Abstract

Various families of Gaussian beams have been explored previously to represent the propagation of nearly plane electromagnetic waves in media having at most quadratic transverse variations of the index of refraction and the gain or loss in the vicinity of the beam. However, such beams cannot directly represent the wave solutions for propagation in planar or rectangular waveguides, and sinusoidal mode functions are more commonly used for such waveguides. On the other hand, it is also useful to consider the possibility of recurring Gaussian beams that have an approximately Gaussian transverse profile at certain distinct planes along the propagation path. It is shown here that under some conditions recurring Gaussian beams can describe wave propagation in hollow metal waveguides, and they can also lead to efficient coupling between the waveguide fields and free-space beams.

© 2000 Optical Society of America

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  29. 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).
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    [CrossRef] [PubMed]
  33. Y. Matsuura, M. Miyagi, “Er:YAG, CO, and CO2 laser delivery by ZnS-coated Ag hollow waveguides,” Appl. Opt. 32, 6598–6601 (1993).
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  34. T. Abel, J. Hirsch, J. A. Harrington, “Hollow glass waveguides for broadband infrared transmission,” Opt. Lett. 19, 1034–1036 (1994).
    [CrossRef] [PubMed]
  35. 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]
  36. R. K. Nubling, J. A. Harrington, “Hollow-waveguide delivery systems for high-power, industrial CO2 lasers,” Appl. Opt. 35, 372–380 (1996).
    [CrossRef] [PubMed]
  37. 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]
  38. Jiwang Dal, J. A. Harrington, “High-peak-power, pulsed CO2 laser light delivery by hollow glass waveguides,” Appl. Opt. 36, 5072–5077 (1997).
    [CrossRef]
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    [CrossRef]
  40. L. W. Casperson, “Gaussian light beams in inhomogeneous media,” Appl. Opt. 12, 2434–2441 (1973).
    [CrossRef] [PubMed]
  41. A. A. Tovar, L. W. Casperson, “Generalized beam matrices: Gaussian beam propagation in misaligned complex optical systems,” J. Opt. Soc. Am. A 12, 1522–1533 (1995), Eq. (24).
    [CrossRef]
  42. Y. Matsura, M. Miyagi, “Flexible hollow waveguides for delivery of excimer-laser light,” Opt. Lett. 23, 1226–1228 (1998).
    [CrossRef]
  43. J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
    [CrossRef]
  44. D. L. Aronstein, C. R. Stroud, “Fractional wave-function revivals in the infinite square well,” Phys. Rev. A 55, 4526–4537 (1997), and references therein.
    [CrossRef]

1999 (1)

1998 (1)

1997 (3)

1996 (5)

1995 (3)

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 (2)

1992 (3)

1991 (3)

E. R. Dobrovinskaya, L. A. Litvinov, Y. A. Rubinov, “Influence of thermal and mechanical effects on the properties of a sapphire hollow waveguide of IR waveguide lasers,” Sov. J. Opt. Technol. 58, 411–413 (1991).

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, 392–393 (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 J72C-I, 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]

1984 (2)

V. G. Artyushenko, L. N. Butvina, V. V. Voitsekhovskii, E. M. Dianov, I. S. Lisitskii, A. M. Prokhorov, V. K. Sysoev, “Polycrystalline waveguides with 0.35 dB/m losses at the 10.6 μm wavelength,” Sov. J. Quantum Electron. 11, 1–2 (1984).
[CrossRef]

K. Takahashi, N. Yoshida, M. Yokota, “Optical fibers for transmitting high-power CO2 laser beam,” Sumitomo Electr. Tech. Rev. 23, 203–210 (1984).

1981 (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]

1980 (1)

J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

1978 (1)

B. B. Chaudhuri, D. K. Paul, “Wave propagation through a hollow rectangular anisotropic dielectric guide,” IEEE J. Quantum Electron. QE-14, 557–560 (1978).
[CrossRef]

1977 (2)

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

1976 (3)

1975 (1)

1973 (1)

1965 (2)

1961 (1)

G. D. Boyd, J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508 (1961).
[CrossRef]

Abel, T.

