Abstract

For optical and near-optical applications in electromagnetics, the directed propagation of waves in free space and in lenslike media is often in the Cartesian form of Gaussian or more general Hermite-sinusoidal-Gaussian beams. It has been shown that recurring (rather than continuing) forms of such beams are possible in the paraxial approximation for certain hollow metal waveguides, in which multiple reflections from the waveguide walls may occur. Limitations on this recurrence behavior implicit in use of the paraxial approximation are considered here, and estimates are obtained for the maximum propagation distance before the onset of significant distortion of the recurring beams.

© 2002 Optical Society of America

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  1. E. Garmire, T. McMahon, M. Bass, “Propagation of infrared light in flexible hollow waveguides,” Appl. Opt. 15, 145–150 (1976).
    [CrossRef] [PubMed]
  2. E. Garmire, “Propagation of IR light in flexible hollow waveguides: further discussion,” Appl. Opt. 15, 3037–3039 (1976).
    [CrossRef] [PubMed]
  3. E. Garmire, T. McMahon, M. Bass, “Low-loss optical transmission through bent hollow metal waveguides,” Appl. Phys. Lett. 31, 92–94 (1977).
    [CrossRef]
  4. E. Garmire, T. McMahon, M. Bass, “Measurements of propagation in flexible infrared transmissive (FIT) waveguides,” IEEE J. Quantum Electron. QE-13, 21–22 (1977).
  5. T. Matsushima, I. Yamauchi, T. Sueta, “Flexible infrared-transmissive plastic waveguides coated with evaporated aluminum,” Jpn. J. Appl. Phys. 20, 1345–1346 (1981).
    [CrossRef]
  6. J. Gombert, M. Gazard, “Attenuation characteristics of a planar dielectric coated metallic waveguide for 10.6-µm radiation,” Opt. Commun. 58, 307–310 (1986).
    [CrossRef]
  7. M. Miyagi, S. Karasawa, “A comparative study of rectangular and circular dielectric-coated metallic waveguides for CO2 laser light: theory,” Opt. Commun. 68, 18–20 (1988).
    [CrossRef]
  8. S. V. Azizbekyan, V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, I. L. Pyl’nov, “Bending loss of hollow metal waveguides for mid-infrared range,” Sov. Tech. Phys. Lett. 15, 602–603 (1989).
  9. S. Karasawa, M. Miyagi, T. Nakamura, H. Ishikawa, “Fabrication of dielectric-coated rectangular hollow waveguides for CO2 laser light transmission,” Trans. Inst. Electron. Inf. Commun. Eng. C-I J72, 637–641 (1989).
  10. S. V. Azizbekyan, V. G. Artyushenko, E. M. Dianov, K. I. Kalaidzhyan, M. M. Mirakyan, “Transmission of hollow metal waveguides in the mid-infrared region,” Sov. Phys. Tech. Phys. 35, 196–198 (1990).
  11. V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, “Flexible hollow waveguides for the mid-IR range,” Sov. Phys. Tech. Phys. 36, 46–49 (1991).
  12. H. Machida, H. Ishikawa, M. Miyagi, “Low-loss lead fluoride-coated square waveguide for CO2 laser light transmission,” Electron. Lett. 27, 2068–2070 (1991).
    [CrossRef]
  13. Y. Matsuura, M. Miyagi, “Bending losses and beam profiles of zinc selenide-coated silver waveguides for carbon dioxide laser light,” Appl. Opt. 31, 6441–6445 (1992).
    [CrossRef] [PubMed]
  14. H. Machida, Y. Matsuura, H. Ishikawa, M. Miyagi, “Transmission properties of rectangular hollow waveguides for CO2 laser light,” Appl. Opt. 31, 7616–7622 (1992).
    [CrossRef]
  15. Y. Matsuura, M. Miyagi, “Er:YAG, CO, and CO2 laser delivery by ZnS-coated Ag hollow waveguides,” Appl. Opt. 32, 6598–6601 (1993).
    [CrossRef] [PubMed]
  16. T. Abel, J. Hirsch, J. A. Harrington, “Hollow glass waveguides for broadband infrared transmission,” Opt. Lett. 19, 1034–1036 (1994).
    [CrossRef] [PubMed]
  17. 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]
  18. R. K. Nubling, J. A. Harrington, “Hollow-waveguide delivery systems for high-power, industrial CO2 lasers,” Appl. Opt. 35, 372–380 (1996).
    [CrossRef] [PubMed]
  19. D. Su, S. Somkuarnpanit, D. R. Hall, J. D. C. Jones, “Thermal effects in a hollow waveguide beam launch for CO2 laser power delivery,” Appl. Opt. 35, 4787–4789 (1996).
    [CrossRef] [PubMed]
  20. J. Dal, J. A. Harrington, “High-peak-power, pulsed CO2 laser light delivery by hollow glass waveguides,” Appl. Opt. 36, 5072–5077 (1997).
    [CrossRef]
  21. D. C. Chang, E. F. Kuester, “A hybrid method for paraxial beam propagation in multimode optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 923–933 (1981).
    [CrossRef]
  22. L. W. Casperson, “Gaussian beams in hollow metal waveguides,” J. Opt. Soc. Am. A 17, 1115–1123 (2000).
    [CrossRef]
  23. M. Ghita, L. W. Casperson, “Gaussian beams in hollow metal waveguides: experiment,” Appl. Opt. 40, 5459–5462 (2001).
    [CrossRef]
  24. L. A. Rivlin, V. S. Shul’dyaev, “Multimode waveguides for coherent light,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 572–578 (1968).
  25. E. E. Grigor’eva, A. T. Semenov, “Waveguide image transmission in coherent light (review),” Sov. J. Quantum Electron. 8, 1063–1073 (1978).
    [CrossRef]
  26. L. W. Casperson, “Gaussian light beams in inhomogeneous media,” Appl. Opt. 12, 2434–2441 (1973).
    [CrossRef] [PubMed]
  27. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965), Eq. (3.896-1).

