Abstract

The theoretical and experimental investigation of the kinetics of photoanisotropy induction in polarization-sensitive media with significant dark relaxation on the basis of azo dyes in polymer matrices is considered. For improving dynamic characteristics of polarization-sensitive materials, new azo dye N,N-dimethyl-4((4-nitrophenyl)diazenyl)aniline has been specially synthesized, and the kinetics of photoanisotropy induction and relaxation in materials on the basis of this dye has been compared with materials on the basis of Dimethyl Yellow. It is shown that spectral sensitivity of the material with new azo dye is in the range of 470520nm, the working range is both in the visible and in the infrared range (from 520nm at least up to 3400nm), the maximum meaning of effective anisotropy is 38% (Δn0.022), and the time of photoanisotropy inducing and erasing is approximately 18ms. It is shown that, if we confine ourselves to meanings of effective anisotropy of approximately 1–2% (Δn0.007), the time of inducing/erasing will be of the order of microseconds. The use of such dynamic polarization-sensitive materials gives the possibility of a new direction—dynamic polarization holography to be developed that com bines the possibilities of both dynamic and polarization holography and that opens new prospects for applications.

© 2009 Optical Society of America

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  2. S. Kakichashvili, Polarization Holography (Nauka, 1989).
  3. S. Kakichashvili and V. Shaverdova, “Photoanisotropy in Mordant Yellow azo-dyes,” J. Sci. Appl. Photogr. Cinematogr. (USSR) 24, 342-345 (1979).
  4. S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172-2183 (1995).
    [CrossRef]
  5. S. Kakichashvili, B. Kilosanidze, and V. Shaverdova, “Anisotropy and gyrotropy of dye mordant pure-yellow induced by linear polarized light,” J. Opt. Spectrosc. (USSR) 68, 1309-1312 (1990).
  6. F. Lagugne Labarthet, S. Freiberg, C. Pellerin, M. Pézolet, A. Natansohn, and P. Rochon, “Spectroscopic and optical characterization of a series of azobenzene-containing side-chain liquid crystalline polymers,” Macromolecules 33, 6815-6823(2000).
    [CrossRef]
  7. Z. Sekkat and M. Dumont, “Polarization effects in photoisomerization of azo dyes in polymeric films,” Appl. Phys. B 53, 121-123 (1991).
    [CrossRef]
  8. L. Nedelchev, A. S. Matharu, S. Hvilsted, and P. S. Ramanujam, “Photoinduced anisotropy in a family of amorphous azobenzene polyesters for optical storage,” Appl. Opt. 42, 5918-5927 (2003).
    [CrossRef] [PubMed]
  9. I. Shatalin, V. Kakichashvili, and Sh. Kakichashvili, “Polarization hologram of 100% diffraction efficiency (polarization kinoform),” Lett. J. Tech. Phys. (USSR) 13, 1051-1055 (1987).
  10. A. Mendez and J. M. C. Jonathan, “Anisotropic gratings recorded from two circularly polarized coherent waves,” Opt. Commun. 47, 85-90 (1983).
    [CrossRef]
  11. B. Kilosanidze and G. Kakauridze, “Polarization-holographic gratings for analysis and transformations of light. 1. The analysis of completely polarized light,” Appl. Opt. 46, 1040-1049 (2007).
    [CrossRef] [PubMed]
  12. 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]
  13. B. Kilosanidze, G. Kakauridze, L. Margolin, and I. Kobulashvili, “Real-time objects recognition by photoanisotropic copies,” Appl. Opt. 46, 7537-7543 (2007).
    [CrossRef] [PubMed]
  14. S. Kakichashvili and B. Kilosanidze, “Polarization holographic memory of superhigh capacity,” J. Opt. Technol. 64, 64-67(1997).
  15. B. Stepanov, E. Ivakin, and A. Rubanov, “Registration of thin and volume dynamic holograms in bleaching media,” Doklady Acad. Nauk USSR 196, 567 (1971).
  16. V. Vinetskii, N. Kukhtarev, S. Odulov, and M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 129, 113-137 (1979).
  17. V. Vinetskii and N. Kukhtarev, Dynamic Holography (Naukova Dumka, 1983).
  18. D. Staselko, Y. Denisyuk, and V. Sizov, “Image formation by inertialess dynamic holograms recorded in a medium with quadratic nonlinearity at different frequencies of the object and reference waves,” Opt. Spectrosc. 93, 457-468(2002).
    [CrossRef]
  19. B. Kilosanidze and G. Kakauridze, “On the model consideration of photoanisotropy in media with dark relaxation,” Bull. Georgian Acad. Sci. 169, 282-286 (2004).
  20. G. Kakauridze, B. Kilosanidze, S. Petrova, and V. Shaverdova, “Photoanisotropy in relaxing media on the basis of asodye Dimethyl-Yellow,” Bull. Georgian Acad. Sci. 170, 249-252 (2004).
  21. B. Kilosanidze and G. Kakauridze, “Relaxing polarization media for dynamic polarization holography,” Proc. SPIE 5742, 224-233 (2005).
  22. B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization-sensitive media,” Opt. Mem. Neural Netw. 16, 17-23 (2007).
    [CrossRef]
  23. E. Korchemskaya, D. Stepanchikov, and N. Burykin, “Potentials of dynamic holography on bacteriorhodospin films for real-time optical processing,” in Bioelectronic Applications of Photochromic Pigments, A. Der and L. Keszthelyi, eds. (IOS, 2001), pp. 74-89.
  24. H. Wang, Y. Huang, Z. Liu, F. Zhao, W. Lin, J. Wang, and Z. Liang, “Ultrafast photoinduced anisotropy and optical switching in azobenzene sidechain polymers,” Appl. Phys. Lett. 82, 3394-3396 (2003).
    [CrossRef]
  25. A. Rubanov, A. Tolstik, S. Karpur, and O. Ormachea, “Nonlinear formation of dynamic holograms and multiwave mixing in resonant media,” Opt. Commun. 181, 183-190 (2000).
    [CrossRef]
  26. A. Miniewicz, A. Kochalska, J. My?liwiec, A. Samoc, M. Samo?, and J. G. Grote, “Deoxyribonucleic acid-based photochromic material for fast dynamic holography,” Appl. Phys. Lett. 91, 041118 (2007).
    [CrossRef]
  27. D. V. Uraev, V. Shmalhausen, A. Simonov, V. Shibaev, and A. Stakhanov, “Photoreversible holographic recording in azo-dye-containing polymer films,” Proc. SPIE 5135, 142-150 (2003).
    [CrossRef]
  28. C. Sheng, R. A. Norwood, J. Thomas, Y. Wu, Z. Zheng, N. Tabirian, D. Steeves, B. Kimball, and N. Peyghambarian, “Time-resolved studies of photoinduced birefringence in azobenzene dye-doped polymer films,” Appl. Opt. 47, 5074-5077 (2008).
    [CrossRef] [PubMed]
  29. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488-493 (1941).
    [CrossRef]
  30. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).
  31. A. Balabanov, G. Kakauridze, S. Kakichashvili, A. Savitskii, V. Shaverdova, and J. Shvaitser, “On the investigation of spectral characteristics of photoanisotropy,” J. Opt. Spectrosc. (USSR) 67, 409-412 (1989).
  32. R. Hildebrandt, M. Hegelich, H.-M. Keller, G. Marowsky, S. Hvilsted, N. C. R. Holme, and P. S. Ramanujam, “Time-resolved investigation of photoinduced birefringence in azobenzene side-chain polyester films,” Phys. Rev. Lett. 81, 5548-5551 (1998).
    [CrossRef]
  33. P. F. Gordon and P. Gregory, Organic Chemistry in Colour (Springer-Verlag, 1982).
  34. J. A. Baltrop and J. D. Coyle, Excited States in Organic Chemistry (Wiley, 1974).
  35. T. G. Pedersen, P. S. Ramanujam, P. M. Johansen, and S. Hvilsted, “Quantum theory and experimental studies of absorption spectra and photoisomerization of azobenzene polymers,” J. Opt. Soc. Am. B 15, 2721-2730 (1998).
    [CrossRef]

