Abstract

The formation of a periodic transverse structure in the light field in a resonator consisting of mirrors and a thin layer of a nonlinear medium is considered. It is shown that, when the resonator length is a multiple of one half of the Talbot length, there exist periodic structures that are self-imaged under propagation through both the empty part of the resonator and the nonlinear medium. The influence of aperture losses is estimated. It is suggested that this type of a resonator may be useful for diode-array-pumped solid-state lasers.

© 1990 Optical Society of America

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  1. V. V. Antyuhov, A. F. Glova, O. P. Katchurin, F. V. Lebedev, V. V. Likhansky, A. P. Napartovich, and V. D. Pysmennyi, “An effective phase synchronization of a laser set,” JETP Lett. 44, 78 (1986).
  2. S. A. Akhmanov, M. A. Vorontsov, and V. Yu. Ivanov, “Large-scale transverse nonlinear interactions in laser beams: new types of nonlinear waves, onset of ‘optical turbulence,’ ” JETP Lett. 47, 707 (1988).
  3. L. A. Lugiato, L. M. Narducci, M. A. Pernigo, J. R. Tredicce, E. J. Quel, M. Ghazzawi, and C. Green, “Spatial and temporal instabilities in a CO2laser,” Phys. Rev. Lett. 62, 1274 (1989).
    [CrossRef]
  4. W. J. Firth and E. M. Wright, “Theory of Gaussian beam optical bistability,” Opt. Commun. 40, 233 (1982).
    [CrossRef]
  5. L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, G.-L. Oppo, and M. A. Pernigo, “Spontaneous spatial pattern formation in laser and cooperative frequency locking,” Opt. Commun. 68, 63 (1988); L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, F. Prati, and P. Ru, “Role of transverse effects on laser instabilities,” Phys. Rev. A 37, 3847 (1988).
    [CrossRef] [PubMed]
  6. H. Adachihara, A. Aceves, C. Jones, J. C. Lerman, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Chaos and coherent structures in partial differential equations,” Physica D 18, 85 (1986); H. Adachihara, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Solitary waves as a fixed points of an infinite dimensional maps: an analysis,” J. Math. Phys. 29, 63 (1988).
    [CrossRef]
  7. W. J. Firth, “Optical memory and spatial chaos,” Phys. Rev. Lett. 62, 1274 (1988); “Optically bistable arrays and chaotic dynamics,” Phys. Lett. A 125, 375 (1987).
  8. A. Yu. Okulov and A. N. Oraevsky, “Spatio-temporal dynamics of a wave packet in nonlinear media and discrete maps,” in Proceedings of the Lebedev Physics Institute, N. G. Basov, ed. (Nova-Science, New York, 1988), Vol. 187, p. 202.
  9. Yu. M. Azyan and V. V. Migulin, “On the self-oscillations in delayed feedback system,” Radiotekh. Elektron. 1, 418 (1956).
  10. N. N. Rozanov and V. E. Semenov, “The kinetics of histeresis of the beam profile in nonlinear interferometer,” Opt. Commun. 38, 435 (1981); “Histeretic and chaotic phenomena in nonlinear optical systems,” Izv. Akad. Nauk SSR Ser. Fiz. 46, 1886 (1982).
    [CrossRef]
  11. P. Meystre, E. M. Wright, and W. J. Firth, “Nonlinear theory of self-oscillations in a phase-conjugate resonator,” Opt. Commun. 51, 428 (1984); P. Meystre, E. M. Wright, and M. Belic, “Optical turbulence in a phase-conjugate resonator,” J. Opt. Soc. Am. B 5, 1193 (1988).
    [CrossRef]
  12. A. Yu. Okulov and A. N. Oraevsky, “Spatio-temporal behavior of a light pulse in nonlinear nondispersive media,” J. Opt. Soc. Am. B 3, 741 (1986).
    [CrossRef]
  13. H. F. Talbot, “The facts relating to optical science,” Philos. Mag. J. Sci. (London) 9, 401 (1836); Rayleigh, “On copying diffraction-gratings and on some phenomena connected therewith,” Philos. Mag. 2 (5), 196 (1881).
  14. J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334 (1989); J. Z. Wilcox, W. W. Simmons, D. Botez, M. Jansen, L. J. Mawst, G. Peterson, T. J. Wilcox, and J. J. Yang, “Design considerations for diffraction coupled arrays with monolithically integrated self-imaging cavities,” Appl. Phys. Lett. 54, 1848 (1989).
    [CrossRef]
  15. A. Maitland and M. H. Dunn, Laser Physics (Mir, Moscow, 1978), Chap. 6.
  16. J. Durnin, “Exact solutions for nondiffracting optical beams. I. Scalar theory,” J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  17. G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6, 150 (1989).
    [CrossRef]
  18. A. A. Golubentsev, V. V. Likhansky, and A. P. Napartovich, “Theory of the phase locking of an array of lasers,” Sov. Phys. JETP,  66, 676 (1987).
  19. V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).
  20. F. Hanson and D. Haddock, “Laser diode side pumping of neodymium rods,” Appl. Opt. 27, 80 (1988).
    [CrossRef] [PubMed]
  21. L. Allen and J. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1978), Chap. 4.
  22. L. A. Lugiato, “Theory of optical bistability,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1984), Vol. 21, p. 71.
    [CrossRef]
  23. I. Galbraith and H. Haug, “Spatiotemporal chaos in a ring cavity,” J. Opt. Soc. Am. B 4, 1116 (1987).
    [CrossRef]
  24. V. M. Marchenko, T. M. Makhviladize, A. M. Prokhorov, and M. E. Sarytchev, “Optical resonators with periodic boundaries,” Sov. Phys. JETP 74, 455 (1978).
  25. O. V. Bogdankevich, S. A. Darznek, A. N. Pechenov, B. I. Vasiliev, and M. M. Zverev, “Semiconductor electron-beam pumped laser of the radiating mirror type,” IEEE J. Quantum Electron. QE-9, 342 (1973).
    [CrossRef]

