Abstract

Dynamic polarization-holographic gratings with a different profile of anisotropy in the band are presented. Polarization-sensitive recording materials of two types are used: material possessing high dark relaxation and highly reversible material without dark relaxation in which the recorded grating is erased by a circularly polarized beam. For a grating recorded by two orthogonally circularly polarized beams a diffraction efficiency of 20% has been obtained at 3.5W/cm2 power density during 1 ms recording/erasing time. An all-optical cross commutator based on the matrix of dynamic reprogrammable polarization-holographic microholograms is considered. The amplification of the weak beam at two-wave mixing in polarization-sensitive materials has been shown, with an obtained amplification coefficient of 4.95.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  5. I. Chaganava, G. Kakauridze, and B. Kilosanidze, “Development of high-performance, stable and moisture-resistant polarization-sensitive materials,” Proc. SPIE 8126, 812651 (2011).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011

I. Chaganava, G. Kakauridze, and B. Kilosanidze, “Development of high-performance, stable and moisture-resistant polarization-sensitive materials,” Proc. SPIE 8126, 812651 (2011).
[CrossRef]

G. Kakauridze and B. Kilosanidze, “Polarization-holographic diffraction element-based real-time imaging Stokes spectropolarimetry,” Proc. SPIE 7957, 795728 (2011).
[CrossRef]

2009

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization holography: methods and applications,” J. Holography Speckle 5, 52–61 (2009).
[CrossRef]

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization holography. 1. Dynamic polarization-sensitive materials on the basis of azo-dye-containing polymers,” Appl. Opt. 48, 1861–1868 (2009).
[CrossRef]

2008

C. X. Sheng, R. A. Norwood, J. Wang, J. Thomas, Y. Wu, Z. Zheng, N. Tabirian, D. M. Steeves, B. R. Kimball, and N. Peyghambarian, “Time-resolved studies of photoinduced birefringence in azobenzene dye-doped polymer films,” Appl. Opt. 47, 5074–5077 (2008).
[CrossRef]

S. Takeuchi, S. Ruhman, T. Tsuneda, M. Chiba, T. Taketsugu, and T. Tahara, “Spectroscopic tracking of structural evolution in ultrafast stilbene photoisomerization,” Science 322, 1073–1077 (2008).
[CrossRef]

2007

J. Woo, E. Kim, B. Kim, and Y. Cho, “Morphology and switching of holographic gratings containing an azo dye,” Liq. Cryst. 34, 527–533 (2007).
[CrossRef]

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, “Polarization-holographic gratings for analysis and transformations of light: 1. the analysis of completely polarized light,” Appl. Opt. 46, 1040–1049 (2007).
[CrossRef]

2006

2005

2001

2000

F. L. 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]

1999

N. Wollfer, B. Vinouze, and P. Gravey, “Holographic switching between single mode fibres based on electrically addressed nematic liquid crystal gratings with high deflection accuracy,” Opt. Commun. 160, 42–46 (1999).
[CrossRef]

1997

1996

1995

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]

1994

1992

A. Mikaelian and V. Salakhutdinov, “Using of dynamic holograms for information channel switching,” Opt. Mem. Neural Netw. 1, 315–324 (1992).

A. G. Chen and D. Brady, “Real-time holography in azo-dye-doped liquid crystals,” Opt. Lett. 17, 441–443 (1992).
[CrossRef]

1987

Sh. Kakichashvili, “On the regularity in the phenomena of photoanisotropy and photogyrotropy,” Opt. Spectrosc. 63, 911–917 (1987).

1986

I. C. Khoo, “Dynamic gratings and the associated self diffractions and wavefront conjugation processes in nematic liquid crystals,” IEEE J. Quantum Electron. 22, 1268–1275 (1986).
[CrossRef]

1984

Sh. Kakichashvili, “On the effect of the rotation of an axis of photoinduced anisotropy,” Opt. Spectrosc. 56, 977–978 (1984).

1982

B. Y. Zel’dovich and N. V. Tabiryan, “Orientational effect of a light wave on a cholesteric mesophase,” Sov. Phys. JETP 55, 167–176 (1982).

Sh. Kakichashvili, “On the regularity in photoanisotropic phenomena,” Opt. Spectrosc. 52, 317–322 (1982).

1979

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

1941

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]

Bieringer, T.

R. Hagen and T. Bieringer, “Photoaddressable polymers for optical data storage,” Adv. Mater. 13, 1805–1810 (2001).
[CrossRef]

Brady, D.

Busch, S.

Carns, J. L.

Chaganava, I.

