Abstract

We consider some features of spatial solitary-wave switching in a unidirectional ring cavity that is partially filled with a fast and saturably self-focusing nonlinear medium. Large (part-beam switched) solitary arrays are considered. It is found that prescribed binary patterns may be encoded in the duration of a single cavity transit and subsequently remain stable over thousands of transits. Beam interrupt allows pixels to be switched off in fewer than ten cavity transits. Pixel instabilities on an unpixelated beam are shown to arise from spatial solitary attractive forces and intensity gradients.

© 1990 Optical Society of America

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References

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  1. S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
    [CrossRef]
  2. S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, P. S. Smith, Opt. Lett. 13, 904 (1988).
    [CrossRef] [PubMed]
  3. P. Li, Kam Wa, J. E. Sitch, N. J. Mason, J. S. Roberts, P. N. Robson, Electron. Lett. 21, 26 (1985).
    [CrossRef]
  4. N. J. Doran, D. Wood, J. Opt. Soc. Am. B 4, 1843 (1987).
    [CrossRef]
  5. N. J. Doran, D. Wood, Opt. Lett. 13, 56 (1988).
    [CrossRef] [PubMed]
  6. K. J. Blow, N. J. Doran, B. K. Nayar, Opt. Lett. 14, 754 (1989).
    [CrossRef] [PubMed]
  7. S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
    [CrossRef]
  8. S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Commun. 70, 166 (1989).
    [CrossRef]
  9. H. Adachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
    [CrossRef]
  10. A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985).
    [CrossRef]
  11. S. Maneuf, R. Descilly, C. Froehly, Opt. Commun. 65, 193 (1988).
    [CrossRef]
  12. J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, P. W. E. Smith, Opt. Lett. 15, 471 (1990).
    [CrossRef] [PubMed]
  13. E. Abraham, C. Godsalve, B. S. Wherrett, J. Phys. 49, 43 (1988).
  14. A. K. Kar, R. M. Harris, G. S. Buller, S. D. Smith, A. C. Walker, J. Phys. 49, 443 (1988).
  15. W. J. Firth, I. Galbraith, IEEE J. Quantum Electron. QE-21, 1399 (1985).
    [CrossRef]
  16. D. J. Hagan, H. A. Mackenzie, H. A. Al-Attar, W. J. Firth, Opt. Lett. 10, 187 (1985).
    [CrossRef] [PubMed]
  17. K. Tai, J. V. Moloney, H. M. Gibbs, Opt. Lett. 7, 429 (1982).
    [CrossRef] [PubMed]
  18. K. Ikeda, Opt. Commun. 30, 257 (1979).
    [CrossRef]
  19. R. H. Hardin, F. D. Tappert, SIAM Rev. 15, 423 (1973).
  20. J. V. Moloney, H. M. Gibbs, Phys. Rev. Lett. 48, 1607 (1982).
    [CrossRef]
  21. G. S. McDonald, W. J. Firth, “All-optical switching in a nonlinear resonator,” J. Mod. Opt. (to be published).
  22. G. S. McDonald, “Spatial solitary wave optical memory,” Ph.D. dissertation (Strathclyde University, Glasgow, 1989).
  23. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  24. J. P. Gordon, Opt. Lett. 8, 596 (1983).
    [CrossRef] [PubMed]
  25. P. L. Chu, C. Desem, Electron. Lett. 21, 1133 (1985).
    [CrossRef]
  26. B. Hermansson, D. Yerick, Electron. Lett. 19, 570 (1983).
    [CrossRef]
  27. E. Shiojiri, Y. Fujii, Appl. Opt. 24, 358 (1985).
    [CrossRef]
  28. D. Anderson, M. Lisak, Opt. Lett. 11, 174 (1986).
    [CrossRef]
  29. P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985).
    [CrossRef]
  30. E. M. Dianov, Z. S. Mikonova, V. N. Serkin, Sov. J. Quantum Electron. 16, 1148 (1986).
    [CrossRef]
  31. D. W. McLaughlin, J. V. Moloney, A. C. Newell, Phys. Rev. Lett. 7, 681 (1985).
    [CrossRef]
  32. I. Galbraith, “Diffractive and diffusive phenomena in optically bistable devices,” Ph.D. dissertation (Heriot-Watt University, Edinburgh, 1985).

