Abstract

When an external magnetic field is applied parallel to the film surface of a magnetic fluid film, a high-quality one-dimensional periodic chain structure is formed when the field strength reaches a certain level. With a periodic chain structure in the magnetic fluid film, an incident light is diffracted onto the magnetic thin film. The results show that the one-dimensional periodic chain structure in the magnetic fluid film can serve as an optical grating. Further investigations reveal the feasibility of developing tunable coarse wavelength-division multiplexing by utilizing a periodic chain structure.

© 2004 Optical Society of America

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  1. R. E. Rosensweig, Sci. Am. 247, 124 (1982).
    [CrossRef]
  2. C.-Y. Hong, I. J. Jang, H. E. Horng, C. J. Hsu, Y. D. Yao, and H. C. Yang, J. Appl. Phys. 81, 275 (1997).
    [CrossRef]
  3. H. E. Horng, C. Y. Hong, W. B. Yeung, and H. C. Yang, Appl. Opt. 37, 2674 (19989).
    [CrossRef]
  4. C. Y. Hong, H. E. Horng, F. C. Kuo, S. Y. Yang, H. C. Yang, and J. M. Wu, Appl. Phys. Lett. 75, 2196 (1999).
    [CrossRef]
  5. S. Y. Yang, Y. H. Ke, W. S. Tse, H. E. Horng, C.-Y. Hong, and H. C. Yang, J. Magn. Magn. Mater. 252, 290 (2002).
    [CrossRef]
  6. S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, J. Appl. Phys. 93, 3457 (2003).
    [CrossRef]
  7. S. Y. Yang, I. J. Jang, H. E. Horng, C.-Y. Hong, and H. C. Yang, Magn. Gidrodin. 36, 19 (2000).
  8. R. E. Rosensweig, M. Zahn, and R. Shumovich, J. Magn. Magn. Mater. 39, 127 (1983).
    [CrossRef]
  9. S. Y. Yang, Y. P. Chiu, H. E. Horng, C.-Y. Hong, B. Y. Jeang, and H. C. Yang, Appl. Phys. Lett. 79, 2372 (2001).
    [CrossRef]
  10. H. E. Horng, S. Y. Yang, W. S. Tse, H. C. Yang, W. Luo, and C.-Y. Hong, J. Magn. Magn. Mater 252, 104 (2002).
    [CrossRef]
  11. S. Y. Yang, Y. F. Chen, H. E. Horng, C.-Y. Hong, W. S. Tsu, and H. C. Yang, Appl. Phys. Lett. 81, 4931 (2002).
    [CrossRef]
  12. H. E. Horng, S. Y. Yang, S. L. Lee, C. Y. Hong, and H. C. Yang, Appl. Phys. Lett. 79, 350 (2001).
    [CrossRef]
  13. C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, J. Appl. Phys. 94, 2188 (2003).
    [CrossRef]
  14. C. F. Hayes, J. Colloid Interface Sci. 52, 239 (1975).
    [CrossRef]
  15. N. A. Yusuf, J. Phys. D Appl. Phys. 22, 1916 (1989).
    [CrossRef]
  16. S. Taketomi, H. Takahashi, N. Inaba, and H. Miyajima, J. Phys. Soc. Jpn. 60, 1689 (1991).
    [CrossRef]

2003 (2)

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, J. Appl. Phys. 93, 3457 (2003).
[CrossRef]

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

2002 (3)

H. E. Horng, S. Y. Yang, W. S. Tse, H. C. Yang, W. Luo, and C.-Y. Hong, J. Magn. Magn. Mater 252, 104 (2002).
[CrossRef]

S. Y. Yang, Y. F. Chen, H. E. Horng, C.-Y. Hong, W. S. Tsu, and H. C. Yang, Appl. Phys. Lett. 81, 4931 (2002).
[CrossRef]

S. Y. Yang, Y. H. Ke, W. S. Tse, H. E. Horng, C.-Y. Hong, and H. C. Yang, J. Magn. Magn. Mater. 252, 290 (2002).
[CrossRef]

2001 (2)

H. E. Horng, S. Y. Yang, S. L. Lee, C. Y. Hong, and H. C. Yang, Appl. Phys. Lett. 79, 350 (2001).
[CrossRef]

S. Y. Yang, Y. P. Chiu, H. E. Horng, C.-Y. Hong, B. Y. Jeang, and H. C. Yang, Appl. Phys. Lett. 79, 2372 (2001).
[CrossRef]

2000 (1)

S. Y. Yang, I. J. Jang, H. E. Horng, C.-Y. Hong, and H. C. Yang, Magn. Gidrodin. 36, 19 (2000).

1999 (1)

