Abstract

A systematic experimental and theoretical study of first-order grating coupling to surface plasma waves existing at an air–Ag interface is presented. The experiment extends beyond previous work to grating depths comparable with the grating period. The grating profiles range from sinusoidal to rectangular. For TM-polarized incident radiation this grating depth range includes the entire spectrum of surface-plasma-wave-radiation coupling—from underdamped, to nearly 100% coupling, to overdamped and the disappearance of the resonance from the zero-order reflectance measurements. Strong polarization and absorption effects are observed for the deepest gratings. A simple theoretical model, based on the Rayleigh hypothesis and retaining only resonant diffraction terms without a small-signal approximation being made, provides good agreement with the experimental results.

© 1991 Optical Society of America

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References

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  1. R. W. Wood, Philos. Mag. 4, 396 (1902).
  2. Rayleigh, Philos. Mag. 14, 60 (1907).
  3. Rayleigh, Proc. R. Soc. London Ser. A 79, 399 (1907).
  4. U. Fano, J. Opt. Soc. Am. 31, 213 (1941).
    [Crossref]
  5. A. Sommerfeld, Ann. Phys. (Leipzig) 28, 665 (1909).
  6. A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, New York, 1982).
  7. E. A. Stern, as quoted in R. A. Ferrel, Phys. Rev. 111, 1214 (1958).
    [Crossref]
  8. Y. Y. Teng and E. A. Stern, Phys. Rev. Lett. 19, 511 (1967).
    [Crossref]
  9. J. J. Cowan and E. T. Arakawa, Z. Phys. 235, 97 (1970).
    [Crossref]
  10. M. C. Hutley, Opt. Acta 20, 607 (1973).
    [Crossref]
  11. M. C. Hutley and V. M. Bird, Opt. Acta 20, 771 (1973).
    [Crossref]
  12. M. C. Hutley and D. Maystre, Opt. Commun. 19, 431 (1976).
    [Crossref]
  13. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [Crossref]
  14. I. Pockrand, Phys. Lett. A 49, 259 (1974).
    [Crossref]
  15. I. Pockrand and H. Raether, Opt. Commun. 18, 395 (1976).
    [Crossref]
  16. I. Pockrand, J. Phys. D 9, 2423 (1976).
    [Crossref]
  17. I. Pockrand and H. Raether, Appl. Opt. 16, 1784 (1977).
    [Crossref] [PubMed]
  18. H. Raether, Opt. Commun. 42, 217 (1982).
    [Crossref]
  19. E. Kroger and E. Kretschmann, Phys. Status Solidi B 76, 515 (1976).
    [Crossref]
  20. V. M. Agranovich and D. L. Mills, eds., Surface Polaritons (North-Holland, Amsterdam, 1982).
  21. M. Weber and D. L. Mills, Phys. Rev. B 27, 2698 (1983).
    [Crossref]
  22. F. Toigo, A. Marvin, V. Celli, and N. R. Hill, Phys. Rev. B 15, 5618 (1977).
    [Crossref]
  23. N. E. Glass, M. Weber, and D. L. Mills, Phys. Rev. B 29, 6548 (1984).
    [Crossref]
  24. M. G. Weber, Phys. Rev. B 33, 909 (1986).
    [Crossref]
  25. M. Yamashita and M. Tsuji, J. Phys. Soc. Jpn. 52, 2462 (1983).
    [Crossref]
  26. S. D. Gupta, G. V. Varada, and G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
    [Crossref]
  27. S. H. Zaidi and S. R. J. Brueck, Appl. Opt. 27, 2999 (1988).
    [Crossref] [PubMed]
  28. J. L. Roumiguieres, D. Maystre, and R. Petit, J. Opt. Soc. Am. 67, 557 (1977).
    [Crossref]
  29. J. L. Roumiguieres, Opt. Commun. 19, 76 (1976).
    [Crossref]
  30. K. Knop, Opt. Commun. 26, 28 (1978).
    [Crossref]
  31. K. Utagawa, J. Opt. Soc. Am. 69, 333 (1979).
    [Crossref]
  32. M. Naviere, P. Vincent, R. Petit, and M. Cadilhac, Opt. Commun. 9, 48 (1973).
    [Crossref]
  33. H. Numata, J. Phys. Soc. Jpn. 51, 2575 (1982).
    [Crossref]
  34. S. S. Jha, J. R. Kirtley, and J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
    [Crossref]
  35. P. M. Van den Berg and J. T. Fokkema, J. Opt. Soc. Am. 69, 27 (1979).
    [Crossref]
  36. R. Petit and M. Cadilhac, C. R. Acad. Sci. 262, 468 (1966).
  37. T. C. Paulick, Phys. Rev. B 42, 2801 (1990).
    [Crossref]
  38. N. Garcia, Opt. Commun. 45, 307 (1983).
    [Crossref]
  39. G. P. Motulevich, Optical Properties of Metals (Consultants Bureau, New York, 1973).
  40. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [Crossref]
  41. R. Weast and D. Lide, eds., Handbook of Physics and Chemistry, 70th ed. (CRC, Boca Raton, Fla., 1989).

