Abstract

A Gaussian-reflectivity mirror resonator is proposed to achieve high-quality laser beams. To analyze the laser fields in a Gaussian-reflectivity mirror resonator, the diffraction integral equations of a Gaussian-reflectivity mirror resonator are converted to the finite-sum matrix equations. Consequently, according to the Fox–Li laser self-reproducing principle, we describe the mode fields and their losses in the proposed resonator as eigenvectors and eigenvalues of a transfer matrix. The conclusion can be drawn from the numerical results that, if a Gaussian-reflectivity mirror is adopted for a plano–concave resonator, a fundamental mode can easily be obtained from a transverse-flow CO2 laser and high-quality laser beams can be expected.

© 2006 Optical Society of America

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References

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  1. G. Bostanjoglo and N. Hodgson, "Unstable multi-rod Nd:YAG lasers with variable reflectivity mirrors," in High-Power Gas and Solid State Lasers, M. Bohrer, T. Letardi, D. Schuoecker, H. Weber, eds., Proc. SPIE 2206, 459-468 (1994).
    [CrossRef]
  2. G. Bostanjoglo, N. Hodgson, and H. Weber, "Design of variable reflectivity mirrors and unstable resonators for Nd:YAG lasers with high average power," J. Opt. A Pure Appl. Opt. 3, 497-506 (1994).
  3. C. Pare and P. A. Belanger, "Custom laser resonator using graded-phase mirrors," IEEE J. Quantum Electron. 28, 355-363 (1992).
    [CrossRef]
  4. R. Van Neste, C. Pare, R. L. Lachance, and P. A. Belanger, "Graded-phase mirror resonator with a super-Gaussian output in a CW-CO2 laser," IEEE J. Quantum Electron. 30, 2663-2670 (1994).
    [CrossRef]
  5. S. Yu and W. Gu, "Generation of elegant Hermite-Gaussian beams using the graded-phase mirror," J. Opt. A Pure Appl. Opt. 5, 460-463 (2003).
    [CrossRef]
  6. M. Gerber and T. Graf, "Generation of super-Gaussian modes in Nd:YAG lasers with graded-phase mirrors," in ALT'02 International Conference on Advanced Laser Technologies, H. P. Weber, V. I. Konov, T. Graf, eds., Proc. SPIE 5147, 13-20 (2003).
    [CrossRef]
  7. N. A. Generalov, N. G. Solov'yov, M. Yu Yakimov, and V. P. Zimakov, "High power industrial CO2 laser 'Lantan-5' with graded reflectivity mirror resonator," J. Opt. A Pure Appl. Opt. 3, 533-540 (1994).
  8. J. Li, J. F. Coutouly, Y. Lu, and J. Merlin, "Correction and quantitative analysis of the output signal of a laser beam analyzer (LBA)," Meas. Sci. Technol. 5, 120-126 (1994).
    [CrossRef]
  9. S. A. Collins, Jr., "Lens-system diffraction integral written in terms of matrix optics," J. Opt. Soc. Am. 60, 1168-1177 (1970).
    [CrossRef]
  10. B. Lü, Propagation and Control of High-Power Lasers (National Defense Industry Press, 1999), pp. 77-108.
  11. Z. Wei, R. Wang, and Z. Wang, "Numerical analysis of mode-fields of unstable ring resonators 90° beam rotation," Acta Opt. Sin. 15, 696-702 (1995).
  12. J. Li, J. Merlin, J. Chen, and Z. Fan, "Quick Approximate Calculation on the Transient Temperature Field of Laser Heat Treatment," Chin. J. Lasers B 6, 280-288 (1997).
  13. J. Li, X. Li, Z. Fan, Q. Chen, and J. Chen, "Processing time and the temperature field of laser quenching on material surfaces," in Laser Processing of Materials and Industrial Applications II, S. Deng and S. C. Wang, eds., Proc. SPIE 3550, 190-194 (1998).
    [CrossRef]
  14. J. Li, X. Li, J. Chen, Z. Fan, and Q. Chen, "Discussion for the semi-infinite medium approximation and the thermal diffusion velocity in laser heat treatment," Chin. J. Lasers B 8, 377-383 (1999).
  15. B. Lü, H. Ma, and B. Zhang, "Propagation properties of cosh-Gaussian beams," Opt. Commun. 164, 165-170 (1999).
    [CrossRef]
  16. A. Belafhal and M. Ibnchaikh, "Propagation properties of Hermite-cosh-Gaussian laser beams," Opt. Commun. 186, 269-272 (2000).
    [CrossRef]
  17. A. Piegari and G. Emiliani, "Laser mirrors with variable reflected intensity and uniform phase shift: design and process," Appl. Opt. 32, 5454-5461 (1993).
    [CrossRef] [PubMed]
  18. R. Medianu, M. L. Pascu, and I. Gutu, "Coating method for variable reflectivity mirrors to be used in high power CW CO2 lasers," J. Opt. A: Pure Appl. Opt. 3, 449-455 (1994).