1990 (1)

1989 (2)

K. J. Blow, N. J. Doran, B. K. Nayar, Opt. Lett. 14, 754 (1989).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Commun. 70, 166 (1989).
[CrossRef]

1988 (7)

H. Adachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
[CrossRef]

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, P. S. Smith, Opt. Lett. 13, 904 (1988).
[CrossRef] [PubMed]

E. Abraham, C. Godsalve, B. S. Wherrett, J. Phys. 49, 43 (1988).

A. K. Kar, R. M. Harris, G. S. Buller, S. D. Smith, A. C. Walker, J. Phys. 49, 443 (1988).

N. J. Doran, D. Wood, Opt. Lett. 13, 56 (1988).
[CrossRef] [PubMed]

S. Maneuf, R. Descilly, C. Froehly, Opt. Commun. 65, 193 (1988).
[CrossRef]

1987 (1)

1986 (2)

D. Anderson, M. Lisak, Opt. Lett. 11, 174 (1986).
[CrossRef]

E. M. Dianov, Z. S. Mikonova, V. N. Serkin, Sov. J. Quantum Electron. 16, 1148 (1986).
[CrossRef]

1985 (8)

D. W. McLaughlin, J. V. Moloney, A. C. Newell, Phys. Rev. Lett. 7, 681 (1985).
[CrossRef]

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985).
[CrossRef]

P. L. Chu, C. Desem, Electron. Lett. 21, 1133 (1985).
[CrossRef]

E. Shiojiri, Y. Fujii, Appl. Opt. 24, 358 (1985).
[CrossRef]

P. Li, Kam Wa, J. E. Sitch, N. J. Mason, J. S. Roberts, P. N. Robson, Electron. Lett. 21, 26 (1985).
[CrossRef]

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

W. J. Firth, I. Galbraith, IEEE J. Quantum Electron. QE-21, 1399 (1985).
[CrossRef]

D. J. Hagan, H. A. Mackenzie, H. A. Al-Attar, W. J. Firth, Opt. Lett. 10, 187 (1985).
[CrossRef] [PubMed]

1983 (2)

J. P. Gordon, Opt. Lett. 8, 596 (1983).
[CrossRef] [PubMed]

B. Hermansson, D. Yerick, Electron. Lett. 19, 570 (1983).
[CrossRef]

1982 (3)

J. V. Moloney, H. M. Gibbs, Phys. Rev. Lett. 48, 1607 (1982).
[CrossRef]

K. Tai, J. V. Moloney, H. M. Gibbs, Opt. Lett. 7, 429 (1982).
[CrossRef] [PubMed]

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

1979 (1)

K. Ikeda, Opt. Commun. 30, 257 (1979).
[CrossRef]

1973 (1)

R. H. Hardin, F. D. Tappert, SIAM Rev. 15, 423 (1973).

1972 (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Abraham, E.

E. Abraham, C. Godsalve, B. S. Wherrett, J. Phys. 49, 43 (1988).

Adachihara, H.

H. Adachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

Aitchison, J. S.

Al-Attar, H. A.

Anderson, D.

Barthelemy, A.

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

Blow, K. J.

Buller, G. S.

A. K. Kar, R. M. Harris, G. S. Buller, S. D. Smith, A. C. Walker, J. Phys. 49, 443 (1988).

Chu, P. L.

P. L. Chu, C. Desem, Electron. Lett. 21, 1133 (1985).
[CrossRef]

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985).
[CrossRef]

Descilly, R.

S. Maneuf, R. Descilly, C. Froehly, Opt. Commun. 65, 193 (1988).
[CrossRef]

Desem, C.

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985).
[CrossRef]

P. L. Chu, C. Desem, Electron. Lett. 21, 1133 (1985).
[CrossRef]

Dianov, E. M.

E. M. Dianov, Z. S. Mikonova, V. N. Serkin, Sov. J. Quantum Electron. 16, 1148 (1986).
[CrossRef]

Doran, N. J.

Firth, W. J.