2008 (1)

2007 (4)

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization-sensitive media,” Opt. Mem. Neural Netw. 16, 17-23 (2007).
[CrossRef]

A. Miniewicz, A. Kochalska, J. My?liwiec, A. Samoc, M. Samo?, and J. G. Grote, “Deoxyribonucleic acid-based photochromic material for fast dynamic holography,” Appl. Phys. Lett. 91, 041118 (2007).
[CrossRef]

B. Kilosanidze and G. Kakauridze, “Polarization-holographic gratings for analysis and transformations of light. 1. The analysis of completely polarized light,” Appl. Opt. 46, 1040-1049 (2007).
[CrossRef] [PubMed]

B. Kilosanidze, G. Kakauridze, L. Margolin, and I. Kobulashvili, “Real-time objects recognition by photoanisotropic copies,” Appl. Opt. 46, 7537-7543 (2007).
[CrossRef] [PubMed]

2005 (1)

B. Kilosanidze and G. Kakauridze, “Relaxing polarization media for dynamic polarization holography,” Proc. SPIE 5742, 224-233 (2005).

2004 (2)

B. Kilosanidze and G. Kakauridze, “On the model consideration of photoanisotropy in media with dark relaxation,” Bull. Georgian Acad. Sci. 169, 282-286 (2004).

G. Kakauridze, B. Kilosanidze, S. Petrova, and V. Shaverdova, “Photoanisotropy in relaxing media on the basis of asodye Dimethyl-Yellow,” Bull. Georgian Acad. Sci. 170, 249-252 (2004).

2003 (3)

H. Wang, Y. Huang, Z. Liu, F. Zhao, W. Lin, J. Wang, and Z. Liang, “Ultrafast photoinduced anisotropy and optical switching in azobenzene sidechain polymers,” Appl. Phys. Lett. 82, 3394-3396 (2003).
[CrossRef]

D. V. Uraev, V. Shmalhausen, A. Simonov, V. Shibaev, and A. Stakhanov, “Photoreversible holographic recording in azo-dye-containing polymer films,” Proc. SPIE 5135, 142-150 (2003).
[CrossRef]

L. Nedelchev, A. S. Matharu, S. Hvilsted, and P. S. Ramanujam, “Photoinduced anisotropy in a family of amorphous azobenzene polyesters for optical storage,” Appl. Opt. 42, 5918-5927 (2003).
[CrossRef] [PubMed]

2002 (1)

D. Staselko, Y. Denisyuk, and V. Sizov, “Image formation by inertialess dynamic holograms recorded in a medium with quadratic nonlinearity at different frequencies of the object and reference waves,” Opt. Spectrosc. 93, 457-468(2002).
[CrossRef]

2001 (2)

E. Korchemskaya, D. Stepanchikov, and N. Burykin, “Potentials of dynamic holography on bacteriorhodospin films for real-time optical processing,” in Bioelectronic Applications of Photochromic Pigments, A. Der and L. Keszthelyi, eds. (IOS, 2001), pp. 74-89.

