Abstract

We have analyzed the propagation properties of the field produced by circular arrays of coherent optical sources, obtaining the conditions for the generation of good-quality global beams. Such conditions can be obtained by the use of resonators based on the Talbot effect. This appears to be a practical method for the construction of simple, low-cost resonators for compact diffusion-cooled high-power lasers with annular format. Low-loss annular Talbot cavity configurations have also been studied.

© 1999 Optical Society of America

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References

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  1. R. J. Freiberg, P. P. Chenausky, C. J. Buczek, “An experimental study of unstable confocal CO2 lasers,” IEEE J. Quantum Electron. QE-8, 882–888 (1972).
    [CrossRef]
  2. U. Wittrock, H. Weber, B. Heppich, “Inside pumped Nd:YAG tube laser,” Opt. Lett. 16, 1092–1094 (1991).
    [CrossRef] [PubMed]
  3. P. Burlamacchi, R. Pratesi, L. Ronchi, “Self-guiding flashlamp-pumped dye lasers,” Appl. Opt. 14, 79–93 (1975).
    [CrossRef] [PubMed]
  4. See, for instance, D. R. Hall, H. J. Baker, “Diffusion-cooled large surface area CO2–CO lasers,” in Gas Flow and Chemical Lasers: Tenth International Symposium, W. L. Bohn, Huegel, eds., Proc. SPIE2502, 12–19 (1994), and references therein.
  5. D. Ehrlichmann, U. Habich, H. D. Plum, “Azimuthal mode discrimination of annular resonators,” Appl. Opt. 32, 6582–6586 (1993).
    [CrossRef] [PubMed]
  6. H. Bochum, “Near- and far-field properties of annular CO2 waveguide lasers,” Appl. Opt. 36, 3349–3356 (1997).
    [CrossRef] [PubMed]
  7. A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an rf-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
    [CrossRef]
  8. A. Lapucci, M. Ciofini, S. Mascalchi, E. Di Fabrizio, M. Gentili, “Beam quality enhancement for an rf-excited annular CO2 laser,” Appl. Phys. Lett. 73, 2549–2551 (1998).
    [CrossRef]
  9. A. Lapucci, F. Quercioli, D. Jafrancesco, “Optimal phase filtering for high-power laser array far-field distribution,” Opt. Lett. 18, 1694–1696 (1993).
    [CrossRef] [PubMed]
  10. G. Lescroart, G. L. Bourdet, “Effects of binary phase plates on the far field diffraction pattern of an out of phase coupled linear array of waveguide lasers,” Opt. Commun. 119, 373–380 (1995).
    [CrossRef]
  11. A. Lapucci, “Risonatore e metodo di filtraggio per ottenere fasci di buona qualità ottica da laser a sezione anulare,” Italian patentFI98A-130 (1June1998).
  12. M. Morin, P.-A. Bélanger, “Diffractive analysis of annular resonators,” Appl. Opt. 31, 1942–1947 (1992).
    [CrossRef] [PubMed]
  13. H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401 (1836); Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196 (1881).
    [CrossRef]
  14. F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
    [CrossRef]
  15. V. V. Antyukov, A. F. Glova, O. R. Kachurin, F. W. Lebedev, V. V. Likanskii, A. P. Napartovich, V. D. Pis’mennyi, “Effective phase-locking of an array of lasers,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 63–65 (1986).
  16. L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
    [CrossRef]
  17. E. F. Yelden, H. J. J. Seguin, C. E. Capjack, H. Reshef, “Phase-locking phenomena in a radial multislot CO2 laser array,” J. Opt. Soc. Am. B 10, 1475–1482 (1993).
    [CrossRef]
  18. H. J. Baker, D. R. Hall, A. M. Hornby, R. J. Morley, M. R. Taghizadeh, E. F. Yelden, “Propagation characteristics of coherent array beams from carbon dioxide waveguide lasers,” IEEE J. Quantum Electron. 32, 400–407 (1996).
    [CrossRef]
  19. A. Lapucci, A. Labate, F. Rossetti, S. Mascalchi, “Hybrid stable-unstable resonators for diffusion-cooled CO2 slab lasers,” Appl. Opt. 35, 3185–3192 (1996).
    [CrossRef] [PubMed]
  20. A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, “Theory of phase locking of an array of lasers,” Zh. Eksp. Teor. Fiz. 93, 1199–1209 (1987) [reprinted in CIS Selected Papers: High-Power Multibeam Lasers and Their Phase Locking, F. V. Lebedev and A. P. Napartovich, eds., Proc. SPIE 2109, 205–218 (1993)].

