulla, and G. Cipparrone, “Permanent polarization gratings in elastomer comparison of layered and mixed samples,” J. Opt. Soc. Am. B 19, 2531–2537 (2002).
    [CrossRef]
  8. H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
    [CrossRef]
  9. H. Ono, A. Emoto, and N. Kawatsuki, “Anisotropic photonic gratings formed in photocross-linkable polymer liquid crystals,” J. Appl. Phys. 100, 013522 (2006).
    [CrossRef]
  10. C. Provenzano, P. Pagliusi, and G. Cipparrone, “Electrically tunable two-dimensional liquid crystals gratings induced y polarization holography,” Opt. Express 15, 5872–5878 (2007).
    [CrossRef]
  11. B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization holography. 1. Dynamic polarization-sensitive materials on the basis of azo-dye-containing polymers,” Appl. Opt. 48, 1861–1868 (2009).
    [CrossRef]
  12. T. Sasaki, H. Ono, and N. Kawatsuki, “Three-dimensional vector holograms in anisotropic photoreactive liquid-crystal composites,” Appl. Opt. 47, 2192–2200 (2008).
    [CrossRef]
  13. T. Sasaki, H. Ono, and N. Kawatsuki, “Anisotropic photonic structures induced by three-dimensional vector holography in dye-doped liquid crystals,” J. Appl. Phys. 104, 043524 (2008).
    [CrossRef]
  14. T. Sasaki, A. Emoto, K. Miura, O. Hanaizumi, N. Kawatsuki, and H. Ono, “Three-dimensional vector holograms in photoreactive anisotropic media,” in Holograms: Recording Materials and Applications, I. Naydenova ed. (InTech, 2011), 179–196.
  15. C. M. Titus, J. R. Kelly, E. C. Gartland, S. V. Shiyanovskii, J. A. Anderson, and P. J. Bos, “Asymmetric transmissive behavior of liquid-crystal diffraction gratings,” Opt. Lett. 26, 1188–1190 (2001).
    [CrossRef]
  16. C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
    [CrossRef]
  17. H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation in polarization holograms formed in photoreactive polymer liquid crystals,” Jpn. J. Appl. Phys. 47, 3559–3563 (2008).
    [CrossRef]
  18. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  19. G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55, 1035–1047(1997).
    [CrossRef]
  20. R. L. Sutherland, “Polarization and switching properties of holographic polymer-dispersed liquid-crystal gratings. I. Theoretical model,” J. Opt. Soc. Am. B 19, 2995–3003(2002).
    [CrossRef]
  21. D. E. Lucchetta, L. Criante, and F. Simoni, “Determination of small anisotropy of holographic phase gratings,” Opt. Lett. 28, 725–727 (2003).
    [CrossRef]
  22. H. Sarkissian, B. Ya. Zeldovich, and N. Tabiryan, “Longitudinally modulated nematic bandgap structure,” J. Opt. Soc. Am. B 23, 1712–1717 (2006).
    [CrossRef]
  23. T. Sasaki, K. Miura, O. Hanaizumi, A. Emoto, and H. Ono, “Coupled-wave analysis of vector holograms: effects of modulation depth of anisotropic phase retardation,” Appl. Opt. 49, 5205–5211 (2010).
    [CrossRef]
  24. T. Sasaki, K. Miura, O. Hanaizumi, A. Emoto, and H. Ono, “Coupled-wave analysis of vector holograms. 2. Reflective gratings formed in photoanisotropic medium with uniaxial birefringence,” Appl. Opt. 50, 454–459 (2011).
    [CrossRef]
  25. P. Yeh and G. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).
  26. T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).

2011 (1)

2010 (1)

2009 (1)

2008 (3)

T. Sasaki, H. Ono, and N. Kawatsuki, “Three-dimensional vector holograms in anisotropic photoreactive liquid-crystal composites,” Appl. Opt. 47, 2192–2200 (2008).
[CrossRef]

T. Sasaki, H. Ono, and N. Kawatsuki, “Anisotropic photonic structures induced by three-dimensional vector holography in dye-doped liquid crystals,” J. Appl. Phys. 104, 043524 (2008).
[CrossRef]

H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation in polarization holograms formed in photoreactive polymer liquid crystals,” Jpn. J. Appl. Phys. 47, 3559–3563 (2008).
[CrossRef]

2007 (2)

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Electrically tunable two-dimensional liquid crystals gratings induced y polarization holography,” Opt. Express 15, 5872–5878 (2007).
[CrossRef]

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

2006 (2)

H. Ono, A. Emoto, and N. Kawatsuki, “Anisotropic photonic gratings formed in photocross-linkable polymer liquid crystals,” J. Appl. Phys. 100, 013522 (2006).
[CrossRef]