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]

2000 (2)

A. Rubanov, A. Tolstik, S. Karpur, and O. Ormachea, “Nonlinear formation of dynamic holograms and multiwave mixing in resonant media,” Opt. Commun. 181, 183-190 (2000).
[CrossRef]

F. Lagugne Labarthet, S. Freiberg, C. Pellerin, M. Pézolet, A. Natansohn, and P. Rochon, “Spectroscopic and optical characterization of a series of azobenzene-containing side-chain liquid crystalline polymers,” Macromolecules 33, 6815-6823(2000).
[CrossRef]

1998 (2)

R. Hildebrandt, M. Hegelich, H.-M. Keller, G. Marowsky, S. Hvilsted, N. C. R. Holme, and P. S. Ramanujam, “Time-resolved investigation of photoinduced birefringence in azobenzene side-chain polyester films,” Phys. Rev. Lett. 81, 5548-5551 (1998).
[CrossRef]

T. G. Pedersen, P. S. Ramanujam, P. M. Johansen, and S. Hvilsted, “Quantum theory and experimental studies of absorption spectra and photoisomerization of azobenzene polymers,” J. Opt. Soc. Am. B 15, 2721-2730 (1998).
[CrossRef]

1997 (1)

S. Kakichashvili and B. Kilosanidze, “Polarization holographic memory of superhigh capacity,” J. Opt. Technol. 64, 64-67(1997).

1995 (1)

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172-2183 (1995).
[CrossRef]

1991 (1)

Z. Sekkat and M. Dumont, “Polarization effects in photoisomerization of azo dyes in polymeric films,” Appl. Phys. B 53, 121-123 (1991).
[CrossRef]

1990 (1)

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

1989 (2)

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

A. Balabanov, G. Kakauridze, S. Kakichashvili, A. Savitskii, V. Shaverdova, and J. Shvaitser, “On the investigation of spectral characteristics of photoanisotropy,” J. Opt. Spectrosc. (USSR) 67, 409-412 (1989).

1987 (1)

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

1983 (2)

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

V. Vinetskii and N. Kukhtarev, Dynamic Holography (Naukova Dumka, 1983).

1982 (1)

P. F. Gordon and P. Gregory, Organic Chemistry in Colour (Springer-Verlag, 1982).

1979 (2)

V. Vinetskii, N. Kukhtarev, S. Odulov, and M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 129, 113-137 (1979).

S. Kakichashvili and V. Shaverdova, “Photoanisotropy in Mordant Yellow azo-dyes,” J. Sci. Appl. Photogr. Cinematogr. (USSR) 24, 342-345 (1979).

1975 (1)

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

1974 (1)

J. A. Baltrop and J. D. Coyle, Excited States in Organic Chemistry (Wiley, 1974).

1972 (1)

S. Kakichashvili, “On polarization recording of holograms,” J. Opt. Spectrosc. (USSR) 33, 324-327 (1972).

1971 (1)

B. Stepanov, E. Ivakin, and A. Rubanov, “Registration of thin and volume dynamic holograms in bleaching media,” Doklady Acad. Nauk USSR 196, 567 (1971).

1941 (1)

Andruzzi, F.

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172-2183 (1995).
[CrossRef]

Balabanov, A.

A. Balabanov, G. Kakauridze, S. Kakichashvili, A. Savitskii, V. Shaverdova, and J. Shvaitser, “On the investigation of spectral characteristics of photoanisotropy,” J. Opt. Spectrosc. (USSR) 67, 409-412 (1989).

Baltrop, J. A.

J. A. Baltrop and J. D. Coyle, Excited States in Organic Chemistry (Wiley, 1974).

Born, M.

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

Burykin, N.

E. Korchemskaya, D. Stepanchikov, and N. Burykin, “Potentials of dynamic holography on bacteriorhodospin films for real-time optical processing,” in Bioelectronic Applications of Photochromic Pigments, A. Der and L. Keszthelyi, eds. (IOS, 2001), pp. 74-89.

Chaganava, I.

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization-sensitive media,” Opt. Mem. Neural Netw. 16, 17-23 (2007).
[CrossRef]

Cipparrone, G.

Coyle, J. D.

J. A. Baltrop and J. D. Coyle, Excited States in Organic Chemistry (Wiley, 1974).

Denisyuk, Y.

D. Staselko, Y. Denisyuk, and V. Sizov, “Image formation by inertialess dynamic holograms recorded in a medium with quadratic nonlinearity at different frequencies of the object and reference waves,” Opt. Spectrosc. 93, 457-468(2002).
[CrossRef]

Dumont, M.

Z. Sekkat and M. Dumont, “Polarization effects in photoisomerization of azo dyes in polymeric films,” Appl. Phys. B 53, 121-123 (1991).
[CrossRef]

Freiberg, S.

F. Lagugne Labarthet, S. Freiberg, C. Pellerin, M. Pézolet, A. Natansohn, and P. Rochon, “Spectroscopic and optical characterization of a series of azobenzene-containing side-chain liquid crystalline polymers,” Macromolecules 33, 6815-6823(2000).
[CrossRef]

Gordon, P. F.

P. F. Gordon and P. Gregory, Organic Chemistry in Colour (Springer-Verlag, 1982).

Gregory, P.

P. F. Gordon and P. Gregory, Organic Chemistry in Colour (Springer-Verlag, 1982).

Grote, J. G.

A. Miniewicz, A. Kochalska, J. My?liwiec, A. Samoc, M. Samo?, and J. G. Grote, “Deoxyribonucleic acid-based photochromic material for fast dynamic holography,” Appl. Phys. Lett. 91, 041118 (2007).
[CrossRef]

Hegelich, M.

R. Hildebrandt, M. Hegelich, H.-M. Keller, G. Marowsky, S. Hvilsted, N. C. R. Holme, and P. S. Ramanujam, “Time-resolved investigation of photoinduced birefringence in azobenzene side-chain polyester films,” Phys. Rev. Lett. 81, 5548-5551 (1998).
[CrossRef]

Hildebrandt, R.