1989 (3)

L. A. Lugiato, L. M. Narducci, M. A. Pernigo, J. R. Tredicce, E. J. Quel, M. Ghazzawi, and C. Green, “Spatial and temporal instabilities in a CO2laser,” Phys. Rev. Lett. 62, 1274 (1989).
[CrossRef]

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334 (1989); J. Z. Wilcox, W. W. Simmons, D. Botez, M. Jansen, L. J. Mawst, G. Peterson, T. J. Wilcox, and J. J. Yang, “Design considerations for diffraction coupled arrays with monolithically integrated self-imaging cavities,” Appl. Phys. Lett. 54, 1848 (1989).
[CrossRef]

G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6, 150 (1989).
[CrossRef]

1988 (5)

S. A. Akhmanov, M. A. Vorontsov, and V. Yu. Ivanov, “Large-scale transverse nonlinear interactions in laser beams: new types of nonlinear waves, onset of ‘optical turbulence,’ ” JETP Lett. 47, 707 (1988).

L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, G.-L. Oppo, and M. A. Pernigo, “Spontaneous spatial pattern formation in laser and cooperative frequency locking,” Opt. Commun. 68, 63 (1988); L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, F. Prati, and P. Ru, “Role of transverse effects on laser instabilities,” Phys. Rev. A 37, 3847 (1988).
[CrossRef] [PubMed]

W. J. Firth, “Optical memory and spatial chaos,” Phys. Rev. Lett. 62, 1274 (1988); “Optically bistable arrays and chaotic dynamics,” Phys. Lett. A 125, 375 (1987).

V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).

F. Hanson and D. Haddock, “Laser diode side pumping of neodymium rods,” Appl. Opt. 27, 80 (1988).
[CrossRef] [PubMed]

1987 (3)

1986 (3)

A. Yu. Okulov and A. N. Oraevsky, “Spatio-temporal behavior of a light pulse in nonlinear nondispersive media,” J. Opt. Soc. Am. B 3, 741 (1986).
[CrossRef]

H. Adachihara, A. Aceves, C. Jones, J. C. Lerman, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Chaos and coherent structures in partial differential equations,” Physica D 18, 85 (1986); H. Adachihara, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Solitary waves as a fixed points of an infinite dimensional maps: an analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

V. V. Antyuhov, A. F. Glova, O. P. Katchurin, F. V. Lebedev, V. V. Likhansky, A. P. Napartovich, and V. D. Pysmennyi, “An effective phase synchronization of a laser set,” JETP Lett. 44, 78 (1986).

1984 (1)

P. Meystre, E. M. Wright, and W. J. Firth, “Nonlinear theory of self-oscillations in a phase-conjugate resonator,” Opt. Commun. 51, 428 (1984); P. Meystre, E. M. Wright, and M. Belic, “Optical turbulence in a phase-conjugate resonator,” J. Opt. Soc. Am. B 5, 1193 (1988).
[CrossRef]

1982 (1)

W. J. Firth and E. M. Wright, “Theory of Gaussian beam optical bistability,” Opt. Commun. 40, 233 (1982).
[CrossRef]

1981 (1)

N. N. Rozanov and V. E. Semenov, “The kinetics of histeresis of the beam profile in nonlinear interferometer,” Opt. Commun. 38, 435 (1981); “Histeretic and chaotic phenomena in nonlinear optical systems,” Izv. Akad. Nauk SSR Ser. Fiz. 46, 1886 (1982).
[CrossRef]

1978 (1)

V. M. Marchenko, T. M. Makhviladize, A. M. Prokhorov, and M. E. Sarytchev, “Optical resonators with periodic boundaries,” Sov. Phys. JETP 74, 455 (1978).