1998 (1)

A. Lapucci, M. Ciofini, S. Mascalchi, E. Di Fabrizio, M. Gentili, “Beam quality enhancement for an rf-excited annular CO2 laser,” Appl. Phys. Lett. 73, 2549–2551 (1998).
[CrossRef]

1997 (1)

1996 (2)

H. J. Baker, D. R. Hall, A. M. Hornby, R. J. Morley, M. R. Taghizadeh, E. F. Yelden, “Propagation characteristics of coherent array beams from carbon dioxide waveguide lasers,” IEEE J. Quantum Electron. 32, 400–407 (1996).
[CrossRef]

A. Lapucci, A. Labate, F. Rossetti, S. Mascalchi, “Hybrid stable-unstable resonators for diffusion-cooled CO2 slab lasers,” Appl. Opt. 35, 3185–3192 (1996).
[CrossRef] [PubMed]

1995 (1)

G. Lescroart, G. L. Bourdet, “Effects of binary phase plates on the far field diffraction pattern of an out of phase coupled linear array of waveguide lasers,” Opt. Commun. 119, 373–380 (1995).
[CrossRef]

1994 (1)

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an rf-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

1993 (3)

1992 (1)

1991 (1)

1989 (1)

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

1987 (1)

A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, “Theory of phase locking of an array of lasers,” Zh. Eksp. Teor. Fiz. 93, 1199–1209 (1987) [reprinted in CIS Selected Papers: High-Power Multibeam Lasers and Their Phase Locking, F. V. Lebedev and A. P. Napartovich, eds., Proc. SPIE 2109, 205–218 (1993)].

1986 (2)

V. V. Antyukov, A. F. Glova, O. R. Kachurin, F. W. Lebedev, V. V. Likanskii, A. P. Napartovich, V. D. Pis’mennyi, “Effective phase-locking of an array of lasers,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 63–65 (1986).

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

1975 (1)

1972 (1)

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, “An experimental study of unstable confocal CO2 lasers,” IEEE J. Quantum Electron. QE-8, 882–888 (1972).
[CrossRef]

1836 (1)

H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401 (1836); Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196 (1881).
[CrossRef]

Antyukov, V. V.

V. V. Antyukov, A. F. Glova, O. R. Kachurin, F. W. Lebedev, V. V. Likanskii, A. P. Napartovich, V. D. Pis’mennyi, “Effective phase-locking of an array of lasers,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 63–65 (1986).

Baker, H. J.

H. J. Baker, D. R. Hall, A. M. Hornby, R. J. Morley, M. R. Taghizadeh, E. F. Yelden, “Propagation characteristics of coherent array beams from carbon dioxide waveguide lasers,” IEEE J. Quantum Electron. 32, 400–407 (1996).
[CrossRef]

See, for instance, D. R. Hall, H. J. Baker, “Diffusion-cooled large surface area CO2–CO lasers,” in Gas Flow and Chemical Lasers: Tenth International Symposium, W. L. Bohn, Huegel, eds., Proc. SPIE2502, 12–19 (1994), and references therein.

Bélanger, P.-A.

Bochum, H.

Bourdet, G. L.

G. Lescroart, G. L. Bourdet, “Effects of binary phase plates on the far field diffraction pattern of an out of phase coupled linear array of waveguide lasers,” Opt. Commun. 119, 373–380 (1995).
[CrossRef]

Buczek, C. J.

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, “An experimental study of unstable confocal CO2 lasers,” IEEE J. Quantum Electron. QE-8, 882–888 (1972).
[CrossRef]

Burlamacchi, P.

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an rf-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

P. Burlamacchi, R. Pratesi, L. Ronchi, “Self-guiding flashlamp-pumped dye lasers,” Appl. Opt. 14, 79–93 (1975).
[CrossRef] [PubMed]

Cantor, A. J.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

Capjack, C. E.

Chenausky, P. P.

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, “An experimental study of unstable confocal CO2 lasers,” IEEE J. Quantum Electron. QE-8, 882–888 (1972).
[CrossRef]

Ciofini, M.

A. Lapucci, M. Ciofini, S. Mascalchi, E. Di Fabrizio, M. Gentili, “Beam quality enhancement for an rf-excited annular CO2 laser,” Appl. Phys. Lett. 73, 2549–2551 (1998).
[CrossRef]

D’Amato, F. X.