I. Chaganava, G. Kakauridze, and B. Kilosanidze, “Development of high-performance, stable and moisture-resistant polarization-sensitive materials,” Proc. SPIE 8126, 812651 (2011).
[CrossRef]

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization holography: methods and applications,” J. Holography Speckle 5, 52–61 (2009).
[CrossRef]

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization holography. 1. Dynamic polarization-sensitive materials on the basis of azo-dye-containing polymers,” Appl. Opt. 48, 1861–1868 (2009).
[CrossRef]

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

Chen, A. G.

Chen, P.

Chiba, M.

S. Takeuchi, S. Ruhman, T. Tsuneda, M. Chiba, T. Taketsugu, and T. Tahara, “Spectroscopic tracking of structural evolution in ultrafast stilbene photoisomerization,” Science 322, 1073–1077 (2008).
[CrossRef]

Cho, Y.

J. Woo, E. Kim, B. Kim, and Y. Cho, “Morphology and switching of holographic gratings containing an azo dye,” Liq. Cryst. 34, 527–533 (2007).
[CrossRef]

Cipparrone, G.

Cook, G.

Evans, D. R.

Freiberg, S.

F. L. 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]

Fuh, A.

Gravey, P.

N. Wollfer, B. Vinouze, and P. Gravey, “Holographic switching between single mode fibres based on electrically addressed nematic liquid crystal gratings with high deflection accuracy,” Opt. Commun. 160, 42–46 (1999).
[CrossRef]

Guenther, B. D.

Guha, S.

Hagen, R.

R. Hagen and T. Bieringer, “Photoaddressable polymers for optical data storage,” Adv. Mater. 13, 1805–1810 (2001).
[CrossRef]

Hall, H. K.

Holme, N. C. R.

Holmstrom, S. A.

Hsieh, D.-M.

Hvilsted, S.

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]

Jones, R. C.

Kakauridze, G.

I. Chaganava, G. Kakauridze, and B. Kilosanidze, “Development of high-performance, stable and moisture-resistant polarization-sensitive materials,” Proc. SPIE 8126, 812651 (2011).
[CrossRef]

G. Kakauridze and B. Kilosanidze, “Polarization-holographic diffraction element-based real-time imaging Stokes spectropolarimetry,” Proc. SPIE 7957, 795728 (2011).
[CrossRef]

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization holography: methods and applications,” J. Holography Speckle 5, 52–61 (2009).
[CrossRef]

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization holography. 1. Dynamic polarization-sensitive materials on the basis of azo-dye-containing polymers,” Appl. Opt. 48, 1861–1868 (2009).
[CrossRef]

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]

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

G. Kakauridze and B. Kilosanidze, “Polarization-holographic gratings that form plane-polarized orders of diffraction,” J. Opt. Technol. 73, 188–192 (2006).
[CrossRef]

Kakichashvili, Sh.

Sh. Kakichashvili, “On the regularity in the phenomena of photoanisotropy and photogyrotropy,” Opt. Spectrosc. 63, 911–917 (1987).

Sh. Kakichashvili, “On the effect of the rotation of an axis of photoinduced anisotropy,” Opt. Spectrosc. 56, 977–978 (1984).

Sh. Kakichashvili, “On the regularity in photoanisotropic phenomena,” Opt. Spectrosc. 52, 317–322 (1982).

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

Khoo, I. C.

I. C. Khoo, B. D. Guenther, M. V. Wood, P. Chen, and M.-Y. Shih, “Coherent beam amplification with a photorefractive liquid crystal,” Opt. Lett. 22, 1229–1231 (1997).
[CrossRef]

I. C. Khoo, “Dynamic gratings and the associated self diffractions and wavefront conjugation processes in nematic liquid crystals,” IEEE J. Quantum Electron. 22, 1268–1275 (1986).
[CrossRef]

Kilosanidze, B.

I. Chaganava, G. Kakauridze, and B. Kilosanidze, “Development of high-performance, stable and moisture-resistant polarization-sensitive materials,” Proc. SPIE 8126, 812651 (2011).
[CrossRef]

G. Kakauridze and B. Kilosanidze, “Polarization-holographic diffraction element-based real-time imaging Stokes spectropolarimetry,” Proc. SPIE 7957, 795728 (2011).
[CrossRef]

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization holography: methods and applications,” J. Holography Speckle 5, 52–61 (2009).
[CrossRef]

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization holography. 1. Dynamic polarization-sensitive materials on the basis of azo-dye-containing polymers,” Appl. Opt. 48, 1861–1868 (2009).
[CrossRef]

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]

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

G. Kakauridze and B. Kilosanidze, “Polarization-holographic gratings that form plane-polarized orders of diffraction,” J. Opt. Technol. 73, 188–192 (2006).
[CrossRef]

Kim, B.

