Abstract

The theoretical and experimental investigation of field properties of annular waveguide lasers with a Fabry–Perot resonator is presented. Oscillation with high azimuthal mode order leads to an annular intensity distribution in the far field with almost linear dependence of the annular diameter on the mode order. Low-order fields form a distinct focal spot in the far field. A laser device with a discharge area of 6-cm diameter and 53-cm length yields an output power of 600 W.

© 1997 Optical Society of America

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  1. R. Nowack, H. Opower, K. Wessel, H. Kruger, W. Haas, N. Wenzel, “Diffusion-cooled compact CO2 high power laser,” Laser Optoelectron. 23(3), 68–81 (1991), in German.
  2. P. Jackson, H. Baker, D. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
    [CrossRef]
  3. C. Shackleton, K. Abramski, H. Baker, D. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
    [CrossRef]
  4. V. Svich, V. Tkachenko, A. Topkov, “Waveguide coaxial rf-excited CO2 laser,” Sov. J. Quantum Electron. 20(6) , 612–614 (1990).
    [CrossRef]
  5. D. Ehrlichmann, U. Habich, H. Plum, “High-power CO2 laser with coaxial waveguide and diffusion cooling,” IEEE J. Quantum Electron. 29, 2211–2219 (1993).
    [CrossRef]
  6. P. Burlamati, R. Pratesi, “High-efficiency coaxial waveguide dye laser with internal excitation,” Appl. Phys. Lett. 23, 475–476 (1973).
    [CrossRef]
  7. N. Hodgson, Q. Lu, S. Dong, B. Eppich, U. Wittrock, “High power solid state lasers in rod-, slab- and tube geometry,” Laser + Optoelectron. 23(3), 82–92, (1991), in German.
  8. J. Xin, D. Hall, “Multipass coaxial radiofrequency discharge CO2 laser,” Opt. Commun. 58, 420–422 (1986).
    [CrossRef]
  9. D. Ehrlichmann, U. Habich, H. Plum, P. Loosen, G. Herziger, “Azimuthally unstable resonators for high-power CO2 lasers with annular gain media,” IEEE J. Quantum Electron. 30, 1441–1447 (1994).
    [CrossRef]
  10. V. Pruzhanovskii, “Asymmetric modes in metal coaxial optical waveguides,” Sov. Phys. Tech. Phys. 15(6) , 897–900 (1970).
  11. A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an RF-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
    [CrossRef]
  12. R. Abrams, A. Chester, “Resonator theory for hollow waveguide lasers,” Appl. Opt. 13, 2117–2125 (1974).
    [CrossRef] [PubMed]

1994 (2)

D. Ehrlichmann, U. Habich, H. Plum, P. Loosen, G. Herziger, “Azimuthally unstable resonators for high-power CO2 lasers with annular gain media,” IEEE J. Quantum Electron. 30, 1441–1447 (1994).
[CrossRef]

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an RF-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

1993 (1)

D. Ehrlichmann, U. Habich, H. Plum, “High-power CO2 laser with coaxial waveguide and diffusion cooling,” IEEE J. Quantum Electron. 29, 2211–2219 (1993).
[CrossRef]

1992 (1)

C. Shackleton, K. Abramski, H. Baker, D. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

1991 (2)

R. Nowack, H. Opower, K. Wessel, H. Kruger, W. Haas, N. Wenzel, “Diffusion-cooled compact CO2 high power laser,” Laser Optoelectron. 23(3), 68–81 (1991), in German.

N. Hodgson, Q. Lu, S. Dong, B. Eppich, U. Wittrock, “High power solid state lasers in rod-, slab- and tube geometry,” Laser + Optoelectron. 23(3), 82–92, (1991), in German.

1990 (1)

V. Svich, V. Tkachenko, A. Topkov, “Waveguide coaxial rf-excited CO2 laser,” Sov. J. Quantum Electron. 20(6) , 612–614 (1990).
[CrossRef]

1989 (1)

P. Jackson, H. Baker, D. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

1986 (1)

J. Xin, D. Hall, “Multipass coaxial radiofrequency discharge CO2 laser,” Opt. Commun. 58, 420–422 (1986).
[CrossRef]

1974 (1)

1973 (1)

P. Burlamati, R. Pratesi, “High-efficiency coaxial waveguide dye laser with internal excitation,” Appl. Phys. Lett. 23, 475–476 (1973).
[CrossRef]

1970 (1)

V. Pruzhanovskii, “Asymmetric modes in metal coaxial optical waveguides,” Sov. Phys. Tech. Phys. 15(6) , 897–900 (1970).

Abrams, R.

Abramski, K.