2003 (2)

S. Yu and W. Gu, "Generation of elegant Hermite-Gaussian beams using the graded-phase mirror," J. Opt. A Pure Appl. Opt. 5, 460-463 (2003).
[CrossRef]

M. Gerber and T. Graf, "Generation of super-Gaussian modes in Nd:YAG lasers with graded-phase mirrors," in ALT'02 International Conference on Advanced Laser Technologies, H. P. Weber, V. I. Konov, T. Graf, eds., Proc. SPIE 5147, 13-20 (2003).
[CrossRef]

2000 (1)

A. Belafhal and M. Ibnchaikh, "Propagation properties of Hermite-cosh-Gaussian laser beams," Opt. Commun. 186, 269-272 (2000).
[CrossRef]

1999 (2)

J. Li, X. Li, J. Chen, Z. Fan, and Q. Chen, "Discussion for the semi-infinite medium approximation and the thermal diffusion velocity in laser heat treatment," Chin. J. Lasers B 8, 377-383 (1999).

B. Lü, H. Ma, and B. Zhang, "Propagation properties of cosh-Gaussian beams," Opt. Commun. 164, 165-170 (1999).
[CrossRef]

1998 (1)

J. Li, X. Li, Z. Fan, Q. Chen, and J. Chen, "Processing time and the temperature field of laser quenching on material surfaces," in Laser Processing of Materials and Industrial Applications II, S. Deng and S. C. Wang, eds., Proc. SPIE 3550, 190-194 (1998).
[CrossRef]

1997 (1)

J. Li, J. Merlin, J. Chen, and Z. Fan, "Quick Approximate Calculation on the Transient Temperature Field of Laser Heat Treatment," Chin. J. Lasers B 6, 280-288 (1997).

1995 (1)

Z. Wei, R. Wang, and Z. Wang, "Numerical analysis of mode-fields of unstable ring resonators 90° beam rotation," Acta Opt. Sin. 15, 696-702 (1995).

1994 (6)

R. Van Neste, C. Pare, R. L. Lachance, and P. A. Belanger, "Graded-phase mirror resonator with a super-Gaussian output in a CW-CO2 laser," IEEE J. Quantum Electron. 30, 2663-2670 (1994).
[CrossRef]

G. Bostanjoglo and N. Hodgson, "Unstable multi-rod Nd:YAG lasers with variable reflectivity mirrors," in High-Power Gas and Solid State Lasers, M. Bohrer, T. Letardi, D. Schuoecker, H. Weber, eds., Proc. SPIE 2206, 459-468 (1994).
[CrossRef]

G. Bostanjoglo, N. Hodgson, and H. Weber, "Design of variable reflectivity mirrors and unstable resonators for Nd:YAG lasers with high average power," J. Opt. A Pure Appl. Opt. 3, 497-506 (1994).

N. A. Generalov, N. G. Solov'yov, M. Yu Yakimov, and V. P. Zimakov, "High power industrial CO2 laser 'Lantan-5' with graded reflectivity mirror resonator," J. Opt. A Pure Appl. Opt. 3, 533-540 (1994).

J. Li, J. F. Coutouly, Y. Lu, and J. Merlin, "Correction and quantitative analysis of the output signal of a laser beam analyzer (LBA)," Meas. Sci. Technol. 5, 120-126 (1994).
[CrossRef]

R. Medianu, M. L. Pascu, and I. Gutu, "Coating method for variable reflectivity mirrors to be used in high power CW CO2 lasers," J. Opt. A: Pure Appl. Opt. 3, 449-455 (1994).