J. Woo, E. Kim, B. Kim, and Y. Cho, “Morphology and switching of holographic gratings containing an azo dye,” Liq. Cryst. 34, 527–533 (2007).
[CrossRef]

Kim, E.

J. Woo, E. Kim, B. Kim, and Y. Cho, “Morphology and switching of holographic gratings containing an azo dye,” Liq. Cryst. 34, 527–533 (2007).
[CrossRef]

Kimball, B. R.

Kippelen, B.

Kreuzer, M.

Kukhtarev, N.

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

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

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. L.

F. L. 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]

Liao, C.-C.

Lu, C.-L.

Lyon, S. R.

Macdonald, R.

Mikaelian, A.

A. Mikaelian and V. Salakhutdinov, “Using of dynamic holograms for information channel switching,” Opt. Mem. Neural Netw. 1, 315–324 (1992).

Natansohn, A.

F. L. 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]

Nersisyan, S.

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).
[CrossRef]

Padias, A. B.

Pagliusi, P.

Pellerin, C.

F. L. 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]

Peyghambarian, N.

Pézolet, M.

F. L. 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.

N. C. R. Holme and P. S. Ramanujam, “10,000 optical write, read, and erase cycles in an azobenzene sidechain liquid-crystalline polyester,” Opt. Lett. 21, 902–904 (1996).
[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. L. 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]

Ruhman, S.

S. Takeuchi, S. Ruhman, T. Tsuneda, M. Chiba, T. Taketsugu, and T. Tahara, “Spectroscopic tracking of structural evolution in ultrafast stilbene photoisomerization,” Science 322, 1073–1077 (2008).
[CrossRef]

Salakhutdinov, V.

A. Mikaelian and V. Salakhutdinov, “Using of dynamic holograms for information channel switching,” Opt. Mem. Neural Netw. 1, 315–324 (1992).

Saleh, M. A.

Sandalphon,

Sheng, C. X.

Shih, M.-Y.

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]

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).
[CrossRef]

Steeves, D. M.

Stickley, C. M.

Tabirian, N.

Tabiryan, N.

Tabiryan, N. V.

B. Y. Zel’dovich and N. V. Tabiryan, “Orientational effect of a light wave on a cholesteric mesophase,” Sov. Phys. JETP 55, 167–176 (1982).

Tahara, T.

S. Takeuchi, S. Ruhman, T. Tsuneda, M. Chiba, T. Taketsugu, and T. Tahara, “Spectroscopic tracking of structural evolution in ultrafast stilbene photoisomerization,” Science 322, 1073–1077 (2008).
[CrossRef]

Taketsugu, T.

S. Takeuchi, S. Ruhman, T. Tsuneda, M. Chiba, T. Taketsugu, and T. Tahara, “Spectroscopic tracking of structural evolution in ultrafast stilbene photoisomerization,” Science 322, 1073–1077 (2008).
[CrossRef]

Takeuchi, S.

S. Takeuchi, S. Ruhman, T. Tsuneda, M. Chiba, T. Taketsugu, and T. Tahara, “Spectroscopic tracking of structural evolution in ultrafast stilbene photoisomerization,” Science 322, 1073–1077 (2008).
[CrossRef]

Thomas, J.

Tsai, C.-Y.

Tsuneda, T.

S. Takeuchi, S. Ruhman, T. Tsuneda, M. Chiba, T. Taketsugu, and T. Tahara, “Spectroscopic tracking of structural evolution in ultrafast stilbene photoisomerization,” Science 322, 1073–1077 (2008).
[CrossRef]

Vinetskii, V.

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

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

Vinouze, B.

N. Wollfer, B. Vinouze, and P. Gravey, “Holographic switching between single mode fibres based on electrically addressed nematic liquid crystal gratings with high deflection accuracy,” Opt. Commun. 160, 42–46 (1999).
[CrossRef]

Wang, J.

Wollfer, N.

N. Wollfer, B. Vinouze, and P. Gravey, “Holographic switching between single mode fibres based on electrically addressed nematic liquid crystal gratings with high deflection accuracy,” Opt. Commun. 160, 42–46 (1999).
[CrossRef]

Woo, J.

J. Woo, E. Kim, B. Kim, and Y. Cho, “Morphology and switching of holographic gratings containing an azo dye,” Liq. Cryst. 34, 527–533 (2007).
[CrossRef]

Wood, M. V.

Wu, Y.

Zel’dovich, B. Y.

B. Y. Zel’dovich and N. V. Tabiryan, “Orientational effect of a light wave on a cholesteric mesophase,” Sov. Phys. JETP 55, 167–176 (1982).

