Abstract

Losses in the general class of sharply bent circular hollow waveguides are evaluated theoretically for linearly polarized modes. A theory presented in this paper confirms the experimental results for metallic waveguides obtained previously, when the polarization is perpendicular to the plane of curvature.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Krammer, “Propagation of Modes in Curved Hollow Metallic Waveguides for the Infrared,” Appl. Opt. 16, 2163–2165 (1977).
    [CrossRef] [PubMed]
  2. E. Garmire, T. McMahon, M. Bass, “Flexible Infrared Waveguides for High-Power Transmission,” IEEE J. Quantum Electron. QE-16, 23–32 (1980).
    [CrossRef]
  3. M. Miyagi, “Bending Losses in Hollow and Dielectric Tube Leaky Waveguides,” Appl. Opt. 20, 1221–1229 (1981).
    [CrossRef] [PubMed]
  4. M. E. Marhic, “Mode-Coupling Analysis of Bending Losses in IR Metallic Waveguides,” Appl. Opt. 20, 3436–3441 (1981).
    [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. M. Miyagi, K. Harada, Y. Aizawa, S. Kawakami, “Transmission Properties of Circular Dielectric-Coated Metallic Waveguides for Infrared Transmission,” Proc. Soc. Photo-Opt. Instrum. Eng. 484, 117–123 (1984).
  8. R. M. Jenkins, R. W. J. Devereux, “Transmission Characteristics of a Curved Hollow Silica Waveguide at 10.6 μm,” IEEE J. Quantum Electron. QE-22, 718–722 (1986).
    [CrossRef]
  9. S. J. Wilson, R. M. Jenkins, R. W. J. Devereux, “Hollow-Core Silica Waveguides,” IEEE J. Quantum Electron. QE-23, 52–58 (1987).
    [CrossRef]
  10. N. Croitoru, J. Dror, E. Goldenberg, D. Mendlovic, S. Ruschin, “Use of Metallic and Dielectric Films for Hollow Fibers,” Fiber and Integrated Opt. 6, 347–361 (1987).
    [CrossRef]
  11. J. Jiao, W. L. Kath, X. Fang, M. E. Marhic, “Losses of Infrared Biconcave Metallic Whispering-Gallery Guides,” paper presented at Fourth International Conference on Infrared Physics, Zurich, Aug. 22–26 (1988).
  12. M. Miyagi, S. Kawakami, “Waveguide Loss Evaluation by the Ray-Optics Method,” J. Opt. Soc. Am. 73, 486–489 (1983).
    [CrossRef]
  13. M. Miyagi, A. Hongo, S. Kawakami, “Transmission Characteristics of Dielectric-Coated Metallic Waveguide for Infrared Transmission: Slab Waveguide Model,” IEEE J Quantum Electron. QE-19, 136–145 (1983).
    [CrossRef]
  14. M. E. Marhic, L. I. Kwan, M. Epstein, “Whispering-Gallery CO2 Laser,” IEEE J. Quantum Electron. QE-15, 487–490 (1979).
    [CrossRef]
  15. K. Harada, Master Thesis, Tohoku University (1984).
  16. S. Abe, M. Miyagi, unpublished.

1989

1987

S. J. Wilson, R. M. Jenkins, R. W. J. Devereux, “Hollow-Core Silica Waveguides,” IEEE J. Quantum Electron. QE-23, 52–58 (1987).
[CrossRef]

N. Croitoru, J. Dror, E. Goldenberg, D. Mendlovic, S. Ruschin, “Use of Metallic and Dielectric Films for Hollow Fibers,” Fiber and Integrated Opt. 6, 347–361 (1987).
[CrossRef]

1986

R. M. Jenkins, R. W. J. Devereux, “Transmission Characteristics of a Curved Hollow Silica Waveguide at 10.6 μm,” IEEE J. Quantum Electron. QE-22, 718–722 (1986).
[CrossRef]

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]

M. Miyagi, K. Harada, Y. Aizawa, S. Kawakami, “Transmission Properties of Circular Dielectric-Coated Metallic Waveguides for Infrared Transmission,” Proc. Soc. Photo-Opt. Instrum. Eng. 484, 117–123 (1984).

1983

M. Miyagi, A. Hongo, S. Kawakami, “Transmission Characteristics of Dielectric-Coated Metallic Waveguide for Infrared Transmission: Slab Waveguide Model,” IEEE J Quantum Electron. QE-19, 136–145 (1983).
[CrossRef]

M. Miyagi, S. Kawakami, “Waveguide Loss Evaluation by the Ray-Optics Method,” J. Opt. Soc. Am. 73, 486–489 (1983).
[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

M. E. Marhic, L. I. Kwan, M. Epstein, “Whispering-Gallery CO2 Laser,” IEEE J. Quantum Electron. QE-15, 487–490 (1979).
[CrossRef]

1977

Abe, S.