Aronstein, D. L.

D. L. Aronstein, C. R. Stroud, “Fractional wave-function revivals in the infinite square well,” Phys. Rev. A 55, 4526–4537 (1997), and references therein.
[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, 392–393 (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).

V. G. Artyushenko, L. N. Butvina, V. V. Voitsekhovskii, E. M. Dianov, I. S. Lisitskii, A. M. Prokhorov, V. K. Sysoev, “Polycrystalline waveguides with 0.35 dB/m losses at the 10.6 μm wavelength,” Sov. J. Quantum Electron. 11, 1–2 (1984).
[CrossRef]

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, 392–393 (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. McMahan, 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, “Measurement 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 laser light in flexible hollow waveguides,” Appl. Opt. 15, 145–150 (1976).
[CrossRef] [PubMed]

Boyd, G. D.

G. D. Boyd, J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508 (1961).
[CrossRef]

Butvina, L. N.

V. G. Artyushenko, L. N. Butvina, V. V. Voitsekhovskii, E. M. Dianov, I. S. Lisitskii, A. M. Prokhorov, V. K. Sysoev, “Polycrystalline waveguides with 0.35 dB/m losses at the 10.6 μm wavelength,” Sov. J. Quantum Electron. 11, 1–2 (1984).
[CrossRef]

Casperson, L. W.

Chaudhuri, B. B.

B. B. Chaudhuri, D. K. Paul, “Wave propagation through a hollow rectangular anisotropic dielectric guide,” IEEE J. Quantum Electron. QE-14, 557–560 (1978).
[CrossRef]

Croitoru, N.

J. Dror, A. Inberg, R. Dahan, A. Elboim, N. Croitoru, “Influence of heating on performances of flexible hollow waveguides for the mid-infrared,” J. Phys. D 29, 569–577 (1996).
[CrossRef]

Dahan, R.

J. Dror, A. Inberg, R. Dahan, A. Elboim, N. Croitoru, “Influence of heating on performances of flexible hollow waveguides for the mid-infrared,” J. Phys. D 29, 569–577 (1996).
[CrossRef]

Dal, Jiwang

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, 392–393 (1990).

V. G. Artyushenko, L. N. Butvina, V. V. Voitsekhovskii, E. M. Dianov, I. S. Lisitskii, A. M. Prokhorov, V. K. Sysoev, “Polycrystalline waveguides with 0.35 dB/m losses at the 10.6 μm wavelength,” Sov. J. Quantum Electron. 11, 1–2 (1984).
[CrossRef]

Dobrovinskaya, E. R.

E. R. Dobrovinskaya, L. A. Litvinov, Y. A. Rubinov, “Influence of thermal and mechanical effects on the properties of a sapphire hollow waveguide of IR waveguide lasers,” Sov. J. Opt. Technol. 58, 411–413 (1991).

Dror, J.

J. Dror, A. Inberg, R. Dahan, A. Elboim, N. Croitoru, “Influence of heating on performances of flexible hollow waveguides for the mid-infrared,” J. Phys. D 29, 569–577 (1996).
[CrossRef]

Eberly, J. H.

J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

Elboim, A.

J. Dror, A. Inberg, R. Dahan, A. Elboim, N. Croitoru, “Influence of heating on performances of flexible hollow waveguides for the mid-infrared,” J. Phys. D 29, 569–577 (1996).
[CrossRef]

Garmire, E.

E. Garmire, T. McMahan, 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, “Measurement 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 laser 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]

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]

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]

Gordon, J. P.

G. D. Boyd, J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508 (1961).
[CrossRef]

Gregory, C. C.

