Abstract

Hollow-sapphire and metal–dielectric-coated hollow-glass waveguides have been used to deliver CO2 laser power for industrial laser applications. The transmission, bending loss, and output-beam properties of these waveguides are described. The bore sizes of the hollow-sapphire waveguides were 1070 and 790 μm, and the hollow-glass waveguide had a bore of 700 μm. The waveguides ranged in length from 1.1 to 1.5 m. The sapphire waveguides were bent to 90°, and the hollow-glass waveguides were bent into a full 360° loop. We delivered a maximum of 1.8 kW through the 1070-μm-bore sapphire waveguide and 1.0 kW through the hollow-glass waveguide. All the hollow waveguides incorporated a water jacket to prevent overheating.

© 1996 Optical Society of America

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References

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  1. J. A. Harrington, ed., Selected Papers on Infrared Fiber Optics, Vol. MS09 of the SPIE Milestone Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990).
  2. N. Croitoru, J. Dror, I. Gannot, “Characterization of hollow fibers for the transmission of infrared radiation,” Appl. Opt. 29, 1805–1809 (1990).
    [CrossRef] [PubMed]
  3. K. D. Laakmann, M. Levy, “Hollow lightpipe and lightpipe tip using a low refractive index inner layer” U.S. Patent5,005,944 (9April1991).
  4. J. A. Harrington, C. C. Gregory, “Hollow sapphire fibers for the delivery of CO2 laser energy,” Opt. Lett. 15, 541–543 (1990).
    [CrossRef] [PubMed]
  5. M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
    [CrossRef]
  6. A. Hongo, K. Morosawa, T. Shiota, Y. Matsuura, M. Miyagi, “Transmission characteristics of germanium thin-film-coated metlalic hollow waveguides for high-powered CO2 laser light,” IEEE J. Quantum Electron. 26, 1510–1515 (1990).
    [CrossRef]
  7. A. Hongo, K. Morosawa, T. Shiota, K. Suzuki, S. Iwasaki, “Transmission of 1 kW-class CO2 laser light through cicular hollow waveguides for material processing,” Appl. Phys. Lett. 58, 1582–1584 (1991).
    [CrossRef]
  8. A. Hongo, K. Morosawa, K. Matsumoto, T. Shiota, T. Hashimoto, “Transmission of kilowatt-class CO2 laser light through dielectric-coated metallic hollow waveguides for material procesing,” Appl. Opt. 31, 5114–5120 (1992).
    [CrossRef] [PubMed]
  9. T. Matsumoto, Y. Seki, K. Yasuda, “Evaluation of the transmission characteristics of CO2 laser beam in a hollow waveguide,” in Proceedings of International Conference on Laser Advanced Materials Processing (High Temperature Society of Japan, Osaka, Japan, 1992), pp. 225–229.
  10. R. Nubling, C. C. Gregory, J. A. Harrington, “Hollow sapphire fiber system for high-power CO2 lasers,” in Lasers as Tools for Manufacturing, L. R. Migliore, R. W. Walker, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2062, 69–76 (1994).
  11. C. C. Gregory, J. A. Harrington, “Attenuation, modal, polarization properties of n < 1, hollow dielectric waveguides,” Appl. Opt. 32, 5302–5309 (1993).
    [CrossRef] [PubMed]
  12. T. Abel, J. Hirsch, J. A. Harrington, “Hollow glass waveguides for broadband infrared transmission,” Opt. Lett. 19, 1034–1036 (1994).
    [CrossRef] [PubMed]
  13. Y. Matsuura, T. Abel, J. Hirsch, J. A. Harrington, “Small-bore hollow waveguide for delivery of near singlemode IR laser radiation,” Electron. Lett. 30, 1688–1690 (1994).
    [CrossRef]
  14. E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).
  15. M. Miyagi, S. Karasawa, “Waveguide losses in sharply bent circular hollow waveguides,” Appl. Opt. 29, 367–370 (1990).
    [CrossRef] [PubMed]
  16. Y. Hiratani, M. Miyagi, S. Nishida, “Power handling capability of dielectric-coated, metallic, hollow waveguides for CO2 laser light,” Opt. Laser Technol. 17, 135–138 (1985).
    [CrossRef]
  17. S. Karasawa, M. Miyagi, S. Nishida, “Temperature distribution along oversized hollow-core waveguides for infrared radiation,” Appl. Opt. 26, 4581–4586 (1987).
    [CrossRef] [PubMed]
  18. A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increase in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
    [CrossRef]
  19. C. C. Gregory, “Hollow dielectric waveguides for carbon dioxide laser power delivery,” Ph.D. dissertation (Rutgers University, Piscataway N.J., 1992).
  20. A. Chester, R. Abrams, “Mode losses in hollow-waveguide lasers,” Appl. Phys. Lett. 21, 576–578 (1972).
    [CrossRef]
  21. R. Jenkins, R. Devereux, “Effect of field regeneration on the TEM00 transmission characteristics of a circular-section waveguide,” Appl. Opt. 31, 5086–5091 (1992).
    [CrossRef] [PubMed]

