Abstract

The beam quality of a radial laser array, quantified in terms of the M 2 propagation constant, is determined as a function of array element configuration. A lower bound on array M 2 is estimated for both phase-locked and nonphase-locked conditions. It is shown that, to achieve near-unity M 2 array, either aperture filling or spatial filtering is required in addition to phase locking. An aperture-filling method suitable for radial arrays of CO2 slab lasers is presented.

© 1998 Optical Society of America

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  1. 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) and references therein.
    [CrossRef]
  2. K. M. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “High-power two-dimensional waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 32, 340–349 (1996).
    [CrossRef]
  3. E. F. Yelden, H. J. J. Seguin, C. E. Capjack, S. K. Nikumb, “Multichannel slab discharge for CO2 laser excitation,” Appl. Phys. Lett. 58, 693–695 (1991).
    [CrossRef]
  4. W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, “High-power 24 channel radial array slab RF-excited carbon dioxide laser,” in Gas and Chemical Lasers and Applications II, R. C. Sze, E. A. Dorko, eds., Proc. SPIE2987, 13–21 (1997).
    [CrossRef]
  5. W. D. Bilida, “Radial array slab laser excitation with a resonant cavity,” Ph.D. dissertation (University of Alberta, Edmonton, Alberta, Canada, 1996).
  6. E. F. Yelden, S. W. C. Scott, J. D. Strohschein, H. J. J. Seguin, C. E. Capjack, H. W. Reshef, “Symmetry enhancement and spot-size reduction through radial beam stacking in a multichannel CO2 laser array,” IEEE J. Quantum Electron. 30, 1868–1875 (1994).
    [CrossRef]
  7. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
    [CrossRef]
  8. A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable cavity resonator,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
    [CrossRef]
  9. J. R. Leger, M. Holtz, G. J. Swanson, W. B. Veldkamp, “Coherent laser beam addition: an application of binary-optics technology,” Lincoln Lab. J. 1, 225–245 (1988).
  10. J. D. Strohschein, “Simulation and design of advanced high power CO2 laser systems,” Ph.D. dissertation, (University of Alberta, Edmonton, Alberta, Canada, 1996).
  11. W. D. Bilida, University of Alberta, Edmonton, Alberta, Canada (personal communication).
  12. E. F. Yelden, H. J. J. Seguin, C. E. Capjack, H. Reshef, “Phase-locking phenomenon in a radial multislot CO2 laser array,” J. Opt. Soc. Am. B. 10, 1475–1482 (1993).
    [CrossRef]
  13. A. E. Siegman, “Binary phase plates cannot improve laser beam quality,” Opt. Lett. 18, 675–677 (1993).
    [CrossRef] [PubMed]
  14. G. Lescroart, R. Muller, G. L. Bourdet, “Phase filter design for efficient side lobe suppression in phase coupled CO2 waveguide laser arrays,” Opt. Commun. 115, 233–240 (1995).
    [CrossRef]

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) and references therein.
[CrossRef]

K. M. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “High-power two-dimensional waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 32, 340–349 (1996).
[CrossRef]

1995 (1)

G. Lescroart, R. Muller, G. L. Bourdet, “Phase filter design for efficient side lobe suppression in phase coupled CO2 waveguide laser arrays,” Opt. Commun. 115, 233–240 (1995).
[CrossRef]

1994 (1)

E. F. Yelden, S. W. C. Scott, J. D. Strohschein, H. J. J. Seguin, C. E. Capjack, H. W. Reshef, “Symmetry enhancement and spot-size reduction through radial beam stacking in a multichannel CO2 laser array,” IEEE J. Quantum Electron. 30, 1868–1875 (1994).
[CrossRef]

1993 (3)

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable cavity resonator,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

A. E. Siegman, “Binary phase plates cannot improve laser beam quality,” Opt. Lett. 18, 675–677 (1993).
[CrossRef] [PubMed]

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

1991 (1)

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, S. K. Nikumb, “Multichannel slab discharge for CO2 laser excitation,” Appl. Phys. Lett. 58, 693–695 (1991).
[CrossRef]

1988 (1)

J. R. Leger, M. Holtz, G. J. Swanson, W. B. Veldkamp, “Coherent laser beam addition: an application of binary-optics technology,” Lincoln Lab. J. 1, 225–245 (1988).

Abramski, K. M.

K. M. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “High-power two-dimensional waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 32, 340–349 (1996).
[CrossRef]

Baker, H. J.

K. M. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “High-power two-dimensional waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 32, 340–349 (1996).
[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) and references therein.
[CrossRef]

Bilida, W. D.