C. Shackleton, K. Abramski, H. Baker, D. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

Baker, H.

C. Shackleton, K. Abramski, H. Baker, D. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

P. Jackson, H. Baker, D. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

Burlamacchi, P.

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an RF-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

Burlamati, P.

P. Burlamati, R. Pratesi, “High-efficiency coaxial waveguide dye laser with internal excitation,” Appl. Phys. Lett. 23, 475–476 (1973).
[CrossRef]

Chester, A.

Dong, S.

N. Hodgson, Q. Lu, S. Dong, B. Eppich, U. Wittrock, “High power solid state lasers in rod-, slab- and tube geometry,” Laser + Optoelectron. 23(3), 82–92, (1991), in German.

Ehrlichmann, D.

D. Ehrlichmann, U. Habich, H. Plum, P. Loosen, G. Herziger, “Azimuthally unstable resonators for high-power CO2 lasers with annular gain media,” IEEE J. Quantum Electron. 30, 1441–1447 (1994).
[CrossRef]

D. Ehrlichmann, U. Habich, H. Plum, “High-power CO2 laser with coaxial waveguide and diffusion cooling,” IEEE J. Quantum Electron. 29, 2211–2219 (1993).
[CrossRef]

Eppich, B.

N. Hodgson, Q. Lu, S. Dong, B. Eppich, U. Wittrock, “High power solid state lasers in rod-, slab- and tube geometry,” Laser + Optoelectron. 23(3), 82–92, (1991), in German.

Haas, W.

R. Nowack, H. Opower, K. Wessel, H. Kruger, W. Haas, N. Wenzel, “Diffusion-cooled compact CO2 high power laser,” Laser Optoelectron. 23(3), 68–81 (1991), in German.

Habich, U.

D. Ehrlichmann, U. Habich, H. Plum, P. Loosen, G. Herziger, “Azimuthally unstable resonators for high-power CO2 lasers with annular gain media,” IEEE J. Quantum Electron. 30, 1441–1447 (1994).
[CrossRef]

D. Ehrlichmann, U. Habich, H. Plum, “High-power CO2 laser with coaxial waveguide and diffusion cooling,” IEEE J. Quantum Electron. 29, 2211–2219 (1993).
[CrossRef]

Hall, D.

C. Shackleton, K. Abramski, H. Baker, D. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

P. Jackson, H. Baker, D. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

J. Xin, D. Hall, “Multipass coaxial radiofrequency discharge CO2 laser,” Opt. Commun. 58, 420–422 (1986).
[CrossRef]

Herziger, G.

D. Ehrlichmann, U. Habich, H. Plum, P. Loosen, G. Herziger, “Azimuthally unstable resonators for high-power CO2 lasers with annular gain media,” IEEE J. Quantum Electron. 30, 1441–1447 (1994).
[CrossRef]

Hodgson, N.

N. Hodgson, Q. Lu, S. Dong, B. Eppich, U. Wittrock, “High power solid state lasers in rod-, slab- and tube geometry,” Laser + Optoelectron. 23(3), 82–92, (1991), in German.

Jackson, P.

P. Jackson, H. Baker, D. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

Kruger, H.

R. Nowack, H. Opower, K. Wessel, H. Kruger, W. Haas, N. Wenzel, “Diffusion-cooled compact CO2 high power laser,” Laser Optoelectron. 23(3), 68–81 (1991), in German.

Lapucci, A.

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an RF-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

Loosen, P.

D. Ehrlichmann, U. Habich, H. Plum, P. Loosen, G. Herziger, “Azimuthally unstable resonators for high-power CO2 lasers with annular gain media,” IEEE J. Quantum Electron. 30, 1441–1447 (1994).
[CrossRef]

Lu, Q.

N. Hodgson, Q. Lu, S. Dong, B. Eppich, U. Wittrock, “High power solid state lasers in rod-, slab- and tube geometry,” Laser + Optoelectron. 23(3), 82–92, (1991), in German.

Nowack, R.

R. Nowack, H. Opower, K. Wessel, H. Kruger, W. Haas, N. Wenzel, “Diffusion-cooled compact CO2 high power laser,” Laser Optoelectron. 23(3), 68–81 (1991), in German.

Opower, H.

R. Nowack, H. Opower, K. Wessel, H. Kruger, W. Haas, N. Wenzel, “Diffusion-cooled compact CO2 high power laser,” Laser Optoelectron. 23(3), 68–81 (1991), in German.

Plum, H.