C. C. Gregory, J. A. Harrington, “High peak power CO2 laser transmission by hollow sapphire waveguides,” Appl. Opt. 32, 3978–3980 (1993).
[CrossRef] [PubMed]

J. A. Harrington, J. C. Harrington, C. C. Gregory, S. Harman, “Properties of alkali halide optical fibers,” in Optical Fibers in Medicine III, A. Katzir, ed., Proc. SPIE906, 176–182 (1988).
[CrossRef]

Hall, D. G.

Hall, D. R.

Harman, S.

J. A. Harrington, J. C. Harrington, C. C. Gregory, S. Harman, “Properties of alkali halide optical fibers,” in Optical Fibers in Medicine III, A. Katzir, ed., Proc. SPIE906, 176–182 (1988).
[CrossRef]

Harrington, J. A.

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

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

C. D. Rabii, J. A. Harrington, “Optical properties of dual core hollow waveguides,” Appl. Opt. 35, 6249–6252 (1996).
[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]

Y. Matsuura, T. Abel, J. A. Harrington, “Optical properties of small-bore hollow glass waveguides,” Appl. Opt. 34, 6842–6847 (1995).
[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]

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, “High peak power CO2 laser transmission by hollow sapphire waveguides,” Appl. Opt. 32, 3978–3980 (1993).
[CrossRef] [PubMed]

J. A. Harrington, J. C. Harrington, C. C. Gregory, S. Harman, “Properties of alkali halide optical fibers,” in Optical Fibers in Medicine III, A. Katzir, ed., Proc. SPIE906, 176–182 (1988).
[CrossRef]

Harrington, J. C.

J. A. Harrington, J. C. Harrington, C. C. Gregory, S. Harman, “Properties of alkali halide optical fibers,” in Optical Fibers in Medicine III, A. Katzir, ed., Proc. SPIE906, 176–182 (1988).
[CrossRef]

Herlemont, F.

M. Khelkhal, F. Herlemont, “Effective optical constants of alumina, silica and beryllia at CO2 laser wavelengths,” J. Opt. 23, 225–228 (1992).
[CrossRef]

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]

Inberg, A.

J. Dror, A. Inberg, R. Dahan, A. Elboim, N. Croitoru, “Influence of heating on performances of flexible hollow waveguides for the mid-infrared,” J. Phys. D 29, 569–577 (1996).
[CrossRef]

Ishikawa, H.

H. Machida, Y. Matsuura, H. Ishikawa, M. Miyagi, “Transmission properties of rectangular hollow waveguides for CO2 laser light,” Appl. Opt. 31, 7617–7622 (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 J72C-I, 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, 392–393 (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 J72C-I, 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]

Khelkhal, M.

M. Khelkhal, F. Herlemont, “Effective optical constants of alumina, silica and beryllia at CO2 laser wavelengths,” J. Opt. 23, 225–228 (1992).
[CrossRef]

Kogelnik, H.

Lisitskii, I. S.

V. G. Artyushenko, L. N. Butvina, V. V. Voitsekhovskii, E. M. Dianov, I. S. Lisitskii, A. M. Prokhorov, V. K. Sysoev, “Polycrystalline waveguides with 0.35 dB/m losses at the 10.6 μm wavelength,” Sov. J. Quantum Electron. 11, 1–2 (1984).
[CrossRef]

Litvinov, L. A.

E. R. Dobrovinskaya, L. A. Litvinov, Y. A. Rubinov, “Influence of thermal and mechanical effects on the properties of a sapphire hollow waveguide of IR waveguide lasers,” Sov. J. Opt. Technol. 58, 411–413 (1991).

Lunnam, S. D.

Machida, H.

H. Machida, Y. Matsuura, H. Ishikawa, M. Miyagi, “Transmission properties of rectangular hollow waveguides for CO2 laser light,” Appl. Opt. 31, 7617–7622 (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]

Matsura, Y.

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.

McMahan, T.

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

McMahon, T.

E. Garmire, T. McMahon, M. Bass, “Measurement 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 laser 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, 392–393 (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. Matsura, M. Miyagi, “Flexible hollow waveguides for delivery of excimer-laser light,” Opt. Lett. 23, 1226–1228 (1998).
[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, 7617–7622 (1992).
[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, 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 J72C-I, 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 J72C-I, 637–641 (1989).

