Abstract

Propagation of TE-waves along a single curved metallic surface with radius of curvature much larger than wavelength is investigated both theoretically and experimentally. Approximate analytic expressions for the field configuration yield that power concentrates in a small region near the metal. The attenuation constant per unit angle of bend (radian) is given by the real part of the inverse of the refractive index, independent of the radius of curvature and of the mode number. In agreement with theory experiments with 10-μm radiation showed that low loss guiding can be realized.

© 1978 Optical Society of America

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References

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  1. E. Garmire, T. McMahon, M. Bass, Appl. Phys. Lett. 31, 92 (1977).
    [CrossRef]
  2. H. Krammer, Appl. Opt. 16, 2163 (1977).
    [CrossRef] [PubMed]
  3. S. Sheem, J. R. Whinnery, Wave Electron. 1, 61 (1974).
  4. M. Heiblum, J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
    [CrossRef]
  5. L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1955), pp. 184–193.
  6. H. Nishihara, T. Inoue, J. Koyoma, Appl. Phys. Lett. 25, 391 (1974).
    [CrossRef]

1977 (2)

E. Garmire, T. McMahon, M. Bass, Appl. Phys. Lett. 31, 92 (1977).
[CrossRef]

H. Krammer, Appl. Opt. 16, 2163 (1977).
[CrossRef] [PubMed]

1975 (1)

M. Heiblum, J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

1974 (2)

H. Nishihara, T. Inoue, J. Koyoma, Appl. Phys. Lett. 25, 391 (1974).
[CrossRef]

S. Sheem, J. R. Whinnery, Wave Electron. 1, 61 (1974).

Bass, M.

E. Garmire, T. McMahon, M. Bass, Appl. Phys. Lett. 31, 92 (1977).
[CrossRef]

Garmire, E.

E. Garmire, T. McMahon, M. Bass, Appl. Phys. Lett. 31, 92 (1977).
[CrossRef]

Harris, J. H.

M. Heiblum, J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

Heiblum, M.

M. Heiblum, J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

Inoue, T.

H. Nishihara, T. Inoue, J. Koyoma, Appl. Phys. Lett. 25, 391 (1974).
[CrossRef]

Koyoma, J.

H. Nishihara, T. Inoue, J. Koyoma, Appl. Phys. Lett. 25, 391 (1974).
[CrossRef]

Krammer, H.

McMahon, T.

E. Garmire, T. McMahon, M. Bass, Appl. Phys. Lett. 31, 92 (1977).
[CrossRef]

Nishihara, H.

H. Nishihara, T. Inoue, J. Koyoma, Appl. Phys. Lett. 25, 391 (1974).
[CrossRef]

Schiff, L. I.

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1955), pp. 184–193.

Sheem, S.

S. Sheem, J. R. Whinnery, Wave Electron. 1, 61 (1974).

Whinnery, J. R.

S. Sheem, J. R. Whinnery, Wave Electron. 1, 61 (1974).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

E. Garmire, T. McMahon, M. Bass, Appl. Phys. Lett. 31, 92 (1977).
[CrossRef]

H. Nishihara, T. Inoue, J. Koyoma, Appl. Phys. Lett. 25, 391 (1974).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Heiblum, J. H. Harris, IEEE J. Quantum Electron. QE-11, 75 (1975).
[CrossRef]

Wave Electron. (1)

S. Sheem, J. R. Whinnery, Wave Electron. 1, 61 (1974).

Other (1)

L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1955), pp. 184–193.

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Figures (4)

Fig. 1
Fig. 1

(a) Curved metallic plate. The arrangement infinitely extends normal to the plane of drawing. (b) Conformal transformation. The region rR is transformed to the half-plane u ≤ 0.

Fig. 2
Fig. 2

Electric field of TE-modes dependent on the normalized coordinate ξ according to Eq. (9) for ξ > 0, Eq. (10) for ξ < 0, Eq. (11) for ξ ≈ 0. For the pth mode the metallic surface is at the pth zero ξp. For ξξp the function E(ξ) gives the field distribution.

Fig. 3
Fig. 3

Experimental arrangements. (a) Experiment to demonstrate guiding of a TE-wave along a curved metallic plate; (b) arrangement to measure the transmitted power in dependence of the angle of bend (resp. number of turns). PM = power meter; FM = focusing mirror; PP1, PP2 = parallel plate waveguide; CP = curved plate.

Fig. 4
Fig. 4

Transmitted power as a function of angle of bend. Experimental data (×) and best fitting theoretical result ln(P/P0) = −2φ Re{n−l} where Re{n−1} = 0.008.

Equations (22)

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d 2 E d r 2 + 1 r d E d r + ( k 2 ν 2 r 2 ) E = 0
υ = R φ , u = R ln ( r / R ) .
[ u , υ 2 + k 2 exp ( 2 u / R ) ] E = 0
[ u , υ 2 + ( 1 + 2 u / R ) k 2 ] E = 0 .
d 2 E / d u 2 + [ ( k 2 β 2 ) + ( 2 k 2 / R ) u ] E = 0.
ξ = ( 2 k 2 / R ) 1 / 3 u + ξ p
ξ p = ( 2 k 2 / R ) 2 / 3 ( k 2 β 2 )
d 2 E / d ξ 2 + ξ E = 0.
E ( ξ ) = A ξ 1 / 4 cos ( 2 3 ξ 3 / 2 π / 4 ) for ξ > 0
E ( ξ ) = A 2 | ξ | 1 / 4 exp ( 2 3 | ξ | 3 / 2 ) for ξ < 0.
E ( ξ ) = A ( π 1 / 2 / 3 ) [ 3 1 / 3 / Γ ( 2 3 ) + 3 2 / 3 ξ / Γ ( 1 3 ) ] = A ( 0.62927 + 0.45875 ξ )
ξ p = [ 3 ( 4 p 1 ) π / 8 ] 2 / 3 ( p = 1 , 2 , . . . ) .
| u o | = [ 3 ( 4 p 1 ) π / 8 ] 2 / 3 ( R / 2 k 2 ) 1 / 3 R ,
2 α = P r / P φ ,
P r = 1 2 Re { E z H φ * } r = R ,
P φ = 1 2 Re { 0 R E z H r * d r } .
E ( 0 ) = j n k ( d E d u ) u = 0 .
α = a p R 1 Re { n 1 } ,
a p = A 2 ξ p 1 / 2 / ξ p 1 [ E ( ξ ) ] 2 d ξ
ξ p E 2 d ξ = ξ 1 E 2 d ξ + ξ 1 ξ 2 E 2 d ξ + . . . + ξ 1 ξ p E 2 d ξ .
ξ 1 E 2 d ξ A 2 ξ 1 1 / 2 , ξ m 1 ξ m E 2 d ξ = A 2 ( ξ m 1 / 2 ξ m 1 1 / 2
α = R 1 Re { n 1 } .

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