1973 (1)

O. V. Bogdankevich, S. A. Darznek, A. N. Pechenov, B. I. Vasiliev, and M. M. Zverev, “Semiconductor electron-beam pumped laser of the radiating mirror type,” IEEE J. Quantum Electron. QE-9, 342 (1973).
[CrossRef]

1956 (1)

Yu. M. Azyan and V. V. Migulin, “On the self-oscillations in delayed feedback system,” Radiotekh. Elektron. 1, 418 (1956).

1836 (1)

H. F. Talbot, “The facts relating to optical science,” Philos. Mag. J. Sci. (London) 9, 401 (1836); Rayleigh, “On copying diffraction-gratings and on some phenomena connected therewith,” Philos. Mag. 2 (5), 196 (1881).

Aceves, A.

H. Adachihara, A. Aceves, C. Jones, J. C. Lerman, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Chaos and coherent structures in partial differential equations,” Physica D 18, 85 (1986); H. Adachihara, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Solitary waves as a fixed points of an infinite dimensional maps: an analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

Adachihara, H.

H. Adachihara, A. Aceves, C. Jones, J. C. Lerman, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Chaos and coherent structures in partial differential equations,” Physica D 18, 85 (1986); H. Adachihara, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Solitary waves as a fixed points of an infinite dimensional maps: an analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, M. A. Vorontsov, and V. Yu. Ivanov, “Large-scale transverse nonlinear interactions in laser beams: new types of nonlinear waves, onset of ‘optical turbulence,’ ” JETP Lett. 47, 707 (1988).

Allen, L.

L. Allen and J. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1978), Chap. 4.

Antyuhov, V. V.

V. V. Antyuhov, A. F. Glova, O. P. Katchurin, F. V. Lebedev, V. V. Likhansky, A. P. Napartovich, and V. D. Pysmennyi, “An effective phase synchronization of a laser set,” JETP Lett. 44, 78 (1986).

Azyan, Yu. M.

Yu. M. Azyan and V. V. Migulin, “On the self-oscillations in delayed feedback system,” Radiotekh. Elektron. 1, 418 (1956).

Bandy, D. K.

L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, G.-L. Oppo, and M. A. Pernigo, “Spontaneous spatial pattern formation in laser and cooperative frequency locking,” Opt. Commun. 68, 63 (1988); L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, F. Prati, and P. Ru, “Role of transverse effects on laser instabilities,” Phys. Rev. A 37, 3847 (1988).
[CrossRef] [PubMed]

Bogdankevich, O. V.

O. V. Bogdankevich, S. A. Darznek, A. N. Pechenov, B. I. Vasiliev, and M. M. Zverev, “Semiconductor electron-beam pumped laser of the radiating mirror type,” IEEE J. Quantum Electron. QE-9, 342 (1973).
[CrossRef]

Darznek, S. A.

O. V. Bogdankevich, S. A. Darznek, A. N. Pechenov, B. I. Vasiliev, and M. M. Zverev, “Semiconductor electron-beam pumped laser of the radiating mirror type,” IEEE J. Quantum Electron. QE-9, 342 (1973).
[CrossRef]

Divak, A. A.

V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).

Dunn, M. H.

A. Maitland and M. H. Dunn, Laser Physics (Mir, Moscow, 1978), Chap. 6.

Durnin, J.

Eberly, J.

L. Allen and J. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1978), Chap. 4.

Firth, W. J.

W. J. Firth, “Optical memory and spatial chaos,” Phys. Rev. Lett. 62, 1274 (1988); “Optically bistable arrays and chaotic dynamics,” Phys. Lett. A 125, 375 (1987).

P. Meystre, E. M. Wright, and W. J. Firth, “Nonlinear theory of self-oscillations in a phase-conjugate resonator,” Opt. Commun. 51, 428 (1984); P. Meystre, E. M. Wright, and M. Belic, “Optical turbulence in a phase-conjugate resonator,” J. Opt. Soc. Am. B 5, 1193 (1988).
[CrossRef]

W. J. Firth and E. M. Wright, “Theory of Gaussian beam optical bistability,” Opt. Commun. 40, 233 (1982).
[CrossRef]

Galbraith, I.

Garmash, V. M.

V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).

Ghazzawi, M.

