Abstract

The self-deflection of slab laser beams with right-triangular and semi-Gaussian intensity profiles that pass through a thin nonlinear film are compared, and semi-Gaussian beam profiles are found to produce near-maximum self-deflection angles. We also analyze symmetric profiles (both triangular and Gaussian), which, instead of self-(de)focusing, exhibit strongly counter-self-deflected beams in the far-field region. This evidence indicates that the self-deflection effect can dominate over self-focusing.

© 1988 Optical Society of America

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  1. A. E. Kaplan, JETP Lett. 9, 33 (1969) [Pis’ma Zh. Eksp. Teor. Fiz. 9, 58 (1969)].
  2. M. S. Brodin and A. M. Kamuz, JETP Lett. 9, 351 (1969) [Pis’ma Zh. Eksp. Teor. Fiz. 9, 577 (1969)].
  3. L. I. Gudzenko, C. D. Kaitmazov, A. A. Medvedev, and E. I. Schklovsky, Lebedev Inst. Phys. Brief Commun. Phys. 1, 64 (1970, in Russian).
  4. A. E. Kaplan, Opt. Lett. 6, 360 (1981).
    [Crossref] [PubMed]
  5. J. A. Hermann, Opt. Commun. 62, 367 (1987);Opt. Quantum Electron. 19, 169 (1987).
    [Crossref]
  6. P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965);S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi and E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, p. 1151;Y. R. Shen, Rev. Mod. Phys. 48, 1 (1976).
    [Crossref]
  7. P. D. McWane, Nature 211, 1081 (1966).
    [Crossref]
  8. A. E. Kaplan, Radiophys. Quantum Electron. 12, 692 (1969) [Izv. Vyash. Ucheb. Zaved. Radiofiz. 12, 869 (1969)];F. S. Felber, Appl. Phys. Lett. 36, 723 (1980).
    [Crossref]
  9. T. F. Boggess, S. C. Moss, I. W. Boyd, and A. L. Smirl, Opt. Lett. 9, 291 (1984);T. F. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, and E. W. Van Stryland, IEEE J. Quantum Electron. QE-21, 488 (1985).
    [Crossref] [PubMed]
  10. J. A. Hermann, J. Opt. Soc. Am. B 1, 729 (1984).
    [Crossref]
  11. G. A. Swartzlander, M. S. thesis (Purdue U., West Lafayette, Indiana, 1985) (unpublished).
  12. D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, and W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982);D. S. Chemla and D. A. B. Miller, J. Opt. Soc. Am. B 2, 1155 (1985).
    [Crossref]
  13. M. Dagenais and H. G. Winful, Appl. Phys. Lett. 44, 574 (1984);M. Dagenais and W. F. Sharfin, J. Opt. Soc. Am. B 2, 1179 (1985).
    [Crossref]
  14. I. C. Khoo, Phys. Rev. A 25, 1636 (1982).
    [Crossref]
  15. A. Ashkin, J. M. Dziedzic, and P. W. Smith, Opt. Lett. 7, 276 (1982);P. W. Smith, P. J. Maloney, and A. Ashkin, Opt. Lett. 7, 347 (1982).
    [Crossref] [PubMed]
  16. S. Friberg and P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
    [Crossref]
  17. I. C. Khoo, R. R. Michael, T. H. Liu, G. Finn, and A. E. Kaplan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 43 (1986).
  18. We use the following definition of the Fresnel integrals: S(u)=(1/2π)∫0u2[sin(t)/t]dt and C(u)=(1/2π)∫0u2[cos(t)t]dt. [See Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, eds. (Dover, New York, 1972).]
  19. J. E. Bjorkholm, P. W. Smith, W. J. Tomlinson, and A. E. Kaplan, Opt. Lett. 6, 345 (1981);I. C. Khoo, P. J. Yan, T. H. Liu, S. Shepard, and J. Y. Hou, Phys. Rev. A 29, 2756 (1984);K. Tai, M. M. Gibbs, N. Peyghambarian, and A. Mysyrowicz, Opt. Lett. 10, 220 (1985);M. Le Berre, E. Ressayre, A. Tallet, K. Tai, and H. M. Gibbs, IEEE J. Quantum Electron. QE-21, 1404 (1985).
    [Crossref] [PubMed]

1987 (2)

J. A. Hermann, Opt. Commun. 62, 367 (1987);Opt. Quantum Electron. 19, 169 (1987).
[Crossref]

S. Friberg and P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
[Crossref]

1986 (1)

I. C. Khoo, R. R. Michael, T. H. Liu, G. Finn, and A. E. Kaplan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 43 (1986).