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

DeMaria, A. J.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

Di Fabrizio, E.

A. Lapucci, M. Ciofini, S. Mascalchi, E. Di Fabrizio, M. Gentili, “Beam quality enhancement for an rf-excited annular CO2 laser,” Appl. Phys. Lett. 73, 2549–2551 (1998).
[CrossRef]

Ehrlichmann, D.

Freiberg, R. J.

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, “An experimental study of unstable confocal CO2 lasers,” IEEE J. Quantum Electron. QE-8, 882–888 (1972).
[CrossRef]

Gentili, M.

A. Lapucci, M. Ciofini, S. Mascalchi, E. Di Fabrizio, M. Gentili, “Beam quality enhancement for an rf-excited annular CO2 laser,” Appl. Phys. Lett. 73, 2549–2551 (1998).
[CrossRef]

Glova, A. F.

V. V. Antyukov, A. F. Glova, O. R. Kachurin, F. W. Lebedev, V. V. Likanskii, A. P. Napartovich, V. D. Pis’mennyi, “Effective phase-locking of an array of lasers,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 63–65 (1986).

Golubentsev, A. A.

A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, “Theory of phase locking of an array of lasers,” Zh. Eksp. Teor. Fiz. 93, 1199–1209 (1987) [reprinted in CIS Selected Papers: High-Power Multibeam Lasers and Their Phase Locking, F. V. Lebedev and A. P. Napartovich, eds., Proc. SPIE 2109, 205–218 (1993)].

Habich, U.

Hall, D. R.

H. J. Baker, D. R. Hall, A. M. Hornby, R. J. Morley, M. R. Taghizadeh, E. F. Yelden, “Propagation characteristics of coherent array beams from carbon dioxide waveguide lasers,” IEEE J. Quantum Electron. 32, 400–407 (1996).
[CrossRef]

See, for instance, D. R. Hall, H. J. Baker, “Diffusion-cooled large surface area CO2–CO lasers,” in Gas Flow and Chemical Lasers: Tenth International Symposium, W. L. Bohn, Huegel, eds., Proc. SPIE2502, 12–19 (1994), and references therein.

Hart, R. A.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

Heppich, B.

Hornby, A. M.

H. J. Baker, D. R. Hall, A. M. Hornby, R. J. Morley, M. R. Taghizadeh, E. F. Yelden, “Propagation characteristics of coherent array beams from carbon dioxide waveguide lasers,” IEEE J. Quantum Electron. 32, 400–407 (1996).
[CrossRef]

Jafrancesco, D.

Kachurin, O. R.

V. V. Antyukov, A. F. Glova, O. R. Kachurin, F. W. Lebedev, V. V. Likanskii, A. P. Napartovich, V. D. Pis’mennyi, “Effective phase-locking of an array of lasers,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 63–65 (1986).

Kennedy, J. T.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

Labate, A.

Lapucci, A.

A. Lapucci, M. Ciofini, S. Mascalchi, E. Di Fabrizio, M. Gentili, “Beam quality enhancement for an rf-excited annular CO2 laser,” Appl. Phys. Lett. 73, 2549–2551 (1998).
[CrossRef]

A. Lapucci, A. Labate, F. Rossetti, S. Mascalchi, “Hybrid stable-unstable resonators for diffusion-cooled CO2 slab lasers,” Appl. Opt. 35, 3185–3192 (1996).
[CrossRef] [PubMed]

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an rf-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

A. Lapucci, F. Quercioli, D. Jafrancesco, “Optimal phase filtering for high-power laser array far-field distribution,” Opt. Lett. 18, 1694–1696 (1993).
[CrossRef] [PubMed]

A. Lapucci, “Risonatore e metodo di filtraggio per ottenere fasci di buona qualità ottica da laser a sezione anulare,” Italian patentFI98A-130 (1June1998).

Lebedev, F. W.

V. V. Antyukov, A. F. Glova, O. R. Kachurin, F. W. Lebedev, V. V. Likanskii, A. P. Napartovich, V. D. Pis’mennyi, “Effective phase-locking of an array of lasers,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 63–65 (1986).

Lescroart, G.

G. Lescroart, G. L. Bourdet, “Effects of binary phase plates on the far field diffraction pattern of an out of phase coupled linear array of waveguide lasers,” Opt. Commun. 119, 373–380 (1995).
[CrossRef]

Likanskii, V. V.