1994

Y. Matsuura, T. Abel, J. Hirsch, J. A. Harrington, “Small-bore hollow waveguide for delivery of near singlemode IR laser radiation,” Electron. Lett. 30, 1688–1690 (1994).
[CrossRef]

T. Abel, J. Hirsch, J. A. Harrington, “Hollow glass waveguides for broadband infrared transmission,” Opt. Lett. 19, 1034–1036 (1994).
[CrossRef] [PubMed]

1993

1992

1991

A. Hongo, K. Morosawa, T. Shiota, K. Suzuki, S. Iwasaki, “Transmission of 1 kW-class CO2 laser light through cicular hollow waveguides for material processing,” Appl. Phys. Lett. 58, 1582–1584 (1991).
[CrossRef]

1990

1987

S. Karasawa, M. Miyagi, S. Nishida, “Temperature distribution along oversized hollow-core waveguides for infrared radiation,” Appl. Opt. 26, 4581–4586 (1987).
[CrossRef] [PubMed]

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increase in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

1985

Y. Hiratani, M. Miyagi, S. Nishida, “Power handling capability of dielectric-coated, metallic, hollow waveguides for CO2 laser light,” Opt. Laser Technol. 17, 135–138 (1985).
[CrossRef]

1984

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

1972

A. Chester, R. Abrams, “Mode losses in hollow-waveguide lasers,” Appl. Phys. Lett. 21, 576–578 (1972).
[CrossRef]

1964

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).

Abel, T.

T. Abel, J. Hirsch, J. A. Harrington, “Hollow glass waveguides for broadband infrared transmission,” Opt. Lett. 19, 1034–1036 (1994).
[CrossRef] [PubMed]

Y. Matsuura, T. Abel, J. Hirsch, J. A. Harrington, “Small-bore hollow waveguide for delivery of near singlemode IR laser radiation,” Electron. Lett. 30, 1688–1690 (1994).
[CrossRef]

Abrams, R.

A. Chester, R. Abrams, “Mode losses in hollow-waveguide lasers,” Appl. Phys. Lett. 21, 576–578 (1972).
[CrossRef]

Chester, A.

A. Chester, R. Abrams, “Mode losses in hollow-waveguide lasers,” Appl. Phys. Lett. 21, 576–578 (1972).
[CrossRef]

Croitoru, N.

Devereux, R.

Dror, J.

Gannot, I.

Gregory, C. C.

C. C. Gregory, J. A. Harrington, “Attenuation, modal, polarization properties of n < 1, hollow dielectric waveguides,” Appl. Opt. 32, 5302–5309 (1993).
[CrossRef] [PubMed]

J. A. Harrington, C. C. Gregory, “Hollow sapphire fibers for the delivery of CO2 laser energy,” Opt. Lett. 15, 541–543 (1990).
[CrossRef] [PubMed]

R. Nubling, C. C. Gregory, J. A. Harrington, “Hollow sapphire fiber system for high-power CO2 lasers,” in Lasers as Tools for Manufacturing, L. R. Migliore, R. W. Walker, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2062, 69–76 (1994).