L. A. Lugiato, L. M. Narducci, M. A. Pernigo, J. R. Tredicce, E. J. Quel, M. Ghazzawi, and C. Green, “Spatial and temporal instabilities in a CO2laser,” Phys. Rev. Lett. 62, 1274 (1989).
[CrossRef]

Glova, A. F.

V. V. Antyuhov, A. F. Glova, O. P. Katchurin, F. V. Lebedev, V. V. Likhansky, A. P. Napartovich, and V. D. Pysmennyi, “An effective phase synchronization of a laser set,” JETP Lett. 44, 78 (1986).

Golubentsev, A. A.

A. A. Golubentsev, V. V. Likhansky, and A. P. Napartovich, “Theory of the phase locking of an array of lasers,” Sov. Phys. JETP,  66, 676 (1987).

Green, C.

L. A. Lugiato, L. M. Narducci, M. A. Pernigo, J. R. Tredicce, E. J. Quel, M. Ghazzawi, and C. Green, “Spatial and temporal instabilities in a CO2laser,” Phys. Rev. Lett. 62, 1274 (1989).
[CrossRef]

Haddock, D.

Hanson, F.

Haug, H.

Indebetouw, G.

Ivanov, V. Yu.

S. A. Akhmanov, M. A. Vorontsov, and V. Yu. Ivanov, “Large-scale transverse nonlinear interactions in laser beams: new types of nonlinear waves, onset of ‘optical turbulence,’ ” JETP Lett. 47, 707 (1988).

Jones, C.

H. Adachihara, A. Aceves, C. Jones, J. C. Lerman, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Chaos and coherent structures in partial differential equations,” Physica D 18, 85 (1986); H. Adachihara, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Solitary waves as a fixed points of an infinite dimensional maps: an analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

Katchurin, O. P.

V. V. Antyuhov, A. F. Glova, O. P. Katchurin, F. V. Lebedev, V. V. Likhansky, A. P. Napartovich, and V. D. Pysmennyi, “An effective phase synchronization of a laser set,” JETP Lett. 44, 78 (1986).

Kovyzenko, N. A.

V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).

Kuratev, I. I.

V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).

Lebedev, F. V.

V. V. Antyuhov, A. F. Glova, O. P. Katchurin, F. V. Lebedev, V. V. Likhansky, A. P. Napartovich, and V. D. Pysmennyi, “An effective phase synchronization of a laser set,” JETP Lett. 44, 78 (1986).

Leger, J. R.

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334 (1989); J. Z. Wilcox, W. W. Simmons, D. Botez, M. Jansen, L. J. Mawst, G. Peterson, T. J. Wilcox, and J. J. Yang, “Design considerations for diffraction coupled arrays with monolithically integrated self-imaging cavities,” Appl. Phys. Lett. 54, 1848 (1989).
[CrossRef]

Lerman, J. C.

H. Adachihara, A. Aceves, C. Jones, J. C. Lerman, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Chaos and coherent structures in partial differential equations,” Physica D 18, 85 (1986); H. Adachihara, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Solitary waves as a fixed points of an infinite dimensional maps: an analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

Likhansky, V. V.

A. A. Golubentsev, V. V. Likhansky, and A. P. Napartovich, “Theory of the phase locking of an array of lasers,” Sov. Phys. JETP,  66, 676 (1987).

V. V. Antyuhov, A. F. Glova, O. P. Katchurin, F. V. Lebedev, V. V. Likhansky, A. P. Napartovich, and V. D. Pysmennyi, “An effective phase synchronization of a laser set,” JETP Lett. 44, 78 (1986).

Lugiato, L. A.

L. A. Lugiato, L. M. Narducci, M. A. Pernigo, J. R. Tredicce, E. J. Quel, M. Ghazzawi, and C. Green, “Spatial and temporal instabilities in a CO2laser,” Phys. Rev. Lett. 62, 1274 (1989).
[CrossRef]

L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, G.-L. Oppo, and M. A. Pernigo, “Spontaneous spatial pattern formation in laser and cooperative frequency locking,” Opt. Commun. 68, 63 (1988); L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, F. Prati, and P. Ru, “Role of transverse effects on laser instabilities,” Phys. Rev. A 37, 3847 (1988).
[CrossRef] [PubMed]

L. A. Lugiato, “Theory of optical bistability,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1984), Vol. 21, p. 71.
[CrossRef]

Maitland, A.

A. Maitland and M. H. Dunn, Laser Physics (Mir, Moscow, 1978), Chap. 6.

Makhviladize, T. M.

V. M. Marchenko, T. M. Makhviladize, A. M. Prokhorov, and M. E. Sarytchev, “Optical resonators with periodic boundaries,” Sov. Phys. JETP 74, 455 (1978).

Marchenko, V. M.

