Abstract

A polarization grating (PG) written in an azo-dye-doped film of polymer-ball-type polymer-dispersed liquid crystals was investigated. The writing beams were two mutually orthogonal (s- and p-polarized) polarized beams. The PG resulted from molecular reorientation of the liquid crystals as a result of their interaction with the dye molecules adsorbed on the surface of the polymer balls. Polarization characteristics of the diffracted beams and the grating pattern were studied under a polarizing optical microscope with a crossed analyzer. The results indicate that the PG diffracts the linearly polarized incident light into beams with various polarizations. Accordingly, the grating can be used as an unpolarized or a polarized beam splitter, depending on the polarization of the incident light. A model based on the Jones matrix approach was developed, and it closely fits the experimental results.

© 2002 Optical Society of America

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  1. J. W. Doane, N. A. Vaz, B.-G. Wu, and S. Zumer, “Field controlled light scattering from nematic microdroplet,” Appl. Phys. Lett. 48, 269–272 (1986).
    [CrossRef]
  2. R. Yamaguchi and S. Sato, “Memory effects of light transmission properties in polymer-dispersed liquid crystal (PDLC) films,” Jpn. J. Appl. Phys. 30, L616–L618 (1991).
    [CrossRef]
  3. R. L. Sutherland, V. P. Tondiglia, and L. V. Natarajan, “Electrically switchable volume gratings in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
    [CrossRef]
  4. A. Y.-G. Fuh, T.-C. Ko, M.-S. Tsai, C.-Y. Huang, and L.-C. Chien, “Dynamical studies of gratings formed in polymer-dispersed liquid crystal films,” J. Appl. Phys. 83, 679–683 (1998).
    [CrossRef]
  5. A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, “Optically switchable gratings based on polymer-dispersed liquid crystal films doped with a guest–host dye,” Appl. Phys. Lett. 74, 2572–2574 (1999).
    [CrossRef]
  6. B. I. Sturman, M. Yu. Goul’kov, and S. G. Odoulov, “Phenomenological analysis of the parametric scattering processes in photorefractive crystals,” J. Opt. Soc. Am. B 13, 577–583 (1996).
    [CrossRef]
  7. I. C. Khoo, “Temporal dependence of optical nonlinearities of nematic liquid crystals and the unusual polarization dependence of self diffraction in 4–4-bis(heptyloxy) azoxybenzene,” Mol. Cryst. Liq. Cryst. 207, 317–329 (1991).
    [CrossRef]
  8. S. Slussarenko, O. Francescangeli, and F. Simoni, “High resolution polarization gratings in liquid crystals,” Appl. Phys. Lett. 71, 3613–3615 (1997).
    [CrossRef]
  9. L. Nikolova and T. Todorv, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579–588 (1984).
    [CrossRef]
  10. K. Anderle and J. H. Wendorff, “Holographic recording, using liquid crystalline side chain polymers,” Mol. Cryst. Liq. Cryst. 243, 51–75 (1994).
    [CrossRef]
  11. I. Naydenova, L. Nikolova, T. Todorov, N. C. Holme, P. S. Ramanujan, and S. Hvilsted, “Diffraction from polarization holographic gratings with surface relief in side-chain azobenzene polyesters,” J. Opt. Soc. Am. B 15, 1257–1265 (1998).
    [CrossRef]
  12. F. Lagugne Labarthet and P. Rochon, “Polarization analysis of diffracted orders from a birefringence grating recorded on azobenzene containing polymer,” Appl. Phys. Lett. 75, 1377–1379 (1999).
    [CrossRef]
  13. G. Cipparrone, A. Mazzulla, and G. Russo, “Diffraction gratings in polymer-dispersed liquid crystals recorded by means of polarization holographic technique,” Appl. Phys. Lett. 78, 1186–1188 (2001).
    [CrossRef]
  14. A. Y.-G. Fuh, C.-R. Lee, Y.-H. Ho, T.-S. Mo, and P.-M. Liu, “Study of a holographic grating based on dye-doped polymer-ball-type polymer dispersed liquid crystal films,” Jpn. J. Appl. Phys. 40, 6868–6871 (2001).
    [CrossRef]
  15. D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, Boston, Mass., 1990).
  16. J. Tervo and J. Turunen, “Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings,” Opt. Lett. 25, 785–786 (2000).
    [CrossRef]
  17. J. Turunen, F. Wyrowski, and E. Noponen, “Transition from paraxial to non-paraxial domain in diffractive optics,” in Diffractive and Holographic Optics Technology, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2152, 34–43 (1994).
    [CrossRef]
  18. A. Y.-G. Fuh, C.-C. Liao, K.-C. Hsu, C.-L. Lu, and C.-Y. Tsai, “Dynamic studies of holographic gratings in dye-doped liquid crystal films,” Opt. Lett. 26, 1767–1769 (2001).
    [CrossRef]