C. C. Gregory, “Hollow dielectric waveguides for carbon dioxide laser power delivery,” Ph.D. dissertation (Rutgers University, Piscataway N.J., 1992).

Harrington, J. A.

Y. Matsuura, T. Abel, J. Hirsch, J. A. Harrington, “Small-bore hollow waveguide for delivery of near singlemode IR laser radiation,” Electron. Lett. 30, 1688–1690 (1994).
[CrossRef]

T. Abel, J. Hirsch, J. A. Harrington, “Hollow glass waveguides for broadband infrared transmission,” Opt. Lett. 19, 1034–1036 (1994).
[CrossRef] [PubMed]

C. C. Gregory, J. A. Harrington, “Attenuation, modal, polarization properties of n < 1, hollow dielectric waveguides,” Appl. Opt. 32, 5302–5309 (1993).
[CrossRef] [PubMed]

J. A. Harrington, C. C. Gregory, “Hollow sapphire fibers for the delivery of CO2 laser energy,” Opt. Lett. 15, 541–543 (1990).
[CrossRef] [PubMed]

R. Nubling, C. C. Gregory, J. A. Harrington, “Hollow sapphire fiber system for high-power CO2 lasers,” in Lasers as Tools for Manufacturing, L. R. Migliore, R. W. Walker, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2062, 69–76 (1994).

Hashimoto, T.

Hiratani, Y.

Y. Hiratani, M. Miyagi, S. Nishida, “Power handling capability of dielectric-coated, metallic, hollow waveguides for CO2 laser light,” Opt. Laser Technol. 17, 135–138 (1985).
[CrossRef]

Hirsch, J.

Y. Matsuura, T. Abel, J. Hirsch, J. A. Harrington, “Small-bore hollow waveguide for delivery of near singlemode IR laser radiation,” Electron. Lett. 30, 1688–1690 (1994).
[CrossRef]

T. Abel, J. Hirsch, J. A. Harrington, “Hollow glass waveguides for broadband infrared transmission,” Opt. Lett. 19, 1034–1036 (1994).
[CrossRef] [PubMed]

Hongo, A.

A. Hongo, K. Morosawa, K. Matsumoto, T. Shiota, T. Hashimoto, “Transmission of kilowatt-class CO2 laser light through dielectric-coated metallic hollow waveguides for material procesing,” Appl. Opt. 31, 5114–5120 (1992).
[CrossRef] [PubMed]

A. Hongo, K. Morosawa, T. Shiota, K. Suzuki, S. Iwasaki, “Transmission of 1 kW-class CO2 laser light through cicular hollow waveguides for material processing,” Appl. Phys. Lett. 58, 1582–1584 (1991).
[CrossRef]

A. Hongo, K. Morosawa, T. Shiota, Y. Matsuura, M. Miyagi, “Transmission characteristics of germanium thin-film-coated metlalic hollow waveguides for high-powered CO2 laser light,” IEEE J. Quantum Electron. 26, 1510–1515 (1990).
[CrossRef]

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increase in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

Iwasaki, S.

A. Hongo, K. Morosawa, T. Shiota, K. Suzuki, S. Iwasaki, “Transmission of 1 kW-class CO2 laser light through cicular hollow waveguides for material processing,” Appl. Phys. Lett. 58, 1582–1584 (1991).
[CrossRef]

Jenkins, R.

Karasawa, S.

Kawakami, S.

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

Laakmann, K. D.

K. D. Laakmann, M. Levy, “Hollow lightpipe and lightpipe tip using a low refractive index inner layer” U.S. Patent5,005,944 (9April1991).

Levy, M.

K. D. Laakmann, M. Levy, “Hollow lightpipe and lightpipe tip using a low refractive index inner layer” U.S. Patent5,005,944 (9April1991).

Marcatili, E. A. J.

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).

Matsumoto, K.

Matsumoto, T.

T. Matsumoto, Y. Seki, K. Yasuda, “Evaluation of the transmission characteristics of CO2 laser beam in a hollow waveguide,” in Proceedings of International Conference on Laser Advanced Materials Processing (High Temperature Society of Japan, Osaka, Japan, 1992), pp. 225–229.