Zheng, Z.

Adv. Mater.

R. Hagen and T. Bieringer, “Photoaddressable polymers for optical data storage,” Adv. Mater. 13, 1805–1810 (2001).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

I. C. Khoo, “Dynamic gratings and the associated self diffractions and wavefront conjugation processes in nematic liquid crystals,” IEEE J. Quantum Electron. 22, 1268–1275 (1986).
[CrossRef]

J. Holography Speckle

B. Kilosanidze, G. Kakauridze, and I. Chaganava, “Dynamic polarization holography: methods and applications,” J. Holography Speckle 5, 52–61 (2009).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Opt. Technol.

Liq. Cryst.

J. Woo, E. Kim, B. Kim, and Y. Cho, “Morphology and switching of holographic gratings containing an azo dye,” Liq. Cryst. 34, 527–533 (2007).
[CrossRef]

Macromolecules

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

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Figures (8)

Fig. 1.
Fig. 1.

Experimental setup for recording and erasing dynamic polarization-holographic gratings and for the investigation of time dependence of DE. WP, Wollaston prism; QWP, quarter-wave plates; P, polarizers; O, objective; RM, dynamic polarization-sensitive recording material; M, mirror; PD, photodetectors; PC, computer with ADC.

Fig. 2.
Fig. 2.

Time dependence of DE for different types of gratings recorded on different materials in conditions of (a) recording and free relaxation, (b) recording and forced erasing.

Fig. 3.
Fig. 3.

Optical scheme of a laboratory model of an all-optical commutator. QWP, quarter-wave plates; WP, Wollastone prism; M1, controllable mirrors; M2, mirror.

Fig. 4.
Fig. 4.

Time dependence of the DE of microholograms while switching one of the input channels. “1” corresponds to the recording/connection/erasing of a microhologram with one value of the grating vector (Section AB corresponds to the recording of a microhologram, BC to the connection, and CD to the erasing of a microhologram); “2” is the same for a microhologram with another value of the grating vector.

Fig. 5.
Fig. 5.

Optical scheme for studying the phenomenon of energy transfer in the dynamic polarization hologram at two-wave mixing of the strong I0,1 and week I0,2 beams. PD, photodetectors; PC, computer with integrated ADC; I1 and I2, the intensities of the transmitted beams; I±1, the intensities of the diffracted beams.

Fig. 6.
Fig. 6.

Dependence of the amplification coefficient on the weak-to-strong beam intensity ratio.

Fig. 7.
Fig. 7.

Kinetic curves of the intensity of the transmitted beam I2 for (a) NDMR in PMMA and (b) MY-M in gelatin.

Fig. 8.
Fig. 8.

Time dependence of the amplification of a weak beam at different conditions of using a microshift: (a) with repeatedly switching an electromagnet on and off, and (b) with a single long switching on of an electromagnet. The arrows indicate the moments of switching an electromagnet on and off. The intensity of the weak beam is 2% relative to the intensity of the strong one.

Equations (13)

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EΣ=(ψxexp(iax)+ξxexp(ibx)exp(iδ)ψyexp(iay)+ξyexp(iby)exp(iδ))exp(iωt)+(φxexp(icx)φyexp(icy))exp(iωt),
Δn^1,212n^0[s^(I1+I2)±[v^L(I1I2)]2+[v^G(I+I)]2]exp[2γ(It1+t2)],
Mexp(2iκdn^0)exp[iκds^2n^0(I1+I2)exp[2γ(It1+t2)]](m11m12m21m22),
m11,22=1cosθ[iκdv^L2n^0(I1I2)]exp[2γ(It1+t2)],
m12,21={sin2θ[iκdv^L2n^0(I1I2)]κdv^G2n^0(I+I)}exp[2γ(It1+t2)].
M1Aexp(±δ)((m11)1(m12)1(m21)1(m22)1),
A=iκd2n^0exp(2iκdn^0)exp[2γ(It1+t2)],
(m11,22)1=(s^±v^L)ψ^x*ξ^x+(s^v^L)ψ^y*ξ^y,
(m12,21)1=(v^L±v^G)ψ^x*ξ^y+(v^Lv^G)ψ^y*ξ^x,
(m11,22)+1=(s^±v^L)ψ^xξ^x*+(s^v^L)ψ^yξ^y*,
(m12,21)+1=(v^L±v^G)ψ^yξ^x*+(v^Lv^G)ψ^xξ^y*.
(M1)CAn^0v^Lψ2exp(±iδ)exp[i(axby)](1ii1).
(M1)LAn^0v^Lψ2exp(±iδ)exp[i(axbx)](cos2φcosφsinφcosφsinφsin2φ).

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