Abstract

The diffraction efficiency of phase gratings recorded by two s-polarized waves in a polymer is modeled. The molecular orientation distribution along the grating period is seen to become homogeneous as a function of time due to saturation. Experimental data is presented, in agreement with the model.

©2009 Optical Society of America

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References

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  1. A. Natansohn and P. Rochon, “Photoinduced Motions in Azo-Containing Polymers,” Chem. Rev. 102, 4139–4175 (2002).
    [Crossref] [PubMed]
  2. N. K. Viswanathan, S. Balasubramanian, J. Kumar, and S. K. Tripathy, “Investigation of Birefringence and Surface Relief Grating Formation in Azopolymer Films,” J. Macomol. Sci. Pure Appl. Chem. A 38, 1445–1462 (2001).
    [Crossref]
  3. 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,” J. Phys. Chem. B 103, 6690–6699 (1999).
    [Crossref]
  4. U. Pietsch, P. Rochon, and A. Natansohn, “Formation of a Buried Lateral Density Grating in Azobenzene Polymer Films,” Adv. Mater. 12, 1129–1132 (2000).
    [Crossref]
  5. D. Y. Kim, L. Li, X. L. Jiang, V. Shivshankar, J. Kumar, and S. K. Tripathy, “Polarized Laser Induced Holographic Surface Relief Gratings on Polymer Films,” Macromolecules 28, 8835–8839 (1995).
    [Crossref]
  6. A. Sobolewska and S. Bartkiewicz, “Analysis of the Kinetics of Diffraction Efficiency during the Holographic Grating Recording in Azobenzene Functionalized Polymers,” J. Phys. Chem. B 111, 1536–1544 (2007).
    [Crossref] [PubMed]
  7. N.C.R. Holme, L. Nikolova, and P. S. Ramanujam, “An Analysis of the Anisotropic and Topographic Gratings in a Side-chain Liquid Cristalline Azobenzene Polyester,” Appl. Phys. Lett. 70, 1518–1520 (1997).
    [Crossref]
  8. M. Helgert, B. Fleck, L. Wenke, S. Hvilsted, and P. S. Ramanujam, “An Improved Method for Separating the Kinetics of Anisotropic and Topographic Grating in Side-chain Azobenzene Polyesters,” Appl. Phys. B 70, 803–807 (2000).
  9. M. Dumont, “Photoinduced Orientational Order in Dye-doped Amorphous Polymeric Films,” Mol. Cryst. Liq. Cryst. 282, 437–450 (1996).
    [Crossref]
  10. M.S. Ho, A. Natansohn, and P. Rochon, “Azo polymers for reversible optical storage. 9, copolymers containing two types of azobenzene side groups,” Macromolecules 29, 44–49 (1996).
    [Crossref]
  11. N. K. Viswanathan, S. Balasubramanian, L. Liang, J. Kumar, and S. K. Tripathy, “Surface-Initiated Mechanism for the Formation of Relief Gratings on Azo-Polymer Films,” J. Phys. Chem B,  102, 6064–6060 (1998).
    [Crossref]

2007 (1)

A. Sobolewska and S. Bartkiewicz, “Analysis of the Kinetics of Diffraction Efficiency during the Holographic Grating Recording in Azobenzene Functionalized Polymers,” J. Phys. Chem. B 111, 1536–1544 (2007).
[Crossref] [PubMed]

2002 (1)

A. Natansohn and P. Rochon, “Photoinduced Motions in Azo-Containing Polymers,” Chem. Rev. 102, 4139–4175 (2002).
[Crossref] [PubMed]

2001 (1)

N. K. Viswanathan, S. Balasubramanian, J. Kumar, and S. K. Tripathy, “Investigation of Birefringence and Surface Relief Grating Formation in Azopolymer Films,” J. Macomol. Sci. Pure Appl. Chem. A 38, 1445–1462 (2001).
[Crossref]

2000 (2)

U. Pietsch, P. Rochon, and A. Natansohn, “Formation of a Buried Lateral Density Grating in Azobenzene Polymer Films,” Adv. Mater. 12, 1129–1132 (2000).
[Crossref]

M. Helgert, B. Fleck, L. Wenke, S. Hvilsted, and P. S. Ramanujam, “An Improved Method for Separating the Kinetics of Anisotropic and Topographic Grating in Side-chain Azobenzene Polyesters,” Appl. Phys. B 70, 803–807 (2000).