V. M. Marchenko, T. M. Makhviladize, A. M. Prokhorov, and M. E. Sarytchev, “Optical resonators with periodic boundaries,” Sov. Phys. JETP 74, 455 (1978).

McLaughlin, D. W.

H. Adachihara, A. Aceves, C. Jones, J. C. Lerman, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Chaos and coherent structures in partial differential equations,” Physica D 18, 85 (1986); H. Adachihara, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Solitary waves as a fixed points of an infinite dimensional maps: an analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

Meystre, P.

P. Meystre, E. M. Wright, and W. J. Firth, “Nonlinear theory of self-oscillations in a phase-conjugate resonator,” Opt. Commun. 51, 428 (1984); P. Meystre, E. M. Wright, and M. Belic, “Optical turbulence in a phase-conjugate resonator,” J. Opt. Soc. Am. B 5, 1193 (1988).
[CrossRef]

Migulin, V. V.

Yu. M. Azyan and V. V. Migulin, “On the self-oscillations in delayed feedback system,” Radiotekh. Elektron. 1, 418 (1956).

Moloney, J. V.

H. Adachihara, A. Aceves, C. Jones, J. C. Lerman, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Chaos and coherent structures in partial differential equations,” Physica D 18, 85 (1986); H. Adachihara, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Solitary waves as a fixed points of an infinite dimensional maps: an analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

Napartovich, A. P.

A. A. Golubentsev, V. V. Likhansky, and A. P. Napartovich, “Theory of the phase locking of an array of lasers,” Sov. Phys. JETP,  66, 676 (1987).

V. V. Antyuhov, A. F. Glova, O. P. Katchurin, F. V. Lebedev, V. V. Likhansky, A. P. Napartovich, and V. D. Pysmennyi, “An effective phase synchronization of a laser set,” JETP Lett. 44, 78 (1986).

Narducci, L. M.

L. A. Lugiato, L. M. Narducci, M. A. Pernigo, J. R. Tredicce, E. J. Quel, M. Ghazzawi, and C. Green, “Spatial and temporal instabilities in a CO2laser,” Phys. Rev. Lett. 62, 1274 (1989).
[CrossRef]

L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, G.-L. Oppo, and M. A. Pernigo, “Spontaneous spatial pattern formation in laser and cooperative frequency locking,” Opt. Commun. 68, 63 (1988); L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, F. Prati, and P. Ru, “Role of transverse effects on laser instabilities,” Phys. Rev. A 37, 3847 (1988).
[CrossRef] [PubMed]

Newell, A. C.

H. Adachihara, A. Aceves, C. Jones, J. C. Lerman, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Chaos and coherent structures in partial differential equations,” Physica D 18, 85 (1986); H. Adachihara, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Solitary waves as a fixed points of an infinite dimensional maps: an analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

Okulov, A. Yu.

A. Yu. Okulov and A. N. Oraevsky, “Spatio-temporal behavior of a light pulse in nonlinear nondispersive media,” J. Opt. Soc. Am. B 3, 741 (1986).
[CrossRef]

A. Yu. Okulov and A. N. Oraevsky, “Spatio-temporal dynamics of a wave packet in nonlinear media and discrete maps,” in Proceedings of the Lebedev Physics Institute, N. G. Basov, ed. (Nova-Science, New York, 1988), Vol. 187, p. 202.

Oppo, G.-L.

L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, G.-L. Oppo, and M. A. Pernigo, “Spontaneous spatial pattern formation in laser and cooperative frequency locking,” Opt. Commun. 68, 63 (1988); L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, F. Prati, and P. Ru, “Role of transverse effects on laser instabilities,” Phys. Rev. A 37, 3847 (1988).
[CrossRef] [PubMed]

Oraevsky, A. N.

A. Yu. Okulov and A. N. Oraevsky, “Spatio-temporal behavior of a light pulse in nonlinear nondispersive media,” J. Opt. Soc. Am. B 3, 741 (1986).
[CrossRef]

A. Yu. Okulov and A. N. Oraevsky, “Spatio-temporal dynamics of a wave packet in nonlinear media and discrete maps,” in Proceedings of the Lebedev Physics Institute, N. G. Basov, ed. (Nova-Science, New York, 1988), Vol. 187, p. 202.

Pechenov, A. N.

O. V. Bogdankevich, S. A. Darznek, A. N. Pechenov, B. I. Vasiliev, and M. M. Zverev, “Semiconductor electron-beam pumped laser of the radiating mirror type,” IEEE J. Quantum Electron. QE-9, 342 (1973).
[CrossRef]

Pernigo, M. A.