1990 (1)

T. C. Paulick, Phys. Rev. B 42, 2801 (1990).
[Crossref]

1988 (1)

1987 (1)

S. D. Gupta, G. V. Varada, and G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[Crossref]

1986 (1)

M. G. Weber, Phys. Rev. B 33, 909 (1986).
[Crossref]

1984 (1)

N. E. Glass, M. Weber, and D. L. Mills, Phys. Rev. B 29, 6548 (1984).
[Crossref]

1983 (3)

N. Garcia, Opt. Commun. 45, 307 (1983).
[Crossref]

M. Yamashita and M. Tsuji, J. Phys. Soc. Jpn. 52, 2462 (1983).
[Crossref]

M. Weber and D. L. Mills, Phys. Rev. B 27, 2698 (1983).
[Crossref]

1982 (2)

H. Raether, Opt. Commun. 42, 217 (1982).
[Crossref]

H. Numata, J. Phys. Soc. Jpn. 51, 2575 (1982).
[Crossref]

1980 (1)

S. S. Jha, J. R. Kirtley, and J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
[Crossref]

1979 (2)

1978 (1)

K. Knop, Opt. Commun. 26, 28 (1978).
[Crossref]

1977 (3)

1976 (5)

E. Kroger and E. Kretschmann, Phys. Status Solidi B 76, 515 (1976).
[Crossref]

I. Pockrand and H. Raether, Opt. Commun. 18, 395 (1976).
[Crossref]

I. Pockrand, J. Phys. D 9, 2423 (1976).
[Crossref]

M. C. Hutley and D. Maystre, Opt. Commun. 19, 431 (1976).
[Crossref]

J. L. Roumiguieres, Opt. Commun. 19, 76 (1976).
[Crossref]

1974 (1)

I. Pockrand, Phys. Lett. A 49, 259 (1974).
[Crossref]

1973 (3)

M. C. Hutley, Opt. Acta 20, 607 (1973).
[Crossref]

M. C. Hutley and V. M. Bird, Opt. Acta 20, 771 (1973).
[Crossref]

M. Naviere, P. Vincent, R. Petit, and M. Cadilhac, Opt. Commun. 9, 48 (1973).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

1970 (1)

J. J. Cowan and E. T. Arakawa, Z. Phys. 235, 97 (1970).
[Crossref]

1967 (1)

Y. Y. Teng and E. A. Stern, Phys. Rev. Lett. 19, 511 (1967).
[Crossref]

1966 (1)

R. Petit and M. Cadilhac, C. R. Acad. Sci. 262, 468 (1966).

1958 (1)

E. A. Stern, as quoted in R. A. Ferrel, Phys. Rev. 111, 1214 (1958).
[Crossref]

E. A. Stern, as quoted in R. A. Ferrel, Phys. Rev. 111, 1214 (1958).
[Crossref]

1941 (1)

1909 (1)

A. Sommerfeld, Ann. Phys. (Leipzig) 28, 665 (1909).

1907 (2)

Rayleigh, Philos. Mag. 14, 60 (1907).