S. Abe, M. Miyagi, unpublished.

Aizawa, Y.

M. Miyagi, K. Harada, Y. Aizawa, S. Kawakami, “Transmission Properties of Circular Dielectric-Coated Metallic Waveguides for Infrared Transmission,” Proc. Soc. Photo-Opt. Instrum. Eng. 484, 117–123 (1984).

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]

Croitoru, N.

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]

N. Croitoru, J. Dror, E. Goldenberg, D. Mendlovic, S. Ruschin, “Use of Metallic and Dielectric Films for Hollow Fibers,” Fiber and Integrated Opt. 6, 347–361 (1987).
[CrossRef]

Devereux, R. W. J.

S. J. Wilson, R. M. Jenkins, R. W. J. Devereux, “Hollow-Core Silica Waveguides,” IEEE J. Quantum Electron. QE-23, 52–58 (1987).
[CrossRef]

R. M. Jenkins, R. W. J. Devereux, “Transmission Characteristics of a Curved Hollow Silica Waveguide at 10.6 μm,” IEEE J. Quantum Electron. QE-22, 718–722 (1986).
[CrossRef]

Dror, J.

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]

N. Croitoru, J. Dror, E. Goldenberg, D. Mendlovic, S. Ruschin, “Use of Metallic and Dielectric Films for Hollow Fibers,” Fiber and Integrated Opt. 6, 347–361 (1987).
[CrossRef]

Epstein, M.

M. E. Marhic, L. I. Kwan, M. Epstein, “Whispering-Gallery CO2 Laser,” IEEE J. Quantum Electron. QE-15, 487–490 (1979).
[CrossRef]

Fang, X.

J. Jiao, W. L. Kath, X. Fang, M. E. Marhic, “Losses of Infrared Biconcave Metallic Whispering-Gallery Guides,” paper presented at Fourth International Conference on Infrared Physics, Zurich, Aug. 22–26 (1988).

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]

Goldenberg, E.

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]

N. Croitoru, J. Dror, E. Goldenberg, D. Mendlovic, S. Ruschin, “Use of Metallic and Dielectric Films for Hollow Fibers,” Fiber and Integrated Opt. 6, 347–361 (1987).
[CrossRef]

Harada, K.

M. Miyagi, K. Harada, Y. Aizawa, S. Kawakami, “Transmission Properties of Circular Dielectric-Coated Metallic Waveguides for Infrared Transmission,” Proc. Soc. Photo-Opt. Instrum. Eng. 484, 117–123 (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]

K. Harada, Master Thesis, Tohoku University (1984).

Hongo, A.

M. Miyagi, A. Hongo, S. Kawakami, “Transmission Characteristics of Dielectric-Coated Metallic Waveguide for Infrared Transmission: Slab Waveguide Model,” IEEE J Quantum Electron. QE-19, 136–145 (1983).
[CrossRef]

Jenkins, R. M.

S. J. Wilson, R. M. Jenkins, R. W. J. Devereux, “Hollow-Core Silica Waveguides,” IEEE J. Quantum Electron. QE-23, 52–58 (1987).
[CrossRef]

R. M. Jenkins, R. W. J. Devereux, “Transmission Characteristics of a Curved Hollow Silica Waveguide at 10.6 μm,” IEEE J. Quantum Electron. QE-22, 718–722 (1986).
[CrossRef]

Jiao, J.

J. Jiao, W. L. Kath, X. Fang, M. E. Marhic, “Losses of Infrared Biconcave Metallic Whispering-Gallery Guides,” paper presented at Fourth International Conference on Infrared Physics, Zurich, Aug. 22–26 (1988).

Kath, W. L.

J. Jiao, W. L. Kath, X. Fang, M. E. Marhic, “Losses of Infrared Biconcave Metallic Whispering-Gallery Guides,” paper presented at Fourth International Conference on Infrared Physics, Zurich, Aug. 22–26 (1988).

Kawakami, S.

