Abstract

Transmission losses in quartz hollow waveguides with rough inner surfaces have been measured, and an anomalous loss decrease has been observed just beyond the resonance wavelength at the infrared. Detailed analyses have been conducted to check the applicability of available theories in the prediction of additional loss increases or decreases in wide infrared-wavelength regions. A new theory based on a thin-film-coating model has also been presented for the first time, to our knowledge, to describe the additional loss behavior.

© 1995 Optical Society of America

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  1. 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 processing,” Appl. Opt. 31, 5114–5120 (1992).
    [CrossRef] [PubMed]
  2. C. C. Gregory, J. A. Harrington, “High peak power CO2 laser transmission by hollow sapphire waveguides,” Appl. Opt. 32, 3978–3980 (1993).
    [CrossRef] [PubMed]
  3. 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]
  4. S. Wuthrich, W. Luthy, H. P. Wever, “Optical damage thresholds at 2.94 μm in fluoride glass fibers,” Appl. Opt. 29, 5833–5837 (1992).
    [CrossRef]
  5. M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. 2, 116–126 (1994).
    [CrossRef]
  6. T. Hidaka, “Loss calculation of the hollow-core, oxide-glass-cladding, middle-infrared optical waveguides,” J. Appl. Phys. 53, 93–97 (1982).
    [CrossRef]
  7. E. Garmire, T. McMahon, M. Bass, “Flexible infrared waveguides for high-power transmission,” IEEE J. Quantum Electron. QE-16, 23–32 (1980).
    [CrossRef]
  8. M. E. Marhic, “Mode-coupling analysis of bending losses in IR metallic waveguides,” Appl. Opt. 20, 3436–3441 (1981).
    [CrossRef] [PubMed]
  9. M. E. Marhic, “Loss increases in multimode rectangular infrared waveguides due to helical deformations,” IEEE Trans. Microwave Theory Tech. MTT-30, 671–678 (1982).
    [CrossRef]
  10. M. Miyagi, K. Harada, S. Kawakami, “Wave propagation and attenuation in the general class of circular hollow waveguides with uniform curvature,” IEEE Trans. Microwave Theory Tech. MTT-32, 513–521 (1984).
    [CrossRef]
  11. C. A. Hill, R. M. Jenkins, R. W. J. Devereux, “Transmission of linearly polarized infrared light through curved hollow dielectric waveguides,” IEEE J. Quantum Electron. 24, 618–624 (1988).
    [CrossRef]
  12. D. Mendlovic, E. Goldenberg, S. Ruschin, J. Dror, N. Croitoru, “Ray model for transmission of metallic–dielectric hollow bent cylindrical waveguides,” Appl. Opt. 28, 708–712 (1989).
    [CrossRef] [PubMed]
  13. S. Abe, M. Miyagi, “Transmission and attenuation of vector modes in uniformly bent circular hollow waveguides for the infrared,” IEEE Trans. Microwave Theory Tech. 40, 903–909 (1992).
    [CrossRef]
  14. M. Miyagi, Y. Matsuura, M. Saito, A. Hongo, “Spectral attenuation of IR light in circular hollow waveguides,” Appl. Opt. 27, 4169–4170 (1988).
    [CrossRef] [PubMed]
  15. Y. Matsuura, M. Saito, M. Miyagi, A. Hongo, “Loss characteristics of circular hollow waveguides for incoherent infrared light,” J. Opt. Soc. Am. A 6, 423–427 (1989).
    [CrossRef]
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    [CrossRef]
  27. T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high-spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
    [CrossRef] [PubMed]
  28. T. K. Gaylord, E. N. Glytsis, M. G. Moharam, “Zero-reflectivity homogeneous layers and high-spatial-frequency surface-relief gratings on lossy materials,” Appl. Opt. 26, 3123–3135 (1987).
    [CrossRef] [PubMed]

1994

1993

1992

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 processing,” Appl. Opt. 31, 5114–5120 (1992).
[CrossRef] [PubMed]

S. Wuthrich, W. Luthy, H. P. Wever, “Optical damage thresholds at 2.94 μm in fluoride glass fibers,” Appl. Opt. 29, 5833–5837 (1992).
[CrossRef]

S. Abe, M. Miyagi, “Transmission and attenuation of vector modes in uniformly bent circular hollow waveguides for the infrared,” IEEE Trans. Microwave Theory Tech. 40, 903–909 (1992).
[CrossRef]

1991

1990

1989

1988

M. Miyagi, Y. Matsuura, M. Saito, A. Hongo, “Spectral attenuation of IR light in circular hollow waveguides,” Appl. Opt. 27, 4169–4170 (1988).
[CrossRef] [PubMed]