L. A. Lugiato, L. M. Narducci, M. A. Pernigo, J. R. Tredicce, E. J. Quel, M. Ghazzawi, and C. Green, “Spatial and temporal instabilities in a CO2laser,” Phys. Rev. Lett. 62, 1274 (1989).
[CrossRef]

L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, G.-L. Oppo, and M. A. Pernigo, “Spontaneous spatial pattern formation in laser and cooperative frequency locking,” Opt. Commun. 68, 63 (1988); L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, F. Prati, and P. Ru, “Role of transverse effects on laser instabilities,” Phys. Rev. A 37, 3847 (1988).
[CrossRef] [PubMed]

Prokhorov, A. M.

V. M. Marchenko, T. M. Makhviladize, A. M. Prokhorov, and M. E. Sarytchev, “Optical resonators with periodic boundaries,” Sov. Phys. JETP 74, 455 (1978).

Pysmennyi, V. D.

V. V. Antyuhov, A. F. Glova, O. P. Katchurin, F. V. Lebedev, V. V. Likhansky, A. P. Napartovich, and V. D. Pysmennyi, “An effective phase synchronization of a laser set,” JETP Lett. 44, 78 (1986).

Quel, E. J.

L. A. Lugiato, L. M. Narducci, M. A. Pernigo, J. R. Tredicce, E. J. Quel, M. Ghazzawi, and C. Green, “Spatial and temporal instabilities in a CO2laser,” Phys. Rev. Lett. 62, 1274 (1989).
[CrossRef]

Rozanov, N. N.

N. N. Rozanov and V. E. Semenov, “The kinetics of histeresis of the beam profile in nonlinear interferometer,” Opt. Commun. 38, 435 (1981); “Histeretic and chaotic phenomena in nonlinear optical systems,” Izv. Akad. Nauk SSR Ser. Fiz. 46, 1886 (1982).
[CrossRef]

Sarytchev, M. E.

V. M. Marchenko, T. M. Makhviladize, A. M. Prokhorov, and M. E. Sarytchev, “Optical resonators with periodic boundaries,” Sov. Phys. JETP 74, 455 (1978).

Semenenko, A. V.

V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).

Semenov, V. E.

N. N. Rozanov and V. E. Semenov, “The kinetics of histeresis of the beam profile in nonlinear interferometer,” Opt. Commun. 38, 435 (1981); “Histeretic and chaotic phenomena in nonlinear optical systems,” Izv. Akad. Nauk SSR Ser. Fiz. 46, 1886 (1982).
[CrossRef]

Shveikin, V. I.

V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).

Talbot, H. F.

H. F. Talbot, “The facts relating to optical science,” Philos. Mag. J. Sci. (London) 9, 401 (1836); Rayleigh, “On copying diffraction-gratings and on some phenomena connected therewith,” Philos. Mag. 2 (5), 196 (1881).

Tarasov, A. V.

V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).

Tredicce, J. R.

L. A. Lugiato, L. M. Narducci, M. A. Pernigo, J. R. Tredicce, E. J. Quel, M. Ghazzawi, and C. Green, “Spatial and temporal instabilities in a CO2laser,” Phys. Rev. Lett. 62, 1274 (1989).
[CrossRef]

L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, G.-L. Oppo, and M. A. Pernigo, “Spontaneous spatial pattern formation in laser and cooperative frequency locking,” Opt. Commun. 68, 63 (1988); L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, F. Prati, and P. Ru, “Role of transverse effects on laser instabilities,” Phys. Rev. A 37, 3847 (1988).
[CrossRef] [PubMed]

Tsvetkov, Y. V.

V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).

Vasiliev, B. I.

O. V. Bogdankevich, S. A. Darznek, A. N. Pechenov, B. I. Vasiliev, and M. M. Zverev, “Semiconductor electron-beam pumped laser of the radiating mirror type,” IEEE J. Quantum Electron. QE-9, 342 (1973).
[CrossRef]

Vorontsov, M. A.

S. A. Akhmanov, M. A. Vorontsov, and V. Yu. Ivanov, “Large-scale transverse nonlinear interactions in laser beams: new types of nonlinear waves, onset of ‘optical turbulence,’ ” JETP Lett. 47, 707 (1988).

Wright, E. M.

P. Meystre, E. M. Wright, and W. J. Firth, “Nonlinear theory of self-oscillations in a phase-conjugate resonator,” Opt. Commun. 51, 428 (1984); P. Meystre, E. M. Wright, and M. Belic, “Optical turbulence in a phase-conjugate resonator,” J. Opt. Soc. Am. B 5, 1193 (1988).
[CrossRef]

W. J. Firth and E. M. Wright, “Theory of Gaussian beam optical bistability,” Opt. Commun. 40, 233 (1982).
[CrossRef]

Yanchuk, V. G.