Matsuura, Y.

Y. Matsuura, T. Abel, J. Hirsch, J. A. Harrington, “Small-bore hollow waveguide for delivery of near singlemode IR laser radiation,” Electron. Lett. 30, 1688–1690 (1994).
[CrossRef]

A. Hongo, K. Morosawa, T. Shiota, Y. Matsuura, M. Miyagi, “Transmission characteristics of germanium thin-film-coated metlalic hollow waveguides for high-powered CO2 laser light,” IEEE J. Quantum Electron. 26, 1510–1515 (1990).
[CrossRef]

Miyagi, M.

A. Hongo, K. Morosawa, T. Shiota, Y. Matsuura, M. Miyagi, “Transmission characteristics of germanium thin-film-coated metlalic hollow waveguides for high-powered CO2 laser light,” IEEE J. Quantum Electron. 26, 1510–1515 (1990).
[CrossRef]

M. Miyagi, S. Karasawa, “Waveguide losses in sharply bent circular hollow waveguides,” Appl. Opt. 29, 367–370 (1990).
[CrossRef] [PubMed]

S. Karasawa, M. Miyagi, S. Nishida, “Temperature distribution along oversized hollow-core waveguides for infrared radiation,” Appl. Opt. 26, 4581–4586 (1987).
[CrossRef] [PubMed]

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increase in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

Y. Hiratani, M. Miyagi, S. Nishida, “Power handling capability of dielectric-coated, metallic, hollow waveguides for CO2 laser light,” Opt. Laser Technol. 17, 135–138 (1985).
[CrossRef]

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

Morosawa, K.

A. Hongo, K. Morosawa, K. Matsumoto, T. Shiota, T. Hashimoto, “Transmission of kilowatt-class CO2 laser light through dielectric-coated metallic hollow waveguides for material procesing,” Appl. Opt. 31, 5114–5120 (1992).
[CrossRef] [PubMed]

A. Hongo, K. Morosawa, T. Shiota, K. Suzuki, S. Iwasaki, “Transmission of 1 kW-class CO2 laser light through cicular hollow waveguides for material processing,” Appl. Phys. Lett. 58, 1582–1584 (1991).
[CrossRef]

A. Hongo, K. Morosawa, T. Shiota, Y. Matsuura, M. Miyagi, “Transmission characteristics of germanium thin-film-coated metlalic hollow waveguides for high-powered CO2 laser light,” IEEE J. Quantum Electron. 26, 1510–1515 (1990).
[CrossRef]

Nishida, S.

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increase in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

S. Karasawa, M. Miyagi, S. Nishida, “Temperature distribution along oversized hollow-core waveguides for infrared radiation,” Appl. Opt. 26, 4581–4586 (1987).
[CrossRef] [PubMed]

Y. Hiratani, M. Miyagi, S. Nishida, “Power handling capability of dielectric-coated, metallic, hollow waveguides for CO2 laser light,” Opt. Laser Technol. 17, 135–138 (1985).
[CrossRef]

Nubling, R.

R. Nubling, C. C. Gregory, J. A. Harrington, “Hollow sapphire fiber system for high-power CO2 lasers,” in Lasers as Tools for Manufacturing, L. R. Migliore, R. W. Walker, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2062, 69–76 (1994).

Sakamoto, K.

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increase in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

Schmeltzer, R. A.

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).

Seki, Y.

T. Matsumoto, Y. Seki, K. Yasuda, “Evaluation of the transmission characteristics of CO2 laser beam in a hollow waveguide,” in Proceedings of International Conference on Laser Advanced Materials Processing (High Temperature Society of Japan, Osaka, Japan, 1992), pp. 225–229.

Shiota, T.

