Abstract

The cavity modes of metal strip waveguide lasers are most simply expressed in terms of Airy-Hermite-Gaussian functions. The free space propagation of the resulting beam modes has been examined, and both near- and far-field patterns have been calculated and measured. Phase plates may be useful for enhancing the far-field intensity.

© 1984 Optical Society of America

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References

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  1. K. D. Laakman, U.S. Patent4,169,251 (1979).
  2. J. G. Grossman, “RF Excited CO2 Metal Waveguide Laser,” Ph.D. Dissertation, U. California, Los Angeles (Mar.1982).
    [PubMed]
  3. J. G. Grossman, L. W. Casperson, O. M. Stafsudd, Appl. Opt. 22, 1298 (1983).
    [Crossref] [PubMed]
  4. M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 609 (1978).
    [Crossref]
  5. M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 874 (1978).
    [Crossref]
  6. L. W. Casperson, T. S. Garfield, IEEE J. Quantum Electron. QE-15, 491 (1979).
    [Crossref]
  7. M. E. Marhic, J. Opt. Soc. Am. 69, 1218 (1979).
    [Crossref]
  8. M. E. Marhic, L. I. Kwan, M. Epstein, IEEE J. Quantum Electron. QE-15, 487 (1979).
    [Crossref]
  9. Handbook of Mathematical Functions, NBS Applied Math. Ser. 55 (U.S. GPO, Washington, D.C., 1964), Chap. 10.
  10. In Ref. 9, Chap. 22.
  11. A. Yariv, Quantum Electronics (Wiley, New York, 1975), p. 111.
  12. R. L. Abrams, “Waveguide Gas Lasers,” in Laser Handbook (North-Holland, Amsterdam, 1979), Chap. A2.
  13. L. W. Casperson, Opt. Quantum Electron. 8, 537 (1976).
    [Crossref]

1983 (1)

1979 (3)

L. W. Casperson, T. S. Garfield, IEEE J. Quantum Electron. QE-15, 491 (1979).
[Crossref]

M. E. Marhic, J. Opt. Soc. Am. 69, 1218 (1979).
[Crossref]

M. E. Marhic, L. I. Kwan, M. Epstein, IEEE J. Quantum Electron. QE-15, 487 (1979).
[Crossref]

1978 (2)

M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 609 (1978).
[Crossref]

M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 874 (1978).
[Crossref]

1976 (1)

L. W. Casperson, Opt. Quantum Electron. 8, 537 (1976).
[Crossref]

Abrams, R. L.

R. L. Abrams, “Waveguide Gas Lasers,” in Laser Handbook (North-Holland, Amsterdam, 1979), Chap. A2.

Casperson, L. W.

J. G. Grossman, L. W. Casperson, O. M. Stafsudd, Appl. Opt. 22, 1298 (1983).
[Crossref] [PubMed]

L. W. Casperson, T. S. Garfield, IEEE J. Quantum Electron. QE-15, 491 (1979).
[Crossref]

L. W. Casperson, Opt. Quantum Electron. 8, 537 (1976).
[Crossref]

Epstein, M.

M. E. Marhic, L. I. Kwan, M. Epstein, IEEE J. Quantum Electron. QE-15, 487 (1979).
[Crossref]

M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 874 (1978).
[Crossref]

M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 609 (1978).
[Crossref]

Garfield, T. S.

L. W. Casperson, T. S. Garfield, IEEE J. Quantum Electron. QE-15, 491 (1979).
[Crossref]

Grossman, J. G.

J. G. Grossman, L. W. Casperson, O. M. Stafsudd, Appl. Opt. 22, 1298 (1983).
[Crossref] [PubMed]

J. G. Grossman, “RF Excited CO2 Metal Waveguide Laser,” Ph.D. Dissertation, U. California, Los Angeles (Mar.1982).
[PubMed]

Kwan, L. I.

M. E. Marhic, L. I. Kwan, M. Epstein, IEEE J. Quantum Electron. QE-15, 487 (1979).
[Crossref]

M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 874 (1978).
[Crossref]

M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 609 (1978).
[Crossref]

Laakman, K. D.

K. D. Laakman, U.S. Patent4,169,251 (1979).

Marhic, M. E.