V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).

Zverev, M. M.

O. V. Bogdankevich, S. A. Darznek, A. N. Pechenov, B. I. Vasiliev, and M. M. Zverev, “Semiconductor electron-beam pumped laser of the radiating mirror type,” IEEE J. Quantum Electron. QE-9, 342 (1973).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. R. Leger, “Lateral mode control of an AlGaAs laser array in a Talbot cavity,” Appl. Phys. Lett. 55, 334 (1989); J. Z. Wilcox, W. W. Simmons, D. Botez, M. Jansen, L. J. Mawst, G. Peterson, T. J. Wilcox, and J. J. Yang, “Design considerations for diffraction coupled arrays with monolithically integrated self-imaging cavities,” Appl. Phys. Lett. 54, 1848 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

O. V. Bogdankevich, S. A. Darznek, A. N. Pechenov, B. I. Vasiliev, and M. M. Zverev, “Semiconductor electron-beam pumped laser of the radiating mirror type,” IEEE J. Quantum Electron. QE-9, 342 (1973).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

JETP Lett. (2)

V. V. Antyuhov, A. F. Glova, O. P. Katchurin, F. V. Lebedev, V. V. Likhansky, A. P. Napartovich, and V. D. Pysmennyi, “An effective phase synchronization of a laser set,” JETP Lett. 44, 78 (1986).

S. A. Akhmanov, M. A. Vorontsov, and V. Yu. Ivanov, “Large-scale transverse nonlinear interactions in laser beams: new types of nonlinear waves, onset of ‘optical turbulence,’ ” JETP Lett. 47, 707 (1988).

Opt. Commun. (4)

W. J. Firth and E. M. Wright, “Theory of Gaussian beam optical bistability,” Opt. Commun. 40, 233 (1982).
[CrossRef]

L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, G.-L. Oppo, and M. A. Pernigo, “Spontaneous spatial pattern formation in laser and cooperative frequency locking,” Opt. Commun. 68, 63 (1988); L. A. Lugiato, L. M. Narducci, D. K. Bandy, J. R. Tredicce, F. Prati, and P. Ru, “Role of transverse effects on laser instabilities,” Phys. Rev. A 37, 3847 (1988).
[CrossRef] [PubMed]

N. N. Rozanov and V. E. Semenov, “The kinetics of histeresis of the beam profile in nonlinear interferometer,” Opt. Commun. 38, 435 (1981); “Histeretic and chaotic phenomena in nonlinear optical systems,” Izv. Akad. Nauk SSR Ser. Fiz. 46, 1886 (1982).
[CrossRef]

P. Meystre, E. M. Wright, and W. J. Firth, “Nonlinear theory of self-oscillations in a phase-conjugate resonator,” Opt. Commun. 51, 428 (1984); P. Meystre, E. M. Wright, and M. Belic, “Optical turbulence in a phase-conjugate resonator,” J. Opt. Soc. Am. B 5, 1193 (1988).
[CrossRef]

Philos. Mag. J. Sci. (London) (1)

H. F. Talbot, “The facts relating to optical science,” Philos. Mag. J. Sci. (London) 9, 401 (1836); Rayleigh, “On copying diffraction-gratings and on some phenomena connected therewith,” Philos. Mag. 2 (5), 196 (1881).

Phys. Rev. Lett. (2)

W. J. Firth, “Optical memory and spatial chaos,” Phys. Rev. Lett. 62, 1274 (1988); “Optically bistable arrays and chaotic dynamics,” Phys. Lett. A 125, 375 (1987).

L. A. Lugiato, L. M. Narducci, M. A. Pernigo, J. R. Tredicce, E. J. Quel, M. Ghazzawi, and C. Green, “Spatial and temporal instabilities in a CO2laser,” Phys. Rev. Lett. 62, 1274 (1989).
[CrossRef]

Physica D (1)

H. Adachihara, A. Aceves, C. Jones, J. C. Lerman, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Chaos and coherent structures in partial differential equations,” Physica D 18, 85 (1986); H. Adachihara, J. V. Moloney, D. W. McLaughlin, and A. C. Newell, “Solitary waves as a fixed points of an infinite dimensional maps: an analysis,” J. Math. Phys. 29, 63 (1988).
[CrossRef]

Radiotekh. Elektron. (1)

Yu. M. Azyan and V. V. Migulin, “On the self-oscillations in delayed feedback system,” Radiotekh. Elektron. 1, 418 (1956).

Sov. J. Quantum Electron. (1)

V. M. Garmash, A. A. Divak, N. A. Kovyzenko, I. I. Kuratev, A. V. Semenenko, A. V. Tarasov, Y. V. Tsvetkov, V. I. Shveikin, and V. G. Yanchuk, “Miniature solid-state laser with semiconductor pump radiating in UV region,” Sov. J. Quantum Electron. 15, 1323 (1988).