2001 (3)

G. Cipparrone, A. Mazzulla, and G. Russo, “Diffraction gratings in polymer-dispersed liquid crystals recorded by means of polarization holographic technique,” Appl. Phys. Lett. 78, 1186–1188 (2001).
[CrossRef]

A. Y.-G. Fuh, C.-R. Lee, Y.-H. Ho, T.-S. Mo, and P.-M. Liu, “Study of a holographic grating based on dye-doped polymer-ball-type polymer dispersed liquid crystal films,” Jpn. J. Appl. Phys. 40, 6868–6871 (2001).
[CrossRef]

A. Y.-G. Fuh, C.-C. Liao, K.-C. Hsu, C.-L. Lu, and C.-Y. Tsai, “Dynamic studies of holographic gratings in dye-doped liquid crystal films,” Opt. Lett. 26, 1767–1769 (2001).
[CrossRef]

2000 (1)

1999 (2)

F. Lagugne Labarthet and P. Rochon, “Polarization analysis of diffracted orders from a birefringence grating recorded on azobenzene containing polymer,” Appl. Phys. Lett. 75, 1377–1379 (1999).
[CrossRef]

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, “Optically switchable gratings based on polymer-dispersed liquid crystal films doped with a guest–host dye,” Appl. Phys. Lett. 74, 2572–2574 (1999).
[CrossRef]

1998 (2)

A. Y.-G. Fuh, T.-C. Ko, M.-S. Tsai, C.-Y. Huang, and L.-C. Chien, “Dynamical studies of gratings formed in polymer-dispersed liquid crystal films,” J. Appl. Phys. 83, 679–683 (1998).
[CrossRef]

I. Naydenova, L. Nikolova, T. Todorov, N. C. Holme, P. S. Ramanujan, and S. Hvilsted, “Diffraction from polarization holographic gratings with surface relief in side-chain azobenzene polyesters,” J. Opt. Soc. Am. B 15, 1257–1265 (1998).
[CrossRef]

1997 (1)

S. Slussarenko, O. Francescangeli, and F. Simoni, “High resolution polarization gratings in liquid crystals,” Appl. Phys. Lett. 71, 3613–3615 (1997).
[CrossRef]

1996 (1)

1994 (3)

K. Anderle and J. H. Wendorff, “Holographic recording, using liquid crystalline side chain polymers,” Mol. Cryst. Liq. Cryst. 243, 51–75 (1994).
[CrossRef]

J. Turunen, F. Wyrowski, and E. Noponen, “Transition from paraxial to non-paraxial domain in diffractive optics,” in Diffractive and Holographic Optics Technology, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2152, 34–43 (1994).
[CrossRef]

R. L. Sutherland, V. P. Tondiglia, and L. V. Natarajan, “Electrically switchable volume gratings in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

1991 (2)

R. Yamaguchi and S. Sato, “Memory effects of light transmission properties in polymer-dispersed liquid crystal (PDLC) films,” Jpn. J. Appl. Phys. 30, L616–L618 (1991).
[CrossRef]

I. C. Khoo, “Temporal dependence of optical nonlinearities of nematic liquid crystals and the unusual polarization dependence of self diffraction in 4–4-bis(heptyloxy) azoxybenzene,” Mol. Cryst. Liq. Cryst. 207, 317–329 (1991).
[CrossRef]

1986 (1)

J. W. Doane, N. A. Vaz, B.-G. Wu, and S. Zumer, “Field controlled light scattering from nematic microdroplet,” Appl. Phys. Lett. 48, 269–272 (1986).
[CrossRef]

1984 (1)

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

Anderle, K.