1993 (1)

1992 (1)

C. Pare and P. A. Belanger, "Custom laser resonator using graded-phase mirrors," IEEE J. Quantum Electron. 28, 355-363 (1992).
[CrossRef]

1970 (1)

Belafhal, A.

A. Belafhal and M. Ibnchaikh, "Propagation properties of Hermite-cosh-Gaussian laser beams," Opt. Commun. 186, 269-272 (2000).
[CrossRef]

Belanger, P. A.

R. Van Neste, C. Pare, R. L. Lachance, and P. A. Belanger, "Graded-phase mirror resonator with a super-Gaussian output in a CW-CO2 laser," IEEE J. Quantum Electron. 30, 2663-2670 (1994).
[CrossRef]

C. Pare and P. A. Belanger, "Custom laser resonator using graded-phase mirrors," IEEE J. Quantum Electron. 28, 355-363 (1992).
[CrossRef]

Bostanjoglo, G.

G. Bostanjoglo and N. Hodgson, "Unstable multi-rod Nd:YAG lasers with variable reflectivity mirrors," in High-Power Gas and Solid State Lasers, M. Bohrer, T. Letardi, D. Schuoecker, H. Weber, eds., Proc. SPIE 2206, 459-468 (1994).
[CrossRef]

G. Bostanjoglo, N. Hodgson, and H. Weber, "Design of variable reflectivity mirrors and unstable resonators for Nd:YAG lasers with high average power," J. Opt. A Pure Appl. Opt. 3, 497-506 (1994).

Chen, J.

J. Li, X. Li, J. Chen, Z. Fan, and Q. Chen, "Discussion for the semi-infinite medium approximation and the thermal diffusion velocity in laser heat treatment," Chin. J. Lasers B 8, 377-383 (1999).

J. Li, X. Li, Z. Fan, Q. Chen, and J. Chen, "Processing time and the temperature field of laser quenching on material surfaces," in Laser Processing of Materials and Industrial Applications II, S. Deng and S. C. Wang, eds., Proc. SPIE 3550, 190-194 (1998).
[CrossRef]

J. Li, J. Merlin, J. Chen, and Z. Fan, "Quick Approximate Calculation on the Transient Temperature Field of Laser Heat Treatment," Chin. J. Lasers B 6, 280-288 (1997).

Chen, Q.

J. Li, X. Li, J. Chen, Z. Fan, and Q. Chen, "Discussion for the semi-infinite medium approximation and the thermal diffusion velocity in laser heat treatment," Chin. J. Lasers B 8, 377-383 (1999).

J. Li, X. Li, Z. Fan, Q. Chen, and J. Chen, "Processing time and the temperature field of laser quenching on material surfaces," in Laser Processing of Materials and Industrial Applications II, S. Deng and S. C. Wang, eds., Proc. SPIE 3550, 190-194 (1998).
[CrossRef]

Collins, S. A.

Coutouly, J. F.

J. Li, J. F. Coutouly, Y. Lu, and J. Merlin, "Correction and quantitative analysis of the output signal of a laser beam analyzer (LBA)," Meas. Sci. Technol. 5, 120-126 (1994).
[CrossRef]

Emiliani, G.

Fan, Z.

J. Li, X. Li, J. Chen, Z. Fan, and Q. Chen, "Discussion for the semi-infinite medium approximation and the thermal diffusion velocity in laser heat treatment," Chin. J. Lasers B 8, 377-383 (1999).

J. Li, X. Li, Z. Fan, Q. Chen, and J. Chen, "Processing time and the temperature field of laser quenching on material surfaces," in Laser Processing of Materials and Industrial Applications II, S. Deng and S. C. Wang, eds., Proc. SPIE 3550, 190-194 (1998).
[CrossRef]

J. Li, J. Merlin, J. Chen, and Z. Fan, "Quick Approximate Calculation on the Transient Temperature Field of Laser Heat Treatment," Chin. J. Lasers B 6, 280-288 (1997).

Generalov, N. A.

N. A. Generalov, N. G. Solov'yov, M. Yu Yakimov, and V. P. Zimakov, "High power industrial CO2 laser 'Lantan-5' with graded reflectivity mirror resonator," J. Opt. A Pure Appl. Opt. 3, 533-540 (1994).