1999 (1)

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,” J. Phys. Chem. B 103, 6690–6699 (1999).
[Crossref]

1998 (1)

N. K. Viswanathan, S. Balasubramanian, L. Liang, J. Kumar, and S. K. Tripathy, “Surface-Initiated Mechanism for the Formation of Relief Gratings on Azo-Polymer Films,” J. Phys. Chem B,  102, 6064–6060 (1998).
[Crossref]

1997 (1)

N.C.R. Holme, L. Nikolova, and P. S. Ramanujam, “An Analysis of the Anisotropic and Topographic Gratings in a Side-chain Liquid Cristalline Azobenzene Polyester,” Appl. Phys. Lett. 70, 1518–1520 (1997).
[Crossref]

1996 (2)

M. Dumont, “Photoinduced Orientational Order in Dye-doped Amorphous Polymeric Films,” Mol. Cryst. Liq. Cryst. 282, 437–450 (1996).
[Crossref]

M.S. Ho, A. Natansohn, and P. Rochon, “Azo polymers for reversible optical storage. 9, copolymers containing two types of azobenzene side groups,” Macromolecules 29, 44–49 (1996).
[Crossref]

1995 (1)

D. Y. Kim, L. Li, X. L. Jiang, V. Shivshankar, J. Kumar, and S. K. Tripathy, “Polarized Laser Induced Holographic Surface Relief Gratings on Polymer Films,” Macromolecules 28, 8835–8839 (1995).
[Crossref]

Balasubramanian, S.

N. K. Viswanathan, S. Balasubramanian, J. Kumar, and S. K. Tripathy, “Investigation of Birefringence and Surface Relief Grating Formation in Azopolymer Films,” J. Macomol. Sci. Pure Appl. Chem. A 38, 1445–1462 (2001).
[Crossref]

N. K. Viswanathan, S. Balasubramanian, L. Liang, J. Kumar, and S. K. Tripathy, “Surface-Initiated Mechanism for the Formation of Relief Gratings on Azo-Polymer Films,” J. Phys. Chem B,  102, 6064–6060 (1998).
[Crossref]

Bartkiewicz, S.

A. Sobolewska and S. Bartkiewicz, “Analysis of the Kinetics of Diffraction Efficiency during the Holographic Grating Recording in Azobenzene Functionalized Polymers,” J. Phys. Chem. B 111, 1536–1544 (2007).
[Crossref] [PubMed]

Buffeteau, T.

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,” J. Phys. Chem. B 103, 6690–6699 (1999).
[Crossref]

Dumont, M.

M. Dumont, “Photoinduced Orientational Order in Dye-doped Amorphous Polymeric Films,” Mol. Cryst. Liq. Cryst. 282, 437–450 (1996).
[Crossref]

Fleck, B.

M. Helgert, B. Fleck, L. Wenke, S. Hvilsted, and P. S. Ramanujam, “An Improved Method for Separating the Kinetics of Anisotropic and Topographic Grating in Side-chain Azobenzene Polyesters,” Appl. Phys. B 70, 803–807 (2000).

Helgert, M.

M. Helgert, B. Fleck, L. Wenke, S. Hvilsted, and P. S. Ramanujam, “An Improved Method for Separating the Kinetics of Anisotropic and Topographic Grating in Side-chain Azobenzene Polyesters,” Appl. Phys. B 70, 803–807 (2000).

Ho, M.S.

M.S. Ho, A. Natansohn, and P. Rochon, “Azo polymers for reversible optical storage. 9, copolymers containing two types of azobenzene side groups,” Macromolecules 29, 44–49 (1996).
[Crossref]

Holme, N.C.R.