H. Sarkissian, B. Ya. Zeldovich, and N. Tabiryan, “Longitudinally modulated nematic bandgap structure,” J. Opt. Soc. Am. B 23, 1712–1717 (2006).
[CrossRef]

2003 (2)

D. E. Lucchetta, L. Criante, and F. Simoni, “Determination of small anisotropy of holographic phase gratings,” Opt. Lett. 28, 725–727 (2003).
[CrossRef]

H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
[CrossRef]

2002 (4)

2001 (2)

1997 (1)

G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55, 1035–1047(1997).
[CrossRef]

1996 (1)

1993 (1)

1984 (1)

L. Nikolova and T. Todorov, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579–588 (1984).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Anderson, J. A.

Andruzzi, F.

Bian, S.

Birabassov, R.

Bos, P. J.

Buffeteau, T.

F. L. Labarthet, T. Buffeteau, and C. Sourisseau, “Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on birefringence and surface relief grating properties,” Appl. Phys. B 74, 129–137 (2002).
[CrossRef]

Chaganava, I.

Cipparrone, G.

Ciuchi, F.

Criante, L.

Emoto, A.

T. Sasaki, K. Miura, O. Hanaizumi, A. Emoto, and H. Ono, “Coupled-wave analysis of vector holograms. 2. Reflective gratings formed in photoanisotropic medium with uniaxial birefringence,” Appl. Opt. 50, 454–459 (2011).
[CrossRef]

T. Sasaki, K. Miura, O. Hanaizumi, A. Emoto, and H. Ono, “Coupled-wave analysis of vector holograms: effects of modulation depth of anisotropic phase retardation,” Appl. Opt. 49, 5205–5211 (2010).
[CrossRef]

H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation in polarization holograms formed in photoreactive polymer liquid crystals,” Jpn. J. Appl. Phys. 47, 3559–3563 (2008).
[CrossRef]

H. Ono, A. Emoto, and N. Kawatsuki, “Anisotropic photonic gratings formed in photocross-linkable polymer liquid crystals,” J. Appl. Phys. 100, 013522 (2006).
[CrossRef]

H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
[CrossRef]

T. Sasaki, A. Emoto, K. Miura, O. Hanaizumi, N. Kawatsuki, and H. Ono, “Three-dimensional vector holograms in photoreactive anisotropic media,” in Holograms: Recording Materials and Applications, I. Naydenova ed. (InTech, 2011), 179–196.

Escuti, M. J.

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

Galstian, T. V.

Gartland, E. C.

Gu, G.

P. Yeh and G. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

Hanaizumi, O.

Hasegawa, T.

H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
[CrossRef]

Huang, T.

Hvilsted, S.

Ivanov, M.

Kakauridze, G.

Kawatsuki, N.

T. Sasaki, H. Ono, and N. Kawatsuki, “Three-dimensional vector holograms in anisotropic photoreactive liquid-crystal composites,” Appl. Opt. 47, 2192–2200 (2008).
[CrossRef]

T. Sasaki, H. Ono, and N. Kawatsuki, “Anisotropic photonic structures induced by three-dimensional vector holography in dye-doped liquid crystals,” J. Appl. Phys. 104, 043524 (2008).
[CrossRef]

H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation in polarization holograms formed in photoreactive polymer liquid crystals,” Jpn. J. Appl. Phys. 47, 3559–3563 (2008).
[CrossRef]

H. Ono, A. Emoto, and N. Kawatsuki, “Anisotropic photonic gratings formed in photocross-linkable polymer liquid crystals,” J. Appl. Phys. 100, 013522 (2006).
[CrossRef]

H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
[CrossRef]

T. Sasaki, A. Emoto, K. Miura, O. Hanaizumi, N. Kawatsuki, and H. Ono, “Three-dimensional vector holograms in photoreactive anisotropic media,” in Holograms: Recording Materials and Applications, I. Naydenova ed. (InTech, 2011), 179–196.

Kelly, J. R.

Kilosanidze, B.

Kim, S. I.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kuzyk, M. G.

Labarthet, F. L.

F. L. Labarthet, T. Buffeteau, and C. Sourisseau, “Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on birefringence and surface relief grating properties,” Appl. Phys. B 74, 129–137 (2002).
[CrossRef]

Lucchetta, D. E.

Mazzulla, A.

Miura, K.

Montemezzani, G.

G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55, 1035–1047(1997).
[CrossRef]

Nikolova, L.

Oh, C.

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

Ono, H.