K. Anderle and J. H. Wendorff, “Holographic recording, using liquid crystalline side chain polymers,” Mol. Cryst. Liq. Cryst. 243, 51–75 (1994).
[CrossRef]

Chien, L.-C.

A. Y.-G. Fuh, T.-C. Ko, M.-S. Tsai, C.-Y. Huang, and L.-C. Chien, “Dynamical studies of gratings formed in polymer-dispersed liquid crystal films,” J. Appl. Phys. 83, 679–683 (1998).
[CrossRef]

Cipparrone, G.

G. Cipparrone, A. Mazzulla, and G. Russo, “Diffraction gratings in polymer-dispersed liquid crystals recorded by means of polarization holographic technique,” Appl. Phys. Lett. 78, 1186–1188 (2001).
[CrossRef]

Doane, J. W.

J. W. Doane, N. A. Vaz, B.-G. Wu, and S. Zumer, “Field controlled light scattering from nematic microdroplet,” Appl. Phys. Lett. 48, 269–272 (1986).
[CrossRef]

Francescangeli, O.

S. Slussarenko, O. Francescangeli, and F. Simoni, “High resolution polarization gratings in liquid crystals,” Appl. Phys. Lett. 71, 3613–3615 (1997).
[CrossRef]

Fuh, A. Y.-G.

A. Y.-G. Fuh, C.-R. Lee, Y.-H. Ho, T.-S. Mo, and P.-M. Liu, “Study of a holographic grating based on dye-doped polymer-ball-type polymer dispersed liquid crystal films,” Jpn. J. Appl. Phys. 40, 6868–6871 (2001).
[CrossRef]

A. Y.-G. Fuh, C.-C. Liao, K.-C. Hsu, C.-L. Lu, and C.-Y. Tsai, “Dynamic studies of holographic gratings in dye-doped liquid crystal films,” Opt. Lett. 26, 1767–1769 (2001).
[CrossRef]

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, “Optically switchable gratings based on polymer-dispersed liquid crystal films doped with a guest–host dye,” Appl. Phys. Lett. 74, 2572–2574 (1999).
[CrossRef]

A. Y.-G. Fuh, T.-C. Ko, M.-S. Tsai, C.-Y. Huang, and L.-C. Chien, “Dynamical studies of gratings formed in polymer-dispersed liquid crystal films,” J. Appl. Phys. 83, 679–683 (1998).
[CrossRef]

Goul’kov, M. Yu.

Ho, Y.-H.

A. Y.-G. Fuh, C.-R. Lee, Y.-H. Ho, T.-S. Mo, and P.-M. Liu, “Study of a holographic grating based on dye-doped polymer-ball-type polymer dispersed liquid crystal films,” Jpn. J. Appl. Phys. 40, 6868–6871 (2001).
[CrossRef]

Holme, N. C.

Hsu, K.-C.

Huang, C.-Y.

A. Y.-G. Fuh, T.-C. Ko, M.-S. Tsai, C.-Y. Huang, and L.-C. Chien, “Dynamical studies of gratings formed in polymer-dispersed liquid crystal films,” J. Appl. Phys. 83, 679–683 (1998).
[CrossRef]

Huang, L.-J.

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, “Optically switchable gratings based on polymer-dispersed liquid crystal films doped with a guest–host dye,” Appl. Phys. Lett. 74, 2572–2574 (1999).
[CrossRef]

Hvilsted, S.

Khoo, I. C.

I. C. Khoo, “Temporal dependence of optical nonlinearities of nematic liquid crystals and the unusual polarization dependence of self diffraction in 4–4-bis(heptyloxy) azoxybenzene,” Mol. Cryst. Liq. Cryst. 207, 317–329 (1991).
[CrossRef]

Ko, T.-C.

A. Y.-G. Fuh, T.-C. Ko, M.-S. Tsai, C.-Y. Huang, and L.-C. Chien, “Dynamical studies of gratings formed in polymer-dispersed liquid crystal films,” J. Appl. Phys. 83, 679–683 (1998).
[CrossRef]

Lagugne Labarthet, F.