R. Hildebrandt, M. Hegelich, H.-M. Keller, G. Marowsky, S. Hvilsted, N. C. R. Holme, and P. S. Ramanujam, “Time-resolved investigation of photoinduced birefringence in azobenzene side-chain polyester films,” Phys. Rev. Lett. 81, 5548-5551 (1998).
[CrossRef]

Holme, N. C. R.

R. Hildebrandt, M. Hegelich, H.-M. Keller, G. Marowsky, S. Hvilsted, N. C. R. Holme, and P. S. Ramanujam, “Time-resolved investigation of photoinduced birefringence in azobenzene side-chain polyester films,” Phys. Rev. Lett. 81, 5548-5551 (1998).
[CrossRef]

Huang, Y.

H. Wang, Y. Huang, Z. Liu, F. Zhao, W. Lin, J. Wang, and Z. Liang, “Ultrafast photoinduced anisotropy and optical switching in azobenzene sidechain polymers,” Appl. Phys. Lett. 82, 3394-3396 (2003).
[CrossRef]

Hvilsted, S.

L. Nedelchev, A. S. Matharu, S. Hvilsted, and P. S. Ramanujam, “Photoinduced anisotropy in a family of amorphous azobenzene polyesters for optical storage,” Appl. Opt. 42, 5918-5927 (2003).
[CrossRef] [PubMed]

R. Hildebrandt, M. Hegelich, H.-M. Keller, G. Marowsky, S. Hvilsted, N. C. R. Holme, and P. S. Ramanujam, “Time-resolved investigation of photoinduced birefringence in azobenzene side-chain polyester films,” Phys. Rev. Lett. 81, 5548-5551 (1998).
[CrossRef]

T. G. Pedersen, P. S. Ramanujam, P. M. Johansen, and S. Hvilsted, “Quantum theory and experimental studies of absorption spectra and photoisomerization of azobenzene polymers,” J. Opt. Soc. Am. B 15, 2721-2730 (1998).
[CrossRef]

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172-2183 (1995).
[CrossRef]

Ivakin, E.

B. Stepanov, E. Ivakin, and A. Rubanov, “Registration of thin and volume dynamic holograms in bleaching media,” Doklady Acad. Nauk USSR 196, 567 (1971).

Johansen, P. 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.

B. Kilosanidze and G. Kakauridze, “Polarization-holographic gratings for analysis and transformations of light. 1. The analysis of completely polarized light,” Appl. Opt. 46, 1040-1049 (2007).
[CrossRef] [PubMed]

B. Kilosanidze, G. Kakauridze, L. Margolin, and I. Kobulashvili, “Real-time objects recognition by photoanisotropic copies,” Appl. Opt. 46, 7537-7543 (2007).
[CrossRef] [PubMed]

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization-sensitive media,” Opt. Mem. Neural Netw. 16, 17-23 (2007).
[CrossRef]

B. Kilosanidze and G. Kakauridze, “Relaxing polarization media for dynamic polarization holography,” Proc. SPIE 5742, 224-233 (2005).

B. Kilosanidze and G. Kakauridze, “On the model consideration of photoanisotropy in media with dark relaxation,” Bull. Georgian Acad. Sci. 169, 282-286 (2004).

G. Kakauridze, B. Kilosanidze, S. Petrova, and V. Shaverdova, “Photoanisotropy in relaxing media on the basis of asodye Dimethyl-Yellow,” Bull. Georgian Acad. Sci. 170, 249-252 (2004).

A. Balabanov, G. Kakauridze, S. Kakichashvili, A. Savitskii, V. Shaverdova, and J. Shvaitser, “On the investigation of spectral characteristics of photoanisotropy,” J. Opt. Spectrosc. (USSR) 67, 409-412 (1989).

Kakichashvili, S.

S. Kakichashvili and B. Kilosanidze, “Polarization holographic memory of superhigh capacity,” J. Opt. Technol. 64, 64-67(1997).

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

A. Balabanov, G. Kakauridze, S. Kakichashvili, A. Savitskii, V. Shaverdova, and J. Shvaitser, “On the investigation of spectral characteristics of photoanisotropy,” J. Opt. Spectrosc. (USSR) 67, 409-412 (1989).

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

S. Kakichashvili and V. Shaverdova, “Photoanisotropy in Mordant Yellow azo-dyes,” J. Sci. Appl. Photogr. Cinematogr. (USSR) 24, 342-345 (1979).

S. Kakichashvili, “On polarization recording of holograms,” J. Opt. Spectrosc. (USSR) 33, 324-327 (1972).

Kakichashvili, Sh.

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

Kakichashvili, V.

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

Karpur, S.

A. Rubanov, A. Tolstik, S. Karpur, and O. Ormachea, “Nonlinear formation of dynamic holograms and multiwave mixing in resonant media,” Opt. Commun. 181, 183-190 (2000).
[CrossRef]

Keller, H.-M.

R. Hildebrandt, M. Hegelich, H.-M. Keller, G. Marowsky, S. Hvilsted, N. C. R. Holme, and P. S. Ramanujam, “Time-resolved investigation of photoinduced birefringence in azobenzene side-chain polyester films,” Phys. Rev. Lett. 81, 5548-5551 (1998).
[CrossRef]

Kilosanidze, B.

B. Kilosanidze and G. Kakauridze, “Polarization-holographic gratings for analysis and transformations of light. 1. The analysis of completely polarized light,” Appl. Opt. 46, 1040-1049 (2007).
[CrossRef] [PubMed]

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization-sensitive media,” Opt. Mem. Neural Netw. 16, 17-23 (2007).
[CrossRef]

B. Kilosanidze, G. Kakauridze, L. Margolin, and I. Kobulashvili, “Real-time objects recognition by photoanisotropic copies,” Appl. Opt. 46, 7537-7543 (2007).
[CrossRef] [PubMed]

B. Kilosanidze and G. Kakauridze, “Relaxing polarization media for dynamic polarization holography,” Proc. SPIE 5742, 224-233 (2005).