Sov. Phys. JETP (2)

A. A. Golubentsev, V. V. Likhansky, and A. P. Napartovich, “Theory of the phase locking of an array of lasers,” Sov. Phys. JETP,  66, 676 (1987).

V. M. Marchenko, T. M. Makhviladize, A. M. Prokhorov, and M. E. Sarytchev, “Optical resonators with periodic boundaries,” Sov. Phys. JETP 74, 455 (1978).

Other (4)

L. Allen and J. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1978), Chap. 4.

L. A. Lugiato, “Theory of optical bistability,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1984), Vol. 21, p. 71.
[CrossRef]

A. Maitland and M. H. Dunn, Laser Physics (Mir, Moscow, 1978), Chap. 6.

A. Yu. Okulov and A. N. Oraevsky, “Spatio-temporal dynamics of a wave packet in nonlinear media and discrete maps,” in Proceedings of the Lebedev Physics Institute, N. G. Basov, ed. (Nova-Science, New York, 1988), Vol. 187, p. 202.

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Figures (4)

Fig. 1
Fig. 1

Transverse profile destruction at z = Lfr and its reconstruction at z = Lt.

Fig. 2
Fig. 2

Configuration of a resonator for a diode-pumped solid-state laser: LDA, laser diode array; Nd:YAG, active medium.

Fig. 3
Fig. 3

a, Boundary conditions for calculation of counterpropagat-ing fields E+(z), E(z). Rb and R0 are the reflectances of the left and the output mirrors, respectively, b, Output intensity F versus 1, input intensity B; 2, its asymptote F = B + NL/T1. c, Output field E+ versus 1, input field E; 2, its asymptote E+ = E(1 + NL/T1E2)1/2.

Fig. 4
Fig. 4

Evolution of transverse structure in the resonator of microlaser (Fig. 2) calculated by successive iterations of the map [Eq. (10)] with a spatially periodic inversion profile (central 4 × 4 spikes).

Equations (12)

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E ( x , y , z ) = i k 2 π z exp ( i k z ) × exp { i k 2 z [ ( x x ) 2 + ( y y ) 2 ] } × D ( x , y ) E ( x , y , z = 0 ) d x d y ,
E ( x , y , z = 0 ) = A m n exp [ i 2 π ( n x / b x + m y / b y ) ] ,
E ( x , y , z ) = exp ( i k z ) A m n exp [ i 2 π ( n x b x + m y b y ) ] × exp [ ( 2 b x n x ) 2 ( 1 + i z / k d x 2 ) 2 d x 2 ( 2 b y m y ) 2 ( 1 + i z / k d y 2 ) 2 d y 2 + i 2 π π z k × ( n 2 b x 2 + m 2 b y 2 ) ] [ ( 1 + i z k d x 2 ) ( 1 + i z k d y 2 ) ] 1 / 2 .
E ( x , y , z ) = exp ( i k z ) A m n exp [ i 2 π ( n x b x + m y b y ) ] × exp [ i 2 π π z k ( n 2 b x 2 + m 2 b y 2 ) ] .
E ( x , y , z ) = exp ( i k z ) A m n exp [ i 2 π ( n x b + m l y b ) ] × exp [ ( 2 b l t n x ) 2 + ( 2 b l l t m y ) 2 2 d 2 ( 1 + i l t b 2 / π d 2 ) ] × [ 1 + i l t b 2 / π d 2 ] 1 .
E n + 1 ( x , y , z ) = f [ x , y , E n ( x , y , z ) ] .
f ( E ) = α E + β E 2 + E 3 + .
f ( E ) = α A m n exp [ i 2 π ( n x b x + m y b y ) ] + β A m n A t s exp [ i 2 π ( n x b x + m y b y + t x b x + s y b y ) ] + .
d F d z = σ N F 1 + σ T 1 ( F + B ) , d B d z = σ N B 1 + σ T 1 ( F + B ) ,
F exp [ σ T 1 ( F C / F ) ] = F ( 0 ) exp { σ T 1 [ F ( 0 ) C / F ( 0 ) ] + σ N L } , B exp [ σ T 1 ( B C / B ) ] = B ( 0 ) exp { σ T 1 [ B ( 0 ) C / B ( 0 ) ] σ N L } ,
F exp ( 2 σ T 1 F ) = B exp ( 2 σ T 1 B + 2 σ N L ) .
( E n + 1 / R 0 1 / 2 ) exp ( σ T 1 E n + 1 2 / R 0 ) = E n exp ( σ T 1 E n 2 + σ N L ) .

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