T. Sasaki, K. Miura, O. Hanaizumi, A. Emoto, and H. Ono, “Coupled-wave analysis of vector holograms. 2. Reflective gratings formed in photoanisotropic medium with uniaxial birefringence,” Appl. Opt. 50, 454–459 (2011).
[CrossRef]

T. Sasaki, K. Miura, O. Hanaizumi, A. Emoto, and H. Ono, “Coupled-wave analysis of vector holograms: effects of modulation depth of anisotropic phase retardation,” Appl. Opt. 49, 5205–5211 (2010).
[CrossRef]

H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation in polarization holograms formed in photoreactive polymer liquid crystals,” Jpn. J. Appl. Phys. 47, 3559–3563 (2008).
[CrossRef]

T. Sasaki, H. Ono, and N. Kawatsuki, “Three-dimensional vector holograms in anisotropic photoreactive liquid-crystal composites,” Appl. Opt. 47, 2192–2200 (2008).
[CrossRef]

T. Sasaki, H. Ono, and N. Kawatsuki, “Anisotropic photonic structures induced by three-dimensional vector holography in dye-doped liquid crystals,” J. Appl. Phys. 104, 043524 (2008).
[CrossRef]

H. Ono, A. Emoto, and N. Kawatsuki, “Anisotropic photonic gratings formed in photocross-linkable polymer liquid crystals,” J. Appl. Phys. 100, 013522 (2006).
[CrossRef]

H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
[CrossRef]

T. Sasaki, A. Emoto, K. Miura, O. Hanaizumi, N. Kawatsuki, and H. Ono, “Three-dimensional vector holograms in photoreactive anisotropic media,” in Holograms: Recording Materials and Applications, I. Naydenova ed. (InTech, 2011), 179–196.

Pagliusi, P.

Provenzano, C.

Ramanujam, P. S.

Sarkissian, H.

Sasaki, T.

T. Sasaki, K. Miura, O. Hanaizumi, A. Emoto, and H. Ono, “Coupled-wave analysis of vector holograms. 2. Reflective gratings formed in photoanisotropic medium with uniaxial birefringence,” Appl. Opt. 50, 454–459 (2011).
[CrossRef]

T. Sasaki, K. Miura, O. Hanaizumi, A. Emoto, and H. Ono, “Coupled-wave analysis of vector holograms: effects of modulation depth of anisotropic phase retardation,” Appl. Opt. 49, 5205–5211 (2010).
[CrossRef]

T. Sasaki, H. Ono, and N. Kawatsuki, “Anisotropic photonic structures induced by three-dimensional vector holography in dye-doped liquid crystals,” J. Appl. Phys. 104, 043524 (2008).
[CrossRef]

T. Sasaki, H. Ono, and N. Kawatsuki, “Three-dimensional vector holograms in anisotropic photoreactive liquid-crystal composites,” Appl. Opt. 47, 2192–2200 (2008).
[CrossRef]

T. Sasaki, A. Emoto, K. Miura, O. Hanaizumi, N. Kawatsuki, and H. Ono, “Three-dimensional vector holograms in photoreactive anisotropic media,” in Holograms: Recording Materials and Applications, I. Naydenova ed. (InTech, 2011), 179–196.

Scharf, T.

T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).

Sekiguchi, T.

H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation in polarization holograms formed in photoreactive polymer liquid crystals,” Jpn. J. Appl. Phys. 47, 3559–3563 (2008).
[CrossRef]

Shiyanovskii, S. V.

Simoni, F.

Sourisseau, C.

F. L. Labarthet, T. Buffeteau, and C. Sourisseau, “Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on birefringence and surface relief grating properties,” Appl. Phys. B 74, 129–137 (2002).
[CrossRef]

Sutherland, R. L.

Tabiryan, N.

Titus, C. M.

Todorov, T.

Wagner, K. H.

Yeh, P.

P. Yeh and G. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

Zeldovich, B. Ya.

Zgonik, M.

G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55, 1035–1047(1997).
[CrossRef]

Zhang, W.

Appl. Opt. (5)

Appl. Phys. B (1)

F. L. Labarthet, T. Buffeteau, and C. Sourisseau, “Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on birefringence and surface relief grating properties,” Appl. Phys. B 74, 129–137 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

H. Ono, A. Emoto, N. Kawatsuki, and T. Hasegawa, “Self-organized phase gratings in photoreactive polymer liquid crystals,” Appl. Phys. Lett. 82, 1359–1361 (2003).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

J. Appl. Phys. (2)

T. Sasaki, H. Ono, and N. Kawatsuki, “Anisotropic photonic structures induced by three-dimensional vector holography in dye-doped liquid crystals,” J. Appl. Phys. 104, 043524 (2008).
[CrossRef]

