Abstract

The channel formation by the self-trapping of a (1 + 1)D beam in polymeric media based on a polymethylmethacrylate (PMMA) matrix containing phenanthrenequinone (PQ) molecules is predicted theoretically and observed experimentally for the first time. Particular attention is paid to the effect of thermal beam expansion, which in conjunction with the photorefractive nonlinearity of the medium results in the possibility to control optically the geometrical parameters of the generated channel.

© 2011 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2010 (1)

V. Matusevich, E. Tolstik, A. Winkler, and R. Kowarschik, “Head-Up-Displays from Plexiglas,” J. Photonik 2, 44–45 (2010).

2009 (2)

O. Kashin, E. Tolstik, V. Matusevich, and R. Kowarschik, “Numerical investigation of the (1+1)D self-trapping of laser beams in polymeric films based on polymethylmethacrylate and phenanthrenequinone,” J. Opt. Soc. Am. B 26(11), 2152–2156 (2009).
[CrossRef]

E. Tolstik, A. Winkler, V. Matusevich, R. Kowarschik, U. V. Mahilny, D. N. Marmysh, Y. I. Matusevich, and L. P. Krul, “PMMA-PQ Photopolymers for Head-Up-Displays,” IEEE Photon. Technol. Lett. 21(12), 784–786 (2009).
[CrossRef]

2008 (3)

2007 (2)

2006 (2)

U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006).
[CrossRef]

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer (Guildf.) 47(14), 4893–4896 (2006).
[CrossRef]

2005 (1)

M. Assael, S. Botsios, K. Gialou, and I. Metaxa, “Thermal Conductivity of Polymethyl Methacrylate (PMMA) and Borosilicate Crown Glass BK7,” Int. J. Thermophys. 26(5), 1595–1605 (2005).
[CrossRef]

2004 (2)

K. Smolders and J. Baeyens, “Thermal degradation of PMMA in fluidised beds,” Waste Manag. 24(8), 849–857 (2004).
[CrossRef] [PubMed]

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93(14), 143905 (2004).
[CrossRef] [PubMed]

2001 (1)

J. Lawrence, F. O'Neill, and J. Sheridan, “Photopolymer holographic recording material,” Optik, Int. J. Light 112, 449–463 (2001).
[CrossRef]

2000 (1)

G. Stegeman, D. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000).
[CrossRef]

1999 (1)

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

1996 (1)

1984 (1)

T. R. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical nonlinear Schrödinger equation,” J. Comput. Phys. 55(2), 203–230 (1984).
[CrossRef]

1975 (1)

1968 (1)

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968).
[CrossRef]

Ablowitz, M. J.

T. R. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical nonlinear Schrödinger equation,” J. Comput. Phys. 55(2), 203–230 (1984).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968).
[CrossRef]

Assael, M.

M. Assael, S. Botsios, K. Gialou, and I. Metaxa, “Thermal Conductivity of Polymethyl Methacrylate (PMMA) and Borosilicate Crown Glass BK7,” Int. J. Thermophys. 26(5), 1595–1605 (2005).
[CrossRef]

Baeyens, J.

K. Smolders and J. Baeyens, “Thermal degradation of PMMA in fluidised beds,” Waste Manag. 24(8), 849–857 (2004).
[CrossRef] [PubMed]

Booth, B. L.

Botsios, S.

M. Assael, S. Botsios, K. Gialou, and I. Metaxa, “Thermal Conductivity of Polymethyl Methacrylate (PMMA) and Borosilicate Crown Glass BK7,” Int. J. Thermophys. 26(5), 1595–1605 (2005).
[CrossRef]

Bruendel, M.

Butovskaya, G. V.

Christodoulides, D.

G. Stegeman, D. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000).
[CrossRef]

Crégut, O.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93(14), 143905 (2004).
[CrossRef] [PubMed]

Dorkenoo, K. D.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93(14), 143905 (2004).
[CrossRef] [PubMed]

Fort, A.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93(14), 143905 (2004).
[CrossRef] [PubMed]

Gialou, K.