2001 (1)

2000 (1)

1997 (1)

1996 (2)

1994 (2)

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]

1993 (1)

1992 (2)

Y. Matsuura, M. Miyagi, “Bending losses and beam profiles of zinc selenide-coated silver waveguides for carbon dioxide laser light,” Appl. Opt. 31, 6441–6445 (1992).
[CrossRef] [PubMed]

H. Machida, Y. Matsuura, H. Ishikawa, M. Miyagi, “Transmission properties of rectangular hollow waveguides for CO2 laser light,” Appl. Opt. 31, 7616–7622 (1992).
[CrossRef]

1991 (2)

V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, “Flexible hollow waveguides for the mid-IR range,” Sov. Phys. Tech. Phys. 36, 46–49 (1991).

H. Machida, H. Ishikawa, M. Miyagi, “Low-loss lead fluoride-coated square waveguide for CO2 laser light transmission,” Electron. Lett. 27, 2068–2070 (1991).
[CrossRef]

1990 (1)

S. V. Azizbekyan, V. G. Artyushenko, E. M. Dianov, K. I. Kalaidzhyan, M. M. Mirakyan, “Transmission of hollow metal waveguides in the mid-infrared region,” Sov. Phys. Tech. Phys. 35, 196–198 (1990).

1989 (2)

S. V. Azizbekyan, V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, I. L. Pyl’nov, “Bending loss of hollow metal waveguides for mid-infrared range,” Sov. Tech. Phys. Lett. 15, 602–603 (1989).

S. Karasawa, M. Miyagi, T. Nakamura, H. Ishikawa, “Fabrication of dielectric-coated rectangular hollow waveguides for CO2 laser light transmission,” Trans. Inst. Electron. Inf. Commun. Eng. C-I J72, 637–641 (1989).

1988 (1)

M. Miyagi, S. Karasawa, “A comparative study of rectangular and circular dielectric-coated metallic waveguides for CO2 laser light: theory,” Opt. Commun. 68, 18–20 (1988).
[CrossRef]

1986 (1)

J. Gombert, M. Gazard, “Attenuation characteristics of a planar dielectric coated metallic waveguide for 10.6-µm radiation,” Opt. Commun. 58, 307–310 (1986).
[CrossRef]

1981 (2)

T. Matsushima, I. Yamauchi, T. Sueta, “Flexible infrared-transmissive plastic waveguides coated with evaporated aluminum,” Jpn. J. Appl. Phys. 20, 1345–1346 (1981).
[CrossRef]

