Abstract

The photorefractive properties of single crystals of the organic material 2-cyclooctylamino-5-nitropyridine doped with 7,7,8,8-tetracyanoquinodimethane are investigated with two-wave mixing experiments. Refractive-index gratings with an amplitude of up to 1.8 × 10−6 could be recorded for grating vectors along the twofold axis. The phase gratings showed a phase shift of between 20° and 70° with respect to the intensity grating. An experimental procedure for determining phases and amplitudes of absorption and phase gratings is discussed in detail.

© 1990 Optical Society of America

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1990 (2)

K. Sutter, J. Hulliger, P. Günter, Solid State Commun. 74, 867 (1990).
[CrossRef]

M. Z. Zha, P. Amrhein, P. Günter, IEEE Quantum Electron. 26, 788 (1990).
[CrossRef]

1989 (4)

R. A. Rupp, A. Maillard, J. Walter, Appl. Phys. A 49, 259 (1989).
[CrossRef]

Ch. Bosshard, K. Sutter, P. Günter, G. Chapuis, J. Opt. Soc. Am. B 6, 721 (1989).
[CrossRef]

P. M. Garcia, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[CrossRef]

W. S. Wang, J. Hulliger, H. Arend, Ferroelectrics 92, 1113 (1989).
[CrossRef]

1988 (1)

S. Allen, T. McLean, P. F. Gordon, B. D. Bothwell, M. B. Hursthouse, S. A. Karaulov, J. Appl. Phys. 64, 2583 (1988).
[CrossRef]

1987 (3)

P. Günter, Ch. Bosshard, K. Sutter, H. Arend, G. Chapuis, R. J. Twieg, D. Dobrowolski, Appl. Phys. Lett. 50, 486 (1987).
[CrossRef]

M. Gehrtz, J. Pinsl, C. Bräuchle, Appl. Phys. Lett. B 43, 61 (1987).
[CrossRef]

I. McMichael, P. Yeh, Opt. Lett. 12, (1987).

1986 (1)

R. A. Rupp, Appl. Phys. B 41, 153 (1986).
[CrossRef]

1985 (1)

T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, Prog. Quantum Electron. 10, 77 (1985).
[CrossRef]

1981 (3)

G. F. Lipscomb, A. F. Garito, R. S. Narang, Appl. Phys. Lett. 38, 663 (1981).
[CrossRef]

M. Sigelle, R. Hierle, J. Appl. Phys. 52, 4199 (1981).
[CrossRef]

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

1980 (2)

V. I. Belinicher, B. I. Sturman, Sov. Phys. Usp. 23, 199 (1980).
[CrossRef]

V. I. Belinicher, B. I. Sturman, Sov. Phys. Usp. 3, 199 (1980).
[CrossRef]

1979 (1)

V. Kondilenko, V. Markov, S. Odulov, M. Soskin. Opt. Acta 26, 239 (1979).
[CrossRef]

1975 (1)

J. B. Torrrance, B. A. Scott, F. B. Kaufman, Solid State Commun. 17, 1369 (1975).
[CrossRef]

1973 (1)

J. Ferraris, D. O. Cowan, V. Waltka, J. H. Perlstein, J. Am. Chem. Soc. 95, 948 (1973).
[CrossRef]

1972 (2)

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

1967 (2)

E. Sawicki, C. R. Engel, W. C. Elbert, Talanta 14, 1169 (1967).
[CrossRef] [PubMed]

M. Ottelenghi, D. S. McClure, J. Chem. Phys. 46, 4613 (1967).
[CrossRef]

1965 (1)

R. H. Boyd, W. D. Phillips, J. Chem. Phys. 43, 2927 (1965).
[CrossRef]

1962 (1)

D. S. Acker, W. R. Hertler, J. Am. Chem. Soc. 84, 3370 (1962).
[CrossRef]

Acker, D. S.

D. S. Acker, W. R. Hertler, J. Am. Chem. Soc. 84, 3370 (1962).
[CrossRef]

Albrecht, W.

H. Meier, W. Albrecht, U. Tschirwitz, Photochem. Photobiol. 16, 353 (1972).
[CrossRef]

Allen, S.