W. J. Firth, I. Galbraith, IEEE J. Quantum Electron. QE-21, 1399 (1985).
[CrossRef]

D. J. Hagan, H. A. Mackenzie, H. A. Al-Attar, W. J. Firth, Opt. Lett. 10, 187 (1985).
[CrossRef] [PubMed]

G. S. McDonald, W. J. Firth, “All-optical switching in a nonlinear resonator,” J. Mod. Opt. (to be published).

Friberg, S. R.

Froehly, C.

S. Maneuf, R. Descilly, C. Froehly, Opt. Commun. 65, 193 (1988).
[CrossRef]

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

Fujii, Y.

Galbraith, I.

W. J. Firth, I. Galbraith, IEEE J. Quantum Electron. QE-21, 1399 (1985).
[CrossRef]

I. Galbraith, “Diffractive and diffusive phenomena in optically bistable devices,” Ph.D. dissertation (Heriot-Watt University, Edinburgh, 1985).

Gibbs, H. M.

J. V. Moloney, H. M. Gibbs, Phys. Rev. Lett. 48, 1607 (1982).
[CrossRef]

K. Tai, J. V. Moloney, H. M. Gibbs, Opt. Lett. 7, 429 (1982).
[CrossRef] [PubMed]

Godsalve, C.

E. Abraham, C. Godsalve, B. S. Wherrett, J. Phys. 49, 43 (1988).

Gordon, J. P.

Hagan, D. J.

Hardin, R. H.

R. H. Hardin, F. D. Tappert, SIAM Rev. 15, 423 (1973).

Harris, R. M.

A. K. Kar, R. M. Harris, G. S. Buller, S. D. Smith, A. C. Walker, J. Phys. 49, 443 (1988).

Hermansson, B.

B. Hermansson, D. Yerick, Electron. Lett. 19, 570 (1983).
[CrossRef]

Ikeda, K.

K. Ikeda, Opt. Commun. 30, 257 (1979).
[CrossRef]

Jackel, J. L.

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

Kar, A. K.

A. K. Kar, R. M. Harris, G. S. Buller, S. D. Smith, A. C. Walker, J. Phys. 49, 443 (1988).

Leaird, D. E.

Li, P.

P. Li, Kam Wa, J. E. Sitch, N. J. Mason, J. S. Roberts, P. N. Robson, Electron. Lett. 21, 26 (1985).
[CrossRef]

Lisak, M.

Mackenzie, H. A.

Maneuf, S.

S. Maneuf, R. Descilly, C. Froehly, Opt. Commun. 65, 193 (1988).
[CrossRef]

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

Mason, N. J.

P. Li, Kam Wa, J. E. Sitch, N. J. Mason, J. S. Roberts, P. N. Robson, Electron. Lett. 21, 26 (1985).
[CrossRef]

McDonald, G. S.

G. S. McDonald, W. J. Firth, “All-optical switching in a nonlinear resonator,” J. Mod. Opt. (to be published).

G. S. McDonald, “Spatial solitary wave optical memory,” Ph.D. dissertation (Strathclyde University, Glasgow, 1989).

McLaughlin, D. W.

H. Adachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

D. W. McLaughlin, J. V. Moloney, A. C. Newell, Phys. Rev. Lett. 7, 681 (1985).
[CrossRef]

Mikonova, Z. S.

E. M. Dianov, Z. S. Mikonova, V. N. Serkin, Sov. J. Quantum Electron. 16, 1148 (1986).
[CrossRef]

Moloney, J. V.

H. Adachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

D. W. McLaughlin, J. V. Moloney, A. C. Newell, Phys. Rev. Lett. 7, 681 (1985).
[CrossRef]

J. V. Moloney, H. M. Gibbs, Phys. Rev. Lett. 48, 1607 (1982).
[CrossRef]

K. Tai, J. V. Moloney, H. M. Gibbs, Opt. Lett. 7, 429 (1982).
[CrossRef] [PubMed]

Nayar, B. K.

Newell, A. C.

H. Adachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

D. W. McLaughlin, J. V. Moloney, A. C. Newell, Phys. Rev. Lett. 7, 681 (1985).
[CrossRef]

Oliver, M. K.

Roberts, J. S.