C. Y. Hong, H. E. Horng, F. C. Kuo, S. Y. Yang, H. C. Yang, and J. M. Wu, Appl. Phys. Lett. 75, 2196 (1999).
[CrossRef]

1997 (1)

C.-Y. Hong, I. J. Jang, H. E. Horng, C. J. Hsu, Y. D. Yao, and H. C. Yang, J. Appl. Phys. 81, 275 (1997).
[CrossRef]

1991 (1)

S. Taketomi, H. Takahashi, N. Inaba, and H. Miyajima, J. Phys. Soc. Jpn. 60, 1689 (1991).
[CrossRef]

1989 (1)

N. A. Yusuf, J. Phys. D Appl. Phys. 22, 1916 (1989).
[CrossRef]

1983 (1)

R. E. Rosensweig, M. Zahn, and R. Shumovich, J. Magn. Magn. Mater. 39, 127 (1983).
[CrossRef]

1982 (1)

R. E. Rosensweig, Sci. Am. 247, 124 (1982).
[CrossRef]

1975 (1)

C. F. Hayes, J. Colloid Interface Sci. 52, 239 (1975).
[CrossRef]

Chao, Y. H.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, J. Appl. Phys. 93, 3457 (2003).
[CrossRef]

Chen, Y. F.

S. Y. Yang, Y. F. Chen, H. E. Horng, C.-Y. Hong, W. S. Tsu, and H. C. Yang, Appl. Phys. Lett. 81, 4931 (2002).
[CrossRef]

Chiu, Y. P.

S. Y. Yang, Y. P. Chiu, H. E. Horng, C.-Y. Hong, B. Y. Jeang, and H. C. Yang, Appl. Phys. Lett. 79, 2372 (2001).
[CrossRef]

Chou, M. C.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, J. Appl. Phys. 93, 3457 (2003).
[CrossRef]

Drikis, I.

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

Hayes, C. F.

C. F. Hayes, J. Colloid Interface Sci. 52, 239 (1975).
[CrossRef]

Hong, C. Y.

H. E. Horng, S. Y. Yang, S. L. Lee, C. Y. Hong, and H. C. Yang, Appl. Phys. Lett. 79, 350 (2001).
[CrossRef]

C. Y. Hong, H. E. Horng, F. C. Kuo, S. Y. Yang, H. C. Yang, and J. M. Wu, Appl. Phys. Lett. 75, 2196 (1999).
[CrossRef]

H. E. Horng, C. Y. Hong, W. B. Yeung, and H. C. Yang, Appl. Opt. 37, 2674 (19989).
[CrossRef]

Hong, C.-Y.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, J. Appl. Phys. 93, 3457 (2003).
[CrossRef]

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

S. Y. Yang, Y. H. Ke, W. S. Tse, H. E. Horng, C.-Y. Hong, and H. C. Yang, J. Magn. Magn. Mater. 252, 290 (2002).
[CrossRef]

H. E. Horng, S. Y. Yang, W. S. Tse, H. C. Yang, W. Luo, and C.-Y. Hong, J. Magn. Magn. Mater 252, 104 (2002).
[CrossRef]

S. Y. Yang, Y. F. Chen, H. E. Horng, C.-Y. Hong, W. S. Tsu, and H. C. Yang, Appl. Phys. Lett. 81, 4931 (2002).
[CrossRef]

S. Y. Yang, Y. P. Chiu, H. E. Horng, C.-Y. Hong, B. Y. Jeang, and H. C. Yang, Appl. Phys. Lett. 79, 2372 (2001).
[CrossRef]

S. Y. Yang, I. J. Jang, H. E. Horng, C.-Y. Hong, and H. C. Yang, Magn. Gidrodin. 36, 19 (2000).

C.-Y. Hong, I. J. Jang, H. E. Horng, C. J. Hsu, Y. D. Yao, and H. C. Yang, J. Appl. Phys. 81, 275 (1997).
[CrossRef]

Horng, H. E.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, J. Appl. Phys. 93, 3457 (2003).
[CrossRef]

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

S. Y. Yang, Y. F. Chen, H. E. Horng, C.-Y. Hong, W. S. Tsu, and H. C. Yang, Appl. Phys. Lett. 81, 4931 (2002).
[CrossRef]

H. E. Horng, S. Y. Yang, W. S. Tse, H. C. Yang, W. Luo, and C.-Y. Hong, J. Magn. Magn. Mater 252, 104 (2002).
[CrossRef]

S. Y. Yang, Y. H. Ke, W. S. Tse, H. E. Horng, C.-Y. Hong, and H. C. Yang, J. Magn. Magn. Mater. 252, 290 (2002).
[CrossRef]