M. Assael, S. Botsios, K. Gialou, and I. Metaxa, “Thermal Conductivity of Polymethyl Methacrylate (PMMA) and Borosilicate Crown Glass BK7,” Int. J. Thermophys. 26(5), 1595–1605 (2005).
[CrossRef]

Gillot, F.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93(14), 143905 (2004).
[CrossRef] [PubMed]

Henzi, P.

Hoff, D.

Ichihashi, Y.

Kashin, O.

Kewitsch, A. S.

Khokhlov, R. V.

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968).
[CrossRef]

Kowarschik, R.

V. Matusevich, E. Tolstik, A. Winkler, and R. Kowarschik, “Head-Up-Displays from Plexiglas,” J. Photonik 2, 44–45 (2010).

E. Tolstik, A. Winkler, V. Matusevich, R. Kowarschik, U. V. Mahilny, D. N. Marmysh, Y. I. Matusevich, and L. P. Krul, “PMMA-PQ Photopolymers for Head-Up-Displays,” IEEE Photon. Technol. Lett. 21(12), 784–786 (2009).
[CrossRef]

O. Kashin, E. Tolstik, V. Matusevich, and R. Kowarschik, “Numerical investigation of the (1+1)D self-trapping of laser beams in polymeric films based on polymethylmethacrylate and phenanthrenequinone,” J. Opt. Soc. Am. B 26(11), 2152–2156 (2009).
[CrossRef]

E. Tolstik, O. Kashin, A. Matusevich, V. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Non-local response in glass-like polymer storage materials based on poly (methylmethacrylate) with distributed phenanthrenequinone,” Opt. Express 16(15), 11253–11258 (2008).
[CrossRef] [PubMed]

U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008).
[CrossRef]

V. Matusevich, A. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Holographic volume absorption grating in glass-like polymer recording material,” Opt. Express 16(3), 1552–1558 (2008).
[CrossRef] [PubMed]

L. P. Krul, V. Matusevich, D. Hoff, R. Kowarschik, Y. I. Matusevich, G. V. Butovskaya, and E. A. Murashko, “Modified polymethylmethacrylate as a base for thermostable optical recording media,” Opt. Express 15(14), 8543–8549 (2007).
[CrossRef] [PubMed]

U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006).
[CrossRef]

Krul, L. P.

Lawrence, J.

J. Lawrence, F. O'Neill, and J. Sheridan, “Photopolymer holographic recording material,” Optik, Int. J. Light 112, 449–463 (2001).
[CrossRef]

Leblond, H.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93(14), 143905 (2004).
[CrossRef] [PubMed]

Lin, P.

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer (Guildf.) 47(14), 4893–4896 (2006).
[CrossRef]

Mahilny, U. V.

E. Tolstik, A. Winkler, V. Matusevich, R. Kowarschik, U. V. Mahilny, D. N. Marmysh, Y. I. Matusevich, and L. P. Krul, “PMMA-PQ Photopolymers for Head-Up-Displays,” IEEE Photon. Technol. Lett. 21(12), 784–786 (2009).
[CrossRef]

U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008).
[CrossRef]

U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006).
[CrossRef]

Marmysh, D. N.

E. Tolstik, A. Winkler, V. Matusevich, R. Kowarschik, U. V. Mahilny, D. N. Marmysh, Y. I. Matusevich, and L. P. Krul, “PMMA-PQ Photopolymers for Head-Up-Displays,” IEEE Photon. Technol. Lett. 21(12), 784–786 (2009).
[CrossRef]

U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008).
[CrossRef]

U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006).
[CrossRef]

Matusevich, A.

Matusevich, V.

V. Matusevich, E. Tolstik, A. Winkler, and R. Kowarschik, “Head-Up-Displays from Plexiglas,” J. Photonik 2, 44–45 (2010).