B. Kilosanidze and G. Kakauridze, “On the model consideration of photoanisotropy in media with dark relaxation,” Bull. Georgian Acad. Sci. 169, 282-286 (2004).

G. Kakauridze, B. Kilosanidze, S. Petrova, and V. Shaverdova, “Photoanisotropy in relaxing media on the basis of asodye Dimethyl-Yellow,” Bull. Georgian Acad. Sci. 170, 249-252 (2004).

S. Kakichashvili and B. Kilosanidze, “Polarization holographic memory of superhigh capacity,” J. Opt. Technol. 64, 64-67(1997).

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

Kimball, B.

Kobulashvili, I.

Kochalska, A.

A. Miniewicz, A. Kochalska, J. My?liwiec, A. Samoc, M. Samo?, and J. G. Grote, “Deoxyribonucleic acid-based photochromic material for fast dynamic holography,” Appl. Phys. Lett. 91, 041118 (2007).
[CrossRef]

Korchemskaya, E.

E. Korchemskaya, D. Stepanchikov, and N. Burykin, “Potentials of dynamic holography on bacteriorhodospin films for real-time optical processing,” in Bioelectronic Applications of Photochromic Pigments, A. Der and L. Keszthelyi, eds. (IOS, 2001), pp. 74-89.

Kukhtarev, N.

V. Vinetskii and N. Kukhtarev, Dynamic Holography (Naukova Dumka, 1983).

V. Vinetskii, N. Kukhtarev, S. Odulov, and M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 129, 113-137 (1979).

Kulinna, C.

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172-2183 (1995).
[CrossRef]

Labarthet, F. Lagugne

F. Lagugne Labarthet, S. Freiberg, C. Pellerin, M. Pézolet, A. Natansohn, and P. Rochon, “Spectroscopic and optical characterization of a series of azobenzene-containing side-chain liquid crystalline polymers,” Macromolecules 33, 6815-6823(2000).
[CrossRef]

Liang, Z.

H. Wang, Y. Huang, Z. Liu, F. Zhao, W. Lin, J. Wang, and Z. Liang, “Ultrafast photoinduced anisotropy and optical switching in azobenzene sidechain polymers,” Appl. Phys. Lett. 82, 3394-3396 (2003).
[CrossRef]

Lin, W.

H. Wang, Y. Huang, Z. Liu, F. Zhao, W. Lin, J. Wang, and Z. Liang, “Ultrafast photoinduced anisotropy and optical switching in azobenzene sidechain polymers,” Appl. Phys. Lett. 82, 3394-3396 (2003).
[CrossRef]

Liu, Z.

H. Wang, Y. Huang, Z. Liu, F. Zhao, W. Lin, J. Wang, and Z. Liang, “Ultrafast photoinduced anisotropy and optical switching in azobenzene sidechain polymers,” Appl. Phys. Lett. 82, 3394-3396 (2003).
[CrossRef]

Margolin, L.

Marowsky, G.

R. Hildebrandt, M. Hegelich, H.-M. Keller, G. Marowsky, S. Hvilsted, N. C. R. Holme, and P. S. Ramanujam, “Time-resolved investigation of photoinduced birefringence in azobenzene side-chain polyester films,” Phys. Rev. Lett. 81, 5548-5551 (1998).
[CrossRef]

Matharu, A. S.

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]

Miniewicz, A.

A. Miniewicz, A. Kochalska, J. My?liwiec, A. Samoc, M. Samo?, and J. G. Grote, “Deoxyribonucleic acid-based photochromic material for fast dynamic holography,” Appl. Phys. Lett. 91, 041118 (2007).
[CrossRef]

Mysliwiec, J.

A. Miniewicz, A. Kochalska, J. My?liwiec, A. Samoc, M. Samo?, and J. G. Grote, “Deoxyribonucleic acid-based photochromic material for fast dynamic holography,” Appl. Phys. Lett. 91, 041118 (2007).
[CrossRef]

Natansohn, A.

F. Lagugne Labarthet, S. Freiberg, C. Pellerin, M. Pézolet, A. Natansohn, and P. Rochon, “Spectroscopic and optical characterization of a series of azobenzene-containing side-chain liquid crystalline polymers,” Macromolecules 33, 6815-6823(2000).
[CrossRef]

Nedelchev, L.

Norwood, R. A.

Odulov, S.

V. Vinetskii, N. Kukhtarev, S. Odulov, and M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 129, 113-137 (1979).

Ormachea, O.

A. Rubanov, A. Tolstik, S. Karpur, and O. Ormachea, “Nonlinear formation of dynamic holograms and multiwave mixing in resonant media,” Opt. Commun. 181, 183-190 (2000).
[CrossRef]

Pedersen, T. G.

Pellerin, C.

F. Lagugne Labarthet, S. Freiberg, C. Pellerin, M. Pézolet, A. Natansohn, and P. Rochon, “Spectroscopic and optical characterization of a series of azobenzene-containing side-chain liquid crystalline polymers,” Macromolecules 33, 6815-6823(2000).
[CrossRef]

Petrova, S.

G. Kakauridze, B. Kilosanidze, S. Petrova, and V. Shaverdova, “Photoanisotropy in relaxing media on the basis of asodye Dimethyl-Yellow,” Bull. Georgian Acad. Sci. 170, 249-252 (2004).

Peyghambarian, N.

Pézolet, M.

F. Lagugne Labarthet, S. Freiberg, C. Pellerin, M. Pézolet, A. Natansohn, and P. Rochon, “Spectroscopic and optical characterization of a series of azobenzene-containing side-chain liquid crystalline polymers,” Macromolecules 33, 6815-6823(2000).
[CrossRef]

Ramanujam, P. S.