D. C. Chang, E. F. Kuester, “A hybrid method for paraxial beam propagation in multimode optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 923–933 (1981).
[CrossRef]

1978 (1)

E. E. Grigor’eva, A. T. Semenov, “Waveguide image transmission in coherent light (review),” Sov. J. Quantum Electron. 8, 1063–1073 (1978).
[CrossRef]

1977 (2)

E. Garmire, T. McMahon, M. Bass, “Low-loss optical transmission through bent hollow metal waveguides,” Appl. Phys. Lett. 31, 92–94 (1977).
[CrossRef]

E. Garmire, T. McMahon, M. Bass, “Measurements of propagation in flexible infrared transmissive (FIT) waveguides,” IEEE J. Quantum Electron. QE-13, 21–22 (1977).

1976 (2)

1973 (1)

1968 (1)

L. A. Rivlin, V. S. Shul’dyaev, “Multimode waveguides for coherent light,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 572–578 (1968).

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]

Artyushenko, V. G.

V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, “Flexible hollow waveguides for the mid-IR range,” Sov. Phys. Tech. Phys. 36, 46–49 (1991).

S. V. Azizbekyan, V. G. Artyushenko, E. M. Dianov, K. I. Kalaidzhyan, M. M. Mirakyan, “Transmission of hollow metal waveguides in the mid-infrared region,” Sov. Phys. Tech. Phys. 35, 196–198 (1990).

S. V. Azizbekyan, V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, I. L. Pyl’nov, “Bending loss of hollow metal waveguides for mid-infrared range,” Sov. Tech. Phys. Lett. 15, 602–603 (1989).

Azizbekyan, S. V.

S. V. Azizbekyan, V. G. Artyushenko, E. M. Dianov, K. I. Kalaidzhyan, M. M. Mirakyan, “Transmission of hollow metal waveguides in the mid-infrared region,” Sov. Phys. Tech. Phys. 35, 196–198 (1990).

S. V. Azizbekyan, V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, I. L. Pyl’nov, “Bending loss of hollow metal waveguides for mid-infrared range,” Sov. Tech. Phys. Lett. 15, 602–603 (1989).

Bass, M.

E. Garmire, T. McMahon, M. Bass, “Measurements of propagation in flexible infrared transmissive (FIT) waveguides,” IEEE J. Quantum Electron. QE-13, 21–22 (1977).

E. Garmire, T. McMahon, M. Bass, “Low-loss optical transmission through bent hollow metal waveguides,” Appl. Phys. Lett. 31, 92–94 (1977).
[CrossRef]

E. Garmire, T. McMahon, M. Bass, “Propagation of infrared light in flexible hollow waveguides,” Appl. Opt. 15, 145–150 (1976).
[CrossRef] [PubMed]

Casperson, L. W.

Chang, D. C.

D. C. Chang, E. F. Kuester, “A hybrid method for paraxial beam propagation in multimode optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 923–933 (1981).
[CrossRef]

Dal, J.

Dianov, E. M.

S. V. Azizbekyan, V. G. Artyushenko, E. M. Dianov, K. I. Kalaidzhyan, M. M. Mirakyan, “Transmission of hollow metal waveguides in the mid-infrared region,” Sov. Phys. Tech. Phys. 35, 196–198 (1990).

Garmire, E.

E. Garmire, T. McMahon, M. Bass, “Measurements of propagation in flexible infrared transmissive (FIT) waveguides,” IEEE J. Quantum Electron. QE-13, 21–22 (1977).

E. Garmire, T. McMahon, M. Bass, “Low-loss optical transmission through bent hollow metal waveguides,” Appl. Phys. Lett. 31, 92–94 (1977).
[CrossRef]

E. Garmire, “Propagation of IR light in flexible hollow waveguides: further discussion,” Appl. Opt. 15, 3037–3039 (1976).
[CrossRef] [PubMed]

E. Garmire, T. McMahon, M. Bass, “Propagation of infrared light in flexible hollow waveguides,” Appl. Opt. 15, 145–150 (1976).
[CrossRef] [PubMed]

Gazard, M.