N.C.R. Holme, L. Nikolova, and P. S. Ramanujam, “An Analysis of the Anisotropic and Topographic Gratings in a Side-chain Liquid Cristalline Azobenzene Polyester,” Appl. Phys. Lett. 70, 1518–1520 (1997).
[Crossref]

Hvilsted, S.

M. Helgert, B. Fleck, L. Wenke, S. Hvilsted, and P. S. Ramanujam, “An Improved Method for Separating the Kinetics of Anisotropic and Topographic Grating in Side-chain Azobenzene Polyesters,” Appl. Phys. B 70, 803–807 (2000).

Jiang, X. L.

D. Y. Kim, L. Li, X. L. Jiang, V. Shivshankar, J. Kumar, and S. K. Tripathy, “Polarized Laser Induced Holographic Surface Relief Gratings on Polymer Films,” Macromolecules 28, 8835–8839 (1995).
[Crossref]

Kim, D. Y.

D. Y. Kim, L. Li, X. L. Jiang, V. Shivshankar, J. Kumar, and S. K. Tripathy, “Polarized Laser Induced Holographic Surface Relief Gratings on Polymer Films,” Macromolecules 28, 8835–8839 (1995).
[Crossref]

Kumar, J.

N. K. Viswanathan, S. Balasubramanian, J. Kumar, and S. K. Tripathy, “Investigation of Birefringence and Surface Relief Grating Formation in Azopolymer Films,” J. Macomol. Sci. Pure Appl. Chem. A 38, 1445–1462 (2001).
[Crossref]

N. K. Viswanathan, S. Balasubramanian, L. Liang, J. Kumar, and S. K. Tripathy, “Surface-Initiated Mechanism for the Formation of Relief Gratings on Azo-Polymer Films,” J. Phys. Chem B,  102, 6064–6060 (1998).
[Crossref]

D. Y. Kim, L. Li, X. L. Jiang, V. Shivshankar, J. Kumar, and S. K. Tripathy, “Polarized Laser Induced Holographic Surface Relief Gratings on Polymer Films,” Macromolecules 28, 8835–8839 (1995).
[Crossref]

Labarthet, F. Lagugne

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,” J. Phys. Chem. B 103, 6690–6699 (1999).
[Crossref]

Li, L.

D. Y. Kim, L. Li, X. L. Jiang, V. Shivshankar, J. Kumar, and S. K. Tripathy, “Polarized Laser Induced Holographic Surface Relief Gratings on Polymer Films,” Macromolecules 28, 8835–8839 (1995).
[Crossref]

Liang, L.

N. K. Viswanathan, S. Balasubramanian, L. Liang, J. Kumar, and S. K. Tripathy, “Surface-Initiated Mechanism for the Formation of Relief Gratings on Azo-Polymer Films,” J. Phys. Chem B,  102, 6064–6060 (1998).
[Crossref]

Natansohn, A.

A. Natansohn and P. Rochon, “Photoinduced Motions in Azo-Containing Polymers,” Chem. Rev. 102, 4139–4175 (2002).
[Crossref] [PubMed]

U. Pietsch, P. Rochon, and A. Natansohn, “Formation of a Buried Lateral Density Grating in Azobenzene Polymer Films,” Adv. Mater. 12, 1129–1132 (2000).
[Crossref]

M.S. Ho, A. Natansohn, and P. Rochon, “Azo polymers for reversible optical storage. 9, copolymers containing two types of azobenzene side groups,” Macromolecules 29, 44–49 (1996).
[Crossref]

Nikolova, L.

N.C.R. Holme, L. Nikolova, and P. S. Ramanujam, “An Analysis of the Anisotropic and Topographic Gratings in a Side-chain Liquid Cristalline Azobenzene Polyester,” Appl. Phys. Lett. 70, 1518–1520 (1997).
[Crossref]

Pietsch, U.

U. Pietsch, P. Rochon, and A. Natansohn, “Formation of a Buried Lateral Density Grating in Azobenzene Polymer Films,” Adv. Mater. 12, 1129–1132 (2000).
[Crossref]

Ramanujam, P. S.