M. Miyagi, K. Harada, Y. Aizawa, S. Kawakami, “Transmission Properties of Circular Dielectric-Coated Metallic Waveguides for Infrared Transmission,” Proc. Soc. Photo-Opt. Instrum. Eng. 484, 117–123 (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]

M. Miyagi, A. Hongo, S. Kawakami, “Transmission Characteristics of Dielectric-Coated Metallic Waveguide for Infrared Transmission: Slab Waveguide Model,” IEEE J Quantum Electron. QE-19, 136–145 (1983).
[CrossRef]

M. Miyagi, S. Kawakami, “Waveguide Loss Evaluation by the Ray-Optics Method,” J. Opt. Soc. Am. 73, 486–489 (1983).
[CrossRef]

Krammer, H.

Kwan, L. I.

M. E. Marhic, L. I. Kwan, M. Epstein, “Whispering-Gallery CO2 Laser,” IEEE J. Quantum Electron. QE-15, 487–490 (1979).
[CrossRef]

Marhic, M. E.

M. E. Marhic, “Mode-Coupling Analysis of Bending Losses in IR Metallic Waveguides,” Appl. Opt. 20, 3436–3441 (1981).
[CrossRef] [PubMed]

M. E. Marhic, L. I. Kwan, M. Epstein, “Whispering-Gallery CO2 Laser,” IEEE J. Quantum Electron. QE-15, 487–490 (1979).
[CrossRef]

J. Jiao, W. L. Kath, X. Fang, M. E. Marhic, “Losses of Infrared Biconcave Metallic Whispering-Gallery Guides,” paper presented at Fourth International Conference on Infrared Physics, Zurich, Aug. 22–26 (1988).

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.

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]

N. Croitoru, J. Dror, E. Goldenberg, D. Mendlovic, S. Ruschin, “Use of Metallic and Dielectric Films for Hollow Fibers,” Fiber and Integrated Opt. 6, 347–361 (1987).
[CrossRef]

Miyagi, M.

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]

M. Miyagi, K. Harada, Y. Aizawa, S. Kawakami, “Transmission Properties of Circular Dielectric-Coated Metallic Waveguides for Infrared Transmission,” Proc. Soc. Photo-Opt. Instrum. Eng. 484, 117–123 (1984).

M. Miyagi, A. Hongo, S. Kawakami, “Transmission Characteristics of Dielectric-Coated Metallic Waveguide for Infrared Transmission: Slab Waveguide Model,” IEEE J Quantum Electron. QE-19, 136–145 (1983).
[CrossRef]

M. Miyagi, S. Kawakami, “Waveguide Loss Evaluation by the Ray-Optics Method,” J. Opt. Soc. Am. 73, 486–489 (1983).
[CrossRef]

M. Miyagi, “Bending Losses in Hollow and Dielectric Tube Leaky Waveguides,” Appl. Opt. 20, 1221–1229 (1981).
[CrossRef] [PubMed]

S. Abe, M. Miyagi, unpublished.

Ruschin, S.

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]

N. Croitoru, J. Dror, E. Goldenberg, D. Mendlovic, S. Ruschin, “Use of Metallic and Dielectric Films for Hollow Fibers,” Fiber and Integrated Opt. 6, 347–361 (1987).
[CrossRef]

Wilson, S. J.

S. J. Wilson, R. M. Jenkins, R. W. J. Devereux, “Hollow-Core Silica Waveguides,” IEEE J. Quantum Electron. QE-23, 52–58 (1987).
[CrossRef]

Appl. Opt.

Fiber and Integrated Opt.

N. Croitoru, J. Dror, E. Goldenberg, D. Mendlovic, S. Ruschin, “Use of Metallic and Dielectric Films for Hollow Fibers,” Fiber and Integrated Opt. 6, 347–361 (1987).
[CrossRef]

IEEE J Quantum Electron.

M. Miyagi, A. Hongo, S. Kawakami, “Transmission Characteristics of Dielectric-Coated Metallic Waveguide for Infrared Transmission: Slab Waveguide Model,” IEEE J Quantum Electron. QE-19, 136–145 (1983).
[CrossRef]

IEEE J. Quantum Electron.

M. E. Marhic, L. I. Kwan, M. Epstein, “Whispering-Gallery CO2 Laser,” IEEE J. Quantum Electron. QE-15, 487–490 (1979).
[CrossRef]

E. Garmire, T. McMahon, M. Bass, “Flexible Infrared Waveguides for High-Power Transmission,” IEEE J. Quantum Electron. QE-16, 23–32 (1980).
[CrossRef]

R. M. Jenkins, R. W. J. Devereux, “Transmission Characteristics of a Curved Hollow Silica Waveguide at 10.6 μm,” IEEE J. Quantum Electron. QE-22, 718–722 (1986).
[CrossRef]

S. J. Wilson, R. M. Jenkins, R. W. J. Devereux, “Hollow-Core Silica Waveguides,” IEEE J. Quantum Electron. QE-23, 52–58 (1987).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

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. Opt. Soc. Am.