S. Allen, T. McLean, P. F. Gordon, B. D. Bothwell, M. B. Hursthouse, S. A. Karaulov, J. Appl. Phys. 64, 2583 (1988).
[CrossRef]

Amrhein, P.

M. Z. Zha, P. Amrhein, P. Günter, IEEE Quantum Electron. 26, 788 (1990).
[CrossRef]

Arend, H.

W. S. Wang, J. Hulliger, H. Arend, Ferroelectrics 92, 1113 (1989).
[CrossRef]

P. Günter, Ch. Bosshard, K. Sutter, H. Arend, G. Chapuis, R. J. Twieg, D. Dobrowolski, Appl. Phys. Lett. 50, 486 (1987).
[CrossRef]

Belinicher, V. I.

V. I. Belinicher, B. I. Sturman, Sov. Phys. Usp. 23, 199 (1980).
[CrossRef]

V. I. Belinicher, B. I. Sturman, Sov. Phys. Usp. 3, 199 (1980).
[CrossRef]

Bosshard, Ch.

Ch. Bosshard, K. Sutter, P. Günter, G. Chapuis, J. Opt. Soc. Am. B 6, 721 (1989).
[CrossRef]

P. Günter, Ch. Bosshard, K. Sutter, H. Arend, G. Chapuis, R. J. Twieg, D. Dobrowolski, Appl. Phys. Lett. 50, 486 (1987).
[CrossRef]

Bothwell, B. D.

S. Allen, T. McLean, P. F. Gordon, B. D. Bothwell, M. B. Hursthouse, S. A. Karaulov, J. Appl. Phys. 64, 2583 (1988).
[CrossRef]

Boyd, R. H.

R. H. Boyd, W. D. Phillips, J. Chem. Phys. 43, 2927 (1965).
[CrossRef]

Bräuchle, C.

M. Gehrtz, J. Pinsl, C. Bräuchle, Appl. Phys. Lett. B 43, 61 (1987).
[CrossRef]

Cescato, L.

P. M. Garcia, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[CrossRef]

Chandross, E. A.

Chapuis, G.

Ch. Bosshard, K. Sutter, P. Günter, G. Chapuis, J. Opt. Soc. Am. B 6, 721 (1989).
[CrossRef]

P. Günter, Ch. Bosshard, K. Sutter, H. Arend, G. Chapuis, R. J. Twieg, D. Dobrowolski, Appl. Phys. Lett. 50, 486 (1987).
[CrossRef]

Connors, L. M.

T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, Prog. Quantum Electron. 10, 77 (1985).
[CrossRef]

Cowan, D. O.

J. Ferraris, D. O. Cowan, V. Waltka, J. H. Perlstein, J. Am. Chem. Soc. 95, 948 (1973).
[CrossRef]

Dobrowolski, D.

P. Günter, Ch. Bosshard, K. Sutter, H. Arend, G. Chapuis, R. J. Twieg, D. Dobrowolski, Appl. Phys. Lett. 50, 486 (1987).
[CrossRef]

Eichler, H. J.

H. J. Eichler, P. Günter, D. Phohl, Laser Induced Dynamic Gratings (Springer-Verlag, Heidelberg, 1986).
[CrossRef]

Elbert, W. C.

E. Sawicki, C. R. Engel, W. C. Elbert, Talanta 14, 1169 (1967).
[CrossRef] [PubMed]

Engel, C. R.

E. Sawicki, C. R. Engel, W. C. Elbert, Talanta 14, 1169 (1967).
[CrossRef] [PubMed]

Ferraris, J.

J. Ferraris, D. O. Cowan, V. Waltka, J. H. Perlstein, J. Am. Chem. Soc. 95, 948 (1973).
[CrossRef]

Foote, P. D.

T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, Prog. Quantum Electron. 10, 77 (1985).
[CrossRef]

Fork, R. L.

Frejlich, J.

P. M. Garcia, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[CrossRef]

Fukada, S.

M. Gotoh, T. Tsunekawa, T. Kondoh, S. Fukada, H. Mataki, M. Iwamoto, Y. Maeda, in Proceedings of the International Workshop on Crystal Growth of Organic Materials (Tokyo University of Agriculture and Technology, Tokyo, 1989), pp. 234–237.

Garcia, P. M.

P. M. Garcia, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[CrossRef]

Garito, A. F.