Rayleigh, Proc. R. Soc. London Ser. A 79, 399 (1907).

1902 (1)

R. W. Wood, Philos. Mag. 4, 396 (1902).

Agarwal, G. S.

S. D. Gupta, G. V. Varada, and G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[Crossref]

Arakawa, E. T.

J. J. Cowan and E. T. Arakawa, Z. Phys. 235, 97 (1970).
[Crossref]

Bird, V. M.

M. C. Hutley and V. M. Bird, Opt. Acta 20, 771 (1973).
[Crossref]

Brueck, S. R. J.

Cadilhac, M.

M. Naviere, P. Vincent, R. Petit, and M. Cadilhac, Opt. Commun. 9, 48 (1973).
[Crossref]

R. Petit and M. Cadilhac, C. R. Acad. Sci. 262, 468 (1966).

Celli, V.

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, Phys. Rev. B 15, 5618 (1977).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Cowan, J. J.

J. J. Cowan and E. T. Arakawa, Z. Phys. 235, 97 (1970).
[Crossref]

Fano, U.

Ferrel, R. A.

E. A. Stern, as quoted in R. A. Ferrel, Phys. Rev. 111, 1214 (1958).
[Crossref]

Fokkema, J. T.

Garcia, N.

N. Garcia, Opt. Commun. 45, 307 (1983).
[Crossref]

Glass, N. E.

N. E. Glass, M. Weber, and D. L. Mills, Phys. Rev. B 29, 6548 (1984).
[Crossref]

Gupta, S. D.

S. D. Gupta, G. V. Varada, and G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[Crossref]

Hill, N. R.

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, Phys. Rev. B 15, 5618 (1977).
[Crossref]

Hutley, M. C.

M. C. Hutley and D. Maystre, Opt. Commun. 19, 431 (1976).
[Crossref]

M. C. Hutley, Opt. Acta 20, 607 (1973).
[Crossref]

M. C. Hutley and V. M. Bird, Opt. Acta 20, 771 (1973).
[Crossref]

Jha, S. S.

S. S. Jha, J. R. Kirtley, and J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Kirtley, J. R.

S. S. Jha, J. R. Kirtley, and J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
[Crossref]

Knop, K.

K. Knop, Opt. Commun. 26, 28 (1978).
[Crossref]

Kretschmann, E.

E. Kroger and E. Kretschmann, Phys. Status Solidi B 76, 515 (1976).
[Crossref]

Kroger, E.

E. Kroger and E. Kretschmann, Phys. Status Solidi B 76, 515 (1976).
[Crossref]

Marvin, A.

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, Phys. Rev. B 15, 5618 (1977).
[Crossref]

Maystre, D.

Mills, D. L.

N. E. Glass, M. Weber, and D. L. Mills, Phys. Rev. B 29, 6548 (1984).
[Crossref]

M. Weber and D. L. Mills, Phys. Rev. B 27, 2698 (1983).
[Crossref]

Motulevich, G. P.

G. P. Motulevich, Optical Properties of Metals (Consultants Bureau, New York, 1973).

Naviere, M.

M. Naviere, P. Vincent, R. Petit, and M. Cadilhac, Opt. Commun. 9, 48 (1973).
[Crossref]

Numata, H.

H. Numata, J. Phys. Soc. Jpn. 51, 2575 (1982).
[Crossref]

Paulick, T. C.

T. C. Paulick, Phys. Rev. B 42, 2801 (1990).
[Crossref]

Petit, R.

J. L. Roumiguieres, D. Maystre, and R. Petit, J. Opt. Soc. Am. 67, 557 (1977).
[Crossref]

M. Naviere, P. Vincent, R. Petit, and M. Cadilhac, Opt. Commun. 9, 48 (1973).
[Crossref]

R. Petit and M. Cadilhac, C. R. Acad. Sci. 262, 468 (1966).

Pockrand, I.