D. Ehrlichmann, U. Habich, H. Plum, P. Loosen, G. Herziger, “Azimuthally unstable resonators for high-power CO2 lasers with annular gain media,” IEEE J. Quantum Electron. 30, 1441–1447 (1994).
[CrossRef]

D. Ehrlichmann, U. Habich, H. Plum, “High-power CO2 laser with coaxial waveguide and diffusion cooling,” IEEE J. Quantum Electron. 29, 2211–2219 (1993).
[CrossRef]

Pratesi, R.

P. Burlamati, R. Pratesi, “High-efficiency coaxial waveguide dye laser with internal excitation,” Appl. Phys. Lett. 23, 475–476 (1973).
[CrossRef]

Pruzhanovskii, V.

V. Pruzhanovskii, “Asymmetric modes in metal coaxial optical waveguides,” Sov. Phys. Tech. Phys. 15(6) , 897–900 (1970).

Rossetti, F.

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an RF-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

Shackleton, C.

C. Shackleton, K. Abramski, H. Baker, D. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

Svich, V.

V. Svich, V. Tkachenko, A. Topkov, “Waveguide coaxial rf-excited CO2 laser,” Sov. J. Quantum Electron. 20(6) , 612–614 (1990).
[CrossRef]

Tkachenko, V.

V. Svich, V. Tkachenko, A. Topkov, “Waveguide coaxial rf-excited CO2 laser,” Sov. J. Quantum Electron. 20(6) , 612–614 (1990).
[CrossRef]

Topkov, A.

V. Svich, V. Tkachenko, A. Topkov, “Waveguide coaxial rf-excited CO2 laser,” Sov. J. Quantum Electron. 20(6) , 612–614 (1990).
[CrossRef]

Wenzel, N.

R. Nowack, H. Opower, K. Wessel, H. Kruger, W. Haas, N. Wenzel, “Diffusion-cooled compact CO2 high power laser,” Laser Optoelectron. 23(3), 68–81 (1991), in German.

Wessel, K.

R. Nowack, H. Opower, K. Wessel, H. Kruger, W. Haas, N. Wenzel, “Diffusion-cooled compact CO2 high power laser,” Laser Optoelectron. 23(3), 68–81 (1991), in German.

Wittrock, U.

N. Hodgson, Q. Lu, S. Dong, B. Eppich, U. Wittrock, “High power solid state lasers in rod-, slab- and tube geometry,” Laser + Optoelectron. 23(3), 82–92, (1991), in German.

Xin, J.

J. Xin, D. Hall, “Multipass coaxial radiofrequency discharge CO2 laser,” Opt. Commun. 58, 420–422 (1986).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

P. Jackson, H. Baker, D. Hall, “CO2 large-area discharge laser using an unstable-waveguide hybrid resonator,” Appl. Phys. Lett. 54, 1950–1952 (1989).
[CrossRef]

P. Burlamati, R. Pratesi, “High-efficiency coaxial waveguide dye laser with internal excitation,” Appl. Phys. Lett. 23, 475–476 (1973).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. Ehrlichmann, U. Habich, H. Plum, P. Loosen, G. Herziger, “Azimuthally unstable resonators for high-power CO2 lasers with annular gain media,” IEEE J. Quantum Electron. 30, 1441–1447 (1994).
[CrossRef]

D. Ehrlichmann, U. Habich, H. Plum, “High-power CO2 laser with coaxial waveguide and diffusion cooling,” IEEE J. Quantum Electron. 29, 2211–2219 (1993).
[CrossRef]

Laser + Optoelectron. (1)

N. Hodgson, Q. Lu, S. Dong, B. Eppich, U. Wittrock, “High power solid state lasers in rod-, slab- and tube geometry,” Laser + Optoelectron. 23(3), 82–92, (1991), in German.

Laser Optoelectron. (1)

R. Nowack, H. Opower, K. Wessel, H. Kruger, W. Haas, N. Wenzel, “Diffusion-cooled compact CO2 high power laser,” Laser Optoelectron. 23(3), 68–81 (1991), in German.

Opt. Commun. (3)

C. Shackleton, K. Abramski, H. Baker, D. Hall, “Lateral and transverse mode properties of CO2 slab waveguide lasers,” Opt. Commun. 89, 423–428 (1992).
[CrossRef]

J. Xin, D. Hall, “Multipass coaxial radiofrequency discharge CO2 laser,” Opt. Commun. 58, 420–422 (1986).
[CrossRef]

A. Lapucci, F. Rossetti, P. Burlamacchi, “Beam properties of an RF-discharge annular CO2 laser,” Opt. Commun. 111, 290–296 (1994).
[CrossRef]

Sov. J. Quantum Electron. (1)

V. Svich, V. Tkachenko, A. Topkov, “Waveguide coaxial rf-excited CO2 laser,” Sov. J. Quantum Electron. 20(6) , 612–614 (1990).
[CrossRef]

Sov. Phys. Tech. Phys. (1)

V. Pruzhanovskii, “Asymmetric modes in metal coaxial optical waveguides,” Sov. Phys. Tech. Phys. 15(6) , 897–900 (1970).

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Figures (13)

Fig. 1
Fig. 1

Position of the node lines and principal orientation of the E field for different azimuthal mode orders m inside a thin waveguide.