P. Li, Kam Wa, J. E. Sitch, N. J. Mason, J. S. Roberts, P. N. Robson, Electron. Lett. 21, 26 (1985).
[CrossRef]

Robson, P. N.

P. Li, Kam Wa, J. E. Sitch, N. J. Mason, J. S. Roberts, P. N. Robson, Electron. Lett. 21, 26 (1985).
[CrossRef]

Serkin, V. N.

E. M. Dianov, Z. S. Mikonova, V. N. Serkin, Sov. J. Quantum Electron. 16, 1148 (1986).
[CrossRef]

Sfez, B. G.

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Shiojiri, E.

Silberberg, Y.

Sitch, J. E.

P. Li, Kam Wa, J. E. Sitch, N. J. Mason, J. S. Roberts, P. N. Robson, Electron. Lett. 21, 26 (1985).
[CrossRef]

Smith, P. S.

Smith, P. W. E.

Smith, S. D.

A. K. Kar, R. M. Harris, G. S. Buller, S. D. Smith, A. C. Walker, J. Phys. 49, 443 (1988).

Stegeman, G. I.

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Commun. 70, 166 (1989).
[CrossRef]

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
[CrossRef]

Tai, K.

Tappert, F. D.

R. H. Hardin, F. D. Tappert, SIAM Rev. 15, 423 (1973).

Trillo, S.

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Commun. 70, 166 (1989).
[CrossRef]

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
[CrossRef]

Vogel, E. M.

Wa, Kam

P. Li, Kam Wa, J. E. Sitch, N. J. Mason, J. S. Roberts, P. N. Robson, Electron. Lett. 21, 26 (1985).
[CrossRef]

Wabnitz, S.

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Commun. 70, 166 (1989).
[CrossRef]

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
[CrossRef]

Walker, A. C.

A. K. Kar, R. M. Harris, G. S. Buller, S. D. Smith, A. C. Walker, J. Phys. 49, 443 (1988).

Weiner, A. M.

Wherrett, B. S.

E. Abraham, C. Godsalve, B. S. Wherrett, J. Phys. 49, 43 (1988).

Wood, D.

Wright, E. M.

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Commun. 70, 166 (1989).
[CrossRef]

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Lett. 13, 672 (1988).
[CrossRef]

Yerick, D.

B. Hermansson, D. Yerick, Electron. Lett. 19, 570 (1983).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Appl. Opt. (1)

Electron. Lett. (4)

P. L. Chu, C. Desem, Electron. Lett. 21, 1133 (1985).
[CrossRef]

B. Hermansson, D. Yerick, Electron. Lett. 19, 570 (1983).
[CrossRef]

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985).
[CrossRef]

P. Li, Kam Wa, J. E. Sitch, N. J. Mason, J. S. Roberts, P. N. Robson, Electron. Lett. 21, 26 (1985).
[CrossRef]

IEEE J. Quantum Electron. (2)

S. M. Jensen, IEEE J. Quantum Electron. QE-18, 1580 (1982).
[CrossRef]

W. J. Firth, I. Galbraith, IEEE J. Quantum Electron. QE-21, 1399 (1985).
[CrossRef]

J. Math. Phys. (1)

H. Adachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. (2)

E. Abraham, C. Godsalve, B. S. Wherrett, J. Phys. 49, 43 (1988).

A. K. Kar, R. M. Harris, G. S. Buller, S. D. Smith, A. C. Walker, J. Phys. 49, 443 (1988).

Opt. Commun. (4)

K. Ikeda, Opt. Commun. 30, 257 (1979).
[CrossRef]

A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

S. Maneuf, R. Descilly, C. Froehly, Opt. Commun. 65, 193 (1988).
[CrossRef]

S. Trillo, S. Wabnitz, E. M. Wright, G. I. Stegeman, Opt. Commun. 70, 166 (1989).
[CrossRef]

Opt. Lett. (9)

Phys. Rev. Lett. (2)

D. W. McLaughlin, J. V. Moloney, A. C. Newell, Phys. Rev. Lett. 7, 681 (1985).
[CrossRef]

J. V. Moloney, H. M. Gibbs, Phys. Rev. Lett. 48, 1607 (1982).
[CrossRef]

SIAM Rev. (1)