Narozhny, N. B.

J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

Nubling, R. K.

Paul, D. K.

B. B. Chaudhuri, D. K. Paul, “Wave propagation through a hollow rectangular anisotropic dielectric guide,” IEEE J. Quantum Electron. QE-14, 557–560 (1978).
[CrossRef]

Prokhorov, A. M.

V. G. Artyushenko, L. N. Butvina, V. V. Voitsekhovskii, E. M. Dianov, I. S. Lisitskii, A. M. Prokhorov, V. K. Sysoev, “Polycrystalline waveguides with 0.35 dB/m losses at the 10.6 μm wavelength,” Sov. J. Quantum Electron. 11, 1–2 (1984).
[CrossRef]

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).

Rabii, C. D.

Rubinov, Y. A.

E. R. Dobrovinskaya, L. A. Litvinov, Y. A. Rubinov, “Influence of thermal and mechanical effects on the properties of a sapphire hollow waveguide of IR waveguide lasers,” Sov. J. Opt. Technol. 58, 411–413 (1991).

Sanchez-Mondragon, J. J.

J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

Somkuarnpanit, S.

Stroud, C. R.

D. L. Aronstein, C. R. Stroud, “Fractional wave-function revivals in the infinite square well,” Phys. Rev. A 55, 4526–4537 (1997), and references therein.
[CrossRef]

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]

Sysoev, V. K.

V. G. Artyushenko, L. N. Butvina, V. V. Voitsekhovskii, E. M. Dianov, I. S. Lisitskii, A. M. Prokhorov, V. K. Sysoev, “Polycrystalline waveguides with 0.35 dB/m losses at the 10.6 μm wavelength,” Sov. J. Quantum Electron. 11, 1–2 (1984).
[CrossRef]

Takahashi, K.

K. Takahashi, N. Yoshida, M. Yokota, “Optical fibers for transmitting high-power CO2 laser beam,” Sumitomo Electr. Tech. Rev. 23, 203–210 (1984).

Tovar, A. A.

Voitsekhovskii, V. V.

V. G. Artyushenko, L. N. Butvina, V. V. Voitsekhovskii, E. M. Dianov, I. S. Lisitskii, A. M. Prokhorov, V. K. Sysoev, “Polycrystalline waveguides with 0.35 dB/m losses at the 10.6 μm wavelength,” Sov. J. Quantum Electron. 11, 1–2 (1984).
[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]

Yokota, M.

K. Takahashi, N. Yoshida, M. Yokota, “Optical fibers for transmitting high-power CO2 laser beam,” Sumitomo Electr. Tech. Rev. 23, 203–210 (1984).

Yoshida, N.

K. Takahashi, N. Yoshida, M. Yokota, “Optical fibers for transmitting high-power CO2 laser beam,” Sumitomo Electr. Tech. Rev. 23, 203–210 (1984).

Appl. Opt. (16)

H. Kogelnik, “On the propagation of Gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. 4, 1562–1569 (1965).
[CrossRef]

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

L. W. Casperson, S. D. Lunnam, “Gaussian modes in high loss laser resonators,” Appl. Opt. 14, 1193–1199 (1975), and references therein.
[CrossRef] [PubMed]

E. Garmire, T. McMahon, M. Bass, “Propagation of laser 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]

C. C. Gregory, J. A. Harrington, “High peak power CO2 laser transmission by hollow sapphire waveguides,” Appl. Opt. 32, 3978–3980 (1993).
[CrossRef] [PubMed]

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]

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

Y. Matsuura, T. Abel, J. A. Harrington, “Optical properties of small-bore hollow glass waveguides,” Appl. Opt. 34, 6842–6847 (1995).
[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]

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]

C. D. Rabii, J. A. Harrington, “Optical properties of dual core hollow waveguides,” Appl. Opt. 35, 6249–6252 (1996).
[CrossRef] [PubMed]

