Abstract

We report what we believe to be the first application of diffractive phase elements for transverse mode selection in laser ring resonators. We show that this resonator type offers several advantages over Fabry–Pérot resonators with diffractive mirrors. The design for a regenerative ring resonator that produces an eighth-order super-Gaussian intensity profile beam is presented. Numerical simulations, including modeling of the gain saturation and experimental tests, have been carried out to demonstrate the performance of this approach for cw and pulsed operations.

© 1999 Optical Society of America

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References

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  1. J. R. Leger, D. Chen, G. Mowry, “Design and performance of diffractive optics for custom laser resonators,” Appl. Opt. 34, 2498–2509 (1995).
    [Crossref] [PubMed]
  2. J. R. Leger, D. Chen, Z. Wang, “Diffractive optical element for mode shaping of a Nd:YAG Laser,” Opt. Lett. 19, 108–110 (1994).
    [Crossref] [PubMed]
  3. I. M. Barton, M. R. Taghizadeh, “Application of optimization algorithms to the design of diffractive optical elements for custom laser resonators,” Opt. Lett. 23, 198–200 (1998).
    [Crossref]
  4. I. M. Barton, P. Blair, A. J. Waddie, K. Balluder, M. R. Taghizadeh, H. A. McInnes, T. H. Bett, “Beam-shaping diffractive optical elements for high-power solid-state laser systems,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437–443 (1999).
    [Crossref]
  5. K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, T. H. Bett, “Diffractive optical elements for beam-shaping tasks in solid-state laser systems,” in Conference on Lasers and Electro-Optics (CLEO/Europe) (Optical Society of America, Washington, D.C., Calif., 1998).
  6. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  7. A. Yariv, “Compensation for atmospheric degradation of optical beam transmission,” Opt. Commun. 21, 49–50 (1977).
    [Crossref]
  8. A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
    [Crossref]
  9. K. Ballüder, M. R. Taghizadeh, “Diffractive optical elements for beam-shaping tasks,” in Conference on Postgraduate Research in Electronics, Photonics and Related Fields (Institute of Physics, Manchester, 1999).
  10. K. Ballüder, M. R. Taghizadeh, “Novel intracavity diffractive mode selecting element designs for high-power laser applications,” in Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1999).
  11. K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21 (1989).
    [Crossref]

1998 (1)

1995 (1)

1994 (1)

1989 (1)

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21 (1989).
[Crossref]

1977 (1)

A. Yariv, “Compensation for atmospheric degradation of optical beam transmission,” Opt. Commun. 21, 49–50 (1977).
[Crossref]

1961 (1)

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

Balluder, K.

I. M. Barton, P. Blair, A. J. Waddie, K. Balluder, M. R. Taghizadeh, H. A. McInnes, T. H. Bett, “Beam-shaping diffractive optical elements for high-power solid-state laser systems,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437–443 (1999).
[Crossref]

Ballüder, K.

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, T. H. Bett, “Diffractive optical elements for beam-shaping tasks in solid-state laser systems,” in Conference on Lasers and Electro-Optics (CLEO/Europe) (Optical Society of America, Washington, D.C., Calif., 1998).

K. Ballüder, M. R. Taghizadeh, “Diffractive optical elements for beam-shaping tasks,” in Conference on Postgraduate Research in Electronics, Photonics and Related Fields (Institute of Physics, Manchester, 1999).

K. Ballüder, M. R. Taghizadeh, “Novel intracavity diffractive mode selecting element designs for high-power laser applications,” in Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1999).

Barton, I. M.

I. M. Barton, M. R. Taghizadeh, “Application of optimization algorithms to the design of diffractive optical elements for custom laser resonators,” Opt. Lett. 23, 198–200 (1998).
[Crossref]

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, T. H. Bett, “Diffractive optical elements for beam-shaping tasks in solid-state laser systems,” in Conference on Lasers and Electro-Optics (CLEO/Europe) (Optical Society of America, Washington, D.C., Calif., 1998).

I. M. Barton, P. Blair, A. J. Waddie, K. Balluder, M. R. Taghizadeh, H. A. McInnes, T. H. Bett, “Beam-shaping diffractive optical elements for high-power solid-state laser systems,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437–443 (1999).
[Crossref]

Bett, T. H.

I. M. Barton, P. Blair, A. J. Waddie, K. Balluder, M. R. Taghizadeh, H. A. McInnes, T. H. Bett, “Beam-shaping diffractive optical elements for high-power solid-state laser systems,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437–443 (1999).
[Crossref]

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, T. H. Bett, “Diffractive optical elements for beam-shaping tasks in solid-state laser systems,” in Conference on Lasers and Electro-Optics (CLEO/Europe) (Optical Society of America, Washington, D.C., Calif., 1998).

Blair, P.

I. M. Barton, P. Blair, A. J. Waddie, K. Balluder, M. R. Taghizadeh, H. A. McInnes, T. H. Bett, “Beam-shaping diffractive optical elements for high-power solid-state laser systems,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437–443 (1999).
[Crossref]

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, T. H. Bett, “Diffractive optical elements for beam-shaping tasks in solid-state laser systems,” in Conference on Lasers and Electro-Optics (CLEO/Europe) (Optical Society of America, Washington, D.C., Calif., 1998).

Chen, D.

Fox, A. G.

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

Leger, J. R.

Li, T.

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

McInnes, H.

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, T. H. Bett, “Diffractive optical elements for beam-shaping tasks in solid-state laser systems,” in Conference on Lasers and Electro-Optics (CLEO/Europe) (Optical Society of America, Washington, D.C., Calif., 1998).

McInnes, H. A.