H. E. Horng, S. Y. Yang, S. L. Lee, C. Y. Hong, and H. C. Yang, Appl. Phys. Lett. 79, 350 (2001).
[CrossRef]

S. Y. Yang, Y. P. Chiu, H. E. Horng, C.-Y. Hong, B. Y. Jeang, and H. C. Yang, Appl. Phys. Lett. 79, 2372 (2001).
[CrossRef]

S. Y. Yang, I. J. Jang, H. E. Horng, C.-Y. Hong, and H. C. Yang, Magn. Gidrodin. 36, 19 (2000).

C. Y. Hong, H. E. Horng, F. C. Kuo, S. Y. Yang, H. C. Yang, and J. M. Wu, Appl. Phys. Lett. 75, 2196 (1999).
[CrossRef]

H. E. Horng, C. Y. Hong, W. B. Yeung, and H. C. Yang, Appl. Opt. 37, 2674 (19989).
[CrossRef]

C.-Y. Hong, I. J. Jang, H. E. Horng, C. J. Hsu, Y. D. Yao, and H. C. Yang, J. Appl. Phys. 81, 275 (1997).
[CrossRef]

Hsu, C. J.

C.-Y. Hong, I. J. Jang, H. E. Horng, C. J. Hsu, Y. D. Yao, and H. C. Yang, J. Appl. Phys. 81, 275 (1997).
[CrossRef]

Inaba, N.

S. Taketomi, H. Takahashi, N. Inaba, and H. Miyajima, J. Phys. Soc. Jpn. 60, 1689 (1991).
[CrossRef]

Jang, I. J.

S. Y. Yang, I. J. Jang, H. E. Horng, C.-Y. Hong, and H. C. Yang, Magn. Gidrodin. 36, 19 (2000).

C.-Y. Hong, I. J. Jang, H. E. Horng, C. J. Hsu, Y. D. Yao, and H. C. Yang, J. Appl. Phys. 81, 275 (1997).
[CrossRef]

Jeang, B. Y.

S. Y. Yang, Y. P. Chiu, H. E. Horng, C.-Y. Hong, B. Y. Jeang, and H. C. Yang, Appl. Phys. Lett. 79, 2372 (2001).
[CrossRef]

Ke, Y. H.

S. Y. Yang, Y. H. Ke, W. S. Tse, H. E. Horng, C.-Y. Hong, and H. C. Yang, J. Magn. Magn. Mater. 252, 290 (2002).
[CrossRef]

Kuo, F. C.

C. Y. Hong, H. E. Horng, F. C. Kuo, S. Y. Yang, H. C. Yang, and J. M. Wu, Appl. Phys. Lett. 75, 2196 (1999).
[CrossRef]

Lee, S. L.

H. E. Horng, S. Y. Yang, S. L. Lee, C. Y. Hong, and H. C. Yang, Appl. Phys. Lett. 79, 350 (2001).
[CrossRef]

Luo, W.

H. E. Horng, S. Y. Yang, W. S. Tse, H. C. Yang, W. Luo, and C.-Y. Hong, J. Magn. Magn. Mater 252, 104 (2002).
[CrossRef]

Miyajima, H.

S. Taketomi, H. Takahashi, N. Inaba, and H. Miyajima, J. Phys. Soc. Jpn. 60, 1689 (1991).
[CrossRef]

Pan, C. T.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, J. Appl. Phys. 93, 3457 (2003).
[CrossRef]

Rosensweig, R. E.

R. E. Rosensweig, M. Zahn, and R. Shumovich, J. Magn. Magn. Mater. 39, 127 (1983).
[CrossRef]

R. E. Rosensweig, Sci. Am. 247, 124 (1982).
[CrossRef]

Shumovich, R.

R. E. Rosensweig, M. Zahn, and R. Shumovich, J. Magn. Magn. Mater. 39, 127 (1983).
[CrossRef]

Takahashi, H.

S. Taketomi, H. Takahashi, N. Inaba, and H. Miyajima, J. Phys. Soc. Jpn. 60, 1689 (1991).
[CrossRef]

Taketomi, S.

S. Taketomi, H. Takahashi, N. Inaba, and H. Miyajima, J. Phys. Soc. Jpn. 60, 1689 (1991).
[CrossRef]

Tse, W. S.