L. Nedelchev, A. S. Matharu, S. Hvilsted, and P. S. Ramanujam, “Photoinduced anisotropy in a family of amorphous azobenzene polyesters for optical storage,” Appl. Opt. 42, 5918-5927 (2003).
[CrossRef] [PubMed]

R. Hildebrandt, M. Hegelich, H.-M. Keller, G. Marowsky, S. Hvilsted, N. C. R. Holme, and P. S. Ramanujam, “Time-resolved investigation of photoinduced birefringence in azobenzene side-chain polyester films,” Phys. Rev. Lett. 81, 5548-5551 (1998).
[CrossRef]

T. G. Pedersen, P. S. Ramanujam, P. M. Johansen, and S. Hvilsted, “Quantum theory and experimental studies of absorption spectra and photoisomerization of azobenzene polymers,” J. Opt. Soc. Am. B 15, 2721-2730 (1998).
[CrossRef]

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172-2183 (1995).
[CrossRef]

Rochon, P.

F. Lagugne Labarthet, S. Freiberg, C. Pellerin, M. Pézolet, A. Natansohn, and P. Rochon, “Spectroscopic and optical characterization of a series of azobenzene-containing side-chain liquid crystalline polymers,” Macromolecules 33, 6815-6823(2000).
[CrossRef]

Rubanov, A.

A. Rubanov, A. Tolstik, S. Karpur, and O. Ormachea, “Nonlinear formation of dynamic holograms and multiwave mixing in resonant media,” Opt. Commun. 181, 183-190 (2000).
[CrossRef]

B. Stepanov, E. Ivakin, and A. Rubanov, “Registration of thin and volume dynamic holograms in bleaching media,” Doklady Acad. Nauk USSR 196, 567 (1971).

Russo, G.

Samoc, A.

A. Miniewicz, A. Kochalska, J. My?liwiec, A. Samoc, M. Samo?, and J. G. Grote, “Deoxyribonucleic acid-based photochromic material for fast dynamic holography,” Appl. Phys. Lett. 91, 041118 (2007).
[CrossRef]

Samoc, M.

A. Miniewicz, A. Kochalska, J. My?liwiec, A. Samoc, M. Samo?, and J. G. Grote, “Deoxyribonucleic acid-based photochromic material for fast dynamic holography,” Appl. Phys. Lett. 91, 041118 (2007).
[CrossRef]

Savitskii, A.

A. Balabanov, G. Kakauridze, S. Kakichashvili, A. Savitskii, V. Shaverdova, and J. Shvaitser, “On the investigation of spectral characteristics of photoanisotropy,” J. Opt. Spectrosc. (USSR) 67, 409-412 (1989).

Sekkat, Z.

Z. Sekkat and M. Dumont, “Polarization effects in photoisomerization of azo dyes in polymeric films,” Appl. Phys. B 53, 121-123 (1991).
[CrossRef]

Shatalin, I.

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

Shaverdova, V.

G. Kakauridze, B. Kilosanidze, S. Petrova, and V. Shaverdova, “Photoanisotropy in relaxing media on the basis of asodye Dimethyl-Yellow,” Bull. Georgian Acad. Sci. 170, 249-252 (2004).

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

A. Balabanov, G. Kakauridze, S. Kakichashvili, A. Savitskii, V. Shaverdova, and J. Shvaitser, “On the investigation of spectral characteristics of photoanisotropy,” J. Opt. Spectrosc. (USSR) 67, 409-412 (1989).

S. Kakichashvili and V. Shaverdova, “Photoanisotropy in Mordant Yellow azo-dyes,” J. Sci. Appl. Photogr. Cinematogr. (USSR) 24, 342-345 (1979).

Sheng, C.

Shibaev, V.

D. V. Uraev, V. Shmalhausen, A. Simonov, V. Shibaev, and A. Stakhanov, “Photoreversible holographic recording in azo-dye-containing polymer films,” Proc. SPIE 5135, 142-150 (2003).
[CrossRef]

Shmalhausen, V.

D. V. Uraev, V. Shmalhausen, A. Simonov, V. Shibaev, and A. Stakhanov, “Photoreversible holographic recording in azo-dye-containing polymer films,” Proc. SPIE 5135, 142-150 (2003).
[CrossRef]

Shvaitser, J.

A. Balabanov, G. Kakauridze, S. Kakichashvili, A. Savitskii, V. Shaverdova, and J. Shvaitser, “On the investigation of spectral characteristics of photoanisotropy,” J. Opt. Spectrosc. (USSR) 67, 409-412 (1989).

Siesler, H. W.

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172-2183 (1995).
[CrossRef]

Simonov, A.

D. V. Uraev, V. Shmalhausen, A. Simonov, V. Shibaev, and A. Stakhanov, “Photoreversible holographic recording in azo-dye-containing polymer films,” Proc. SPIE 5135, 142-150 (2003).
[CrossRef]

Sizov, V.

D. Staselko, Y. Denisyuk, and V. Sizov, “Image formation by inertialess dynamic holograms recorded in a medium with quadratic nonlinearity at different frequencies of the object and reference waves,” Opt. Spectrosc. 93, 457-468(2002).
[CrossRef]

Soskin, M.

V. Vinetskii, N. Kukhtarev, S. Odulov, and M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 129, 113-137 (1979).

Stakhanov, A.

D. V. Uraev, V. Shmalhausen, A. Simonov, V. Shibaev, and A. Stakhanov, “Photoreversible holographic recording in azo-dye-containing polymer films,” Proc. SPIE 5135, 142-150 (2003).
[CrossRef]

Staselko, D.

D. Staselko, Y. Denisyuk, and V. Sizov, “Image formation by inertialess dynamic holograms recorded in a medium with quadratic nonlinearity at different frequencies of the object and reference waves,” Opt. Spectrosc. 93, 457-468(2002).
[CrossRef]

Steeves, D.