A. Hongo, K. Morosawa, K. Matsumoto, T. Shiota, T. Hashimoto, “Transmission of kilowatt-class CO2 laser light through dielectric-coated metallic hollow waveguides for material procesing,” Appl. Opt. 31, 5114–5120 (1992).
[CrossRef] [PubMed]

A. Hongo, K. Morosawa, T. Shiota, K. Suzuki, S. Iwasaki, “Transmission of 1 kW-class CO2 laser light through cicular hollow waveguides for material processing,” Appl. Phys. Lett. 58, 1582–1584 (1991).
[CrossRef]

A. Hongo, K. Morosawa, T. Shiota, Y. Matsuura, M. Miyagi, “Transmission characteristics of germanium thin-film-coated metlalic hollow waveguides for high-powered CO2 laser light,” IEEE J. Quantum Electron. 26, 1510–1515 (1990).
[CrossRef]

Suzuki, K.

A. Hongo, K. Morosawa, T. Shiota, K. Suzuki, S. Iwasaki, “Transmission of 1 kW-class CO2 laser light through cicular hollow waveguides for material processing,” Appl. Phys. Lett. 58, 1582–1584 (1991).
[CrossRef]

Yasuda, K.

T. Matsumoto, Y. Seki, K. Yasuda, “Evaluation of the transmission characteristics of CO2 laser beam in a hollow waveguide,” in Proceedings of International Conference on Laser Advanced Materials Processing (High Temperature Society of Japan, Osaka, Japan, 1992), pp. 225–229.

Appl. Opt.

Appl. Phys. Lett.

A. Chester, R. Abrams, “Mode losses in hollow-waveguide lasers,” Appl. Phys. Lett. 21, 576–578 (1972).
[CrossRef]

A. Hongo, K. Morosawa, T. Shiota, K. Suzuki, S. Iwasaki, “Transmission of 1 kW-class CO2 laser light through cicular hollow waveguides for material processing,” Appl. Phys. Lett. 58, 1582–1584 (1991).
[CrossRef]

Bell Syst. Tech. J.

E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964).

Electron. Lett.

Y. Matsuura, T. Abel, J. Hirsch, J. A. Harrington, “Small-bore hollow waveguide for delivery of near singlemode IR laser radiation,” Electron. Lett. 30, 1688–1690 (1994).
[CrossRef]

IEEE J. Quantum Electron.

A. Hongo, K. Morosawa, T. Shiota, Y. Matsuura, M. Miyagi, “Transmission characteristics of germanium thin-film-coated metlalic hollow waveguides for high-powered CO2 laser light,” IEEE J. Quantum Electron. 26, 1510–1515 (1990).
[CrossRef]

J. Lightwave Technol.

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

Opt. Laser Technol.

A. Hongo, M. Miyagi, K. Sakamoto, S. Karasawa, S. Nishida, “Excitation dependent losses and temperature increase in various hollow waveguides at 10.6 μm,” Opt. Laser Technol. 19, 214–216 (1987).
[CrossRef]

Y. Hiratani, M. Miyagi, S. Nishida, “Power handling capability of dielectric-coated, metallic, hollow waveguides for CO2 laser light,” Opt. Laser Technol. 17, 135–138 (1985).
[CrossRef]

Opt. Lett.

Other

J. A. Harrington, ed., Selected Papers on Infrared Fiber Optics, Vol. MS09 of the SPIE Milestone Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1990).

K. D. Laakmann, M. Levy, “Hollow lightpipe and lightpipe tip using a low refractive index inner layer” U.S. Patent5,005,944 (9April1991).

T. Matsumoto, Y. Seki, K. Yasuda, “Evaluation of the transmission characteristics of CO2 laser beam in a hollow waveguide,” in Proceedings of International Conference on Laser Advanced Materials Processing (High Temperature Society of Japan, Osaka, Japan, 1992), pp. 225–229.

R. Nubling, C. C. Gregory, J. A. Harrington, “Hollow sapphire fiber system for high-power CO2 lasers,” in Lasers as Tools for Manufacturing, L. R. Migliore, R. W. Walker, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2062, 69–76 (1994).

C. C. Gregory, “Hollow dielectric waveguides for carbon dioxide laser power delivery,” Ph.D. dissertation (Rutgers University, Piscataway N.J., 1992).

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Figures (14)

Fig. 1
Fig. 1

Theoretical (solid curves) and measured attenuation in straight hollow-glass and hollow-sapphire waveguides at 10.6 μm.