M. Helgert, B. Fleck, L. Wenke, S. Hvilsted, and P. S. Ramanujam, “An Improved Method for Separating the Kinetics of Anisotropic and Topographic Grating in Side-chain Azobenzene Polyesters,” Appl. Phys. B 70, 803–807 (2000).

N.C.R. Holme, L. Nikolova, and P. S. Ramanujam, “An Analysis of the Anisotropic and Topographic Gratings in a Side-chain Liquid Cristalline Azobenzene Polyester,” Appl. Phys. Lett. 70, 1518–1520 (1997).
[Crossref]

Rochon, P.

A. Natansohn and P. Rochon, “Photoinduced Motions in Azo-Containing Polymers,” Chem. Rev. 102, 4139–4175 (2002).
[Crossref] [PubMed]

U. Pietsch, P. Rochon, and A. Natansohn, “Formation of a Buried Lateral Density Grating in Azobenzene Polymer Films,” Adv. Mater. 12, 1129–1132 (2000).
[Crossref]

M.S. Ho, A. Natansohn, and P. Rochon, “Azo polymers for reversible optical storage. 9, copolymers containing two types of azobenzene side groups,” Macromolecules 29, 44–49 (1996).
[Crossref]

Shivshankar, V.

D. Y. Kim, L. Li, X. L. Jiang, V. Shivshankar, J. Kumar, and S. K. Tripathy, “Polarized Laser Induced Holographic Surface Relief Gratings on Polymer Films,” Macromolecules 28, 8835–8839 (1995).
[Crossref]

Sobolewska, A.

A. Sobolewska and S. Bartkiewicz, “Analysis of the Kinetics of Diffraction Efficiency during the Holographic Grating Recording in Azobenzene Functionalized Polymers,” J. Phys. Chem. B 111, 1536–1544 (2007).
[Crossref] [PubMed]

Sourisseau, C.

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,” J. Phys. Chem. B 103, 6690–6699 (1999).
[Crossref]

Tripathy, S. K.

N. K. Viswanathan, S. Balasubramanian, J. Kumar, and S. K. Tripathy, “Investigation of Birefringence and Surface Relief Grating Formation in Azopolymer Films,” J. Macomol. Sci. Pure Appl. Chem. A 38, 1445–1462 (2001).
[Crossref]

N. K. Viswanathan, S. Balasubramanian, L. Liang, J. Kumar, and S. K. Tripathy, “Surface-Initiated Mechanism for the Formation of Relief Gratings on Azo-Polymer Films,” J. Phys. Chem B,  102, 6064–6060 (1998).
[Crossref]

D. Y. Kim, L. Li, X. L. Jiang, V. Shivshankar, J. Kumar, and S. K. Tripathy, “Polarized Laser Induced Holographic Surface Relief Gratings on Polymer Films,” Macromolecules 28, 8835–8839 (1995).
[Crossref]

Viswanathan, N. K.

N. K. Viswanathan, S. Balasubramanian, J. Kumar, and S. K. Tripathy, “Investigation of Birefringence and Surface Relief Grating Formation in Azopolymer Films,” J. Macomol. Sci. Pure Appl. Chem. A 38, 1445–1462 (2001).
[Crossref]

N. K. Viswanathan, S. Balasubramanian, L. Liang, J. Kumar, and S. K. Tripathy, “Surface-Initiated Mechanism for the Formation of Relief Gratings on Azo-Polymer Films,” J. Phys. Chem B,  102, 6064–6060 (1998).
[Crossref]

Wenke, L.

M. Helgert, B. Fleck, L. Wenke, S. Hvilsted, and P. S. Ramanujam, “An Improved Method for Separating the Kinetics of Anisotropic and Topographic Grating in Side-chain Azobenzene Polyesters,” Appl. Phys. B 70, 803–807 (2000).