Gerber, M.

M. Gerber and T. Graf, "Generation of super-Gaussian modes in Nd:YAG lasers with graded-phase mirrors," in ALT'02 International Conference on Advanced Laser Technologies, H. P. Weber, V. I. Konov, T. Graf, eds., Proc. SPIE 5147, 13-20 (2003).
[CrossRef]

Graf, T.

M. Gerber and T. Graf, "Generation of super-Gaussian modes in Nd:YAG lasers with graded-phase mirrors," in ALT'02 International Conference on Advanced Laser Technologies, H. P. Weber, V. I. Konov, T. Graf, eds., Proc. SPIE 5147, 13-20 (2003).
[CrossRef]

Gu, W.

S. Yu and W. Gu, "Generation of elegant Hermite-Gaussian beams using the graded-phase mirror," J. Opt. A Pure Appl. Opt. 5, 460-463 (2003).
[CrossRef]

Gutu, I.

R. Medianu, M. L. Pascu, and I. Gutu, "Coating method for variable reflectivity mirrors to be used in high power CW CO2 lasers," J. Opt. A: Pure Appl. Opt. 3, 449-455 (1994).

Hodgson, N.

G. Bostanjoglo, N. Hodgson, and H. Weber, "Design of variable reflectivity mirrors and unstable resonators for Nd:YAG lasers with high average power," J. Opt. A Pure Appl. Opt. 3, 497-506 (1994).

G. Bostanjoglo and N. Hodgson, "Unstable multi-rod Nd:YAG lasers with variable reflectivity mirrors," in High-Power Gas and Solid State Lasers, M. Bohrer, T. Letardi, D. Schuoecker, H. Weber, eds., Proc. SPIE 2206, 459-468 (1994).
[CrossRef]

Ibnchaikh, M.

A. Belafhal and M. Ibnchaikh, "Propagation properties of Hermite-cosh-Gaussian laser beams," Opt. Commun. 186, 269-272 (2000).
[CrossRef]

Lachance, R. L.

R. Van Neste, C. Pare, R. L. Lachance, and P. A. Belanger, "Graded-phase mirror resonator with a super-Gaussian output in a CW-CO2 laser," IEEE J. Quantum Electron. 30, 2663-2670 (1994).
[CrossRef]

Li, J.

J. Li, X. Li, J. Chen, Z. Fan, and Q. Chen, "Discussion for the semi-infinite medium approximation and the thermal diffusion velocity in laser heat treatment," Chin. J. Lasers B 8, 377-383 (1999).

J. Li, X. Li, Z. Fan, Q. Chen, and J. Chen, "Processing time and the temperature field of laser quenching on material surfaces," in Laser Processing of Materials and Industrial Applications II, S. Deng and S. C. Wang, eds., Proc. SPIE 3550, 190-194 (1998).
[CrossRef]

J. Li, J. Merlin, J. Chen, and Z. Fan, "Quick Approximate Calculation on the Transient Temperature Field of Laser Heat Treatment," Chin. J. Lasers B 6, 280-288 (1997).

J. Li, J. F. Coutouly, Y. Lu, and J. Merlin, "Correction and quantitative analysis of the output signal of a laser beam analyzer (LBA)," Meas. Sci. Technol. 5, 120-126 (1994).
[CrossRef]

Li, X.

J. Li, X. Li, J. Chen, Z. Fan, and Q. Chen, "Discussion for the semi-infinite medium approximation and the thermal diffusion velocity in laser heat treatment," Chin. J. Lasers B 8, 377-383 (1999).

J. Li, X. Li, Z. Fan, Q. Chen, and J. Chen, "Processing time and the temperature field of laser quenching on material surfaces," in Laser Processing of Materials and Industrial Applications II, S. Deng and S. C. Wang, eds., Proc. SPIE 3550, 190-194 (1998).
[CrossRef]

Lu, Y.

J. Li, J. F. Coutouly, Y. Lu, and J. Merlin, "Correction and quantitative analysis of the output signal of a laser beam analyzer (LBA)," Meas. Sci. Technol. 5, 120-126 (1994).
[CrossRef]

Lü, B.