Fig. 2
Fig. 2

Diagram showing power lost, P(z) − P(z + Δz), and heat flow from the outer surface, Q 2z), and inner surface, Q 1z), in a waveguide section of length Δz.

Fig. 3
Fig. 3

Calculated temperature of the inner wall at the input end of a 700-μm-bore hollow-glass waveguide (solid line), a 790-μm-bore hollow-sapphire waveguide (dashed line), and a 1070-μm-bore hollow-sapphire waveguide (dotted line) for an attenuation of 3 dB/m. Calculations were based on forced convective water cooling with a water temperature of 18 °C.

Fig. 4
Fig. 4

Structure of hollow-waveguide cooling jacket and Cu input fitting.

Fig. 5
Fig. 5

Beam patterns of (a) 1500-W laser, (b) 2000-W laser, and (c) 3000-W laser taken from burns made in acrylic blocks.

Fig. 6
Fig. 6

Transmission of a straight, 790-μm-bore, 1.2-m-long hollow-sapphire waveguide on the 1500-W laser (■) and the 2000-W laser (▲).

Fig. 7
Fig. 7

Transmission of a straight, 1070-μm-bore, 1.5-m-long hollow-sapphire waveguide on the 1500-W laser.

Fig. 8
Fig. 8

Transmission of a straight, 1070-μm-bore, 1.2-m-long hollow-sapphire waveguide on the 2000-W laser (▲) and the 3000-W laser (□).

Fig. 9
Fig. 9

Bending loss of a 1070-μm-bore, 1.2-m-long hollow-sapphire waveguide a 3000-W laser operating at 500 W.

Fig. 10
Fig. 10

Output-beam profiles on the 1500-W laser of (a) 790-μm-bore hollow-sapphire and (b) 1070-μm-bore hollow-sapphire waveguides and on the 2000-W laser of (c) 1070-μm-bore hollow-sapphire waveguide.

Fig. 11
Fig. 11

Transmission of a straight, 700-μm-bore, 1.54-m-long hollow-glass waveguide on the 1500-W laser. The maximum output power was 1010 W.

Fig. 12
Fig. 12

Transmission of straight (■) and bent 360° (▲) 700-μm-bore, 1.54-m-long hollow-glass waveguides on the 1500 W laser.

Fig. 13
Fig. 13

Transmission of straight (■), bent 90° (▲), and bent 180° (●) 700-μm-bore, 1.54-m-long hollow-glass waveguides.

Fig. 14
Fig. 14

Output-beam profiles on the 1500-W laser of a 700-μm-bore, 1.54-m-long hollow-glass waveguide (a) straight and (b) bent 360°.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

α 1 a 3 , α 1 R ,
Q 1 = T i T 1 ( 1 2 π h 1 r i Δ z ) ,
Q 2 = T i T 2 ln ( r o / r i ) 2 π k Δ z + 1 2 π h 2 r o Δ z ,
P z = P 0 exp ( α z ) ,
P L ( Δ z ) = P 0 exp ( α z ) P 0 exp [ α ( z + Δ z ) ] ,
P L ( Δ z ) = P 0 exp ( α z ) [ 1 exp ( α Δ z ) ] .
P 0 2 π exp ( α z ) lim Δ z 0 [ 1 exp ( α Δ z ) ] Δ z = T i T 1 R 1 + T i T 2 R + R 2 ,
α 2 π P 0 exp ( α z ) = T i T 1 R 1 + T i T 2 R + R 2 ,
R 1 = 1 h 1 r i , R = ln ( r o r i ) k , R 2 = 1 h 2 r o ,
Q = T i T o R = T i T 2 R + R 2 .
T i = R 1 ( R + R 2 ) R 1 + R + R 2 × [ 0.23 α 2 π P 0 exp ( α z 434 ) + T 2 R + R 2 + T 1 R 1 ] ,
T o = R 1 R 2 R 1 + R + R 2 { 0.23 α 2 π P 0 exp ( α z 434 ) + [ 1 + R ( R 1 + R + R 2 ) R 1 R 2 ] T 2 R + R 2 + T 1 R 1 } ,
d = 1.27 λ f D M 2 ,

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