I. Pockrand and H. Raether, Appl. Opt. 16, 1784 (1977).
[Crossref] [PubMed]

I. Pockrand and H. Raether, Opt. Commun. 18, 395 (1976).
[Crossref]

I. Pockrand, J. Phys. D 9, 2423 (1976).
[Crossref]

I. Pockrand, Phys. Lett. A 49, 259 (1974).
[Crossref]

Raether, H.

H. Raether, Opt. Commun. 42, 217 (1982).
[Crossref]

I. Pockrand and H. Raether, Appl. Opt. 16, 1784 (1977).
[Crossref] [PubMed]

I. Pockrand and H. Raether, Opt. Commun. 18, 395 (1976).
[Crossref]

Rayleigh,

Rayleigh, Philos. Mag. 14, 60 (1907).

Rayleigh, Proc. R. Soc. London Ser. A 79, 399 (1907).

Roumiguieres, J. L.

Sommerfeld, A.

A. Sommerfeld, Ann. Phys. (Leipzig) 28, 665 (1909).

Stern, E. A.

Y. Y. Teng and E. A. Stern, Phys. Rev. Lett. 19, 511 (1967).
[Crossref]

E. A. Stern, as quoted in R. A. Ferrel, Phys. Rev. 111, 1214 (1958).
[Crossref]

Teng, Y. Y.

Y. Y. Teng and E. A. Stern, Phys. Rev. Lett. 19, 511 (1967).
[Crossref]

Toigo, F.

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, Phys. Rev. B 15, 5618 (1977).
[Crossref]

Tsang, J. C.

S. S. Jha, J. R. Kirtley, and J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
[Crossref]

Tsuji, M.

M. Yamashita and M. Tsuji, J. Phys. Soc. Jpn. 52, 2462 (1983).
[Crossref]

Utagawa, K.

Van den Berg, P. M.

Varada, G. V.

S. D. Gupta, G. V. Varada, and G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[Crossref]

Vincent, P.

M. Naviere, P. Vincent, R. Petit, and M. Cadilhac, Opt. Commun. 9, 48 (1973).
[Crossref]

Weber, M.

N. E. Glass, M. Weber, and D. L. Mills, Phys. Rev. B 29, 6548 (1984).
[Crossref]

M. Weber and D. L. Mills, Phys. Rev. B 27, 2698 (1983).
[Crossref]

Weber, M. G.

M. G. Weber, Phys. Rev. B 33, 909 (1986).
[Crossref]

Wood, R. W.

R. W. Wood, Philos. Mag. 4, 396 (1902).

Yamashita, M.

M. Yamashita and M. Tsuji, J. Phys. Soc. Jpn. 52, 2462 (1983).
[Crossref]

Zaidi, S. H.

Ann. Phys. (Leipzig) (1)

A. Sommerfeld, Ann. Phys. (Leipzig) 28, 665 (1909).

Appl. Opt. (2)

C. R. Acad. Sci. (1)

R. Petit and M. Cadilhac, C. R. Acad. Sci. 262, 468 (1966).

J. Opt. Soc. Am. (4)

J. Phys. D (1)

I. Pockrand, J. Phys. D 9, 2423 (1976).
[Crossref]

J. Phys. Soc. Jpn. (2)

M. Yamashita and M. Tsuji, J. Phys. Soc. Jpn. 52, 2462 (1983).
[Crossref]

H. Numata, J. Phys. Soc. Jpn. 51, 2575 (1982).
[Crossref]

Opt. Acta (2)

M. C. Hutley, Opt. Acta 20, 607 (1973).
[Crossref]

M. C. Hutley and V. M. Bird, Opt. Acta 20, 771 (1973).
[Crossref]

Opt. Commun. (7)