G. F. Lipscomb, A. F. Garito, R. S. Narang, Appl. Phys. Lett. 38, 663 (1981).
[CrossRef]

Gehrtz, M.

M. Gehrtz, J. Pinsl, C. Bräuchle, Appl. Phys. Lett. B 43, 61 (1987).
[CrossRef]

Gordon, P. F.

S. Allen, T. McLean, P. F. Gordon, B. D. Bothwell, M. B. Hursthouse, S. A. Karaulov, J. Appl. Phys. 64, 2583 (1988).
[CrossRef]

Gotoh, M.

M. Gotoh, T. Tsunekawa, T. Kondoh, S. Fukada, H. Mataki, M. Iwamoto, Y. Maeda, in Proceedings of the International Workshop on Crystal Growth of Organic Materials (Tokyo University of Agriculture and Technology, Tokyo, 1989), pp. 234–237.

Günter, P.

M. Z. Zha, P. Amrhein, P. Günter, IEEE Quantum Electron. 26, 788 (1990).
[CrossRef]

K. Sutter, J. Hulliger, P. Günter, Solid State Commun. 74, 867 (1990).
[CrossRef]

Ch. Bosshard, K. Sutter, P. Günter, G. Chapuis, J. Opt. Soc. Am. B 6, 721 (1989).
[CrossRef]

P. Günter, Ch. Bosshard, K. Sutter, H. Arend, G. Chapuis, R. J. Twieg, D. Dobrowolski, Appl. Phys. Lett. 50, 486 (1987).
[CrossRef]

H. J. Eichler, P. Günter, D. Phohl, Laser Induced Dynamic Gratings (Springer-Verlag, Heidelberg, 1986).
[CrossRef]

Hall, T. J.

T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, Prog. Quantum Electron. 10, 77 (1985).
[CrossRef]

Hertler, W. R.

D. S. Acker, W. R. Hertler, J. Am. Chem. Soc. 84, 3370 (1962).
[CrossRef]

Hierle, R.

M. Sigelle, R. Hierle, J. Appl. Phys. 52, 4199 (1981).
[CrossRef]

Huignard, J. P.

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Hulliger, J.

K. Sutter, J. Hulliger, P. Günter, Solid State Commun. 74, 867 (1990).
[CrossRef]

W. S. Wang, J. Hulliger, H. Arend, Ferroelectrics 92, 1113 (1989).
[CrossRef]

W. S. Wang, J. Hulliger, “Modified Bridgman–Stockbarger growth of 2-cyclooctylamino-5-nitropyridine (COANP),” presented at the Ninth International Conference on Crystal Growth, Sendai, Japan, 1989.

Hursthouse, M. B.

S. Allen, T. McLean, P. F. Gordon, B. D. Bothwell, M. B. Hursthouse, S. A. Karaulov, J. Appl. Phys. 64, 2583 (1988).
[CrossRef]

Iwamoto, M.

M. Gotoh, T. Tsunekawa, T. Kondoh, S. Fukada, H. Mataki, M. Iwamoto, Y. Maeda, in Proceedings of the International Workshop on Crystal Growth of Organic Materials (Tokyo University of Agriculture and Technology, Tokyo, 1989), pp. 234–237.

Jaura, R.

T. J. Hall, R. Jaura, L. M. Connors, P. D. Foote, Prog. Quantum Electron. 10, 77 (1985).
[CrossRef]

Karaulov, S. A.

S. Allen, T. McLean, P. F. Gordon, B. D. Bothwell, M. B. Hursthouse, S. A. Karaulov, J. Appl. Phys. 64, 2583 (1988).
[CrossRef]

Kaufman, F. B.

J. B. Torrrance, B. A. Scott, F. B. Kaufman, Solid State Commun. 17, 1369 (1975).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Kondilenko, V.

V. Kondilenko, V. Markov, S. Odulov, M. Soskin. Opt. Acta 26, 239 (1979).
[CrossRef]

Kondoh, T.

M. Gotoh, T. Tsunekawa, T. Kondoh, S. Fukada, H. Mataki, M. Iwamoto, Y. Maeda, in Proceedings of the International Workshop on Crystal Growth of Organic Materials (Tokyo University of Agriculture and Technology, Tokyo, 1989), pp. 234–237.