Stepanchikov, D.

E. Korchemskaya, D. Stepanchikov, and N. Burykin, “Potentials of dynamic holography on bacteriorhodospin films for real-time optical processing,” in Bioelectronic Applications of Photochromic Pigments, A. Der and L. Keszthelyi, eds. (IOS, 2001), pp. 74-89.

Stepanov, B.

B. Stepanov, E. Ivakin, and A. Rubanov, “Registration of thin and volume dynamic holograms in bleaching media,” Doklady Acad. Nauk USSR 196, 567 (1971).

Tabirian, N.

Thomas, J.

Tolstik, A.

A. Rubanov, A. Tolstik, S. Karpur, and O. Ormachea, “Nonlinear formation of dynamic holograms and multiwave mixing in resonant media,” Opt. Commun. 181, 183-190 (2000).
[CrossRef]

Uraev, D. V.

D. V. Uraev, V. Shmalhausen, A. Simonov, V. Shibaev, and A. Stakhanov, “Photoreversible holographic recording in azo-dye-containing polymer films,” Proc. SPIE 5135, 142-150 (2003).
[CrossRef]

Vinetskii, V.

V. Vinetskii and N. Kukhtarev, Dynamic Holography (Naukova Dumka, 1983).

V. Vinetskii, N. Kukhtarev, S. Odulov, and M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 129, 113-137 (1979).

Wang, H.

H. Wang, Y. Huang, Z. Liu, F. Zhao, W. Lin, J. Wang, and Z. Liang, “Ultrafast photoinduced anisotropy and optical switching in azobenzene sidechain polymers,” Appl. Phys. Lett. 82, 3394-3396 (2003).
[CrossRef]

Wang, J.

H. Wang, Y. Huang, Z. Liu, F. Zhao, W. Lin, J. Wang, and Z. Liang, “Ultrafast photoinduced anisotropy and optical switching in azobenzene sidechain polymers,” Appl. Phys. Lett. 82, 3394-3396 (2003).
[CrossRef]

Wolf, E.

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

Wu, Y.

Zhao, F.

H. Wang, Y. Huang, Z. Liu, F. Zhao, W. Lin, J. Wang, and Z. Liang, “Ultrafast photoinduced anisotropy and optical switching in azobenzene sidechain polymers,” Appl. Phys. Lett. 82, 3394-3396 (2003).
[CrossRef]

Zheng, Z.

Appl. Opt. (4)

Appl. Phys. B (1)

Z. Sekkat and M. Dumont, “Polarization effects in photoisomerization of azo dyes in polymeric films,” Appl. Phys. B 53, 121-123 (1991).
[CrossRef]

Appl. Phys. Lett. (2)

H. Wang, Y. Huang, Z. Liu, F. Zhao, W. Lin, J. Wang, and Z. Liang, “Ultrafast photoinduced anisotropy and optical switching in azobenzene sidechain polymers,” Appl. Phys. Lett. 82, 3394-3396 (2003).
[CrossRef]

A. Miniewicz, A. Kochalska, J. My?liwiec, A. Samoc, M. Samo?, and J. G. Grote, “Deoxyribonucleic acid-based photochromic material for fast dynamic holography,” Appl. Phys. Lett. 91, 041118 (2007).
[CrossRef]

Bull. Georgian Acad. Sci. (2)

B. Kilosanidze and G. Kakauridze, “On the model consideration of photoanisotropy in media with dark relaxation,” Bull. Georgian Acad. Sci. 169, 282-286 (2004).

G. Kakauridze, B. Kilosanidze, S. Petrova, and V. Shaverdova, “Photoanisotropy in relaxing media on the basis of asodye Dimethyl-Yellow,” Bull. Georgian Acad. Sci. 170, 249-252 (2004).

Doklady Acad. Nauk USSR (1)

B. Stepanov, E. Ivakin, and A. Rubanov, “Registration of thin and volume dynamic holograms in bleaching media,” Doklady Acad. Nauk USSR 196, 567 (1971).

J. Opt. Soc. Am. (1)

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

J. Opt. Spectrosc. (USSR) (3)

A. Balabanov, G. Kakauridze, S. Kakichashvili, A. Savitskii, V. Shaverdova, and J. Shvaitser, “On the investigation of spectral characteristics of photoanisotropy,” J. Opt. Spectrosc. (USSR) 67, 409-412 (1989).

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

S. Kakichashvili, “On polarization recording of holograms,” J. Opt. Spectrosc. (USSR) 33, 324-327 (1972).

J. Opt. Technol. (1)

S. Kakichashvili and B. Kilosanidze, “Polarization holographic memory of superhigh capacity,” J. Opt. Technol. 64, 64-67(1997).

J. Sci. Appl. Photogr. Cinematogr. (USSR) (1)

S. Kakichashvili and V. Shaverdova, “Photoanisotropy in Mordant Yellow azo-dyes,” J. Sci. Appl. Photogr. Cinematogr. (USSR) 24, 342-345 (1979).

