Abstract

A simple and convenient method was proposed for the calculation of transmission loss in a circular hollow waveguide. The method is based on a simple ray theory and is applicable to multimode transmission of incoherent light. In order to confirm the validity of the method, spectral losses of various kinds of hollow waveguide were measured and compared with the theoretical values. For a silica waveguide, good coincidence was obtained between calculated and measured values, whereas, for metallic waveguides, surface irregularities must be taken into account for prediction of optical losses.

© 1989 Optical Society of America

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References

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  1. M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” IEEE J. Lightwave Technol. LT-2, 116–126 (1984).
    [CrossRef]
  2. A. Hongo, T. Shiota, M. Suzuki, M. Miyagi, “Germanium-coated nickel hollow waveguides for high-powered CO2laser light transmission,” in Technical Digest of the 1988 Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WL2.
  3. M. Miyagi, Y. Matsuura, M. Saito, A. Hongo, “Spectral attenuation of incoherent infrared light in circular waveguides,” Appl. Opt. 27, 4169–4170 (1988).
    [CrossRef] [PubMed]
  4. M. Miyagi, “Waveguide loss evaluation in circular hollow waveguides and its ray optical treatment,” IEEE J. Lightwave Technol. LT-3, 303–307 (1985).
    [CrossRef]
  5. H. E. Bennett, “Specular reflectance of aluminized ground glass and the height distribution of surface irregularities,”J. Opt. Soc. Am. 53, 1389–1394 (1963).
    [CrossRef]
  6. D. Beaglehole, O. Hundrei, “Study of the interaction of light with rough metal surface. I. Experiment,” Phys. Rev. B 2, 309–321 (1970).
    [CrossRef]
  7. H. Fujii, J. W. Y. Lit, “Surface roughness measurement using dichromatic speckle pattern: an experimental study,” Appl. Opt. 17, 2690–2694 (1978).
    [CrossRef] [PubMed]
  8. E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985), Part II, pp. 313–323, 749–763.
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1985), pp. 36–66.

1988 (1)

1985 (1)

M. Miyagi, “Waveguide loss evaluation in circular hollow waveguides and its ray optical treatment,” IEEE J. Lightwave Technol. LT-3, 303–307 (1985).
[CrossRef]

1984 (1)

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” IEEE J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

1978 (1)

1970 (1)

D. Beaglehole, O. Hundrei, “Study of the interaction of light with rough metal surface. I. Experiment,” Phys. Rev. B 2, 309–321 (1970).
[CrossRef]

1963 (1)

Beaglehole, D.

D. Beaglehole, O. Hundrei, “Study of the interaction of light with rough metal surface. I. Experiment,” Phys. Rev. B 2, 309–321 (1970).
[CrossRef]

Bennett, H. E.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1985), pp. 36–66.

Fujii, H.

Hongo, A.

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

A. Hongo, T. Shiota, M. Suzuki, M. Miyagi, “Germanium-coated nickel hollow waveguides for high-powered CO2laser light transmission,” in Technical Digest of the 1988 Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WL2.

Hundrei, O.

D. Beaglehole, O. Hundrei, “Study of the interaction of light with rough metal surface. I. Experiment,” Phys. Rev. B 2, 309–321 (1970).
[CrossRef]

Kawakami, S.

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” IEEE J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

Lit, J. W. Y.

Matsuura, Y.

Miyagi, M.

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

M. Miyagi, “Waveguide loss evaluation in circular hollow waveguides and its ray optical treatment,” IEEE J. Lightwave Technol. LT-3, 303–307 (1985).
[CrossRef]

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” IEEE J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

A. Hongo, T. Shiota, M. Suzuki, M. Miyagi, “Germanium-coated nickel hollow waveguides for high-powered CO2laser light transmission,” in Technical Digest of the 1988 Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WL2.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985), Part II, pp. 313–323, 749–763.

Saito, M.

Shiota, T.

A. Hongo, T. Shiota, M. Suzuki, M. Miyagi, “Germanium-coated nickel hollow waveguides for high-powered CO2laser light transmission,” in Technical Digest of the 1988 Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WL2.

Suzuki, M.

A. Hongo, T. Shiota, M. Suzuki, M. Miyagi, “Germanium-coated nickel hollow waveguides for high-powered CO2laser light transmission,” in Technical Digest of the 1988 Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WL2.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1985), pp. 36–66.

Appl. Opt. (2)

IEEE J. Lightwave Technol. (2)

M. Miyagi, S. Kawakami, “Design theory of dielectric-coated circular metallic waveguides for infrared transmission,” IEEE J. Lightwave Technol. LT-2, 116–126 (1984).
[CrossRef]

M. Miyagi, “Waveguide loss evaluation in circular hollow waveguides and its ray optical treatment,” IEEE J. Lightwave Technol. LT-3, 303–307 (1985).
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Rev. B (1)

D. Beaglehole, O. Hundrei, “Study of the interaction of light with rough metal surface. I. Experiment,” Phys. Rev. B 2, 309–321 (1970).
[CrossRef]

Other (3)

A. Hongo, T. Shiota, M. Suzuki, M. Miyagi, “Germanium-coated nickel hollow waveguides for high-powered CO2laser light transmission,” in Technical Digest of the 1988 Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper WL2.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985), Part II, pp. 313–323, 749–763.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1985), pp. 36–66.