C. A. Hill, R. M. Jenkins, R. W. J. Devereux, “Transmission of linearly polarized infrared light through curved hollow dielectric waveguides,” IEEE J. Quantum Electron. 24, 618–624 (1988).
[CrossRef]

1987

1986

1984

M. Miyagi, K. Harada, S. Kawakami, “Wave propagation and attenuation in the general class of circular hollow waveguides with uniform curvature,” IEEE Trans. Microwave Theory Tech. MTT-32, 513–521 (1984).
[CrossRef]

1982

M. E. Marhic, “Loss increases in multimode rectangular infrared waveguides due to helical deformations,” IEEE Trans. Microwave Theory Tech. MTT-30, 671–678 (1982).
[CrossRef]

T. Hidaka, “Loss calculation of the hollow-core, oxide-glass-cladding, middle-infrared optical waveguides,” J. Appl. Phys. 53, 93–97 (1982).
[CrossRef]

1981

1980

E. Garmire, T. McMahon, M. Bass, “Flexible infrared waveguides for high-power transmission,” IEEE J. Quantum Electron. QE-16, 23–32 (1980).
[CrossRef]

1979

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).

1963

Abe, S.

S. Abe, M. Miyagi, “Transmission and attenuation of vector modes in uniformly bent circular hollow waveguides for the infrared,” IEEE Trans. Microwave Theory Tech. 40, 903–909 (1992).
[CrossRef]

Abel, T.

Baird, W. E.

Bass, M.

E. Garmire, T. McMahon, M. Bass, “Flexible infrared waveguides for high-power transmission,” IEEE J. Quantum Electron. QE-16, 23–32 (1980).
[CrossRef]

Benett, H. E.

Carniglia, C. K.

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).

Croitoru, N.

Danilov, O. B.

Devereux, R. W. J.

C. A. Hill, R. M. Jenkins, R. W. J. Devereux, “Transmission of linearly polarized infrared light through curved hollow dielectric waveguides,” IEEE J. Quantum Electron. 24, 618–624 (1988).
[CrossRef]

Dror, J.

Garmire, E.

E. Garmire, T. McMahon, M. Bass, “Flexible infrared waveguides for high-power transmission,” IEEE J. Quantum Electron. QE-16, 23–32 (1980).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Goldenberg, E.

Gregory, C. C.

Gu, Z. H.

Harada, K.

M. Miyagi, K. Harada, S. Kawakami, “Wave propagation and attenuation in the general class of circular hollow waveguides with uniform curvature,” IEEE Trans. Microwave Theory Tech. MTT-32, 513–521 (1984).
[CrossRef]

Harrington, J. A.

Hashimoto, T.

Hidaka, T.

T. Hidaka, “Loss calculation of the hollow-core, oxide-glass-cladding, middle-infrared optical waveguides,” J. Appl. Phys. 53, 93–97 (1982).
[CrossRef]

Hill, C. A.

C. A. Hill, R. M. Jenkins, R. W. J. Devereux, “Transmission of linearly polarized infrared light through curved hollow dielectric waveguides,” IEEE J. Quantum Electron. 24, 618–624 (1988).
[CrossRef]

Hirsch, J.

Hongo, A.

Jaggard, D. L.

Jenkins, R. M.

C. A. Hill, R. M. Jenkins, R. W. J. Devereux, “Transmission of linearly polarized infrared light through curved hollow dielectric waveguides,” IEEE J. Quantum Electron. 24, 618–624 (1988).
[CrossRef]

Kawakami, S.

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. 2, 116–126 (1994).
[CrossRef]

M. Miyagi, K. Harada, S. Kawakami, “Wave propagation and attenuation in the general class of circular hollow waveguides with uniform curvature,” IEEE Trans. Microwave Theory Tech. MTT-32, 513–521 (1984).
[CrossRef]

Lu, J. Q.

Luthy, W.

S. Wuthrich, W. Luthy, H. P. Wever, “Optical damage thresholds at 2.94 μm in fluoride glass fibers,” Appl. Opt. 29, 5833–5837 (1992).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), Chap. 4.

Marhic, M. E.

M. E. Marhic, “Loss increases in multimode rectangular infrared waveguides due to helical deformations,” IEEE Trans. Microwave Theory Tech. MTT-30, 671–678 (1982).
[CrossRef]

M. E. Marhic, “Mode-coupling analysis of bending losses in IR metallic waveguides,” Appl. Opt. 20, 3436–3441 (1981).
[CrossRef] [PubMed]

Matsumoto, K.