H. Ono, A. Emoto, and N. Kawatsuki, “Anisotropic photonic gratings formed in photocross-linkable polymer liquid crystals,” J. Appl. Phys. 100, 013522 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

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

Jpn. J. Appl. Phys. (1)

H. Ono, T. Sekiguchi, A. Emoto, and N. Kawatsuki, “Light wave propagation in polarization holograms formed in photoreactive polymer liquid crystals,” Jpn. J. Appl. Phys. 47, 3559–3563 (2008).
[CrossRef]

Opt. Acta (1)

L. Nikolova and T. Todorov, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579–588 (1984).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

Phys. Rev. E (1)

G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55, 1035–1047(1997).
[CrossRef]

Other (3)

T. Sasaki, A. Emoto, K. Miura, O. Hanaizumi, N. Kawatsuki, and H. Ono, “Three-dimensional vector holograms in photoreactive anisotropic media,” in Holograms: Recording Materials and Applications, I. Naydenova ed. (InTech, 2011), 179–196.

P. Yeh and G. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).

T. Scharf, Polarized Light in Liquid Crystals and Polymers (Wiley, 2007).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Schematic arrangement for holographic recording. Ellipsoids represent the refractive index ellipsoid.

Fig. 2.
Fig. 2.

Calculated Stokes parameters: (a)  d = 10 u , (b)  d = 50 u , (c)  d = 200 u , and (d)  d u .

Fig. 3.
Fig. 3.

Distribution of photoinduced angles. The red and blue curves represent Δ θ and Δ ϕ .

Fig. 4.
Fig. 4.

Polar plots of polarization states of transmitted and diffracted light. The red curves (r) indicate the results calculated by the Jones matrix method and CWA. The blue curves (b) indicate the results calculated by the 4 × 4 matrix method. Incident light is LP with the azimuth of 0 (black curve, i).

Fig. 5.
Fig. 5.

Wavelength dispersion of diffraction efficiency. The red curve (r) indicates the result calculated by CWA. The blue, green, and violet curves indicate the results calculated by the 4 × 4 matrix method for Φ = π / 2 , 4 π , and 6 π .

Fig. 6.
Fig. 6.

Ratio of the diffraction efficiency calculated by the 4 × 4 matrix method ( R ) and CWA ( η ). The red, green, and blue curves are the results for d = 100 Λ , 50 Λ , and 25 Λ .

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

E ( z ) = J + ( z ) E + + J ( z ) E ,
J ± = [ exp ( i 2 π n e z / λ 0 ) 0 0 exp ( i 2 π n o z / λ 0 ) ] ,
E [ exp [ i 2 π ( n e + n o ) z / λ 0 ] 1 ] .
Λ = λ 0 n e + n o .
ϕ = Φ z d ,
d λ 0 2 π | n e n o | Φ u ,
J ± = m = 1 M R ( ϕ ) · [ exp ( i 2 π n e d / λ 0 ) 0 0 exp ( i 2 π n o d / λ 0 ) ] · R ( ϕ ) ,
R ( ϕ ) = [ cos ϕ sin ϕ sin ϕ cos ϕ ] .
E [ A x exp ( i δ x ) A y exp ( i δ y ) ] ,
S 0 = | A x | 2 + | A y | 2 ,
S 1 = | A x | 2 | A y | 2 ,
S 2 = A x A y cos ( δ y δ x ) ,
S 3 = A x A y sin ( δ y δ x ) ,
J + ( z ) E + = R ( ϕ ) · [ exp ( i 2 π n e z / λ 0 ) 0 ] = [ cos ϕ sin ϕ ] exp ( i 2 π n e z / λ 0 ) ,
J ( z ) E = R ( ϕ + π 2 ) · [ exp ( i 2 π n o z / λ 0 ) 0 ] = [ sin ϕ cos ϕ ] exp ( i 2 π n o z / λ 0 ) ,
c = ( ( cos Δ θ ) cos ( ϕ + Δ ϕ ) , ( cos Δ θ ) sin ( ϕ + Δ ϕ ) , sin Δ θ ) ,
Δ θ | c · E | S 0 ,
Δ ϕ | c · E | [ S 1 sin ( 2 ϕ ) S 2 cos ( 2 ϕ ) ] ,
ψ = 2 π P z + ϕ 0 cos ( 2 π Λ z ) K z + ϕ 0 cos ( q z ) ,
Δ ε ( z ) [ 1 i i 1 ] exp ( i 2 ψ ) + [ 1 i i 1 ] exp ( i 2 ψ ) ,
exp ( ± i 2 ψ ) exp ( ± i 2 K z ) ± i ϕ 0 { exp [ i ( q ± 2 K ) z ] + exp [ i ( q 2 K ) z ] } .

Metrics