F. Lagugne Labarthet and P. Rochon, “Polarization analysis of diffracted orders from a birefringence grating recorded on azobenzene containing polymer,” Appl. Phys. Lett. 75, 1377–1379 (1999).
[CrossRef]

Lee, C.-R.

A. Y.-G. Fuh, C.-R. Lee, Y.-H. Ho, T.-S. Mo, and P.-M. Liu, “Study of a holographic grating based on dye-doped polymer-ball-type polymer dispersed liquid crystal films,” Jpn. J. Appl. Phys. 40, 6868–6871 (2001).
[CrossRef]

Liao, C.-C.

Liu, P.-M.

A. Y.-G. Fuh, C.-R. Lee, Y.-H. Ho, T.-S. Mo, and P.-M. Liu, “Study of a holographic grating based on dye-doped polymer-ball-type polymer dispersed liquid crystal films,” Jpn. J. Appl. Phys. 40, 6868–6871 (2001).
[CrossRef]

Liu, T.-C.

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, “Optically switchable gratings based on polymer-dispersed liquid crystal films doped with a guest–host dye,” Appl. Phys. Lett. 74, 2572–2574 (1999).
[CrossRef]

Lu, C.-L.

Mazzulla, A.

G. Cipparrone, A. Mazzulla, and G. Russo, “Diffraction gratings in polymer-dispersed liquid crystals recorded by means of polarization holographic technique,” Appl. Phys. Lett. 78, 1186–1188 (2001).
[CrossRef]

Mo, T.-S.

A. Y.-G. Fuh, C.-R. Lee, Y.-H. Ho, T.-S. Mo, and P.-M. Liu, “Study of a holographic grating based on dye-doped polymer-ball-type polymer dispersed liquid crystal films,” Jpn. J. Appl. Phys. 40, 6868–6871 (2001).
[CrossRef]

Natarajan, L. V.

R. L. Sutherland, V. P. Tondiglia, and L. V. Natarajan, “Electrically switchable volume gratings in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

Naydenova, I.

Nikolova, L.

Noponen, E.

J. Turunen, F. Wyrowski, and E. Noponen, “Transition from paraxial to non-paraxial domain in diffractive optics,” in Diffractive and Holographic Optics Technology, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2152, 34–43 (1994).
[CrossRef]

Odoulov, S. G.

Ramanujan, P. S.

Rochon, P.

F. Lagugne Labarthet and P. Rochon, “Polarization analysis of diffracted orders from a birefringence grating recorded on azobenzene containing polymer,” Appl. Phys. Lett. 75, 1377–1379 (1999).
[CrossRef]

Russo, G.

G. Cipparrone, A. Mazzulla, and G. Russo, “Diffraction gratings in polymer-dispersed liquid crystals recorded by means of polarization holographic technique,” Appl. Phys. Lett. 78, 1186–1188 (2001).
[CrossRef]

Sato, S.

R. Yamaguchi and S. Sato, “Memory effects of light transmission properties in polymer-dispersed liquid crystal (PDLC) films,” Jpn. J. Appl. Phys. 30, L616–L618 (1991).
[CrossRef]

Simoni, F.

S. Slussarenko, O. Francescangeli, and F. Simoni, “High resolution polarization gratings in liquid crystals,” Appl. Phys. Lett. 71, 3613–3615 (1997).
[CrossRef]

Slussarenko, S.

S. Slussarenko, O. Francescangeli, and F. Simoni, “High resolution polarization gratings in liquid crystals,” Appl. Phys. Lett. 71, 3613–3615 (1997).
[CrossRef]

Sturman, B. I.

Sutherland, R. L.

R. L. Sutherland, V. P. Tondiglia, and L. V. Natarajan, “Electrically switchable volume gratings in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

Tervo, J.

Todorov, T.

Todorv, T.

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

Tondiglia, V. P.

R. L. Sutherland, V. P. Tondiglia, and L. V. Natarajan, “Electrically switchable volume gratings in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

Tsai, C.-Y.

Tsai, M.-S.