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Figures (11)

Fig. 1
Fig. 1

Ray model for theoretical evaluation of transmission loss.

Fig. 2
Fig. 2

Illustration for considering an angular distribution of incident rays. The far-field distribution p0(θ) should be weighted by sin θ, since the area of the hatched ring is proportional to sin θ.

Fig. 3
Fig. 3

Experimental setup for measuring waveguide attenuation.

Fig. 4
Fig. 4

Angular profile, or a far-field profile, of the launching beam, which was measured for a coupling waveguide made of nickel, 0.8 mm in diameter and 4 cm in length. Small circles indicate the measured intensity, which is approximated by a Gaussian curve.

Fig. 5
Fig. 5

Attenuation spectra of silica hollow waveguides (a) 1.8 mm in diameter and 100 cm in length and (b) 2.3 mm in diameter and 40 cm in length.

Fig. 6
Fig. 6

Attenuation spectra of nickel hollow waveguides (a) 1.6 mm in diameter and 100 cm in length and (b) 2.2 mm in diameter and 100 cm in length. The dotted–dashed curve indicates the theoretical result calculated by taking surface irregularities into consideration.

Fig. 7
Fig. 7

Attenuation spectra of germanium-coated nickel hollow waveguides 1.5 mm in diameter and 100 cm in length. The coating thicknesses are (a) 0.2 μm, (b) 0.4 μm, and (c) 0.6 μm. Solid curves represent theoretical values without surface irregularities, and dotted–dashed curves represent theoretical values calculated by taking surface irregularities into consideration.

Fig. 8
Fig. 8

Schematic illustration of a ray reflected on an irregular surface.

Fig. 9
Fig. 9

Reflection on a dielectric-coated waveguide surface.

Fig. 10
Fig. 10

Complex refractive index, njκ, of silica glass.8

Fig. 11
Fig. 11

Complex refractive index, njκ, of nickel.8

Equations (18)

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2 α ( θ ) = 1 - R ( θ ) 2 T cot θ ,
R ( θ ) = R s ( θ ) + R p ( θ ) 2 .
P ( z ) = 0 θ max p 0 ( θ ) exp [ - 2 α ( θ ) z ] sin θ d θ
= 0 θ max p 0 ( θ ) exp [ - 1 - R ( θ ) 2 T cot θ z ] sin θ d θ ,
p 0 ( θ ) exp [ - ( θ / θ 0 ) 2 ] ,
R ( θ ) = R ( θ ) exp [ - ( 4 π n i σ sin θ λ ) 2 ] ,
r 1 p = n F cos ψ 1 - cos ψ 2 n F cos ψ 1 + cos ψ 2
r 1 s = cos ψ 1 - n F cos ψ 2 cos ψ 1 + n F cos ψ 2
r 2 = ρ 2 exp ( j ϕ 2 ) .
ρ 2 p 2 = [ ( n 2 - κ 2 ) cos ψ 2 - n F u ] 2 + ( 2 n κ cos ψ 2 - n F v ) 2 [ ( n 2 - κ 2 ) cos ψ 2 + n F u ] 2 + ( 2 n κ cos ψ 2 + n F v ) 2 ,
tan ϕ 2 p = 2 n F cos ψ 2 - 2 n κ u - ( n 2 - κ 2 ) v ( n 2 + κ 2 ) 2 cos 2 ψ 2 - n F 2 ( u 2 + v 2 ) ,
ρ 2 s 2 = ( n F cos ψ 2 - u ) 2 + v 2 ( n F cos ψ 2 + u ) 2 + v 2 ,
tan ϕ 2 s = - 2 v n F cos ψ 2 u 2 + v 2 - n F 2 cos 2 ψ 2 ,
u 2 = ½ { n 2 - κ 2 - n F 2 sin 2 ψ 2 + [ ( n 2 - κ 2 - n F 2 sin 2 ψ 2 ) 2 + 4 n 2 κ 2 ] 1 / 2 } ,
v 2 = ½ { - ( n 2 - κ 2 - n F 2 sin 2 ψ 2 ) + [ ( n 2 - κ 2 - n F 2 sin 2 ψ 2 ) 2 + 4 n 2 κ 2 ] 1 / 2 } .
r = r 1 + r 2 exp ( - j 2 Γ ) 1 + r 1 r 2 exp ( - j 2 Γ ) = r 1 + ρ 2 exp [ j ( ϕ 2 - 2 Γ ) ] 1 + r 1 ρ 2 exp [ j ( ϕ 2 - 2 Γ ) ] ,
Γ = k 0 n F d cos ψ 2 .
r 2 = r 1 2 + ρ 2 2 + 2 r 1 ρ 2 cos ( ϕ 2 - 2 Γ ) 1 + r 1 2 ρ 2 2 + 2 r 1 ρ 2 cos ( ϕ 2 - 2 Γ ) .

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