Lamola, A. A.

Lipscomb, G. F.

G. F. Lipscomb, A. F. Garito, R. S. Narang, Appl. Phys. Lett. 38, 663 (1981).
[CrossRef]

Maeda, Y.

M. Gotoh, T. Tsunekawa, T. Kondoh, S. Fukada, H. Mataki, M. Iwamoto, Y. Maeda, in Proceedings of the International Workshop on Crystal Growth of Organic Materials (Tokyo University of Agriculture and Technology, Tokyo, 1989), pp. 234–237.

Maillard, A.

R. A. Rupp, A. Maillard, J. Walter, Appl. Phys. A 49, 259 (1989).
[CrossRef]

Markov, V.

V. Kondilenko, V. Markov, S. Odulov, M. Soskin. Opt. Acta 26, 239 (1979).
[CrossRef]

Marrakchi, A.

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Mataki, H.

M. Gotoh, T. Tsunekawa, T. Kondoh, S. Fukada, H. Mataki, M. Iwamoto, Y. Maeda, in Proceedings of the International Workshop on Crystal Growth of Organic Materials (Tokyo University of Agriculture and Technology, Tokyo, 1989), pp. 234–237.

McClure, D. S.

M. Ottelenghi, D. S. McClure, J. Chem. Phys. 46, 4613 (1967).
[CrossRef]

McLean, T.

S. Allen, T. McLean, P. F. Gordon, B. D. Bothwell, M. B. Hursthouse, S. A. Karaulov, J. Appl. Phys. 64, 2583 (1988).
[CrossRef]

McMichael, I.

I. McMichael, P. Yeh, Opt. Lett. 12, (1987).

Meier, H.

H. Meier, W. Albrecht, U. Tschirwitz, Photochem. Photobiol. 16, 353 (1972).
[CrossRef]

Narang, R. S.

G. F. Lipscomb, A. F. Garito, R. S. Narang, Appl. Phys. Lett. 38, 663 (1981).
[CrossRef]

Nicoud, J. F.

J. F. Nicoud, R. J. Twieg, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla, J. Zyss, eds. (Academic, Orlando, 1987), Vol. 2, pp. 221–254.
[CrossRef]

Odulov, S.

V. Kondilenko, V. Markov, S. Odulov, M. Soskin. Opt. Acta 26, 239 (1979).
[CrossRef]

Ottelenghi, M.

M. Ottelenghi, D. S. McClure, J. Chem. Phys. 46, 4613 (1967).
[CrossRef]

Perlstein, J. H.

J. Ferraris, D. O. Cowan, V. Waltka, J. H. Perlstein, J. Am. Chem. Soc. 95, 948 (1973).
[CrossRef]

Phillips, W. D.

R. H. Boyd, W. D. Phillips, J. Chem. Phys. 43, 2927 (1965).
[CrossRef]

Phohl, D.

H. J. Eichler, P. Günter, D. Phohl, Laser Induced Dynamic Gratings (Springer-Verlag, Heidelberg, 1986).
[CrossRef]

Pinsl, J.

M. Gehrtz, J. Pinsl, C. Bräuchle, Appl. Phys. Lett. B 43, 61 (1987).
[CrossRef]

Pope, M.

M. Pope, C. E. Swenberg, Electronic Processes in Organic Crystals (Clarendon, Oxford, 1982).

Pryde, C. A.

Rupp, R. A.

R. A. Rupp, A. Maillard, J. Walter, Appl. Phys. A 49, 259 (1989).
[CrossRef]

R. A. Rupp, Appl. Phys. B 41, 153 (1986).
[CrossRef]

Sawicki, E.

E. Sawicki, C. R. Engel, W. C. Elbert, Talanta 14, 1169 (1967).
[CrossRef] [PubMed]

Scott, B. A.

J. B. Torrrance, B. A. Scott, F. B. Kaufman, Solid State Commun. 17, 1369 (1975).
[CrossRef]

Sigelle, M.

M. Sigelle, R. Hierle, J. Appl. Phys. 52, 4199 (1981).
[CrossRef]

Silinsh, E. A.

E. A. Silinsh, Organic Molecular Crystals: Their Electronic States (Springer, New York, 1980).
[CrossRef]

Soskin, M.