M. C. Hutley and D. Maystre, Opt. Commun. 19, 431 (1976).
[Crossref]

H. Raether, Opt. Commun. 42, 217 (1982).
[Crossref]

M. Naviere, P. Vincent, R. Petit, and M. Cadilhac, Opt. Commun. 9, 48 (1973).
[Crossref]

J. L. Roumiguieres, Opt. Commun. 19, 76 (1976).
[Crossref]

K. Knop, Opt. Commun. 26, 28 (1978).
[Crossref]

I. Pockrand and H. Raether, Opt. Commun. 18, 395 (1976).
[Crossref]

N. Garcia, Opt. Commun. 45, 307 (1983).
[Crossref]

Philos. Mag. (2)

R. W. Wood, Philos. Mag. 4, 396 (1902).

Rayleigh, Philos. Mag. 14, 60 (1907).

Phys. Lett. A (1)

I. Pockrand, Phys. Lett. A 49, 259 (1974).
[Crossref]

Phys. Rev. (1)

E. A. Stern, as quoted in R. A. Ferrel, Phys. Rev. 111, 1214 (1958).
[Crossref]

Phys. Rev. B (8)

S. D. Gupta, G. V. Varada, and G. S. Agarwal, Phys. Rev. B 36, 6331 (1987).
[Crossref]

M. Weber and D. L. Mills, Phys. Rev. B 27, 2698 (1983).
[Crossref]

F. Toigo, A. Marvin, V. Celli, and N. R. Hill, Phys. Rev. B 15, 5618 (1977).
[Crossref]

N. E. Glass, M. Weber, and D. L. Mills, Phys. Rev. B 29, 6548 (1984).
[Crossref]

M. G. Weber, Phys. Rev. B 33, 909 (1986).
[Crossref]

S. S. Jha, J. R. Kirtley, and J. C. Tsang, Phys. Rev. B 22, 3973 (1980).
[Crossref]

T. C. Paulick, Phys. Rev. B 42, 2801 (1990).
[Crossref]

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Phys. Rev. Lett. (1)

Y. Y. Teng and E. A. Stern, Phys. Rev. Lett. 19, 511 (1967).
[Crossref]

Phys. Status Solidi B (1)

E. Kroger and E. Kretschmann, Phys. Status Solidi B 76, 515 (1976).
[Crossref]

Proc. R. Soc. London Ser. A (1)

Rayleigh, Proc. R. Soc. London Ser. A 79, 399 (1907).

Z. Phys. (1)

J. J. Cowan and E. T. Arakawa, Z. Phys. 235, 97 (1970).
[Crossref]

Other (5)

V. M. Agranovich and D. L. Mills, eds., Surface Polaritons (North-Holland, Amsterdam, 1982).

A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, New York, 1982).

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[Crossref]

R. Weast and D. Lide, eds., Handbook of Physics and Chemistry, 70th ed. (CRC, Boca Raton, Fla., 1989).

G. P. Motulevich, Optical Properties of Metals (Consultants Bureau, New York, 1973).

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Figures (17)

Fig. 1
Fig. 1

Dispersion relation of SPW’s for a lossless, free-electron metal ( = 1 − ωp2/ω2). The axes are normalized to ωp and kp = ωp/c. The grating wave vectors corresponding to n = ±1 order of a grating of period d are shown as vertical dashed lines. The range of wave vectors accessible by variations in the input angle from normal to grazing incidence for n = 0 and n = ±1 is shown as horizontal lines. Note that for this choice of parameters (λ/d < 1) there is only one SPW coupling resonance, and at this resonance angle there is no propagating diffraction order.

Fig. 2
Fig. 2

Zero-order reflectance at 633 nm for 510-nm-period gratings with varying grating depths. The left side [(a)–(d)] presents experimental results; the right side [(e)–(h)] presents theoretical modeling. See the text for details.