M. E. Marhic, L. I. Kwan, M. Epstein, IEEE J. Quantum Electron. QE-15, 487 (1979).
[Crossref]

M. E. Marhic, J. Opt. Soc. Am. 69, 1218 (1979).
[Crossref]

M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 609 (1978).
[Crossref]

M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 874 (1978).
[Crossref]

Stafsudd, O. M.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975), p. 111.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 609 (1978).
[Crossref]

M. E. Marhic, L. I. Kwan, M. Epstein, Appl. Phys. Lett. 33, 874 (1978).
[Crossref]

IEEE J. Quantum Electron. (2)

L. W. Casperson, T. S. Garfield, IEEE J. Quantum Electron. QE-15, 491 (1979).
[Crossref]

M. E. Marhic, L. I. Kwan, M. Epstein, IEEE J. Quantum Electron. QE-15, 487 (1979).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Quantum Electron. (1)

L. W. Casperson, Opt. Quantum Electron. 8, 537 (1976).
[Crossref]

Other (6)

K. D. Laakman, U.S. Patent4,169,251 (1979).

J. G. Grossman, “RF Excited CO2 Metal Waveguide Laser,” Ph.D. Dissertation, U. California, Los Angeles (Mar.1982).
[PubMed]

Handbook of Mathematical Functions, NBS Applied Math. Ser. 55 (U.S. GPO, Washington, D.C., 1964), Chap. 10.

In Ref. 9, Chap. 22.

A. Yariv, Quantum Electronics (Wiley, New York, 1975), p. 111.

R. L. Abrams, “Waveguide Gas Lasers,” in Laser Handbook (North-Holland, Amsterdam, 1979), Chap. A2.

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Figures (11)

Fig. 1
Fig. 1

Schematic representation of an rf excited metal waveguide laser.

Fig. 2
Fig. 2

Beam intensity perpendicular to the waveguide surface for the first- and second-order Airy-Gaussian modes.

Fig. 3
Fig. 3

Far-field beam divergence of the first- and second-order Airy-Gaussian modes.

Fig. 4
Fig. 4

Beam intensity perpendicular to the waveguide surface for the sixth- and seventh-order Airy-Gaussian modes.

Fig. 5
Fig. 5

Far-field beam divergence of the sixth- and seventh-order Airy-Gaussian modes.

Fig. 6
Fig. 6

Far-field beam divergence for a phase compensated seventh-order Airy-Gaussian mode.

Fig. 7
Fig. 7

Experimental setup for studying free space beam propagation.

Fig. 8
Fig. 8

Near-field beam intensity profile along Airy axis, lowest-order Airy mode (1 m from laser).

Fig. 9
Fig. 9

Far-field beam intensity profile along Airy axis, lowest-order Airy mode (3 m from laser).

Fig. 10
Fig. 10

Near-field beam intensity profile along Airy axis, second-order Airy mode (2 m from laser).

Fig. 11
Fig. 11

Far-field beam intensity profile along Hermite-Gaussian axis, lowest-order Hermite-Gaussian mode (1 m from laser).

Equations (11)

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E ( ρ , ζ ) = E 0 A ( ρ ) H m ( ζ ) exp ( - ζ 2 / 2 ) .
d 2 A d ρ 2 - ρ A = 0 ,
ρ = ( 2 k 0 2 / r 0 ) - 2 / 3 [ ( 2 k 0 2 / r 0 ) r - α ] .
d 2 H d ζ 2 - 2 ζ d H d ζ + 2 m H = 0 ,
ζ = 2 1 / 2 z / w ,
w = [ 2 ( r 0 R 0 ) 1 / 2 / k 0 ] 1 / 2 .
U ( x 0 , y 0 ) = exp ( j k z ) j λ z ( A n ( x 1 ) H m ( 2 y 1 w 0 ) exp ( - y 1 2 w 0 2 ) × exp { j k 2 z [ ( x 0 - x 1 ) 2 + ( y 0 - y 1 ) 2 ] } ) d x 1 d y 1 ,
z 0 = ( n π w 0 2 ) / λ ,
a s = - f [ 3 π ( 4 s - 1 ) / 8 ] ,
f ( z ) z 2 / 3 ( 1 + 5 48 z - 2 - 5 36 z - 4 + 77125 82944 z - 6 - 108056875 z - 8 6967296 ) ,
θ s ( full angle ) = λ n Δ s / 2 π ,

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