V. Kondilenko, V. Markov, S. Odulov, M. Soskin. Opt. Acta 26, 239 (1979).
[CrossRef]

Sturman, B. I.

V. I. Belinicher, B. I. Sturman, Sov. Phys. Usp. 3, 199 (1980).
[CrossRef]

V. I. Belinicher, B. I. Sturman, Sov. Phys. Usp. 23, 199 (1980).
[CrossRef]

Sutter, K.

K. Sutter, J. Hulliger, P. Günter, Solid State Commun. 74, 867 (1990).
[CrossRef]

Ch. Bosshard, K. Sutter, P. Günter, G. Chapuis, J. Opt. Soc. Am. B 6, 721 (1989).
[CrossRef]

P. Günter, Ch. Bosshard, K. Sutter, H. Arend, G. Chapuis, R. J. Twieg, D. Dobrowolski, Appl. Phys. Lett. 50, 486 (1987).
[CrossRef]

Swenberg, C. E.

M. Pope, C. E. Swenberg, Electronic Processes in Organic Crystals (Clarendon, Oxford, 1982).

Tomlinson, W. J.

Torrrance, J. B.

J. B. Torrrance, B. A. Scott, F. B. Kaufman, Solid State Commun. 17, 1369 (1975).
[CrossRef]

Tschirwitz, U.

H. Meier, W. Albrecht, U. Tschirwitz, Photochem. Photobiol. 16, 353 (1972).
[CrossRef]

Tsunekawa, T.

M. Gotoh, T. Tsunekawa, T. Kondoh, S. Fukada, H. Mataki, M. Iwamoto, Y. Maeda, in Proceedings of the International Workshop on Crystal Growth of Organic Materials (Tokyo University of Agriculture and Technology, Tokyo, 1989), pp. 234–237.

Twieg, R. J.

P. Günter, Ch. Bosshard, K. Sutter, H. Arend, G. Chapuis, R. J. Twieg, D. Dobrowolski, Appl. Phys. Lett. 50, 486 (1987).
[CrossRef]

J. F. Nicoud, R. J. Twieg, in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla, J. Zyss, eds. (Academic, Orlando, 1987), Vol. 2, pp. 221–254.
[CrossRef]

Walter, J.

R. A. Rupp, A. Maillard, J. Walter, Appl. Phys. A 49, 259 (1989).
[CrossRef]

Waltka, V.

J. Ferraris, D. O. Cowan, V. Waltka, J. H. Perlstein, J. Am. Chem. Soc. 95, 948 (1973).
[CrossRef]

Wang, W. S.

W. S. Wang, J. Hulliger, H. Arend, Ferroelectrics 92, 1113 (1989).
[CrossRef]

W. S. Wang, J. Hulliger, “Modified Bridgman–Stockbarger growth of 2-cyclooctylamino-5-nitropyridine (COANP),” presented at the Ninth International Conference on Crystal Growth, Sendai, Japan, 1989.

Yeh, P.

I. McMichael, P. Yeh, Opt. Lett. 12, (1987).

Zha, M. Z.

M. Z. Zha, P. Amrhein, P. Günter, IEEE Quantum Electron. 26, 788 (1990).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A (1)

R. A. Rupp, A. Maillard, J. Walter, Appl. Phys. A 49, 259 (1989).
[CrossRef]

Appl. Phys. B (1)

R. A. Rupp, Appl. Phys. B 41, 153 (1986).
[CrossRef]

Appl. Phys. Lett. (2)

P. Günter, Ch. Bosshard, K. Sutter, H. Arend, G. Chapuis, R. J. Twieg, D. Dobrowolski, Appl. Phys. Lett. 50, 486 (1987).
[CrossRef]

G. F. Lipscomb, A. F. Garito, R. S. Narang, Appl. Phys. Lett. 38, 663 (1981).
[CrossRef]

Appl. Phys. Lett. B (1)

M. Gehrtz, J. Pinsl, C. Bräuchle, Appl. Phys. Lett. B 43, 61 (1987).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Ferroelectrics (1)

W. S. Wang, J. Hulliger, H. Arend, Ferroelectrics 92, 1113 (1989).
[CrossRef]

IEEE Quantum Electron. (1)

M. Z. Zha, P. Amrhein, P. Günter, IEEE Quantum Electron. 26, 788 (1990).
[CrossRef]

J. Am. Chem. Soc. (2)

D. S. Acker, W. R. Hertler, J. Am. Chem. Soc. 84, 3370 (1962).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Single molecules of TCNQ and COANP.