O. Kashin, E. Tolstik, V. Matusevich, and R. Kowarschik, “Numerical investigation of the (1+1)D self-trapping of laser beams in polymeric films based on polymethylmethacrylate and phenanthrenequinone,” J. Opt. Soc. Am. B 26(11), 2152–2156 (2009).
[CrossRef]

E. Tolstik, A. Winkler, V. Matusevich, R. Kowarschik, U. V. Mahilny, D. N. Marmysh, Y. I. Matusevich, and L. P. Krul, “PMMA-PQ Photopolymers for Head-Up-Displays,” IEEE Photon. Technol. Lett. 21(12), 784–786 (2009).
[CrossRef]

E. Tolstik, O. Kashin, A. Matusevich, V. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Non-local response in glass-like polymer storage materials based on poly (methylmethacrylate) with distributed phenanthrenequinone,” Opt. Express 16(15), 11253–11258 (2008).
[CrossRef] [PubMed]

V. Matusevich, A. Matusevich, R. Kowarschik, Y. I. Matusevich, and L. P. Krul, “Holographic volume absorption grating in glass-like polymer recording material,” Opt. Express 16(3), 1552–1558 (2008).
[CrossRef] [PubMed]

U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008).
[CrossRef]

L. P. Krul, V. Matusevich, D. Hoff, R. Kowarschik, Y. I. Matusevich, G. V. Butovskaya, and E. A. Murashko, “Modified polymethylmethacrylate as a base for thermostable optical recording media,” Opt. Express 15(14), 8543–8549 (2007).
[CrossRef] [PubMed]

U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006).
[CrossRef]

Matusevich, Y. I.

Metaxa, I.

M. Assael, S. Botsios, K. Gialou, and I. Metaxa, “Thermal Conductivity of Polymethyl Methacrylate (PMMA) and Borosilicate Crown Glass BK7,” Int. J. Thermophys. 26(5), 1595–1605 (2005).
[CrossRef]

Mohr, J.

Murashko, E. A.

O'Neill, F.

J. Lawrence, F. O'Neill, and J. Sheridan, “Photopolymer holographic recording material,” Optik, Int. J. Light 112, 449–463 (2001).
[CrossRef]

Rabus, D. G.

Segev, M.

G. Stegeman, D. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000).
[CrossRef]

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Sheridan, J.

J. Lawrence, F. O'Neill, and J. Sheridan, “Photopolymer holographic recording material,” Optik, Int. J. Light 112, 449–463 (2001).
[CrossRef]

Smolders, K.

K. Smolders and J. Baeyens, “Thermal degradation of PMMA in fluidised beds,” Waste Manag. 24(8), 849–857 (2004).
[CrossRef] [PubMed]

Sonnefraud, Y.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the refractive index in photopolymerizable materials for (2+1)D solitary wave guide formation,” Phys. Rev. Lett. 93(14), 143905 (2004).
[CrossRef] [PubMed]

Stankevich, A. I.

U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006).
[CrossRef]

Stegeman, G.

G. Stegeman, D. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Sukhorukov, A. P.

S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, “Self-focusing and diffraction of light in a nonlinear medium,” Sov. Phys. Usp. 10(5), 609–636 (1968).
[CrossRef]

Sun, F.

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer (Guildf.) 47(14), 4893–4896 (2006).
[CrossRef]

Taha, T. R.

T. R. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical nonlinear Schrödinger equation,” J. Comput. Phys. 55(2), 203–230 (1984).
[CrossRef]

Tolstik, A. L.

U. V. Mahilny, D. N. Marmysh, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Phase hologram formation in highly concentrated phenanthrenequinone–PMMA media,” J. Opt. A, Pure Appl. Opt. 10(8), 085302 (2008).
[CrossRef]

U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006).
[CrossRef]

Tolstik, E.

Winkler, A.

V. Matusevich, E. Tolstik, A. Winkler, and R. Kowarschik, “Head-Up-Displays from Plexiglas,” J. Photonik 2, 44–45 (2010).