V. V. Antyukov, A. F. Glova, O. R. Kachurin, F. W. Lebedev, V. V. Likanskii, A. P. Napartovich, V. D. Pis’mennyi, “Effective phase-locking of an array of lasers,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 63–65 (1986).

Likhanskii, V. V.

A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, “Theory of phase locking of an array of lasers,” Zh. Eksp. Teor. Fiz. 93, 1199–1209 (1987) [reprinted in CIS Selected Papers: High-Power Multibeam Lasers and Their Phase Locking, F. V. Lebedev and A. P. Napartovich, eds., Proc. SPIE 2109, 205–218 (1993)].

Mascalchi, S.

A. Lapucci, M. Ciofini, S. Mascalchi, E. Di Fabrizio, M. Gentili, “Beam quality enhancement for an rf-excited annular CO2 laser,” Appl. Phys. Lett. 73, 2549–2551 (1998).
[CrossRef]

A. Lapucci, A. Labate, F. Rossetti, S. Mascalchi, “Hybrid stable-unstable resonators for diffusion-cooled CO2 slab lasers,” Appl. Opt. 35, 3185–3192 (1996).
[CrossRef] [PubMed]

Morin, M.

Morley, R. J.

H. J. Baker, D. R. Hall, A. M. Hornby, R. J. Morley, M. R. Taghizadeh, E. F. Yelden, “Propagation characteristics of coherent array beams from carbon dioxide waveguide lasers,” IEEE J. Quantum Electron. 32, 400–407 (1996).
[CrossRef]

Napartovich, A. P.

A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, “Theory of phase locking of an array of lasers,” Zh. Eksp. Teor. Fiz. 93, 1199–1209 (1987) [reprinted in CIS Selected Papers: High-Power Multibeam Lasers and Their Phase Locking, F. V. Lebedev and A. P. Napartovich, eds., Proc. SPIE 2109, 205–218 (1993)].

V. V. Antyukov, A. F. Glova, O. R. Kachurin, F. W. Lebedev, V. V. Likanskii, A. P. Napartovich, V. D. Pis’mennyi, “Effective phase-locking of an array of lasers,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 63–65 (1986).

Newman, L. A.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

Pis’mennyi, V. D.

V. V. Antyukov, A. F. Glova, O. R. Kachurin, F. W. Lebedev, V. V. Likanskii, A. P. Napartovich, V. D. Pis’mennyi, “Effective phase-locking of an array of lasers,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 63–65 (1986).

Plum, H. D.

Pratesi, R.

Quercioli, F.

Reshef, H.

Ronchi, L.

Rossetti, F.

A. Lapucci, A. Labate, F. Rossetti, S. Mascalchi, “Hybrid stable-unstable resonators for diffusion-cooled CO2 slab lasers,” Appl. Opt. 35, 3185–3192 (1996).
[CrossRef] [PubMed]

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an rf-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

Roychoudhuri, C.

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

Seguin, H. J. J.

Siebert, E. T.

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

Taghizadeh, M. R.

H. J. Baker, D. R. Hall, A. M. Hornby, R. J. Morley, M. R. Taghizadeh, E. F. Yelden, “Propagation characteristics of coherent array beams from carbon dioxide waveguide lasers,” IEEE J. Quantum Electron. 32, 400–407 (1996).
[CrossRef]

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401 (1836); Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196 (1881).
[CrossRef]

Weber, H.

Wittrock, U.

Yelden, E. F.

H. J. Baker, D. R. Hall, A. M. Hornby, R. J. Morley, M. R. Taghizadeh, E. F. Yelden, “Propagation characteristics of coherent array beams from carbon dioxide waveguide lasers,” IEEE J. Quantum Electron. 32, 400–407 (1996).
[CrossRef]

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, H. Reshef, “Phase-locking phenomena in a radial multislot CO2 laser array,” J. Opt. Soc. Am. B 10, 1475–1482 (1993).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (3)

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, “Coherent operation of an array of diode lasers using a spatial filter in a Talbot cavity,” Appl. Phys. Lett. 55, 816–818 (1989).
[CrossRef]

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Cantor, A. J. DeMaria, “High power coupled CO2 waveguide laser array,” Appl. Phys. Lett. 48, 1701–1703 (1986).
[CrossRef]