Fig. 3
Fig. 3

Continuation of Fig. 2 for deeper gratings. Note the expanded angular scale. Again, the left side [(a)–(d)] presents experimental results; the right side [(e)–(h)], theoretical modeling. The sharp spikes on the experimental data at ~38° correspond to the n = −1 diffraction order entering the collection optics and are not a part of the zero-order reflectivity.

Fig. 4
Fig. 4

Cross-section SEM pictures of the gratings used for the experiments. The measured depths are (a) 43 nm, (b) 57 nm, (c) 88 nm, and (d) 145 nm.

Fig. 5
Fig. 5

Coupling efficiency into the SPW mode for gratings with periods of (a) 392 nm, (b) 440 nm, and (c) 510 nm and varying depths. The solid curves are the result of theoretical modeling; see the text for details.

Fig. 6
Fig. 6

Same as Fig. 5, except here for SPW resonance angle.

Fig. 7
Fig. 7

Same as Fig. 5, except here for SPW resonance linewidth (FWHM).

Fig. 8
Fig. 8

Data of Figs. 57 for the SPW resonance angle, the resonance linewidth, and the coupling efficiency replotted against the dimensionless parameter h/d. Note that this parameter is approximately invariant for these three grating periods.

Fig. 9
Fig. 9

Sequence of zero-order reflectance scans for approximately square gratings (h/d ~ 0.5) showing strong polarizing effects: (a) h = 200 nm, d = 392 nm; (b) h = 170 nm, d = 440 nm; and (c) h = 190 nm, d = 510 nm.

Fig. 10
Fig. 10

SEM pictures of the gratings used for the measurements of Fig. 9.

Fig. 11
Fig. 11

Sequence of zero-order reflectance scans for deeper rectangular gratings (h/d ~ 1) showing strong absorption effects: (a) h = 320 nm, d = 392 nm; (b) h = 330 nm, d = 440 nm; and (c) h = 300 nm, d = 510 nm.

Fig. 12
Fig. 12

SEM pictures of the gratings used for the measurements of Fig. 11.

Fig. 13
Fig. 13

Geometry used in the analysis.

Fig. 14
Fig. 14

Comparison of (a) calculations of Garcia35 with [(b)–(e)] present calculations for 800-nm-period Au gratings at 633 nm (h1 = h/2d).

Fig. 15
Fig. 15

Calculated zero-order reflectivity SPW resonance line shapes for = (−13.65,0.82) at grating depth h = 19 nm. The experimental result (h = 22 nm) is shown as the solid curve.

Fig. 16
Fig. 16

Calculated SPW resonance parameters plotted against the dimensionless parameter h/d.

Fig. 17
Fig. 17

Calculated zero-order reflectivity for deep (h/d ~ 1) sinusoidal gratings in TM polarization (d = 510 nm).

Equations (11)

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

k SPW = k 0 [ m / ( m + 1 ) ] 1 / 2 ,
k 0 sin θ = ± k SPW + n 2 π / d ,
B v = B v e x = { exp [ i ( k y y + k z z ) ] + B v n exp [ i ( k n y - α n z ) ] } e x ,             z < 0
B m = B m e x = B m n exp [ i ( k n y + β n z ) ] e x ,             z > h ,
f ( y ) = u sin ( g y ) ,
exp [ i γ f ( y ) ] = exp [ i γ u sin ( g y ) ] = exp ( i p g y ) J p ( γ u ) .
{ B v ( y , z ) = B m ( y , z ) } z = f ( y )
{ B v ( y , z ) n = 1 m B m ( y , z ) n } | z = f ( y ) ,
n = [ 1 + ( f y ) 2 ] - 1 / 2 ( z - f y y ) .
J p ( k z u ) + B v n ( - 1 ) p - n J p - n ( α n u ) - B m n J p - n ( β n u ) = 0
( k z - p g k y k z ) J p ( k z u ) - [ α n - ( p - n ) g k n α n ] B v n ( - 1 ) p - n J p - n × ( α n u ) - 1 m [ β n - ( p - n ) g k n β n ] B n m J p - n ( β n u ) = 0 ,

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