J. Gombert, M. Gazard, “Attenuation characteristics of a planar dielectric coated metallic waveguide for 10.6-µm radiation,” Opt. Commun. 58, 307–310 (1986).
[CrossRef]

Ghita, M.

Gombert, J.

J. Gombert, M. Gazard, “Attenuation characteristics of a planar dielectric coated metallic waveguide for 10.6-µm radiation,” Opt. Commun. 58, 307–310 (1986).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965), Eq. (3.896-1).

Grigor’eva, E. E.

E. E. Grigor’eva, A. T. Semenov, “Waveguide image transmission in coherent light (review),” Sov. J. Quantum Electron. 8, 1063–1073 (1978).
[CrossRef]

Hall, D. R.

Harrington, J. A.

Hirsch, J.

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]

Ishikawa, H.

H. Machida, Y. Matsuura, H. Ishikawa, M. Miyagi, “Transmission properties of rectangular hollow waveguides for CO2 laser light,” Appl. Opt. 31, 7616–7622 (1992).
[CrossRef]

H. Machida, H. Ishikawa, M. Miyagi, “Low-loss lead fluoride-coated square waveguide for CO2 laser light transmission,” Electron. Lett. 27, 2068–2070 (1991).
[CrossRef]

S. Karasawa, M. Miyagi, T. Nakamura, H. Ishikawa, “Fabrication of dielectric-coated rectangular hollow waveguides for CO2 laser light transmission,” Trans. Inst. Electron. Inf. Commun. Eng. C-I J72, 637–641 (1989).

Jones, J. D. C.

Kalaidzhyan, K. I.

V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, “Flexible hollow waveguides for the mid-IR range,” Sov. Phys. Tech. Phys. 36, 46–49 (1991).

S. V. Azizbekyan, V. G. Artyushenko, E. M. Dianov, K. I. Kalaidzhyan, M. M. Mirakyan, “Transmission of hollow metal waveguides in the mid-infrared region,” Sov. Phys. Tech. Phys. 35, 196–198 (1990).

S. V. Azizbekyan, V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, I. L. Pyl’nov, “Bending loss of hollow metal waveguides for mid-infrared range,” Sov. Tech. Phys. Lett. 15, 602–603 (1989).

Karasawa, S.

S. Karasawa, M. Miyagi, T. Nakamura, H. Ishikawa, “Fabrication of dielectric-coated rectangular hollow waveguides for CO2 laser light transmission,” Trans. Inst. Electron. Inf. Commun. Eng. C-I J72, 637–641 (1989).

M. Miyagi, S. Karasawa, “A comparative study of rectangular and circular dielectric-coated metallic waveguides for CO2 laser light: theory,” Opt. Commun. 68, 18–20 (1988).
[CrossRef]

Kuester, E. F.

D. C. Chang, E. F. Kuester, “A hybrid method for paraxial beam propagation in multimode optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 923–933 (1981).
[CrossRef]

Machida, H.

H. Machida, Y. Matsuura, H. Ishikawa, M. Miyagi, “Transmission properties of rectangular hollow waveguides for CO2 laser light,” Appl. Opt. 31, 7616–7622 (1992).
[CrossRef]

H. Machida, H. Ishikawa, M. Miyagi, “Low-loss lead fluoride-coated square waveguide for CO2 laser light transmission,” Electron. Lett. 27, 2068–2070 (1991).
[CrossRef]

Matsushima, T.

T. Matsushima, I. Yamauchi, T. Sueta, “Flexible infrared-transmissive plastic waveguides coated with evaporated aluminum,” Jpn. J. Appl. Phys. 20, 1345–1346 (1981).
[CrossRef]

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]

Y. Matsuura, M. Miyagi, “Er:YAG, CO, and CO2 laser delivery by ZnS-coated Ag hollow waveguides,” Appl. Opt. 32, 6598–6601 (1993).
[CrossRef] [PubMed]

H. Machida, Y. Matsuura, H. Ishikawa, M. Miyagi, “Transmission properties of rectangular hollow waveguides for CO2 laser light,” Appl. Opt. 31, 7616–7622 (1992).
[CrossRef]

Y. Matsuura, M. Miyagi, “Bending losses and beam profiles of zinc selenide-coated silver waveguides for carbon dioxide laser light,” Appl. Opt. 31, 6441–6445 (1992).
[CrossRef] [PubMed]

McMahon, T.