Fig. 2
Fig. 2

Vector plots of electric field lines of a TE51 mode for different ratios R between inner and outer guide radii. Although a thin guide shows almost perfect azimuthal polarization, with growing R the radial field increases.

Fig. 3
Fig. 3

Polarization defined as azimuthal over radial intensity (both integrated over the whole cross section) versus the azimuthal mode order m for a guide with a ratio of R = 60:57. TE modes with radial orders of as much as 3 and a TM mode with p = 1. Modes with p = 0 are not shown because their polarization ratio does not exceed 10-7.

Fig. 4
Fig. 4

Calculated near-field intensity distribution for (a) a rotating mode of order m and (b) a standing mode as superposition of two counterrotating modes of orders + m and -m.

Fig. 5
Fig. 5

Gain profile and resonator frequencies. The figure shows two longitudinal modes q and q + 1 with their transversal modes. The different heights of the marks symbolize the growing losses with increasing azimuthal mode order m.

Fig. 6
Fig. 6

Calculated far field of modes TE01, TE11, TE101, and TE401. Intensity distribution in one quadrant versus far-field divergence angle.

Fig. 7
Fig. 7

Normalized ratio of encircled power versus the far-field divergence for different azimuthal mode orders in comparison with a linearly polarized annular near field with constant intensity.

Fig. 8
Fig. 8

Calculated multimode far field with mode orders m < ±5.

Fig. 9
Fig. 9

Calculated multimode far field with mode orders m ≈ ±40.

Fig. 10
Fig. 10

Schematic drawing of the experimental setup of the coaxial waveguide laser.

Fig. 11
Fig. 11

Typical near-field patterns on a brick (left) and as a Plexiglas burn pattern (right).

Fig. 12
Fig. 12

Low-order far field as measured with a rotating pinhole (top) and as a Plexiglas burn pattern (bottom).

Fig. 13
Fig. 13

High-order far field as measured with a rotating pinhole.

Tables (2)

Tables Icon

Table 1 Roots χ mp for TE mp Modes

Tables Icon

Table 2 Frequency Differences for Some Adjacent Transversal Modes and for the Longitudinal Modes q and q + 1 for a resonator length of ∼530 mm

Equations (16)

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

E=E0r·expiωt-kzz-mϕ,  H=H0r·expiωt-kzz-mϕ,
E0r=1NikzrE0z+μ0ωmrH0z,  E0ϕ=1NkzmrE0z-iωμ0rH0z,  H0r=1N-ω0mrE0z+ikzrH0z,  H0ϕ=1Niω0rE0z+mrkzH0z,
N=kz2-μ00ω2.
2r2E0z+1rrE0z-m2r2+NE0z=0,  2r2H0z+1rrH0z-m2r2+NH0z=0,
E0zr=C1Jmr-N+C2Ymr-N,  H0zr=C3Jmr-N+C4Ymr-N.
ρ=r/ri,  χ=ri-N.
ω=ckz2+χ2ri2.
Eϕρ=1=Eϕρ=R=0,
Ezρ=1=Ezρ=R=0,
Eρρ, ϕ, z, t=-C3Ymχμ0ωmriρχ2JmρχYmχ-YmρχJmχexp-imϕ×expiωt-kzz=CmρχJmρχYmχ-YmρχJmχexp-imϕ×expiωt-kzz,  Eϕρ, ϕ, z, t=iC3Ymχμ0ωriχJmρχYmχ-YmρχJmχexp-imϕ×expiωt-kzz=-iCJmρχYmχ-YmρχJmχexp-imϕ×expiωt-kzz  Ez=0.
Fm=JmχmpYmRχmp-YmχmpJmRχmp=0.
E=maxωt-mϕ=const  with z=const.
St=ReE×ReHt=const0mρri·Qm2ρkzm2ρ2χ2·Qm2ρ+Rm2ρ,
Qmρ=JmρχYmχ-YmρχJmχ,  Rmρ=JmρχYmχ-YmρχJmχ.
E=E0·expiωt-kzz-mϕ+expiωt-kzz--mϕ=E0r·cosmϕ·expiωt-kzz.
ωqmp=cq2π2L2+χmp2ri21/2.

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