L. W. Casperson, “Grazing reflection of Gaussian beams,” Appl. Opt. 38, 554–562 (1999).
[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, Y. Matsuura, H. Ishikawa, M. Miyagi, “Transmission properties of rectangular hollow waveguides for CO2 laser light,” Appl. Opt. 31, 7617–7622 (1992).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

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

Bell Syst. Tech. J. (2)

G. D. Boyd, J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508 (1961).
[CrossRef]

H. Kogelnik, “Imaging of optical modes—resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
[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. (2)

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

B. B. Chaudhuri, D. K. Paul, “Wave propagation through a hollow rectangular anisotropic dielectric guide,” IEEE J. Quantum Electron. QE-14, 557–560 (1978).
[CrossRef]

J. Opt. (1)

M. Khelkhal, F. Herlemont, “Effective optical constants of alumina, silica and beryllia at CO2 laser wavelengths,” J. Opt. 23, 225–228 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Phys. D (1)

J. Dror, A. Inberg, R. Dahan, A. Elboim, N. Croitoru, “Influence of heating on performances of flexible hollow waveguides for the mid-infrared,” J. Phys. D 29, 569–577 (1996).
[CrossRef]

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. (2)

Phys. Rev. A (1)

D. L. Aronstein, C. R. Stroud, “Fractional wave-function revivals in the infinite square well,” Phys. Rev. A 55, 4526–4537 (1997), and references therein.
[CrossRef]

Phys. Rev. Lett. (1)

J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323–1326 (1980).
[CrossRef]

Sov. J. Opt. Technol. (1)

E. R. Dobrovinskaya, L. A. Litvinov, Y. A. Rubinov, “Influence of thermal and mechanical effects on the properties of a sapphire hollow waveguide of IR waveguide lasers,” Sov. J. Opt. Technol. 58, 411–413 (1991).

Sov. J. Quantum Electron. (1)

V. G. Artyushenko, L. N. Butvina, V. V. Voitsekhovskii, E. M. Dianov, I. S. Lisitskii, A. M. Prokhorov, V. K. Sysoev, “Polycrystalline waveguides with 0.35 dB/m losses at the 10.6 μm wavelength,” Sov. J. Quantum Electron. 11, 1–2 (1984).
[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, 392–393 (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).

Sumitomo Electr. Tech. Rev. (1)

K. Takahashi, N. Yoshida, M. Yokota, “Optical fibers for transmitting high-power CO2 laser beam,” Sumitomo Electr. Tech. Rev. 23, 203–210 (1984).

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 J72C-I, 637–641 (1989).

Other (1)

J. A. Harrington, J. C. Harrington, C. C. Gregory, S. Harman, “Properties of alkali halide optical fibers,” in Optical Fibers in Medicine III, A. Katzir, ed., Proc. SPIE906, 176–182 (1988).
[CrossRef]

Cited By

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Figures (7)

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 Gaussian beam interacting with flat waveguide surfaces located at the positions x=±0.5. The beam is polarized parallel to the surfaces, the waist spot size is w0=0.2, and the propagation distance between successive profiles is z=0.1 (ten plots per Rayleigh length). The original near-Gaussian profile recurs after approximately eight Rayleigh lengths.

Fig. 3
Fig. 3

Transverse intensity profiles of an off-center Gaussian beam whose input waist occurs at the position x=0.25. The beam is polarized parallel to the surface, the waist spot size is w0=0.2, and the propagation distance between successive profiles is z=1.0. Recurrence is after approximately 64 Rayleigh lengths.

Fig. 4
Fig. 4

Transverse intensity profiles of a misaligned Gaussian beam whose input waist occurs at the waveguide center x=0. The beam is polarized parallel to the surface, the waist spot size is w0=0.2, the velocity of the input beam toward the right-hand surface is v1=0.1, and the propagation distance between successive profiles is z=1.0. Recurrence is after approximately 64 Rayleigh lengths.