E. Garmire, T. McMahon, M. Bass, “Low-loss optical transmission through bent hollow metal waveguides,” Appl. Phys. Lett. 31, 92–94 (1977).
[CrossRef]

E. Garmire, T. McMahon, M. Bass, “Measurements of propagation in flexible infrared transmissive (FIT) waveguides,” IEEE J. Quantum Electron. QE-13, 21–22 (1977).

E. Garmire, T. McMahon, M. Bass, “Propagation of infrared light in flexible hollow waveguides,” Appl. Opt. 15, 145–150 (1976).
[CrossRef] [PubMed]

Mirakyan, M. M.

V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, “Flexible hollow waveguides for the mid-IR range,” Sov. Phys. Tech. Phys. 36, 46–49 (1991).

S. V. Azizbekyan, V. G. Artyushenko, E. M. Dianov, K. I. Kalaidzhyan, M. M. Mirakyan, “Transmission of hollow metal waveguides in the mid-infrared region,” Sov. Phys. Tech. Phys. 35, 196–198 (1990).

S. V. Azizbekyan, V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, I. L. Pyl’nov, “Bending loss of hollow metal waveguides for mid-infrared range,” Sov. Tech. Phys. Lett. 15, 602–603 (1989).

Miyagi, M.

Y. Matsuura, M. Miyagi, “Er:YAG, CO, and CO2 laser delivery by ZnS-coated Ag hollow waveguides,” Appl. Opt. 32, 6598–6601 (1993).
[CrossRef] [PubMed]

H. Machida, Y. Matsuura, H. Ishikawa, M. Miyagi, “Transmission properties of rectangular hollow waveguides for CO2 laser light,” Appl. Opt. 31, 7616–7622 (1992).
[CrossRef]

Y. Matsuura, M. Miyagi, “Bending losses and beam profiles of zinc selenide-coated silver waveguides for carbon dioxide laser light,” Appl. Opt. 31, 6441–6445 (1992).
[CrossRef] [PubMed]

H. Machida, H. Ishikawa, M. Miyagi, “Low-loss lead fluoride-coated square waveguide for CO2 laser light transmission,” Electron. Lett. 27, 2068–2070 (1991).
[CrossRef]

S. Karasawa, M. Miyagi, T. Nakamura, H. Ishikawa, “Fabrication of dielectric-coated rectangular hollow waveguides for CO2 laser light transmission,” Trans. Inst. Electron. Inf. Commun. Eng. C-I J72, 637–641 (1989).

M. Miyagi, S. Karasawa, “A comparative study of rectangular and circular dielectric-coated metallic waveguides for CO2 laser light: theory,” Opt. Commun. 68, 18–20 (1988).
[CrossRef]

Nakamura, T.

S. Karasawa, M. Miyagi, T. Nakamura, H. Ishikawa, “Fabrication of dielectric-coated rectangular hollow waveguides for CO2 laser light transmission,” Trans. Inst. Electron. Inf. Commun. Eng. C-I J72, 637–641 (1989).

Nubling, R. K.

Pyl’nov, I. L.

S. V. Azizbekyan, V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, I. L. Pyl’nov, “Bending loss of hollow metal waveguides for mid-infrared range,” Sov. Tech. Phys. Lett. 15, 602–603 (1989).

Rivlin, L. A.

L. A. Rivlin, V. S. Shul’dyaev, “Multimode waveguides for coherent light,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 572–578 (1968).

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965), Eq. (3.896-1).

Semenov, A. T.

E. E. Grigor’eva, A. T. Semenov, “Waveguide image transmission in coherent light (review),” Sov. J. Quantum Electron. 8, 1063–1073 (1978).
[CrossRef]

Shul’dyaev, V. S.

L. A. Rivlin, V. S. Shul’dyaev, “Multimode waveguides for coherent light,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 572–578 (1968).

Somkuarnpanit, S.

Su, D.

Sueta, T.

T. Matsushima, I. Yamauchi, T. Sueta, “Flexible infrared-transmissive plastic waveguides coated with evaporated aluminum,” Jpn. J. Appl. Phys. 20, 1345–1346 (1981).
[CrossRef]

Yamauchi, I.