Proc. Soc. Photo-Opt. Instrum. Eng.

M. Miyagi, K. Harada, Y. Aizawa, S. Kawakami, “Transmission Properties of Circular Dielectric-Coated Metallic Waveguides for Infrared Transmission,” Proc. Soc. Photo-Opt. Instrum. Eng. 484, 117–123 (1984).

Other

K. Harada, Master Thesis, Tohoku University (1984).

S. Abe, M. Miyagi, unpublished.

J. Jiao, W. L. Kath, X. Fang, M. E. Marhic, “Losses of Infrared Biconcave Metallic Whispering-Gallery Guides,” paper presented at Fourth International Conference on Infrared Physics, Zurich, Aug. 22–26 (1988).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Coordinate system for bent circular waveguide.

Fig. 2
Fig. 2

Magnitude of the weighting parameter c as a function of b , where the upper scale corresponds to the bending radius R for T = 0.75mm and λ = 10.6 μm.

Fig. 3
Fig. 3

Bending losses in circular hollow nickel waveguide with T = 0.75mm at λ = 10.6 μm, where n is assumed to be 9.1–j34.4.7 Dashed lines correspond to attenuation when c is not taken into account, i.e., c = 0.

Fig. 4
Fig. 4

Total attenuation (● and ○) obtained experimentally in a bent nickel hollow waveguide with 1.5mm ϕ and 1m long, where the first 20 cm are straight and the remainder are uniformly bent.7 Solid lines correspond to theoretical predictions (m = 1) and dashed lines correspond to theoretical ones with c = 0, where n is assumed to be 13–j34.4.

Equations (26)

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

2 α = Re c E × H * · r ^ d c Re s E × H * · z ^ d S ,
2 α = Re c ( E θ H z * - E z H θ * ) d c Re s ( E r H θ * - E θ H r * ) d S .
2 α T E = Re c E θ H z * d c Re s ( - E θ H r * ) d S Re c E θ H z * d c P T E ,
2 α T M = Re c ( - E z H θ * ) d c Re s E r H θ * d S Re c ( - E z H θ * ) d c P T M ,
α = α T E P T E + α T M P T M P T E + P T M = α T E + c α T M 1 + c ,
c = P T M / P T E .
α T E = Re ( z T E ) / R ,
α T M = Re ( y T M ) / R .
2 E x 2 + 2 E y 2 + ( n 0 2 k 0 2 + 2 n 0 2 k 0 2 x R - β 2 ) E = 0.
ξ = x / T - [ 1 - ( y / T ) 2 ] 1 / 2 ,
η = y / T ,
E = H m - 1 ( b 1 / 4 η ) A i [ - ( 2 b ) 1 / 3 ξ - ζ p ] exp ( - b 1 / 2 η 2 / 2 ) ,
b = ( n 0 k 0 ) 2 T 3 / R ,
ζ p = [ 3 π ( 4 p - 1 ) / 8 ] 2 / 3 .
H m ( x ) = ( - 1 ) m exp ( x 2 ) d m exp ( - x 2 ) d x m .
E θ = x E / x 2 + y 2 ,
E r = y E / x 2 + y 2 ,
c = s y 2 E 2 / ( x 2 + y 2 ) d x d y s x 2 E 2 / ( x 2 + y 2 ) d x d y ,
y 2 x 2 + y 2 ( y / T ) 2 ,
x 2 x 2 + y 2 1 - ( y / T ) 2 ,
ξ x / T - 1 ,
c = - η 2 H m - 1 2 ( b 1 / 4 η ) exp ( - b 1 / 2 η 2 ) d η - ( 1 - η 2 ) H m - 1 2 ( b 1 / 4 η ) exp ( - b 1 / 2 η 2 ) d η = 2 m - 1 2 b - ( 2 m - 1 ) .
α = α T M + c α T E 1 + c ,
α = n R ( 1 + c ) ( 1 n 2 + κ 2 + c )             : E .
α = n R ( 1 + c ) ( c n 2 + κ 2 + 1 ) n / R             : E .
R u = ( n 0 k 0 ) 2 T 3 [ 3 / 8 ( m - 1 / 4 ) π ] 2 [ 1 + ( 2 m - 1 / 2 ) - 2 / 3 ) ] 3 ,

Metrics