1984 (3)

1982 (3)

A. Ashkin, J. M. Dziedzic, and P. W. Smith, Opt. Lett. 7, 276 (1982);P. W. Smith, P. J. Maloney, and A. Ashkin, Opt. Lett. 7, 347 (1982).
[Crossref] [PubMed]

I. C. Khoo, Phys. Rev. A 25, 1636 (1982).
[Crossref]

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, and W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982);D. S. Chemla and D. A. B. Miller, J. Opt. Soc. Am. B 2, 1155 (1985).
[Crossref]

1981 (2)

1970 (1)

L. I. Gudzenko, C. D. Kaitmazov, A. A. Medvedev, and E. I. Schklovsky, Lebedev Inst. Phys. Brief Commun. Phys. 1, 64 (1970, in Russian).

1969 (3)

A. E. Kaplan, Radiophys. Quantum Electron. 12, 692 (1969) [Izv. Vyash. Ucheb. Zaved. Radiofiz. 12, 869 (1969)];F. S. Felber, Appl. Phys. Lett. 36, 723 (1980).
[Crossref]

A. E. Kaplan, JETP Lett. 9, 33 (1969) [Pis’ma Zh. Eksp. Teor. Fiz. 9, 58 (1969)].

M. S. Brodin and A. M. Kamuz, JETP Lett. 9, 351 (1969) [Pis’ma Zh. Eksp. Teor. Fiz. 9, 577 (1969)].

1966 (1)

P. D. McWane, Nature 211, 1081 (1966).
[Crossref]

1965 (1)

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965);S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi and E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, p. 1151;Y. R. Shen, Rev. Mod. Phys. 48, 1 (1976).
[Crossref]

Ashkin, A.

Bjorkholm, J. E.

Boggess, T. F.

Boyd, I. W.

Brodin, M. S.

M. S. Brodin and A. M. Kamuz, JETP Lett. 9, 351 (1969) [Pis’ma Zh. Eksp. Teor. Fiz. 9, 577 (1969)].

Chemla, D. S.

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, and W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982);D. S. Chemla and D. A. B. Miller, J. Opt. Soc. Am. B 2, 1155 (1985).
[Crossref]

Dagenais, M.

M. Dagenais and H. G. Winful, Appl. Phys. Lett. 44, 574 (1984);M. Dagenais and W. F. Sharfin, J. Opt. Soc. Am. B 2, 1179 (1985).
[Crossref]

Dziedzic, J. M.

Eilenberger, D. J.

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, and W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982);D. S. Chemla and D. A. B. Miller, J. Opt. Soc. Am. B 2, 1155 (1985).
[Crossref]

Finn, G.

I. C. Khoo, R. R. Michael, T. H. Liu, G. Finn, and A. E. Kaplan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 43 (1986).

Friberg, S.

S. Friberg and P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
[Crossref]

Gossard, A. C.

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, and W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982);D. S. Chemla and D. A. B. Miller, J. Opt. Soc. Am. B 2, 1155 (1985).
[Crossref]

Gudzenko, L. I.

L. I. Gudzenko, C. D. Kaitmazov, A. A. Medvedev, and E. I. Schklovsky, Lebedev Inst. Phys. Brief Commun. Phys. 1, 64 (1970, in Russian).

Hermann, J. A.

J. A. Hermann, Opt. Commun. 62, 367 (1987);Opt. Quantum Electron. 19, 169 (1987).
[Crossref]

J. A. Hermann, J. Opt. Soc. Am. B 1, 729 (1984).
[Crossref]

Kaitmazov, C. D.

L. I. Gudzenko, C. D. Kaitmazov, A. A. Medvedev, and E. I. Schklovsky, Lebedev Inst. Phys. Brief Commun. Phys. 1, 64 (1970, in Russian).

Kamuz, A. M.

M. S. Brodin and A. M. Kamuz, JETP Lett. 9, 351 (1969) [Pis’ma Zh. Eksp. Teor. Fiz. 9, 577 (1969)].

Kaplan, A. E.

I. C. Khoo, R. R. Michael, T. H. Liu, G. Finn, and A. E. Kaplan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 43 (1986).