T. Matsushima, I. Yamauchi, T. Sueta, “Flexible infrared-transmissive plastic waveguides coated with evaporated aluminum,” Jpn. J. Appl. Phys. 20, 1345–1346 (1981).
[CrossRef]

Appl. Opt. (10)

E. Garmire, T. McMahon, M. Bass, “Propagation of infrared light in flexible hollow waveguides,” Appl. Opt. 15, 145–150 (1976).
[CrossRef] [PubMed]

E. Garmire, “Propagation of IR light in flexible hollow waveguides: further discussion,” Appl. Opt. 15, 3037–3039 (1976).
[CrossRef] [PubMed]

Y. Matsuura, M. Miyagi, “Bending losses and beam profiles of zinc selenide-coated silver waveguides for carbon dioxide laser light,” Appl. Opt. 31, 6441–6445 (1992).
[CrossRef] [PubMed]

H. Machida, Y. Matsuura, H. Ishikawa, M. Miyagi, “Transmission properties of rectangular hollow waveguides for CO2 laser light,” Appl. Opt. 31, 7616–7622 (1992).
[CrossRef]

Y. Matsuura, M. Miyagi, “Er:YAG, CO, and CO2 laser delivery by ZnS-coated Ag hollow waveguides,” Appl. Opt. 32, 6598–6601 (1993).
[CrossRef] [PubMed]

R. K. Nubling, J. A. Harrington, “Hollow-waveguide delivery systems for high-power, industrial CO2 lasers,” Appl. Opt. 35, 372–380 (1996).
[CrossRef] [PubMed]

D. Su, S. Somkuarnpanit, D. R. Hall, J. D. C. Jones, “Thermal effects in a hollow waveguide beam launch for CO2 laser power delivery,” Appl. Opt. 35, 4787–4789 (1996).
[CrossRef] [PubMed]

J. Dal, J. A. Harrington, “High-peak-power, pulsed CO2 laser light delivery by hollow glass waveguides,” Appl. Opt. 36, 5072–5077 (1997).
[CrossRef]

M. Ghita, L. W. Casperson, “Gaussian beams in hollow metal waveguides: experiment,” Appl. Opt. 40, 5459–5462 (2001).
[CrossRef]

L. W. Casperson, “Gaussian light beams in inhomogeneous media,” Appl. Opt. 12, 2434–2441 (1973).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

E. Garmire, T. McMahon, M. Bass, “Low-loss optical transmission through bent hollow metal waveguides,” Appl. Phys. Lett. 31, 92–94 (1977).
[CrossRef]

Electron. Lett. (2)

H. Machida, H. Ishikawa, M. Miyagi, “Low-loss lead fluoride-coated square waveguide for CO2 laser light transmission,” Electron. Lett. 27, 2068–2070 (1991).
[CrossRef]

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. (1)

E. Garmire, T. McMahon, M. Bass, “Measurements of propagation in flexible infrared transmissive (FIT) waveguides,” IEEE J. Quantum Electron. QE-13, 21–22 (1977).

IEEE Trans. Microwave Theory Tech. (1)

D. C. Chang, E. F. Kuester, “A hybrid method for paraxial beam propagation in multimode optical waveguides,” IEEE Trans. Microwave Theory Tech. MTT-29, 923–933 (1981).
[CrossRef]

Izv. Vyssh. Uchebn. Zaved. Radiofiz. (1)

L. A. Rivlin, V. S. Shul’dyaev, “Multimode waveguides for coherent light,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 572–578 (1968).

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

T. Matsushima, I. Yamauchi, T. Sueta, “Flexible infrared-transmissive plastic waveguides coated with evaporated aluminum,” Jpn. J. Appl. Phys. 20, 1345–1346 (1981).
[CrossRef]

Opt. Commun. (2)

J. Gombert, M. Gazard, “Attenuation characteristics of a planar dielectric coated metallic waveguide for 10.6-µm radiation,” Opt. Commun. 58, 307–310 (1986).
[CrossRef]

M. Miyagi, S. Karasawa, “A comparative study of rectangular and circular dielectric-coated metallic waveguides for CO2 laser light: theory,” Opt. Commun. 68, 18–20 (1988).
[CrossRef]

Opt. Lett. (1)

Sov. J. Quantum Electron. (1)

E. E. Grigor’eva, A. T. Semenov, “Waveguide image transmission in coherent light (review),” Sov. J. Quantum Electron. 8, 1063–1073 (1978).
[CrossRef]

Sov. Phys. Tech. Phys. (2)

S. V. Azizbekyan, V. G. Artyushenko, E. M. Dianov, K. I. Kalaidzhyan, M. M. Mirakyan, “Transmission of hollow metal waveguides in the mid-infrared region,” Sov. Phys. Tech. Phys. 35, 196–198 (1990).