A. Lapucci, M. Ciofini, S. Mascalchi, E. Di Fabrizio, M. Gentili, “Beam quality enhancement for an rf-excited annular CO2 laser,” Appl. Phys. Lett. 73, 2549–2551 (1998).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. J. Freiberg, P. P. Chenausky, C. J. Buczek, “An experimental study of unstable confocal CO2 lasers,” IEEE J. Quantum Electron. QE-8, 882–888 (1972).
[CrossRef]

H. J. Baker, D. R. Hall, A. M. Hornby, R. J. Morley, M. R. Taghizadeh, E. F. Yelden, “Propagation characteristics of coherent array beams from carbon dioxide waveguide lasers,” IEEE J. Quantum Electron. 32, 400–407 (1996).
[CrossRef]

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

Opt. Commun. (2)

G. Lescroart, G. L. Bourdet, “Effects of binary phase plates on the far field diffraction pattern of an out of phase coupled linear array of waveguide lasers,” Opt. Commun. 119, 373–380 (1995).
[CrossRef]

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an rf-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

Opt. Lett. (2)

Philos. Mag. (1)

H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401 (1836); Lord Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196 (1881).
[CrossRef]

Pis’ma Zh. Eksp. Teor. Fiz. (1)

V. V. Antyukov, A. F. Glova, O. R. Kachurin, F. W. Lebedev, V. V. Likanskii, A. P. Napartovich, V. D. Pis’mennyi, “Effective phase-locking of an array of lasers,” Pis’ma Zh. Eksp. Teor. Fiz. 44, 63–65 (1986).

Zh. Eksp. Teor. Fiz. (1)

A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, “Theory of phase locking of an array of lasers,” Zh. Eksp. Teor. Fiz. 93, 1199–1209 (1987) [reprinted in CIS Selected Papers: High-Power Multibeam Lasers and Their Phase Locking, F. V. Lebedev and A. P. Napartovich, eds., Proc. SPIE 2109, 205–218 (1993)].

Other (2)

A. Lapucci, “Risonatore e metodo di filtraggio per ottenere fasci di buona qualità ottica da laser a sezione anulare,” Italian patentFI98A-130 (1June1998).

See, for instance, D. R. Hall, H. J. Baker, “Diffusion-cooled large surface area CO2–CO lasers,” in Gas Flow and Chemical Lasers: Tenth International Symposium, W. L. Bohn, Huegel, eds., Proc. SPIE2502, 12–19 (1994), and references therein.

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Figures (9)

Fig. 1
Fig. 1

Azimuthal quasi-Talbot effect observed on numerical propagation of the field emitted by an array of 28 in-phase sources of 10.6-µm radiation. Sources have a 2 mm × 2 mm transverse dimension and are located upon a 27.5-mm-diameter circle. Field distributions (a) on the source plane, (b) on the plane at distance Z T /4 = 456 mm, (c) on the plane at distance Z T /2 = 912 mm, (d) on the plane at distance 0.75 Z T = 1368 mm.

Fig. 2
Fig. 2

Schematic drawings of the numerically simulated annular cavities: case 1, with the Talbot filter close to the toroidal mirror; case 2, with the Talbot filter close to the flat mirror; case 3, for the guided experimental system of Ref. 8. M1’s, M2’s, cavity mirrors; TF’s, Talbot filters; WG, annular waveguide.

Fig. 3
Fig. 3

Cavity diffraction losses in case 2 for three toroidal mirror ROC’s, (a) 3.0 m, (b) 1.0 m, (c) 0.5 m.

Fig. 4
Fig. 4

Detailed behavior of the cavity diffraction losses close to a Talbot-effect magic distance. Cases 1 and 2 have the same meanings as in Fig. 2.

Fig. 5
Fig. 5

Numerically simulated effect of propagation on an annular beam with purely harmonic azimuthal distribution. Patterns are obtained for propagation distances that differ by 10 cm.

Fig. 6
Fig. 6

Numerically simulated effect of propagation on an annular beam generated by a Talbot cavity with a filling factor equal to 0.8. Patterns are again obtained for propagation distances that differ by 10 cm.

Fig. 7
Fig. 7

Near- (left) and far- (right) field distributions of the source patterns of Figs. 5 and 6.

Fig. 8
Fig. 8

Effect on the far-field of the optimal phase filtering on the field shown in Fig. 6 at the output plane (left) and at a distance of 56 cm from the output plane (right).

Fig. 9
Fig. 9

Energy of the fundamental annular distribution obtainable by phase filtering at several propagation distances.

Equations (3)

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FF=A-OA,
gnr, θ=urexpjnϑ,
ur=rectr0-a; r0+acosπr-r02a.

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