B. Lü, H. Ma, and B. Zhang, "Propagation properties of cosh-Gaussian beams," Opt. Commun. 164, 165-170 (1999).
[CrossRef]

B. Lü, Propagation and Control of High-Power Lasers (National Defense Industry Press, 1999), pp. 77-108.

Ma, H.

B. Lü, H. Ma, and B. Zhang, "Propagation properties of cosh-Gaussian beams," Opt. Commun. 164, 165-170 (1999).
[CrossRef]

Medianu, R.

R. Medianu, M. L. Pascu, and I. Gutu, "Coating method for variable reflectivity mirrors to be used in high power CW CO2 lasers," J. Opt. A: Pure Appl. Opt. 3, 449-455 (1994).

Merlin, J.

J. Li, J. Merlin, J. Chen, and Z. Fan, "Quick Approximate Calculation on the Transient Temperature Field of Laser Heat Treatment," Chin. J. Lasers B 6, 280-288 (1997).

J. Li, J. F. Coutouly, Y. Lu, and J. Merlin, "Correction and quantitative analysis of the output signal of a laser beam analyzer (LBA)," Meas. Sci. Technol. 5, 120-126 (1994).
[CrossRef]

Pare, C.

R. Van Neste, C. Pare, R. L. Lachance, and P. A. Belanger, "Graded-phase mirror resonator with a super-Gaussian output in a CW-CO2 laser," IEEE J. Quantum Electron. 30, 2663-2670 (1994).
[CrossRef]

C. Pare and P. A. Belanger, "Custom laser resonator using graded-phase mirrors," IEEE J. Quantum Electron. 28, 355-363 (1992).
[CrossRef]

Pascu, M. L.

R. Medianu, M. L. Pascu, and I. Gutu, "Coating method for variable reflectivity mirrors to be used in high power CW CO2 lasers," J. Opt. A: Pure Appl. Opt. 3, 449-455 (1994).

Piegari, A.

Solov'yov, N. G.

N. A. Generalov, N. G. Solov'yov, M. Yu Yakimov, and V. P. Zimakov, "High power industrial CO2 laser 'Lantan-5' with graded reflectivity mirror resonator," J. Opt. A Pure Appl. Opt. 3, 533-540 (1994).

Van Neste, R.

R. Van Neste, C. Pare, R. L. Lachance, and P. A. Belanger, "Graded-phase mirror resonator with a super-Gaussian output in a CW-CO2 laser," IEEE J. Quantum Electron. 30, 2663-2670 (1994).
[CrossRef]

Wang, R.

Z. Wei, R. Wang, and Z. Wang, "Numerical analysis of mode-fields of unstable ring resonators 90° beam rotation," Acta Opt. Sin. 15, 696-702 (1995).

Wang, Z.

Z. Wei, R. Wang, and Z. Wang, "Numerical analysis of mode-fields of unstable ring resonators 90° beam rotation," Acta Opt. Sin. 15, 696-702 (1995).

Weber, H.

G. Bostanjoglo, N. Hodgson, and H. Weber, "Design of variable reflectivity mirrors and unstable resonators for Nd:YAG lasers with high average power," J. Opt. A Pure Appl. Opt. 3, 497-506 (1994).

Wei, Z.

Z. Wei, R. Wang, and Z. Wang, "Numerical analysis of mode-fields of unstable ring resonators 90° beam rotation," Acta Opt. Sin. 15, 696-702 (1995).

Yakimov, M. Yu

N. A. Generalov, N. G. Solov'yov, M. Yu Yakimov, and V. P. Zimakov, "High power industrial CO2 laser 'Lantan-5' with graded reflectivity mirror resonator," J. Opt. A Pure Appl. Opt. 3, 533-540 (1994).

Yu, S.

S. Yu and W. Gu, "Generation of elegant Hermite-Gaussian beams using the graded-phase mirror," J. Opt. A Pure Appl. Opt. 5, 460-463 (2003).
[CrossRef]

Zhang, B.

B. Lü, H. Ma, and B. Zhang, "Propagation properties of cosh-Gaussian beams," Opt. Commun. 164, 165-170 (1999).
[CrossRef]

Zimakov, V. P.