Matsuura, Y.

Maystre, D.

McMahon, T.

E. Garmire, T. McMahon, M. Bass, “Flexible infrared waveguides for high-power transmission,” IEEE J. Quantum Electron. QE-16, 23–32 (1980).
[CrossRef]

Mendlovic, D.

Miyagi, M.

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

S. Abe, M. Miyagi, “Transmission and attenuation of vector modes in uniformly bent circular hollow waveguides for the infrared,” IEEE Trans. Microwave Theory Tech. 40, 903–909 (1992).
[CrossRef]

Y. Matsuura, M. Saito, M. Miyagi, A. Hongo, “Loss characteristics of circular hollow waveguides for incoherent infrared light,” J. Opt. Soc. Am. A 6, 423–427 (1989).
[CrossRef]

M. Miyagi, Y. Matsuura, M. Saito, A. Hongo, “Spectral attenuation of IR light in circular hollow waveguides,” Appl. Opt. 27, 4169–4170 (1988).
[CrossRef] [PubMed]

M. Miyagi, K. Harada, S. Kawakami, “Wave propagation and attenuation in the general class of circular hollow waveguides with uniform curvature,” IEEE Trans. Microwave Theory Tech. MTT-32, 513–521 (1984).
[CrossRef]

Moharam, M. G.

Morosawa, K.

Nietro-Vesperinas, M.

Rubinov, Yu. A.

Ruschin, S.

Saillard, M.

Saito, M.

Sanchez-Gil, J. A.

Shiota, T.

Sosnov, E. N.

Sun, X.

Wever, H. P.

S. Wuthrich, W. Luthy, H. P. Wever, “Optical damage thresholds at 2.94 μm in fluoride glass fibers,” Appl. Opt. 29, 5833–5837 (1992).
[CrossRef]

Wuthrich, S.

S. Wuthrich, W. Luthy, H. P. Wever, “Optical damage thresholds at 2.94 μm in fluoride glass fibers,” Appl. Opt. 29, 5833–5837 (1992).
[CrossRef]

Zintchenko, M. I.

Appl. Opt.

S. Wuthrich, W. Luthy, H. P. Wever, “Optical damage thresholds at 2.94 μm in fluoride glass fibers,” Appl. Opt. 29, 5833–5837 (1992).
[CrossRef]

M. E. Marhic, “Mode-coupling analysis of bending losses in IR metallic waveguides,” Appl. Opt. 20, 3436–3441 (1981).
[CrossRef] [PubMed]

T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high-spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
[CrossRef] [PubMed]

T. K. Gaylord, E. N. Glytsis, M. G. Moharam, “Zero-reflectivity homogeneous layers and high-spatial-frequency surface-relief gratings on lossy materials,” Appl. Opt. 26, 3123–3135 (1987).
[CrossRef] [PubMed]

M. Miyagi, Y. Matsuura, M. Saito, A. Hongo, “Spectral attenuation of IR light in circular hollow waveguides,” Appl. Opt. 27, 4169–4170 (1988).
[CrossRef] [PubMed]

D. Mendlovic, E. Goldenberg, S. Ruschin, J. Dror, N. Croitoru, “Ray model for transmission of metallic–dielectric hollow bent cylindrical waveguides,” Appl. Opt. 28, 708–712 (1989).
[CrossRef] [PubMed]

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 processing,” Appl. Opt. 31, 5114–5120 (1992).
[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]

IEEE J. Quantum Electron.

E. Garmire, T. McMahon, M. Bass, “Flexible infrared waveguides for high-power transmission,” IEEE J. Quantum Electron. QE-16, 23–32 (1980).
[CrossRef]

C. A. Hill, R. M. Jenkins, R. W. J. Devereux, “Transmission of linearly polarized infrared light through curved hollow dielectric waveguides,” IEEE J. Quantum Electron. 24, 618–624 (1988).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

S. Abe, M. Miyagi, “Transmission and attenuation of vector modes in uniformly bent circular hollow waveguides for the infrared,” IEEE Trans. Microwave Theory Tech. 40, 903–909 (1992).
[CrossRef]

M. E. Marhic, “Loss increases in multimode rectangular infrared waveguides due to helical deformations,” IEEE Trans. Microwave Theory Tech. MTT-30, 671–678 (1982).
[CrossRef]

M. Miyagi, K. Harada, S. Kawakami, “Wave propagation and attenuation in the general class of circular hollow waveguides with uniform curvature,” IEEE Trans. Microwave Theory Tech. MTT-32, 513–521 (1984).
[CrossRef]

J. Appl. Phys.

T. Hidaka, “Loss calculation of the hollow-core, oxide-glass-cladding, middle-infrared optical waveguides,” J. Appl. Phys. 53, 93–97 (1982).
[CrossRef]

J. Lightwave Technol.

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” J. Lightwave Technol. 2, 116–126 (1994).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Eng.