W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, “High-power 24 channel radial array slab RF-excited carbon dioxide laser,” in Gas and Chemical Lasers and Applications II, R. C. Sze, E. A. Dorko, eds., Proc. SPIE2987, 13–21 (1997).
[CrossRef]

W. D. Bilida, “Radial array slab laser excitation with a resonant cavity,” Ph.D. dissertation (University of Alberta, Edmonton, Alberta, Canada, 1996).

W. D. Bilida, University of Alberta, Edmonton, Alberta, Canada (personal communication).

Bourdet, G. L.

G. Lescroart, R. Muller, G. L. Bourdet, “Phase filter design for efficient side lobe suppression in phase coupled CO2 waveguide laser arrays,” Opt. Commun. 115, 233–240 (1995).
[CrossRef]

Capjack, C. E.

E. F. Yelden, S. W. C. Scott, J. D. Strohschein, H. J. J. Seguin, C. E. Capjack, H. W. Reshef, “Symmetry enhancement and spot-size reduction through radial beam stacking in a multichannel CO2 laser array,” IEEE J. Quantum Electron. 30, 1868–1875 (1994).
[CrossRef]

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

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, S. K. Nikumb, “Multichannel slab discharge for CO2 laser excitation,” Appl. Phys. Lett. 58, 693–695 (1991).
[CrossRef]

Colley, A. D.

K. M. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “High-power two-dimensional waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 32, 340–349 (1996).
[CrossRef]

Hall, D. R.

K. M. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “High-power two-dimensional waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 32, 340–349 (1996).
[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) and references therein.
[CrossRef]

Holtz, M.

J. R. Leger, M. Holtz, G. J. Swanson, W. B. Veldkamp, “Coherent laser beam addition: an application of binary-optics technology,” Lincoln Lab. J. 1, 225–245 (1988).

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) and references therein.
[CrossRef]

Leger, J. R.

J. R. Leger, M. Holtz, G. J. Swanson, W. B. Veldkamp, “Coherent laser beam addition: an application of binary-optics technology,” Lincoln Lab. J. 1, 225–245 (1988).

Lescroart, G.

G. Lescroart, R. Muller, G. L. Bourdet, “Phase filter design for efficient side lobe suppression in phase coupled CO2 waveguide laser arrays,” Opt. Commun. 115, 233–240 (1995).
[CrossRef]

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) and references therein.
[CrossRef]

Muller, R.

G. Lescroart, R. Muller, G. L. Bourdet, “Phase filter design for efficient side lobe suppression in phase coupled CO2 waveguide laser arrays,” Opt. Commun. 115, 233–240 (1995).
[CrossRef]

Nikumb, S. K.

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, S. K. Nikumb, “Multichannel slab discharge for CO2 laser excitation,” Appl. Phys. Lett. 58, 693–695 (1991).
[CrossRef]

Reshef, H.

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

Reshef, H. W.

E. F. Yelden, S. W. C. Scott, J. D. Strohschein, H. J. J. Seguin, C. E. Capjack, H. W. Reshef, “Symmetry enhancement and spot-size reduction through radial beam stacking in a multichannel CO2 laser array,” IEEE J. Quantum Electron. 30, 1868–1875 (1994).
[CrossRef]

Scott, S. W. C.

E. F. Yelden, S. W. C. Scott, J. D. Strohschein, H. J. J. Seguin, C. E. Capjack, H. W. Reshef, “Symmetry enhancement and spot-size reduction through radial beam stacking in a multichannel CO2 laser array,” IEEE J. Quantum Electron. 30, 1868–1875 (1994).
[CrossRef]

Seguin, H. J. J.

E. F. Yelden, S. W. C. Scott, J. D. Strohschein, H. J. J. Seguin, C. E. Capjack, H. W. Reshef, “Symmetry enhancement and spot-size reduction through radial beam stacking in a multichannel CO2 laser array,” IEEE J. Quantum Electron. 30, 1868–1875 (1994).
[CrossRef]

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

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, S. K. Nikumb, “Multichannel slab discharge for CO2 laser excitation,” Appl. Phys. Lett. 58, 693–695 (1991).
[CrossRef]

W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, “High-power 24 channel radial array slab RF-excited carbon dioxide laser,” in Gas and Chemical Lasers and Applications II, R. C. Sze, E. A. Dorko, eds., Proc. SPIE2987, 13–21 (1997).
[CrossRef]

Siegman, A. E.

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable cavity resonator,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

A. E. Siegman, “Binary phase plates cannot improve laser beam quality,” Opt. Lett. 18, 675–677 (1993).
[CrossRef] [PubMed]

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

Strohschein, J. D.

E. F. Yelden, S. W. C. Scott, J. D. Strohschein, H. J. J. Seguin, C. E. Capjack, H. W. Reshef, “Symmetry enhancement and spot-size reduction through radial beam stacking in a multichannel CO2 laser array,” IEEE J. Quantum Electron. 30, 1868–1875 (1994).
[CrossRef]

J. D. Strohschein, “Simulation and design of advanced high power CO2 laser systems,” Ph.D. dissertation, (University of Alberta, Edmonton, Alberta, Canada, 1996).