N. A. Generalov, N. G. Solov'yov, M. Yu Yakimov, and V. P. Zimakov, "High power industrial CO2 laser 'Lantan-5' with graded reflectivity mirror resonator," J. Opt. A Pure Appl. Opt. 3, 533-540 (1994).

Acta Opt. Sin. (1)

Z. Wei, R. Wang, and Z. Wang, "Numerical analysis of mode-fields of unstable ring resonators 90° beam rotation," Acta Opt. Sin. 15, 696-702 (1995).

Appl. Opt. (1)

Chin. J. Lasers B (2)

J. Li, X. Li, J. Chen, Z. Fan, and Q. Chen, "Discussion for the semi-infinite medium approximation and the thermal diffusion velocity in laser heat treatment," Chin. J. Lasers B 8, 377-383 (1999).

J. Li, J. Merlin, J. Chen, and Z. Fan, "Quick Approximate Calculation on the Transient Temperature Field of Laser Heat Treatment," Chin. J. Lasers B 6, 280-288 (1997).

IEEE J. Quantum Electron. (2)

C. Pare and P. A. Belanger, "Custom laser resonator using graded-phase mirrors," IEEE J. Quantum Electron. 28, 355-363 (1992).
[CrossRef]

R. Van Neste, C. Pare, R. L. Lachance, and P. A. Belanger, "Graded-phase mirror resonator with a super-Gaussian output in a CW-CO2 laser," IEEE J. Quantum Electron. 30, 2663-2670 (1994).
[CrossRef]

J. Opt. A (3)

S. Yu and W. Gu, "Generation of elegant Hermite-Gaussian beams using the graded-phase mirror," J. Opt. A Pure Appl. Opt. 5, 460-463 (2003).
[CrossRef]

G. Bostanjoglo, N. Hodgson, and H. Weber, "Design of variable reflectivity mirrors and unstable resonators for Nd:YAG lasers with high average power," J. Opt. A Pure Appl. Opt. 3, 497-506 (1994).

N. A. Generalov, N. G. Solov'yov, M. Yu Yakimov, and V. P. Zimakov, "High power industrial CO2 laser 'Lantan-5' with graded reflectivity mirror resonator," J. Opt. A Pure Appl. Opt. 3, 533-540 (1994).

J. Opt. A: Pure Appl. Opt. (1)

R. Medianu, M. L. Pascu, and I. Gutu, "Coating method for variable reflectivity mirrors to be used in high power CW CO2 lasers," J. Opt. A: Pure Appl. Opt. 3, 449-455 (1994).

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

J. Li, J. F. Coutouly, Y. Lu, and J. Merlin, "Correction and quantitative analysis of the output signal of a laser beam analyzer (LBA)," Meas. Sci. Technol. 5, 120-126 (1994).
[CrossRef]

Opt. Commun. (2)

B. Lü, H. Ma, and B. Zhang, "Propagation properties of cosh-Gaussian beams," Opt. Commun. 164, 165-170 (1999).
[CrossRef]

A. Belafhal and M. Ibnchaikh, "Propagation properties of Hermite-cosh-Gaussian laser beams," Opt. Commun. 186, 269-272 (2000).
[CrossRef]

Proc. SPIE (3)

J. Li, X. Li, Z. Fan, Q. Chen, and J. Chen, "Processing time and the temperature field of laser quenching on material surfaces," in Laser Processing of Materials and Industrial Applications II, S. Deng and S. C. Wang, eds., Proc. SPIE 3550, 190-194 (1998).
[CrossRef]

G. Bostanjoglo and N. Hodgson, "Unstable multi-rod Nd:YAG lasers with variable reflectivity mirrors," in High-Power Gas and Solid State Lasers, M. Bohrer, T. Letardi, D. Schuoecker, H. Weber, eds., Proc. SPIE 2206, 459-468 (1994).
[CrossRef]

M. Gerber and T. Graf, "Generation of super-Gaussian modes in Nd:YAG lasers with graded-phase mirrors," in ALT'02 International Conference on Advanced Laser Technologies, H. P. Weber, V. I. Konov, T. Graf, eds., Proc. SPIE 5147, 13-20 (2003).
[CrossRef]

Other (1)

B. Lü, Propagation and Control of High-Power Lasers (National Defense Industry Press, 1999), pp. 77-108.

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Figures (4)

Fig. 1
Fig. 1

Laser intensity profiles of (a) HJ-3 1.5 kW transverse-flow CO 2 laser and (b) HGL-84 5 kW transverse-flow CO 2 laser. Left, measure results; right, processed results.