Fig. 2
Fig. 2

Molecules of COANP in the crystal lattice.

Fig. 3
Fig. 3

Absorption coefficients of undoped (●) and TCNQ-doped (■) COANP.

Fig. 4
Fig. 4

Conductivity as a function of illumination intensity in a sample of COANP:TCNQ. Illumination wavelength, 676 nm; electric fields, 0.5–3 kV/cm along c; silver electrodes.

Fig. 5
Fig. 5

Diffraction experiment for one incident beam (E0 = 0) or two incident beams (E0 = E0).

Fig. 6
Fig. 6

Intensity of outgoing beams during a linear translation of the crystal (starting at t = 100 msec). The shown signals are divided by the laser output intensity, filtered by a low-pass filter (τ = 24 msec) and offset by ~700 mV. The average intensity before offsetting corresponded to 700 mV for each beam.

Fig. 7
Fig. 7

Buildup of the phase gratings for light polarization parallel to b and for grating vectors Kc and Kb. Intensity, 2 × 1.6 W/cm2.

Fig. 8
Fig. 8

Buildup of AG’s for light polarization parallel to b and for grating vectors Kc and Kb. Intensity, 2 × 1.6 W/cm2.

Tables (1)

Tables Icon

Table 1 Amplitudes A, P, Δα, and Δn and Phase Shifts ϕA and ϕP of Absorption and Phase Gratings for Two Directions of the Grating Vector Ka

Equations (12)

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n ( r ) = n 0 + Δ n cos ( Kr ) , α ( r ) = α 0 + Δ α cos ( Kr ) ,
E ( 1 ) = E 0 R exp [ i ( ω t ρ r ) ] , E ( 2 ) = E 0 S exp [ i ( ω t σ r ) ] ,
S = 1 2 exp ( α 0 d 2 cos θ ) [ exp ( i κ d cos θ ) exp ( i κ d cos θ ) ] , R = 1 2 exp ( α 0 d 2 cos θ ) [ exp ( i κ d cos θ ) + exp ( i κ d cos θ ) ] ,
κ = π ( Δ n / λ ) i ( Δ α / 4 ) ,
E ( 1 ) = E 0 D exp [ i ( ω t ρ r ) ] , E ( 2 ) = E 0 D ( i P + A ) exp [ i ( ω t σ r ) ] ,
D = exp ( α 0 d 2 cos θ )
P = π Δ n d λ cos θ , A = Δ α d 4 cos θ .
n ( r ) = n 0 + Δ n cos ( Kr ϕ P ) , α ( r ) = α 0 + Δ α cos ( Kr ϕ A ) , I ( r ) = I 0 [ 1 + cos ( Kr ) ] .
E ( 1 ) = E 0 D { 1 [ i P exp ( i Φ P ) + A exp ( i Φ A ) ] } , E ( 2 ) = E 0 D { 1 [ i P exp ( i Φ P ) + A exp ( i Φ A ) ] } .
I ( 1 ) = E ( 1 ) E ( 1 ) * = I 0 exp ( α 0 d / cos θ ) ( 1 2 A cos ϕ A 2 P sin ϕ P ) , I ( 2 ) = E ( 2 ) E ( 2 ) * = I 0 exp ( α 0 d / cos θ ) ( 1 2 A cos ϕ A + 2 P sin ϕ P ) ,
I + = I ( 1 ) + I ( 2 ) = I 0 exp ( α 0 d / cos θ ) ( 2 4 A cos ϕ A ) , I = I ( 1 ) I ( 2 ) = I 0 exp ( α 0 d / cos θ ) ( 0 4 P sin ϕ P ) .
I + ( ζ ) = I 0 exp ( α 0 d / cos θ ) [ 2 4 A cos ( ϕ A + 2 π ζ / Λ ) ] , I ( ζ ) = I 0 exp ( α 0 d / cos θ ) [ 0 4 P sin ( ϕ P + 2 π ζ / Λ ) ] ,

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