Adv. Mater. (1)

U. Pietsch, P. Rochon, and A. Natansohn, “Formation of a Buried Lateral Density Grating in Azobenzene Polymer Films,” Adv. Mater. 12, 1129–1132 (2000).
[Crossref]

Appl. Phys. B (1)

M. Helgert, B. Fleck, L. Wenke, S. Hvilsted, and P. S. Ramanujam, “An Improved Method for Separating the Kinetics of Anisotropic and Topographic Grating in Side-chain Azobenzene Polyesters,” Appl. Phys. B 70, 803–807 (2000).

Appl. Phys. Lett. (1)

N.C.R. Holme, L. Nikolova, and P. S. Ramanujam, “An Analysis of the Anisotropic and Topographic Gratings in a Side-chain Liquid Cristalline Azobenzene Polyester,” Appl. Phys. Lett. 70, 1518–1520 (1997).
[Crossref]

Chem. Rev. (1)

A. Natansohn and P. Rochon, “Photoinduced Motions in Azo-Containing Polymers,” Chem. Rev. 102, 4139–4175 (2002).
[Crossref] [PubMed]

J. Macomol. Sci. Pure Appl. Chem. (1)

N. K. Viswanathan, S. Balasubramanian, J. Kumar, and S. K. Tripathy, “Investigation of Birefringence and Surface Relief Grating Formation in Azopolymer Films,” J. Macomol. Sci. Pure Appl. Chem. A 38, 1445–1462 (2001).
[Crossref]

J. Phys. Chem B (1)

N. K. Viswanathan, S. Balasubramanian, L. Liang, J. Kumar, and S. K. Tripathy, “Surface-Initiated Mechanism for the Formation of Relief Gratings on Azo-Polymer Films,” J. Phys. Chem B,  102, 6064–6060 (1998).
[Crossref]

J. Phys. Chem. B (2)

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,” J. Phys. Chem. B 103, 6690–6699 (1999).
[Crossref]

A. Sobolewska and S. Bartkiewicz, “Analysis of the Kinetics of Diffraction Efficiency during the Holographic Grating Recording in Azobenzene Functionalized Polymers,” J. Phys. Chem. B 111, 1536–1544 (2007).
[Crossref] [PubMed]

Macromolecules (2)

D. Y. Kim, L. Li, X. L. Jiang, V. Shivshankar, J. Kumar, and S. K. Tripathy, “Polarized Laser Induced Holographic Surface Relief Gratings on Polymer Films,” Macromolecules 28, 8835–8839 (1995).
[Crossref]

M.S. Ho, A. Natansohn, and P. Rochon, “Azo polymers for reversible optical storage. 9, copolymers containing two types of azobenzene side groups,” Macromolecules 29, 44–49 (1996).
[Crossref]

Mol. Cryst. Liq. Cryst. (1)

M. Dumont, “Photoinduced Orientational Order in Dye-doped Amorphous Polymeric Films,” Mol. Cryst. Liq. Cryst. 282, 437–450 (1996).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Light intensity distribution over the polymer along two periods
Fig. 2.
Fig. 2. Concentration of S,P and C states as a function of time. Birefringence is also illustrated.
Fig. 3.
Fig. 3. Distribution of S molecules along one period of the grating for different recording times.
Fig. 4.
Fig. 4. First order diffraction efficiency for S and P probe polarizations.
Fig. 5.
Fig. 5. Experimental setup for optical recording of diffraction gratings.
Fig. 6.
Fig. 6. Diffraction efficiency of the first (a) and second (b) order s- and p- components. Recording is stopped at t=200s
Fig. 7.
Fig. 7. Birefringence curves for different intensities of the excitation light.

Equations (11)

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

dSdt=aIS+Cτ
dCdt=aISCt2Cτ
dPdt=2Cτ
S(t)=S+eα+t+Seαt
C(t)=τ((α++aI)S+eα+t+(α+aI)Seαt
P(t)=3S(t)C(t)
α±=(aIτ+3)±(aIτ+3)28aIτ2τ
S+=α+aαα+ S=1S+
Δn=nsnpSP/2
η1S{P} (t) (S{P}(x,t)cos(2πx)dx)2
η2S{P} (t) (S{P}(x,t)cos(22πx)dx)2

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