Fig. 2
Fig. 2

Scheme of a Gaussian-reflectivity mirror resonator.

Fig. 3
Fig. 3

Field distributions of low-loss modes in the custom plano-concave resonator: (a) E 1 ( r 1 , φ 1 ) 00 , (b) E 1 ( r 1 , φ 1 ) 01 , (c) E 1 ( r 1 , φ 1 ) 10 .

Fig. 4
Fig. 4

Field distributions of low-loss modes in the Gaussian-reflectivity mirror resonator: (a) E 1 ( r 1 , φ 1 ) 00 , (b) E 1 ( r 1 , φ 1 ) 01 , (c) E 1 ( r 1 , φ 1 ) 10 .

Tables (1)

Tables Icon

Table 1 Eigenvalues of Low Loss Modes

Equations (18)

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R ( r ) = R 0 exp [ 2 ( r w ) 2 ] ,
r ( r ) = r 0 exp [ K ( r a ) 2 ] ,
T 1 = [ A 1 B 1 C 1 D 1 ] = [ 1 L 2 / R 1 2 L / R ] .
T 2 = [ A 2 B 2 C 2 D 2 ] = [ 1 L 0 1 ] .
E 2 ( r 2 , φ 2 ) = i k exp ( i k L ) 2 π B S E 1 ( r 1 , φ 1 ) exp { i k 2 B [ A r 1 2 + D r 2 2 2 r 1 r 2 cos ( φ 1 φ 2 ) ] } r 1 d r 1 d φ 1 ,
E 2 ( r 2 , φ 2 ) = i k exp ( i k L ) 2 π B 1 S 1 E 1 ( r 1 , φ 1 ) exp { i k 2 B 1 [ A 1 r 1 2 + D 1 r 2 2 2 r 1 r 2 cos ( φ 1 φ 2 ) ] } r 1 d r 1 d φ 1 .
E 3 ( r 1 , φ 1 ) = i k r ( r 1 ) exp ( i k L ) 2 π B 2 S 2 E 2 ( r 2 , φ 2 ) exp { i k 2 B 2 [ A 2 r 2 2 + D 2 r 1 2 2 r 1 r 2 cos ( φ 1 φ 2 ) ] } r 2 d r 2 d φ 2 .
E 1 ( r 1 , φ 1 ) = E 1 ( r 1 ) e i n φ 1 ,
E 2 ( r 2 , φ 2 ) = E 2 ( r 2 ) e i n φ 2 ,
E 3 ( r 1 , φ 1 ) = E 3 ( r 1 ) e i n φ 1 ,
E 2 ( r 2 ) = ( i ) n + 1 k exp ( i k L ) B 1 0 a E 1 ( r 1 ) J n ( k r 1 r 2 B 1 ) exp [ i k 2 B 1 ( A 1 r 1 2 + D 1 r 2 2 ) ] r 1 d r 1 ,
E 3 ( r 1 ) = ( i ) n + 1 k r ( r 1 ) exp ( i k L ) B 2 0 a E 2 ( r 2 ) J n ( k r 1 r 2 B 2 ) exp [ i k 2 B 2 ( A 2 r 2 2 + D 2 r 1 2 ) ] r 2 d r 2 ,
E 2 , m = n = 1 M X m n E 1 , n ,
E 3 , m = n = 1 M Y m n E 2 , n ,
X m n = ( i ) n n + 1 k n a 2 exp ( i k L ) B 1 M 2 J n n ( k m n a 2 B 1 M 2 ) exp [ i a 2 π B 1 λ M 2 ( A 1 n 2 + D 1 m 2 ) ] ,
Y m n = ( i ) n n + 1 k n a 2 r 0 exp ( i k L ) B 2 M 2 exp [ K ( n / M ) 2 ] J n n ( k m n a 2 B 2 M 2 ) exp [ i a 2 π B 2 λ M 2 ( A 2 n 2 + D 2 m 2 ) ] ,
E 3 = γ E 1 ,
γ E 1 = Z · E 1 = ( Y · X ) · E 1 .

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