Lett. J. Tech. Phys. (USSR) (1)

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

Macromolecules (2)

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172-2183 (1995).
[CrossRef]

F. Lagugne Labarthet, S. Freiberg, C. Pellerin, M. Pézolet, A. Natansohn, and P. Rochon, “Spectroscopic and optical characterization of a series of azobenzene-containing side-chain liquid crystalline polymers,” Macromolecules 33, 6815-6823(2000).
[CrossRef]

Opt. Commun. (2)

A. Rubanov, A. Tolstik, S. Karpur, and O. Ormachea, “Nonlinear formation of dynamic holograms and multiwave mixing in resonant media,” Opt. Commun. 181, 183-190 (2000).
[CrossRef]

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

Opt. Mem. Neural Netw. (1)

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization-sensitive media,” Opt. Mem. Neural Netw. 16, 17-23 (2007).
[CrossRef]

Opt. Spectrosc. (1)

D. Staselko, Y. Denisyuk, and V. Sizov, “Image formation by inertialess dynamic holograms recorded in a medium with quadratic nonlinearity at different frequencies of the object and reference waves,” Opt. Spectrosc. 93, 457-468(2002).
[CrossRef]

Phys. Rev. Lett. (1)

R. Hildebrandt, M. Hegelich, H.-M. Keller, G. Marowsky, S. Hvilsted, N. C. R. Holme, and P. S. Ramanujam, “Time-resolved investigation of photoinduced birefringence in azobenzene side-chain polyester films,” Phys. Rev. Lett. 81, 5548-5551 (1998).
[CrossRef]

Proc. SPIE (2)

D. V. Uraev, V. Shmalhausen, A. Simonov, V. Shibaev, and A. Stakhanov, “Photoreversible holographic recording in azo-dye-containing polymer films,” Proc. SPIE 5135, 142-150 (2003).
[CrossRef]

B. Kilosanidze and G. Kakauridze, “Relaxing polarization media for dynamic polarization holography,” Proc. SPIE 5742, 224-233 (2005).

Sov. Phys. Usp. (1)

V. Vinetskii, N. Kukhtarev, S. Odulov, and M. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 129, 113-137 (1979).

Other (6)

V. Vinetskii and N. Kukhtarev, Dynamic Holography (Naukova Dumka, 1983).

E. Korchemskaya, D. Stepanchikov, and N. Burykin, “Potentials of dynamic holography on bacteriorhodospin films for real-time optical processing,” in Bioelectronic Applications of Photochromic Pigments, A. Der and L. Keszthelyi, eds. (IOS, 2001), pp. 74-89.

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

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

P. F. Gordon and P. Gregory, Organic Chemistry in Colour (Springer-Verlag, 1982).

J. A. Baltrop and J. D. Coyle, Excited States in Organic Chemistry (Wiley, 1974).

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Figures (4)

Fig. 1
Fig. 1

Scheme of experimental setup for the investigation of photoanisotropy kinetics.

Fig. 2
Fig. 2

Spectral dependence of transmission for the dyes. 1, DMY; 2, NDMR.

Fig. 3
Fig. 3

Time dependence of A eff for the dyes in PC matrix. 1, DMY (inducing wavelength 441, 6 nm ); 2, NDMR (inducing wavelength 488 nm ). Inducing beam intensity 1 W / cm 2 . “Off” is the moment of switch-off of inducing light.

Fig. 4
Fig. 4

Time dependence of A eff for the dyes in the PC matrix. 1, DMY; 2, NDMR. The ratio of intensities of the illuminating and additional beams is 4 1 (some cycles of inducing/erasing).

Tables (2)

Tables Icon

Table 1 Dynamic Characteristics of Materials on the Basis of Dimethyl Yellow and Nitrodimethyl Red Dyes

Tables Icon

Table 2 Dynamic Characteristics of Materials on the Basis of Dimethyl Yellow and Nitrodimethyl Red Dyes for the Ratio 4 1 of the Illuminating and Additional Actinic Beams

Equations (10)

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

d N Θ ( I , t + Δ t ) = exp { [ ( α ˜ 1 cos 2 Θ + α ˜ 2 sin 2 Θ ) I + γ ] Δ t } d N Θ ( I , t ) + [ 1 exp { [ ( α ˜ 1 sin 2 Θ + α ˜ 2 cos 2 Θ ) I + γ ] Δ t } d N Θ 9 o ( I , t ) ] .
d 2 [ d N Θ ( I , t ) ] d t 2 + [ ( α ˜ 1 + α ˜ 2 ) I + 2 γ ] d [ d N Θ ( I , t ) ] d t = 0.
d N Θ ( I , t 1 , t 2 ) = 1 π N { ( α ˜ 1 α ˜ 2 ) I ( α ˜ 1 + α ˜ 2 ) I + 2 γ [ exp { [ ( α ˜ 1 + α ˜ 2 ) I + 2 γ ] t 1 } 1 ] exp ( 2 γ t 2 ) cos 2 Θ + 1 } d Θ ,
M Θ = 1 2 ( m 11 m 12 m 21 m 22 ) ,
M = 1 N 0 π M Θ d N Θ ( I , t 1 , t 2 ) .
M = 1 2 [ exp ( i κ d n ^ 1 ) + exp ( i κ d n ^ 2 ) ] × { ( 1 0 0 1 ) + 1 2 ( α ˜ 1 α ˜ 2 ) I ( α ˜ 1 + α ˜ 2 ) I + 2 γ [ exp { [ ( α ˜ 1 + α ˜ 2 ) I + 2 γ ] t 1 } 1 ] exp ( 2 γ t 2 ) ( 1 0 0 1 ) } .
A eff = 1 16 | ( α ˜ 1 α ˜ 2 ) I ( α ˜ 1 + α ˜ 2 ) I + 2 γ ( exp { [ ( α ˜ 1 + α ˜ 2 ) I + 2 γ ] t 1 } 1 ) exp ( 2 γ t 2 ) [ exp ( i κ n ^ 1 ) exp ( i κ n ^ 2 ) ] | 2 .
A eff , max = 1 16 | ( α ˜ 1 α ˜ 2 ) I ( α ˜ 1 + α ˜ 2 ) I + 2 γ [ exp ( i κ d n ^ 1 ) exp ( i κ d n ^ 2 ) ] | 2 .
A eff , rel = A eff , max | exp ( 2 γ t 2 ) | 2 .
γ = 1 4 t 2 ln A eff , max A eff , rel .

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