V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, “Flexible hollow waveguides for the mid-IR range,” Sov. Phys. Tech. Phys. 36, 46–49 (1991).

Sov. Tech. Phys. Lett. (1)

S. V. Azizbekyan, V. G. Artyushenko, K. I. Kalaidzhyan, M. M. Mirakyan, I. L. Pyl’nov, “Bending loss of hollow metal waveguides for mid-infrared range,” Sov. Tech. Phys. Lett. 15, 602–603 (1989).

Trans. Inst. Electron. Inf. Commun. Eng. C-I (1)

S. Karasawa, M. Miyagi, T. Nakamura, H. Ishikawa, “Fabrication of dielectric-coated rectangular hollow waveguides for CO2 laser light transmission,” Trans. Inst. Electron. Inf. Commun. Eng. C-I J72, 637–641 (1989).

Other (1)

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, New York, 1965), Eq. (3.896-1).

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Figures (3)

Fig. 1
Fig. 1

Schematic representation of an off-axis Gaussian beam undergoing diffraction and reflection from the flat parallel surfaces of a waveguide. The coordinate system used in the analysis is also shown.

Fig. 2
Fig. 2

Series of transverse intensity profiles of a normalized on-axis paraxial Gaussian beam interacting with flat waveguide surfaces located at the positions x/ d = 0, 1. The beam is polarized parallel to the surfaces, the waist spot size is w 0/d = 0.2, and the propagation distance between successive profiles is z/ z 0 = 0.1 (ten plots per Rayleigh length). The original near-Gaussian profile recurs after approximately eight Rayleigh lengths.

Fig. 3
Fig. 3

Transverse amplitude profiles of a normalized on-axis Gaussian beam at recurrences s = 0 and s = 100, represented as a summation of nonparaxial waveguide modes.

Equations (30)

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2Ex, y, z+k2x, y, zEx, y, z=0,
Ex, y, z=Ax, zexp-iβ0z,
2Ax2-2iβ0Az=0,
Ax, z=Bxexp-iγparz,
d2Bdx2-2β0γparB=0.
Bx=a sin kxx+b cos kxx.
kx2+2β0γpar=0.
Bx=a sin kxx,
kxd=mπ,
γparz=-12β0m2π2d2z.
z=4β0d2π,
z=β0d22π.
Ex, y, z=Bxexp-iβzz,
d2Bdx2+β02-βz2B=0.
kx2+βz2-β02=0.
βzz=β02-mπ/d21/2z.
γexz=β02-mπ/d21/2-β0z=1-mπ/β0d21/2-1β0z.
γexzs-12mπβ0d2-18mπβ0d4β0zs=-12mπβ0d2-18mπβ0d4β02d22πs,
γexzs=-m2π4-m4π64λnd2s=γparzs-m4π64λnd2s,
m4π64λnd2s<π4.
m<2d/λ1/2 s-1/4.
Ax, 0=m=1am sinmπx/d.
am=2d0dAx, 0sinmπxddx.
Ax, 0=2/π1/2 dw01/2exp-x-d/2w02.
am=2d2/π1/2 dw01/20dexp-x-d/2w02×sinmπxddx.
am=2d2/π1/2 dw01/2-exp-x-d/2w02×sinmπxddx.
am=22π1/2 w0d1/2exp-mπw02d2-1m-1/2,
Δγmz=1-mλ/2nd21/2+1/2×mλ/2nd2-12πn/λz.
Δγmzs=1-mλ/2nd21/2+1/2×mλ/2nd2-12πn2d2/λ2s.
Ax, zs=m odd22π1/2 w0d1/2exp-mπw02d2×-1m-1/2 sinmπxdcosΔγmzs.

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