S. Y. Yang, Y. H. Ke, W. S. Tse, H. E. Horng, C.-Y. Hong, and H. C. Yang, J. Magn. Magn. Mater. 252, 290 (2002).
[CrossRef]

H. E. Horng, S. Y. Yang, W. S. Tse, H. C. Yang, W. Luo, and C.-Y. Hong, J. Magn. Magn. Mater 252, 104 (2002).
[CrossRef]

Tsu, W. S.

S. Y. Yang, Y. F. Chen, H. E. Horng, C.-Y. Hong, W. S. Tsu, and H. C. Yang, Appl. Phys. Lett. 81, 4931 (2002).
[CrossRef]

Wu, J. M.

C. Y. Hong, H. E. Horng, F. C. Kuo, S. Y. Yang, H. C. Yang, and J. M. Wu, Appl. Phys. Lett. 75, 2196 (1999).
[CrossRef]

Yang, H. C.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, J. Appl. Phys. 93, 3457 (2003).
[CrossRef]

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

S. Y. Yang, Y. F. Chen, H. E. Horng, C.-Y. Hong, W. S. Tsu, and H. C. Yang, Appl. Phys. Lett. 81, 4931 (2002).
[CrossRef]

H. E. Horng, S. Y. Yang, W. S. Tse, H. C. Yang, W. Luo, and C.-Y. Hong, J. Magn. Magn. Mater 252, 104 (2002).
[CrossRef]

S. Y. Yang, Y. H. Ke, W. S. Tse, H. E. Horng, C.-Y. Hong, and H. C. Yang, J. Magn. Magn. Mater. 252, 290 (2002).
[CrossRef]

H. E. Horng, S. Y. Yang, S. L. Lee, C. Y. Hong, and H. C. Yang, Appl. Phys. Lett. 79, 350 (2001).
[CrossRef]

S. Y. Yang, Y. P. Chiu, H. E. Horng, C.-Y. Hong, B. Y. Jeang, and H. C. Yang, Appl. Phys. Lett. 79, 2372 (2001).
[CrossRef]

S. Y. Yang, I. J. Jang, H. E. Horng, C.-Y. Hong, and H. C. Yang, Magn. Gidrodin. 36, 19 (2000).

C. Y. Hong, H. E. Horng, F. C. Kuo, S. Y. Yang, H. C. Yang, and J. M. Wu, Appl. Phys. Lett. 75, 2196 (1999).
[CrossRef]

H. E. Horng, C. Y. Hong, W. B. Yeung, and H. C. Yang, Appl. Opt. 37, 2674 (19989).
[CrossRef]

C.-Y. Hong, I. J. Jang, H. E. Horng, C. J. Hsu, Y. D. Yao, and H. C. Yang, J. Appl. Phys. 81, 275 (1997).
[CrossRef]

Yang, S. Y.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, J. Appl. Phys. 93, 3457 (2003).
[CrossRef]

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

S. Y. Yang, Y. H. Ke, W. S. Tse, H. E. Horng, C.-Y. Hong, and H. C. Yang, J. Magn. Magn. Mater. 252, 290 (2002).
[CrossRef]

H. E. Horng, S. Y. Yang, W. S. Tse, H. C. Yang, W. Luo, and C.-Y. Hong, J. Magn. Magn. Mater 252, 104 (2002).
[CrossRef]

S. Y. Yang, Y. F. Chen, H. E. Horng, C.-Y. Hong, W. S. Tsu, and H. C. Yang, Appl. Phys. Lett. 81, 4931 (2002).
[CrossRef]

H. E. Horng, S. Y. Yang, S. L. Lee, C. Y. Hong, and H. C. Yang, Appl. Phys. Lett. 79, 350 (2001).
[CrossRef]

S. Y. Yang, Y. P. Chiu, H. E. Horng, C.-Y. Hong, B. Y. Jeang, and H. C. Yang, Appl. Phys. Lett. 79, 2372 (2001).
[CrossRef]

S. Y. Yang, I. J. Jang, H. E. Horng, C.-Y. Hong, and H. C. Yang, Magn. Gidrodin. 36, 19 (2000).

C. Y. Hong, H. E. Horng, F. C. Kuo, S. Y. Yang, H. C. Yang, and J. M. Wu, Appl. Phys. Lett. 75, 2196 (1999).
[CrossRef]

Yao, Y. D.

C.-Y. Hong, I. J. Jang, H. E. Horng, C. J. Hsu, Y. D. Yao, and H. C. Yang, J. Appl. Phys. 81, 275 (1997).
[CrossRef]

Yeung, W. B.

Yusuf, N. A.