R. H. Hardin, F. D. Tappert, SIAM Rev. 15, 423 (1973).

Sov. J. Quantum Electron. (1)

E. M. Dianov, Z. S. Mikonova, V. N. Serkin, Sov. J. Quantum Electron. 16, 1148 (1986).
[CrossRef]

Sov. Phys. JETP (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Other (3)

G. S. McDonald, W. J. Firth, “All-optical switching in a nonlinear resonator,” J. Mod. Opt. (to be published).

G. S. McDonald, “Spatial solitary wave optical memory,” Ph.D. dissertation (Strathclyde University, Glasgow, 1989).

I. Galbraith, “Diffractive and diffusive phenomena in optically bistable devices,” Ph.D. dissertation (Heriot-Watt University, Edinburgh, 1985).

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Figures (10)

Fig. 1
Fig. 1

Schematic representation of our optical resonator, which is partially filled with a nonlinear medium. The laser beam(s) enters through M1, which, like M2, has an intensity reflectivity of R = 0.9. Output through M2 is monitored.

Fig. 2
Fig. 2

η = +1. (a) Spatial profiles before, during, and after the left-hand site has been addressed. Also shown (dashed curve) is the input, A(x). This full width at half-maximum (intensity) separation of hold beams, X0 = 2.25, is required for independent switching to be maintained when ΔΦ = 0.0. (b) Pixel independence at X0 = 2.0 is achieved through an overall phase differential (ΔΦ = π). Here some intermediate profiles are also given.

Fig. 3
Fig. 3

Spatial motion due to (unbalanced) nonlinear index differentials. Two solitons are symmetrically induced on an F = 800 beam. Subsequent evolution displays a migration of these waves toward the beam center and ultimate coalescence. N is in units of 1000 cavity transits, |G| axis × 10−1.

Fig. 4
Fig. 4

For a separation identical to that used in Fig. 3, a (spatially) periodic plane-wave simulation is performed. Soliton–soliton coupling is increased here (F = 50), and no significant migration is observed. N is in multiples of 1000 transits.

Fig. 5
Fig. 5

Our sinusoidally modulated hold beam with respect to the appropriate upswitching and downswitching amplitudes (M = 0.08). Encoding of binary patterns on the circulating beam is attained by temporally abrupt superimposition of the addressing Gaussians (here shown in the configuration 1101001110101110101).

Fig. 6
Fig. 6

Simulation shown in Fig. 4 is repeated with an additional (central) induced soliton. Coalescence is at approximately 800 transits.

Fig. 7
Fig. 7

Hold-beam initialization and subsequent address of 19-bit patterns. (a) Quasi-random string addressed, T = 5; (b) Full string of 1’s addressed, T = 1. N is in units of 100 cavity transits, |G| axis × 10−1.

Fig. 8
Fig. 8

Overlay of resonator outputs over a period of 2600–3000 cavity transits. In this simulation the hold beam was allowed 30 transits for initialization, and then a full 1111111111111111111 was encoded in the subsequent 5 transits.

Fig. 9
Fig. 9

(a) Overlay of output profiles 800–850 transits after encoding of the string 111111111 on a F = 800 spot. (b) Beam interrupt, implementing reset during eight subsequent transits.

Fig. 10
Fig. 10

Encoding of a periodic zone within an infinite-dimensional binary array. Spatial periodicity ensures that this quasi-random pattern recurs indefinitely in both directions of X. N is in units of 100 transits, |G| axis × 10−1.

Equations (6)

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

2 i G n z + γ p 2 G n x 2 + f ( | G n | 2 ) G n = 0.
G n + 1 ( x , 0 ) = A ( x ) + R exp ( i Φ 0 ) G n ( x , p ) .
A ( x , t ) = a 01 exp [ ( x x 1 ) 2 ] + a 02 ( t ) exp [ ( x + x 1 ) 2 + i Δ Φ ] .
a H = a + c H ( a a ) , a S = c S a H .
A ( x ) = A 0 ( 1 + M cos k m x ) exp ( x 2 ) .
A 0 = A down + C H ( A up A down ) , A S = C S A 0 .

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