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, “Optically switchable gratings based on polymer-dispersed liquid crystal films doped with a guest–host dye,” Appl. Phys. Lett. 74, 2572–2574 (1999).
[CrossRef]

A. Y.-G. Fuh, T.-C. Ko, M.-S. Tsai, C.-Y. Huang, and L.-C. Chien, “Dynamical studies of gratings formed in polymer-dispersed liquid crystal films,” J. Appl. Phys. 83, 679–683 (1998).
[CrossRef]

Turunen, J.

J. Tervo and J. Turunen, “Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings,” Opt. Lett. 25, 785–786 (2000).
[CrossRef]

J. Turunen, F. Wyrowski, and E. Noponen, “Transition from paraxial to non-paraxial domain in diffractive optics,” in Diffractive and Holographic Optics Technology, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2152, 34–43 (1994).
[CrossRef]

Vaz, N. A.

J. W. Doane, N. A. Vaz, B.-G. Wu, and S. Zumer, “Field controlled light scattering from nematic microdroplet,” Appl. Phys. Lett. 48, 269–272 (1986).
[CrossRef]

Wendorff, J. H.

K. Anderle and J. H. Wendorff, “Holographic recording, using liquid crystalline side chain polymers,” Mol. Cryst. Liq. Cryst. 243, 51–75 (1994).
[CrossRef]

Wu, B.-G.

J. W. Doane, N. A. Vaz, B.-G. Wu, and S. Zumer, “Field controlled light scattering from nematic microdroplet,” Appl. Phys. Lett. 48, 269–272 (1986).
[CrossRef]

Wyrowski, F.

J. Turunen, F. Wyrowski, and E. Noponen, “Transition from paraxial to non-paraxial domain in diffractive optics,” in Diffractive and Holographic Optics Technology, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2152, 34–43 (1994).
[CrossRef]

Yamaguchi, R.

R. Yamaguchi and S. Sato, “Memory effects of light transmission properties in polymer-dispersed liquid crystal (PDLC) films,” Jpn. J. Appl. Phys. 30, L616–L618 (1991).
[CrossRef]

Zumer, S.

J. W. Doane, N. A. Vaz, B.-G. Wu, and S. Zumer, “Field controlled light scattering from nematic microdroplet,” Appl. Phys. Lett. 48, 269–272 (1986).
[CrossRef]

Appl. Phys. Lett. (6)

J. W. Doane, N. A. Vaz, B.-G. Wu, and S. Zumer, “Field controlled light scattering from nematic microdroplet,” Appl. Phys. Lett. 48, 269–272 (1986).
[CrossRef]

R. L. Sutherland, V. P. Tondiglia, and L. V. Natarajan, “Electrically switchable volume gratings in polymer-dispersed liquid crystals,” Appl. Phys. Lett. 64, 1074–1076 (1994).
[CrossRef]

A. Y.-G. Fuh, M.-S. Tsai, L.-J. Huang, and T.-C. Liu, “Optically switchable gratings based on polymer-dispersed liquid crystal films doped with a guest–host dye,” Appl. Phys. Lett. 74, 2572–2574 (1999).
[CrossRef]

S. Slussarenko, O. Francescangeli, and F. Simoni, “High resolution polarization gratings in liquid crystals,” Appl. Phys. Lett. 71, 3613–3615 (1997).
[CrossRef]

F. Lagugne Labarthet and P. Rochon, “Polarization analysis of diffracted orders from a birefringence grating recorded on azobenzene containing polymer,” Appl. Phys. Lett. 75, 1377–1379 (1999).
[CrossRef]

G. Cipparrone, A. Mazzulla, and G. Russo, “Diffraction gratings in polymer-dispersed liquid crystals recorded by means of polarization holographic technique,” Appl. Phys. Lett. 78, 1186–1188 (2001).
[CrossRef]

J. Appl. Phys. (1)

A. Y.-G. Fuh, T.-C. Ko, M.-S. Tsai, C.-Y. Huang, and L.-C. Chien, “Dynamical studies of gratings formed in polymer-dispersed liquid crystal films,” J. Appl. Phys. 83, 679–683 (1998).
[CrossRef]

J. Opt. Soc. Am. B (2)

Jpn. J. Appl. Phys. (2)