Fig. 5
Fig. 5

Series of transverse intensity profiles of a normalized on-axis Gaussian beam. The beam is polarized perpendicular to the surfaces, the waist spot size is w0=0.2, and the propagation distance between successive profiles is z=0.1. The original near-Gaussian profile recurs after approximately eight Rayleigh lengths.

Fig. 6
Fig. 6

Transverse intensity profiles of an off-center Gaussian beam whose input waist occurs at the position x=0.25. The beam is polarized perpendicular to the surface, the waist spot size is w0=0.2, and the propagation distance between successive profiles is z=1.0. Recurrence is after approximately 64 Rayleigh lengths.

Fig. 7
Fig. 7

Transverse intensity profiles of a misaligned Gaussian beam whose input waist occurs at the waveguide center x=0. The beam is polarized perpendicular to the surface, the waist spot size is w0=0.2, the velocity of the input beam toward the right-hand surface is v1=0.1, and the propagation distance between successive profiles is z=1.0. Recurrence is after approximately 64 Rayleigh lengths.

Equations (38)

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

2E(x, y, z)+k2(x, y, z)E(x, y, z)=0,
E(x, y, z)=A(x, z)exp(-iβ0z),
2Ax2-2iβ0 Az=0,
A(x, y, z)=A0 exp-iQx(z)x22+Sx(z)x+P(z).
Qx2+β0 dQxdz=0,
QxSx+β0 dSxdz=0,
dPdz=-i Qx2β0-Sx22β0.
Qx(z)β0=1qx(z)=1Rx(z)-2iβ0wx2(z),
Sx(z)=-Qx(z)dxa(z)+β0dxa(0)
=-Qx(z)dxa(0)+[β0-Qx(z)z]dxa (0),
1qx(z)=1/qx11+z/qx1,
Sx(z)=Sx11+z/qx1,
P(z)=P1-i2 ln1+zqx1-Sx12qx12β0 z/qx11+z/qx1,
1qx(z)=-i/z01-iz/z0.
Sx(z)=Sx11-iz/z0,
P(z)=P1-i2 ln1-izz0-Sx12z02β0 z/z01-iz/z0.
A(x, z)
=A0 exp-1w02(1+z2)-i zw02(1+z2)x2+2(p1+zv1)w02(1+z2)+i 2z(p1+zv1)w02(1+z2)-i 2v1w02x+-ln(1+z2)1/4-z2(v12-p12)+2zv1p1w02(1+z2)+i z(v12-p12)-2z2v1p1w02(1+z2)+i2 tan-1(z),
I(x, z)=A*(x, z)A(x, z),
-I(x, z)dx=1.
A(x, y)=(2/π)1/2w0(1+z2)1/21/2×exp-x-(p1+zv1)w0(1+z2)1/22×exp-izx-(p1+zv1)w0(1+z2)1/22+2v1x-zv12w02-12 tan-1(z).
A(x, z)=A(x, z)-A(1-x, z).
A(x, z)=A(x, z)-A(1-x, z)+A(2+x, z)-A(3-x, z)+-A(-1-x, z)+A(-2+x, z)-A(-3-x, z)+=n=-N+N(-1)nA[n+(-1)nx, z].
I(x, z)=A*(x, z)A(x, z),
A(x, z)=A(x, z)+A(1-x, z).
A(x, z)=A(x, z)+A(1-x, z)+A(2+x, z)+A(3-x, z)++A(-1-x, z)+A(-2+x, z)+A(-3-x, z)+=n=-N+NA[n+(-1)nx, z].
I(x, z)=A*(x, z)A(x, z),
A(x, z)=B(x)exp(-iγ z),
d2Bdx2-2β0γB=0.
B(x)=a sin kx x+b cos kx x.
kx2+2β0γ=0.
B(x)=a sin kx x,
kxd=mπ,
-iγ z=i2β0 m2π2d2z.
12β0 m2π 2d2 z=2hπ,
z=4β0d2π.
z=8πw2.
B(x)=b cos kx x,

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