J. E. Bjorkholm, P. W. Smith, W. J. Tomlinson, and A. E. Kaplan, Opt. Lett. 6, 345 (1981);I. C. Khoo, P. J. Yan, T. H. Liu, S. Shepard, and J. Y. Hou, Phys. Rev. A 29, 2756 (1984);K. Tai, M. M. Gibbs, N. Peyghambarian, and A. Mysyrowicz, Opt. Lett. 10, 220 (1985);M. Le Berre, E. Ressayre, A. Tallet, K. Tai, and H. M. Gibbs, IEEE J. Quantum Electron. QE-21, 1404 (1985).
[Crossref] [PubMed]

A. E. Kaplan, Opt. Lett. 6, 360 (1981).
[Crossref] [PubMed]

A. E. Kaplan, Radiophys. Quantum Electron. 12, 692 (1969) [Izv. Vyash. Ucheb. Zaved. Radiofiz. 12, 869 (1969)];F. S. Felber, Appl. Phys. Lett. 36, 723 (1980).
[Crossref]

A. E. Kaplan, JETP Lett. 9, 33 (1969) [Pis’ma Zh. Eksp. Teor. Fiz. 9, 58 (1969)].

Kelley, P. L.

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965);S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi and E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, p. 1151;Y. R. Shen, Rev. Mod. Phys. 48, 1 (1976).
[Crossref]

Khoo, I. C.

I. C. Khoo, R. R. Michael, T. H. Liu, G. Finn, and A. E. Kaplan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 43 (1986).

I. C. Khoo, Phys. Rev. A 25, 1636 (1982).
[Crossref]

Liu, T. H.

I. C. Khoo, R. R. Michael, T. H. Liu, G. Finn, and A. E. Kaplan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 43 (1986).

McWane, P. D.

P. D. McWane, Nature 211, 1081 (1966).
[Crossref]

Medvedev, A. A.

L. I. Gudzenko, C. D. Kaitmazov, A. A. Medvedev, and E. I. Schklovsky, Lebedev Inst. Phys. Brief Commun. Phys. 1, 64 (1970, in Russian).

Michael, R. R.

I. C. Khoo, R. R. Michael, T. H. Liu, G. Finn, and A. E. Kaplan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 43 (1986).

Miller, D. A. B.

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, and W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982);D. S. Chemla and D. A. B. Miller, J. Opt. Soc. Am. B 2, 1155 (1985).
[Crossref]

Moss, S. C.

Schklovsky, E. I.

L. I. Gudzenko, C. D. Kaitmazov, A. A. Medvedev, and E. I. Schklovsky, Lebedev Inst. Phys. Brief Commun. Phys. 1, 64 (1970, in Russian).

Smirl, A. L.

Smith, P. W.

Swartzlander, G. A.

G. A. Swartzlander, M. S. thesis (Purdue U., West Lafayette, Indiana, 1985) (unpublished).

Tomlinson, W. J.

Tsang, W. T.

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, and W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982);D. S. Chemla and D. A. B. Miller, J. Opt. Soc. Am. B 2, 1155 (1985).
[Crossref]

Winful, H. G.

M. Dagenais and H. G. Winful, Appl. Phys. Lett. 44, 574 (1984);M. Dagenais and W. F. Sharfin, J. Opt. Soc. Am. B 2, 1179 (1985).
[Crossref]

Appl. Phys. Lett. (2)

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, and W. T. Tsang, Appl. Phys. Lett. 41, 679 (1982);D. S. Chemla and D. A. B. Miller, J. Opt. Soc. Am. B 2, 1155 (1985).
[Crossref]

M. Dagenais and H. G. Winful, Appl. Phys. Lett. 44, 574 (1984);M. Dagenais and W. F. Sharfin, J. Opt. Soc. Am. B 2, 1179 (1985).
[Crossref]

IEEE J. Quantum Electron. (1)

S. Friberg and P. W. Smith, IEEE J. Quantum Electron. QE-23, 2089 (1987).
[Crossref]

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

JETP Lett. (2)

A. E. Kaplan, JETP Lett. 9, 33 (1969) [Pis’ma Zh. Eksp. Teor. Fiz. 9, 58 (1969)].

M. S. Brodin and A. M. Kamuz, JETP Lett. 9, 351 (1969) [Pis’ma Zh. Eksp. Teor. Fiz. 9, 577 (1969)].

Lebedev Inst. Phys. Brief Commun. Phys. (1)

L. I. Gudzenko, C. D. Kaitmazov, A. A. Medvedev, and E. I. Schklovsky, Lebedev Inst. Phys. Brief Commun. Phys. 1, 64 (1970, in Russian).