E. Tolstik, A. Winkler, V. Matusevich, R. Kowarschik, U. V. Mahilny, D. N. Marmysh, Y. I. Matusevich, and L. P. Krul, “PMMA-PQ Photopolymers for Head-Up-Displays,” IEEE Photon. Technol. Lett. 21(12), 784–786 (2009).
[CrossRef]

Yariv, A.

Zhang, Z.

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer (Guildf.) 47(14), 4893–4896 (2006).
[CrossRef]

Zhao, P.

Z. Zhang, P. Zhao, P. Lin, and F. Sun, “Thermo-optic coefficients of polymers for optical waveguide applications,” Polymer (Guildf.) 47(14), 4893–4896 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

U. V. Mahilny, D. N. Marmysh, A. I. Stankevich, A. L. Tolstik, V. Matusevich, and R. Kowarschik, “Holographic volume gratings in a glass-like polymer material,” Appl. Phys. B 82(2), 299–302 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

G. Stegeman, D. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1419–1427 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

E. Tolstik, A. Winkler, V. Matusevich, R. Kowarschik, U. V. Mahilny, D. N. Marmysh, Y. I. Matusevich, and L. P. Krul, “PMMA-PQ Photopolymers for Head-Up-Displays,” IEEE Photon. Technol. Lett. 21(12), 784–786 (2009).
[CrossRef]

Int. J. Thermophys. (1)

M. Assael, S. Botsios, K. Gialou, and I. Metaxa, “Thermal Conductivity of Polymethyl Methacrylate (PMMA) and Borosilicate Crown Glass BK7,” Int. J. Thermophys. 26(5), 1595–1605 (2005).
[CrossRef]

J. Photonik (1)

V. Matusevich, E. Tolstik, A. Winkler, and R. Kowarschik, “Head-Up-Displays from Plexiglas,” J. Photonik 2, 44–45 (2010).

J. Comput. Phys. (1)

T. R. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical nonlinear Schrödinger equation,” J. Comput. Phys. 55(2), 203–230 (1984).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

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Supplementary Material (1)

» Media 1: MPG (1391 KB)     

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Figures (7)

Fig. 1
Fig. 1

Schematic setup for formation of a self-trapped channel using Ar-laser illumination and a microobjective (a); Self-trapping in a PQ-PMMA polymeric layer, top view (b).

Fig. 2
Fig. 2

Experimental self-trapping formation in the PQ-PMMA layer by Ar-laser illumination during 12 min (a)-(e); and Ar-laser-light propagation in a pure PMMA medium through the microobjective with a magnification factor of 10 and a focal length of 16 mm (f) [laser power is 8 mW, PQ-concentration is 2.5 mol%, layer thickness is 400 µm].

Fig. 3
Fig. 3

Distribution of the thermal changes of the refractive index in dependence on the illumination time for different lengths of the polymeric layer [1.5 mm, 3 mm, 4.5 mm and 6 mm].

Fig. 4
Fig. 4

Formation of the refractive-index profile for illumination times of 120 s (a), 180 s (b), 240 s (c) and 300 s (d).

Fig. 5
Fig. 5

Evolution of the spreading of temperature in the polymeric layer during an illumination period of 300 s (Media 1).

Fig. 6
Fig. 6

Simulation of the refractive-index profiles for input powers of 2 mW (dotted line) and 8 mW (solid line).

Fig. 7
Fig. 7

Measured normalized refractive-index profiles for input beams with a power of 8 mW (a) and of 2 mW (b) and top view of the polymeric layers.

Equations (7)

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Δ n T = α I t C ρ n T ,
Δ T t a T ( 2 Δ T x 2 + 2 Δ T z 2 ) + b Δ T = α I C ρ ,
Δ T L t = a T ( 2 Δ T x 2 + 2 Δ T z 2 ) b Δ T ,
Δ T N L t = α I C ρ .
Δ n T = n T Δ T ,
Δ n P Q = ( n 2 + 2 ) 2 6 n [ R H P Q R C H P Q R ( x , z , t ) R P Q C P Q ( x , z , t ) ] .
Δ n Σ = Δ n P Q + Δ n T .

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