Abstract

We have invented a quasi-Gaussian profile-transmittance filter based on radially varying the phase retardation in a birefringent element. The radial birefringent element has been applied to resonator design and has demonstrated its usefulness in generating an improved resonator spatial-mode profile.

© 1980 Optical Society of America

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References

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  1. L. W. Casperson, “Mode stability of lasers and periodic optical systems,” IEEE J. Quantum Electron. QE-10, 629–634 (1974).
    [CrossRef]
  2. L. W. Casperson, S. D. Lunnam, “Gaussian modes in high loss laser resonators,” Appl. Opt. 14, 1193–1199 (1975).
    [CrossRef] [PubMed]
  3. U. Ganiel, Y. Silberberg, “Stability of optical resonators with an active medium,” Appl. Opt. 14, 306–309 (1975).
    [CrossRef] [PubMed]
  4. A. Yariv, R. Yeh, “Confinement and stability in optical resonators employing mirrors with Gaussian reflectivity tapers,” Opt. Commun. 13, 370–374 (1975).
    [CrossRef]
  5. A. E. Siegman, “Unstable optical resonators for laser applications,” Proc. IEEE 53, 217–287 (1965);“Unstable optical resonators,” Appl. Opt. 13, 353–367 (1974).
    [CrossRef] [PubMed]
  6. A. J. Campillo et al., “Fresnel diffraction effects in the design of high power laser systems,” Appl. Phys. Lett. 23, 85–87 (1973).
    [CrossRef]
  7. S. Sheng, “Studies of laser resonators and beam propagation using fast transform methods,” Ph.D. thesis, Ginzton Laboratory Report #3106 (Stanford U. Press, Stanford, Calif., 1979).
  8. W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
    [CrossRef]
  9. R. L. Herbst, H. Komine, R. L. Byer, “A 200 mJ unstable resonator Nd:YAG oscillator,” Opt. Commun. 21, 5–9 (1977).
    [CrossRef]
  10. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. 32, 486–493 (1942).
    [CrossRef]
  11. G. Giuliani, R. L. Byer, “The radial birefringent element” (to be published).

1977 (1)

R. L. Herbst, H. Komine, R. L. Byer, “A 200 mJ unstable resonator Nd:YAG oscillator,” Opt. Commun. 21, 5–9 (1977).
[CrossRef]

1975 (3)

1974 (1)

L. W. Casperson, “Mode stability of lasers and periodic optical systems,” IEEE J. Quantum Electron. QE-10, 629–634 (1974).
[CrossRef]

1973 (1)

A. J. Campillo et al., “Fresnel diffraction effects in the design of high power laser systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

1969 (1)

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

1965 (1)

A. E. Siegman, “Unstable optical resonators for laser applications,” Proc. IEEE 53, 217–287 (1965);“Unstable optical resonators,” Appl. Opt. 13, 353–367 (1974).
[CrossRef] [PubMed]

1942 (1)

Byer, R. L.

R. L. Herbst, H. Komine, R. L. Byer, “A 200 mJ unstable resonator Nd:YAG oscillator,” Opt. Commun. 21, 5–9 (1977).
[CrossRef]

G. Giuliani, R. L. Byer, “The radial birefringent element” (to be published).

Campillo, A. J.

A. J. Campillo et al., “Fresnel diffraction effects in the design of high power laser systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

Casperson, L. W.

L. W. Casperson, S. D. Lunnam, “Gaussian modes in high loss laser resonators,” Appl. Opt. 14, 1193–1199 (1975).
[CrossRef] [PubMed]

L. W. Casperson, “Mode stability of lasers and periodic optical systems,” IEEE J. Quantum Electron. QE-10, 629–634 (1974).
[CrossRef]

Ganiel, U.

Giuliani, G.

G. Giuliani, R. L. Byer, “The radial birefringent element” (to be published).

Herbst, R. L.

R. L. Herbst, H. Komine, R. L. Byer, “A 200 mJ unstable resonator Nd:YAG oscillator,” Opt. Commun. 21, 5–9 (1977).
[CrossRef]

Jones, R. C.

Komine, H.

R. L. Herbst, H. Komine, R. L. Byer, “A 200 mJ unstable resonator Nd:YAG oscillator,” Opt. Commun. 21, 5–9 (1977).
[CrossRef]

Krupke, W. F.

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

Lunnam, S. D.

Sheng, S.