C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18, 104–115 (1979).

Opt. Lett.

Other

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985), Part 2.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), Chap. 4.

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Figures (11)

Fig. 1
Fig. 1

Inner surface profile along the axial direction and roughened with alumina powder of nominal diameter 34 μm.

Fig. 2
Fig. 2

Radiation field p 0(θ) from a coupling waveguide, where the open circles denote the experimental values and the solid curve an approximation expressed by Eq. (5).

Fig. 3
Fig. 3

Loss spectra of SiO2 waveguides (1.5 mm ϕ × 20 cm) with a smooth and a rough inner surface produced by alumina powder of diameter 34 μm.

Fig. 4
Fig. 4

Additional-loss spectra of SiO2 waveguides (1.5 mm ϕ × 20 cm) with rough inner surfaces produced by alumina powders of diameters 15, 34, and 57 μm.

Fig. 5
Fig. 5

X-ray microanalysis of the inner surface of a SiO2 waveguide roughened by alumina powder.

Fig. 6
Fig. 6

Additional-loss spectrum of an SiO2 waveguide (1.5 mm ϕ × 20 cm) with a rough inner surface produced by SiC powder of nominal diameter 24 μm.

Fig. 7
Fig. 7

Comparison between the additional losses observed experimentally and those predicted theoretically for an SiO2 waveguide (1.5 mm ϕ × 20 cm) with σ = 0.6 μm (dotted–dashed curve) and 2.2 μm (solid curve), respectively.

Fig. 8
Fig. 8

Schematic explanation of a rough surface with σ and S. Λ0 is the axial distance between each reflection of the ray.

Fig. 9
Fig. 9

Comparison between the additional losses observed experimentally and those predicted through the use of Eqs. (8) and (9a) (solid curve) for an SiO2 waveguide (1.5 mm ϕ × 20 cm) with σ = 0.6 μm. The dotted–dashed curve is the same as that in Fig. 7.

Fig. 10
Fig. 10

Thin-film-coating model of a rough surface: the refractive index of the film is a weighted average of refractive indexes of the hollow core n 0 (=1) and the cladding n 0(njκ).

Fig. 11
Fig. 11

Comparison between the additional losses observed experimentally and those predicted through the use of Eqs. (10)(12) for an SiO2 waveguide (1.5 mm ϕ × 20 cm) with σ = 0.6 μm: M = 0.1 (solid curve) and M = 0.5 (dotted–dashed curve).

Equations (12)

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

R ( λ , θ ) = R 0 ( λ , θ ) exp [ - ( 4 π n 0 sin θ / λ ) 2 ] ,
T ( z ) = 0 π / 2 p 0 ( θ ) exp [ - 2 α ( θ ) z ] sin θ d θ / 0 π / 2 p 0 ( θ ) sin θ d θ ,
2 α ( θ ) = 1 - R ( θ ) 2 T cot θ ,
R ( θ ) = [ R p ( θ ) + R s ( θ ) ] / 2 ,
p 0 ( θ ) = { exp [ - ( θ / 2.8 ) 2 ] 0.85 exp [ - ( θ / 4.2 ) 2 ] ,             0 ° < θ < 1.51 ° 1.51 ° < θ < 12.6 ° ,
w ( x ) = ( 2 π σ 2 ) - 1 / 2 exp ( - x 2 / 2 σ 2 ) ,
2 α ( θ ) = 2 α 0 ( θ ) + 2 α r ( θ ) ,
α 0 ( θ ) = ( n 0 k 0 T sin θ 2 π ) 2 λ 2 T 3 Re [ n ^ 2 + 1 2 ( n ^ 2 - 1 ) 1 / 2 ] .
α r ( θ ) = { n 0 k 0 σ 2 sin θ 2 T cot θ ( π n 0 k 0 S ) 1 / 2 π ( n 0 k 0 ) 3 σ 2 sin θ 4 T cot θ S .             n 0 k 0 S 1 n 0 k 0 S 1
n ^ f = ( 1 - M ) n 0 + M ( n - j κ ) n 0 ,
R ( θ ) = 0 R m ( 2 D , θ ) f ( D ) d D ,
f ( D ) = 2 ( 2 π σ 2 ) - 1 / 2 exp ( - D 2 / 2 σ 2 ) .

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