Nature (1)

P. D. McWane, Nature 211, 1081 (1966).
[Crossref]

Opt. Commun. (1)

J. A. Hermann, Opt. Commun. 62, 367 (1987);Opt. Quantum Electron. 19, 169 (1987).
[Crossref]

Opt. Lett. (4)

Phys. Rev. A (1)

I. C. Khoo, Phys. Rev. A 25, 1636 (1982).
[Crossref]

Phys. Rev. Lett. (1)

P. L. Kelley, Phys. Rev. Lett. 15, 1005 (1965);S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov, in Laser Handbook, F. T. Arecchi and E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, p. 1151;Y. R. Shen, Rev. Mod. Phys. 48, 1 (1976).
[Crossref]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

I. C. Khoo, R. R. Michael, T. H. Liu, G. Finn, and A. E. Kaplan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 43 (1986).

Radiophys. Quantum Electron. (1)

A. E. Kaplan, Radiophys. Quantum Electron. 12, 692 (1969) [Izv. Vyash. Ucheb. Zaved. Radiofiz. 12, 869 (1969)];F. S. Felber, Appl. Phys. Lett. 36, 723 (1980).
[Crossref]

Other (2)

We use the following definition of the Fresnel integrals: S(u)=(1/2π)∫0u2[sin(t)/t]dt and C(u)=(1/2π)∫0u2[cos(t)t]dt. [See Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, eds. (Dover, New York, 1972).]

G. A. Swartzlander, M. S. thesis (Purdue U., West Lafayette, Indiana, 1985) (unpublished).

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Figures (4)

Fig. 1
Fig. 1

Right-triangular incident intensity profiles of equal power (|i|2wi/2 = constant), with peak intensities |E|2 and beam size wi (arbitrary units) varying, respectively, as (i) (1, 1), (ii) (1/2, 2), (iii) (1/3, 3), (iv) (1/4, 4). Their corresponding self-deflected beams are also shown. The deflected beams (NL) become resolved more clearly from their linear positions (L) as the beam size wi is reduced. The insert shows a thin, nonlinear film with incident and transmitted rays of light.

Fig. 2
Fig. 2

Self-deflection due to a semi-Gaussian intensity profile for nonlinear parameter ϕNL = 2πj, j = 0, 1, 2, 3. The deflection angle θNL of the largest peak is given by Eq. (7). The number of subpeaks is equal to j.

Fig. 3
Fig. 3

The deflection angle of the peak intensity in the far field versus the nonlinear parameter ϕNL. Indicent intensity profiles are (a) right-triangular, (b) semi-Gaussian, and (c) symmetric Gaussian.

Fig. 4
Fig. 4

Counter-self-deflection due to a symmetric Gaussian intensity profile for different nonlinear parameters; ϕNL = 2πj, where j = 0, 1, 2, 3.

Equations (10)

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

L ( D , R NL ) ,
D = k w 2 / 2 , R NL = w ( n 0 / 4 n 2 | E m | 2 ) 1 / 2 ,
E ( x , L ) E T ( x ) = E 0 ( x ) exp [ i Φ 0 ( x ) ] exp { i [ n 0 + n 2 | E 0 ( x ) | 2 ] k L } .
ξ ( θ ) = d x E T ( x ) exp ( i k x θ ) .
| E ( x ) | 2 = { | E m | 2 ( 1 x / w ) 0 < x < w 0 otherwise ;
ξ L ( θ ) = E m w { i Θ ( π 2 Θ 3 ) 1 / 2 [ S ( Θ 1 / 2 ) + i C ( Θ 1 / 2 ) ] e i Θ } ,
| ξ NL ( θ ) | = | ξ L ( θ θ NL ) | ,
θ NL = n 2 | E m | 2 L / w = ϕ NL θ d / 2 ,
| ξ NL ( θ ) | 2 = | ξ L ( θ θ 1 ) + ξ L ( θ + θ 2 ) | 2 ,
E 0 ( x ) = { E m exp [ ( x / w ) 2 ] x > 0 0 otherwise .

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