A. Y.-G. Fuh, C.-R. Lee, Y.-H. Ho, T.-S. Mo, and P.-M. Liu, “Study of a holographic grating based on dye-doped polymer-ball-type polymer dispersed liquid crystal films,” Jpn. J. Appl. Phys. 40, 6868–6871 (2001).
[CrossRef]

R. Yamaguchi and S. Sato, “Memory effects of light transmission properties in polymer-dispersed liquid crystal (PDLC) films,” Jpn. J. Appl. Phys. 30, L616–L618 (1991).
[CrossRef]

Mol. Cryst. Liq. Cryst. (2)

I. C. Khoo, “Temporal dependence of optical nonlinearities of nematic liquid crystals and the unusual polarization dependence of self diffraction in 4–4-bis(heptyloxy) azoxybenzene,” Mol. Cryst. Liq. Cryst. 207, 317–329 (1991).
[CrossRef]

K. Anderle and J. H. Wendorff, “Holographic recording, using liquid crystalline side chain polymers,” Mol. Cryst. Liq. Cryst. 243, 51–75 (1994).
[CrossRef]

Opt. Acta (1)

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

Opt. Lett. (2)

Proc. SPIE (1)

J. Turunen, F. Wyrowski, and E. Noponen, “Transition from paraxial to non-paraxial domain in diffractive optics,” in Diffractive and Holographic Optics Technology, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2152, 34–43 (1994).
[CrossRef]

Other (1)

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, Boston, Mass., 1990).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic diagram of the experimental setup, (b) configuration of the spatially modulated polarization setup by s- and p-polarized interfering fields.

Fig. 2
Fig. 2

Measured diffraction efficiencies of the probe beam with various polarizations as a function of angle β: (a) α=0°, (b) α=90°, (c) α=45°, (d) α=45°. α (β) is the angle between the transmission axis of the polarizer (analyzer) and the direction of the stripes (x axis; refer to Fig. 1). The magnitude of the second-order diffracted beam intensity has been magnified ten times.

Fig. 3
Fig. 3

Grating patterns observed under a polarizing optical microscope with a crossed analyzer, following the rotation of the stripes of the PG at an angle α with the polarizer axis: (a) α=0°, (b) α=45°, (c) α=90°.

Fig. 4
Fig. 4

Simulated diffraction efficiencies of the sample under the conditions that yielded the results in Fig. 2. The magnitude of the second-order diffracted beam intensity has been magnified ten times.

Equations (17)

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

E[E1 exp(iδ/2)i+E2 cos(θ/2)exp(-iδ/2)j]×exp{i[(2π/λw)z cos(θ/2)-ωt]},
[TP(y)]x-y=exp(iϕ0)×exp(iΔϕ cos δ)00exp(-iΔϕ cos δ),
[TA(y)]x-y=T0+ΔT cos δ00T0-ΔT cos δ,
[T(y)]x-y=[TP(y)]x-y[TA(y)]x-y=[TA(y)]x-y[TP(y)]x-y.
[T(y)]x-y=S(-45°)[T(y)]x-yS(45°),
[T(y)]x-y=exp(iϕ0)/2(a+b)(a-b)(a-b)(a+b),
Et(y)=T(y)Ei,
Ei=Ei0cos αsin α.
Et(y)=m=-m=  Dm exp(i2πmy/Λ),
Dm(α)=(1/Λ)0Λ  Et(y)exp(-i2πmy/Λ)dy,
Dm(α)=Ei0 exp(iϕ0)(a0δm,0+a2δm,±2)cos α+(a1δm,±1+a3δm,±3)sin α(a0δm,0+a2δm,±2)sin α+(a1δm,±1+a3δm,±3)cos α,
D0=Ei0 exp(iϕ0)a0cos αsin α,
D±1=Ei0 exp(iϕ0)a1sin αcos α,
D±2=Ei0 exp(iϕ0)a2cos αsin α,
D±3=Ei0 exp(iϕ0)a3sin αcos α,
Dm(α, β)=A(β)Dm(α)=cos2 βsin β cos βsin β cos βsin2 βDm(α),
ηm|Dm(α, β)|2/|Ei|2.

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