W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, “High-power 24 channel radial array slab RF-excited carbon dioxide laser,” in Gas and Chemical Lasers and Applications II, R. C. Sze, E. A. Dorko, eds., Proc. SPIE2987, 13–21 (1997).
[CrossRef]

Swanson, G. J.

J. R. Leger, M. Holtz, G. J. Swanson, W. B. Veldkamp, “Coherent laser beam addition: an application of binary-optics technology,” Lincoln Lab. J. 1, 225–245 (1988).

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) and references therein.
[CrossRef]

Townsend, S. W.

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable cavity resonator,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

Veldkamp, W. B.

J. R. Leger, M. Holtz, G. J. Swanson, W. B. Veldkamp, “Coherent laser beam addition: an application of binary-optics technology,” Lincoln Lab. J. 1, 225–245 (1988).

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) and references therein.
[CrossRef]

E. F. Yelden, S. W. C. Scott, J. D. Strohschein, H. J. J. Seguin, C. E. Capjack, H. W. Reshef, “Symmetry enhancement and spot-size reduction through radial beam stacking in a multichannel CO2 laser array,” IEEE J. Quantum Electron. 30, 1868–1875 (1994).
[CrossRef]

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

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, S. K. Nikumb, “Multichannel slab discharge for CO2 laser excitation,” Appl. Phys. Lett. 58, 693–695 (1991).
[CrossRef]

Appl. Phys. Lett. (1)

E. F. Yelden, H. J. J. Seguin, C. E. Capjack, S. K. Nikumb, “Multichannel slab discharge for CO2 laser excitation,” Appl. Phys. Lett. 58, 693–695 (1991).
[CrossRef]

IEEE J. Quantum Electron. (4)

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) and references therein.
[CrossRef]

K. M. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “High-power two-dimensional waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 32, 340–349 (1996).
[CrossRef]

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable cavity resonator,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

E. F. Yelden, S. W. C. Scott, J. D. Strohschein, H. J. J. Seguin, C. E. Capjack, H. W. Reshef, “Symmetry enhancement and spot-size reduction through radial beam stacking in a multichannel CO2 laser array,” IEEE J. Quantum Electron. 30, 1868–1875 (1994).
[CrossRef]

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

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

Lincoln Lab. J. (1)

J. R. Leger, M. Holtz, G. J. Swanson, W. B. Veldkamp, “Coherent laser beam addition: an application of binary-optics technology,” Lincoln Lab. J. 1, 225–245 (1988).

Opt. Commun. (1)

G. Lescroart, R. Muller, G. L. Bourdet, “Phase filter design for efficient side lobe suppression in phase coupled CO2 waveguide laser arrays,” Opt. Commun. 115, 233–240 (1995).
[CrossRef]

Opt. Lett. (1)

Other (5)

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
[CrossRef]

J. D. Strohschein, “Simulation and design of advanced high power CO2 laser systems,” Ph.D. dissertation, (University of Alberta, Edmonton, Alberta, Canada, 1996).

W. D. Bilida, University of Alberta, Edmonton, Alberta, Canada (personal communication).

W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, “High-power 24 channel radial array slab RF-excited carbon dioxide laser,” in Gas and Chemical Lasers and Applications II, R. C. Sze, E. A. Dorko, eds., Proc. SPIE2987, 13–21 (1997).
[CrossRef]

W. D. Bilida, “Radial array slab laser excitation with a resonant cavity,” Ph.D. dissertation (University of Alberta, Edmonton, Alberta, Canada, 1996).

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Figures (2)

Fig. 1
Fig. 1

Best case M 2 of a nonphase-locked radial array. Solid curves distinguish between those regions of configuration space that are directly accessible to radial arrays (above the boundary) and those requiring aperture-filling corrections (below). For a given n, boundaries are the locus of configurations for which the azimuthal intensity modulation between beamlets is 99%.

Fig. 2
Fig. 2

M 2 of a phase-locked radial array compared with that of nonphase-locked conditions for a fixed beamlet aspect ratio (a/ b = 4). The range of r/ a where M 2 is reduced by phase locking (different for each n) requires aperture-filling corrections and so is not directly accessible to a radial array. Inset is a characterization of the intensity distribution at the output plane of a radial array.

Equations (3)

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E 0 x ,   y = exp - y / b 2 - x - r a 2 ,
σ r 0 2 = - - ( x 2 + y 2 ) | E 0 ( x ,   y ) | d x d y - -   | E 0 ( x ,   y ) | d x d y .
M r 2 = a 2 b 1 + b a 2 1 + b a 2 + 4 r a 2 1 / 2 .

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