S. Sheng, “Studies of laser resonators and beam propagation using fast transform methods,” Ph.D. thesis, Ginzton Laboratory Report #3106 (Stanford U. Press, Stanford, Calif., 1979).

Siegman, A. E.

A. E. Siegman, “Unstable optical resonators for laser applications,” Proc. IEEE 53, 217–287 (1965);“Unstable optical resonators,” Appl. Opt. 13, 353–367 (1974).
[CrossRef] [PubMed]

Silberberg, Y.

Sooy, W. R.

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

Yariv, A.

A. Yariv, R. Yeh, “Confinement and stability in optical resonators employing mirrors with Gaussian reflectivity tapers,” Opt. Commun. 13, 370–374 (1975).
[CrossRef]

Yeh, R.

A. Yariv, R. Yeh, “Confinement and stability in optical resonators employing mirrors with Gaussian reflectivity tapers,” Opt. Commun. 13, 370–374 (1975).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. J. Campillo et al., “Fresnel diffraction effects in the design of high power laser systems,” Appl. Phys. Lett. 23, 85–87 (1973).
[CrossRef]

IEEE J. Quantum Electron. (2)

W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969).
[CrossRef]

L. W. Casperson, “Mode stability of lasers and periodic optical systems,” IEEE J. Quantum Electron. QE-10, 629–634 (1974).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

R. L. Herbst, H. Komine, R. L. Byer, “A 200 mJ unstable resonator Nd:YAG oscillator,” Opt. Commun. 21, 5–9 (1977).
[CrossRef]

A. Yariv, R. Yeh, “Confinement and stability in optical resonators employing mirrors with Gaussian reflectivity tapers,” Opt. Commun. 13, 370–374 (1975).
[CrossRef]

Proc. IEEE (1)

A. E. Siegman, “Unstable optical resonators for laser applications,” Proc. IEEE 53, 217–287 (1965);“Unstable optical resonators,” Appl. Opt. 13, 353–367 (1974).
[CrossRef] [PubMed]

Other (2)

S. Sheng, “Studies of laser resonators and beam propagation using fast transform methods,” Ph.D. thesis, Ginzton Laboratory Report #3106 (Stanford U. Press, Stanford, Calif., 1979).

G. Giuliani, R. L. Byer, “The radial birefringent element” (to be published).

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Figures (4)

Fig. 1
Fig. 1

The radial birefringent element consisting of a polarizer and a birefringent plate with curvature ρ, within an unstable resonator cavity.

Fig. 2
Fig. 2

Reflectance profiles of the RBE using two crystal-quartz elements. Two elements have equal but opposite curvature ρ. θ1 and θ2 are the angles between the principal axis of the quartz elements and the polarizer axis. The mode radius r0 is chosen equal to the radius of the Nd:YAG rod.

Fig. 3
Fig. 3

Transverse-mode profiles of the RBE and standard confocal unstable resonator configurations. The Polaroid exposures of the output are at the right side and the vidicon-scanned profiles are at the left side. The slightly asymmetric patterns are due to a damage spot on one end of the Nd:YAG rod.

Fig. 4
Fig. 4

Second-harmonic-generation conversion efficiency versus input pump energy for the confocal unstable resonator and for the RBE unstable resonator in Type II KD*P.

Equations (9)

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R = cos 2 ϕ ( r ) + sin 2 ϕ ( r ) cos 2 2 θ ,
T = sin 2 ϕ ( r ) sin 2 2 θ ,
ϕ ( r ) = 2 π Δ n λ l ( r ) = 2 π Δ n λ ( l 0 ± r 2 2 ρ ) ,
R ( r ) = cos 2 2 θ + sin 2 2 θ cos 2 ϕ ( r ) ,
R ( r ) = cos 2 [ 2 π Δ n λ ( l 0 ± r 2 2 ρ ) ] .
l 0 = λ 2 π Δ n { cos 1 [ R ( 0 ) ] 1 / 2 + m π } , ρ = r 0 2 Δ n 2 π 2 λ { cos 1 [ R ( r 0 ) ] 1 / 2 cos 1 [ R ( 0 ) ] 1 / 2 } 1 ,
w m 2 = r 0 2 cos 1 [ R ( 0 ) / e ] 1 / 2 cos 1 [ R ( 0 ) ] 1 / 2 cos 1 [ R ( r 0 ) ] 1 / 2 cos 1 [ R ( 0 ) ] 1 / 2 ,
R ( 0 ) e ( r 2 / w m 2 ) .
R e = ( 1 R m + 1 f ) 1 ,

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