N. A. Yusuf, J. Phys. D Appl. Phys. 22, 1916 (1989).
[CrossRef]

Zahn, M.

R. E. Rosensweig, M. Zahn, and R. Shumovich, J. Magn. Magn. Mater. 39, 127 (1983).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

S. Y. Yang, Y. P. Chiu, H. E. Horng, C.-Y. Hong, B. Y. Jeang, and H. C. Yang, Appl. Phys. Lett. 79, 2372 (2001).
[CrossRef]

C. Y. Hong, H. E. Horng, F. C. Kuo, S. Y. Yang, H. C. Yang, and J. M. Wu, Appl. Phys. Lett. 75, 2196 (1999).
[CrossRef]

S. Y. Yang, Y. F. Chen, H. E. Horng, C.-Y. Hong, W. S. Tsu, and H. C. Yang, Appl. Phys. Lett. 81, 4931 (2002).
[CrossRef]

H. E. Horng, S. Y. Yang, S. L. Lee, C. Y. Hong, and H. C. Yang, Appl. Phys. Lett. 79, 350 (2001).
[CrossRef]

J. Appl. Phys. (3)

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, J. Appl. Phys. 93, 3457 (2003).
[CrossRef]

C.-Y. Hong, I. J. Jang, H. E. Horng, C. J. Hsu, Y. D. Yao, and H. C. Yang, J. Appl. Phys. 81, 275 (1997).
[CrossRef]

J. Colloid Interface Sci. (1)

C. F. Hayes, J. Colloid Interface Sci. 52, 239 (1975).
[CrossRef]

J. Magn. Magn. Mater (1)

H. E. Horng, S. Y. Yang, W. S. Tse, H. C. Yang, W. Luo, and C.-Y. Hong, J. Magn. Magn. Mater 252, 104 (2002).
[CrossRef]

J. Magn. Magn. Mater. (2)

R. E. Rosensweig, M. Zahn, and R. Shumovich, J. Magn. Magn. Mater. 39, 127 (1983).
[CrossRef]

S. Y. Yang, Y. H. Ke, W. S. Tse, H. E. Horng, C.-Y. Hong, and H. C. Yang, J. Magn. Magn. Mater. 252, 290 (2002).
[CrossRef]

J. Phys. D Appl. Phys. (1)

N. A. Yusuf, J. Phys. D Appl. Phys. 22, 1916 (1989).
[CrossRef]

J. Phys. Soc. Jpn. (1)

S. Taketomi, H. Takahashi, N. Inaba, and H. Miyajima, J. Phys. Soc. Jpn. 60, 1689 (1991).
[CrossRef]

Magn. Gidrodin. (1)

S. Y. Yang, I. J. Jang, H. E. Horng, C.-Y. Hong, and H. C. Yang, Magn. Gidrodin. 36, 19 (2000).

Sci. Am. (1)

R. E. Rosensweig, Sci. Am. 247, 124 (1982).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

One-dimensional periodic chain structure in the magnetic fluid film under a parallel magnetic field. The concentration Ms of the fluid is 15.5 emu/g, the film thickness L is 0.3 µm, the width of the cell, W, is 10 µm, the applied field strength H is 150 Oe, and the sweep rate of applying the field is 10 Oe/s.

Fig. 2
Fig. 2

Schematic cross section of the magnetic fluid film possessing a one-dimensional periodic chain structure and a diffracted image of the transmitted light through the film. Each black dot in the schematic represents the cross section of a magnetic chain. The Cr film shown here blocks the incident light outside the cell. The parallel white light is normally incident upon the film. The white spot at the center of the diffracted image is located at a certain distance above the film and is in the normal line of the film. Angle θ denotes the diffracted angle of the transmitted light.

Fig. 3
Fig. 3

Spatial intensity distribution of the diffracted light with a wavelength of 600 nm.

Fig. 4
Fig. 4

Spatial intensity distributions of the first-order diffraction peaks for various wavelengths λ. The concentration of the fluid Ms is 15.5 emu/g, the film thickness L is 0.3 µm, the width of the cell W is 20 µm, the applied field strength H is 150 Oe, and the sweep rate of the field application is 10 Oe/s.

Fig. 5
Fig. 5

Spatial intensity distributions of the two first- order peaks of the diffracted light with wavelengths of 620 and 640 nm under 150 and 200 Oe, respectively. The separation Δθp between the two peaks is increased from 0.57° to 0.94° when the field H increases from 150 to 200 Oe.

Equations (2)

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

Δxsinθth=nλ
Δθp=θth,λ1-θth,λ2=sin-1λ1/Δx-sin-1λ2/Δx,

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