I. M. Barton, P. Blair, A. J. Waddie, K. Balluder, M. R. Taghizadeh, H. A. McInnes, T. H. Bett, “Beam-shaping diffractive optical elements for high-power solid-state laser systems,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437–443 (1999).
[Crossref]

Mowry, G.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Taghizadeh, M. R.

I. M. Barton, M. R. Taghizadeh, “Application of optimization algorithms to the design of diffractive optical elements for custom laser resonators,” Opt. Lett. 23, 198–200 (1998).
[Crossref]

K. Ballüder, M. R. Taghizadeh, “Novel intracavity diffractive mode selecting element designs for high-power laser applications,” in Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1999).

K. Ballüder, M. R. Taghizadeh, “Diffractive optical elements for beam-shaping tasks,” in Conference on Postgraduate Research in Electronics, Photonics and Related Fields (Institute of Physics, Manchester, 1999).

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, T. H. Bett, “Diffractive optical elements for beam-shaping tasks in solid-state laser systems,” in Conference on Lasers and Electro-Optics (CLEO/Europe) (Optical Society of America, Washington, D.C., Calif., 1998).

I. M. Barton, P. Blair, A. J. Waddie, K. Balluder, M. R. Taghizadeh, H. A. McInnes, T. H. Bett, “Beam-shaping diffractive optical elements for high-power solid-state laser systems,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437–443 (1999).
[Crossref]

Tanaka, M.

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21 (1989).
[Crossref]

Waddie, A. J.

I. M. Barton, P. Blair, A. J. Waddie, K. Balluder, M. R. Taghizadeh, H. A. McInnes, T. H. Bett, “Beam-shaping diffractive optical elements for high-power solid-state laser systems,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437–443 (1999).
[Crossref]

Wang, Z.

Yagi, S.

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21 (1989).
[Crossref]

Yariv, A.

A. Yariv, “Compensation for atmospheric degradation of optical beam transmission,” Opt. Commun. 21, 49–50 (1977).
[Crossref]

Yasui, K.

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21 (1989).
[Crossref]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
[Crossref]

J. Appl. Phys. (1)

K. Yasui, M. Tanaka, S. Yagi, “An unstable resonator with a phase-unifying output coupler to extract a large uniphase beam of a filled-in circular pattern,” J. Appl. Phys. 65, 17–21 (1989).
[Crossref]

Opt. Commun. (1)

A. Yariv, “Compensation for atmospheric degradation of optical beam transmission,” Opt. Commun. 21, 49–50 (1977).
[Crossref]

Opt. Lett. (2)

Other (5)

I. M. Barton, P. Blair, A. J. Waddie, K. Balluder, M. R. Taghizadeh, H. A. McInnes, T. H. Bett, “Beam-shaping diffractive optical elements for high-power solid-state laser systems,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437–443 (1999).
[Crossref]

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, T. H. Bett, “Diffractive optical elements for beam-shaping tasks in solid-state laser systems,” in Conference on Lasers and Electro-Optics (CLEO/Europe) (Optical Society of America, Washington, D.C., Calif., 1998).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

K. Ballüder, M. R. Taghizadeh, “Diffractive optical elements for beam-shaping tasks,” in Conference on Postgraduate Research in Electronics, Photonics and Related Fields (Institute of Physics, Manchester, 1999).

K. Ballüder, M. R. Taghizadeh, “Novel intracavity diffractive mode selecting element designs for high-power laser applications,” in Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1999).

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Figures (13)

Fig. 1
Fig. 1

Graph showing both the experimental data and the simulation results for the output of a linear resonator in which a transmissive MSE was used in conjunction with an existing mirror. Inasmuch as the MSE and the mirror could not be brought into direct contact, they had to be mounted separately to allow for adjustment, leading to a 2.5-cm gap that caused the distorted intensity distribution. The measurements are from a scan through the center of the beam profile.

Fig. 2
Fig. 2

Setup used for the simulations.

Fig. 3
Fig. 3

Beam intensity profile evolution. The pictures show the beam intensity profiles after n round trips through the resonator. The graphs for n = 0 show the input beam of the Gaussian intensity profile before it enters the resonator.

Fig. 4
Fig. 4

Other possible beam shapes generated from a circular Gaussian input beam after n = 10 round trips through the resonator.

Fig. 5
Fig. 5

Output of the actual ring resonator with the MSE that builds a mode from noise. The beam asymmetry is caused by asymmetry in the pump head.

Fig. 6
Fig. 6

Line scan through the center of the beam as shown in Fig. 5 and a comparison with the desired flat-top profile.

Fig. 7
Fig. 7

Output from the test setup showing a Gaussian profile beam after a single pass through the MSE.

Fig. 8
Fig. 8

Line scan through the image from Fig. 7, showing the beam after a single pass through the MSE. This test setup has no amplifier rod and does not show the asymmetry caused by the pump head as is visible in Figs. 5 and 6.

Fig. 9
Fig. 9

Beam observed with the second MSE designed to produce a ring-shaped output. This picture shows the beam after one pass through the MSE and features a central maximum surrounded by two rings.

Fig. 10
Fig. 10

Simulated beam produced by the second MSE after one pass. This picture relates to the experimental result from Fig. 9.

Fig. 11
Fig. 11

Beam distortion as observed when the MSE was misaligned horizontally. The dark shadow disappeared when the MSE was being moved back into the central position.

Fig. 12
Fig. 12

Simulated total energy output from the resonator with the inclusion of a simple model for gain saturation.

Fig. 13
Fig. 13

Simulated beam profiles at half-height and full pulse height of the pulse output from the resonator with the inclusion of gain saturation.

Tables (1)

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Table 1 Comparison of Total Intensity Carried in a Beam through a Given Circular Aperturea

Equations (2)

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Ix, y=exp-x2+y2ω02n.
gx, y=g01+Ix, y/Is.

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