Abstract

The expression for transmissivity of submillimeter waves through metal light pipes, T=exp[ν/σ(L/d)] is given. A comparison of the theoretical calculation with the data measured is made. It is shown that these results agree more closely with the experimental values than do the previously calculated theoretical values.

© 1996 Optical Society of America

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References

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  1. R. C. Ohlmann, P. L. Richards, and M. Tinkham, “Farinfrared transmission through metal light pipes,” J. Opt. Soc. Am. 48, 531–533 (1958).
    [CrossRef]
  2. R. E. Harris, R. L. Cappelletti, and D. M. Ginsberg, “Farinfrared transmission through metal light pipes with low thermal conductance,” Appl. Opt. 5, 1083 (1966).
    [CrossRef] [PubMed]
  3. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 8, p. 370.
  4. Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “CwCH3OH far infrared lasers,” Acta Opt. Sin. 2, 9–17 (1982).
  5. Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “Optically pumped submillimeter-wave laser in formic acid vapor and in formic acid–methanol vapor,” Acta Opt. Sin. 3, 603–609 (1983).
  6. In Refs. 1, 2, and 7 this formula reads asT=12exp(−2q)+[1−exp(−q/2F2)]F2/q≃12[1+exp(−2q)]−q/3F2, but the correct formula should be relation (26).
  7. F. K. Kneububl and E. Affolter, in Infrared and Millimeter Waves, K. J. Button, ed. (Academic, New York, 1959), Vol. 1, p. 235.
  8. Xiong Shouren, Su Jinwen, and Shi Guoliang, “A sub-mm and waveguide made of gold-coated glass tube,” Chin. J. Infrared Res. 5, 161–166 (1986).

1986 (1)

Xiong Shouren, Su Jinwen, and Shi Guoliang, “A sub-mm and waveguide made of gold-coated glass tube,” Chin. J. Infrared Res. 5, 161–166 (1986).

1983 (1)

Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “Optically pumped submillimeter-wave laser in formic acid vapor and in formic acid–methanol vapor,” Acta Opt. Sin. 3, 603–609 (1983).

1982 (1)

Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “CwCH3OH far infrared lasers,” Acta Opt. Sin. 2, 9–17 (1982).

1966 (1)

1958 (1)

Affolter, E.

F. K. Kneububl and E. Affolter, in Infrared and Millimeter Waves, K. J. Button, ed. (Academic, New York, 1959), Vol. 1, p. 235.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 8, p. 370.

Cappelletti, R. L.

Ensheng, Fu

Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “Optically pumped submillimeter-wave laser in formic acid vapor and in formic acid–methanol vapor,” Acta Opt. Sin. 3, 603–609 (1983).

Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “CwCH3OH far infrared lasers,” Acta Opt. Sin. 2, 9–17 (1982).

Ginsberg, D. M.

Guoliang, Shi

Xiong Shouren, Su Jinwen, and Shi Guoliang, “A sub-mm and waveguide made of gold-coated glass tube,” Chin. J. Infrared Res. 5, 161–166 (1986).

Harris, R. E.

Jinwen, Su

Xiong Shouren, Su Jinwen, and Shi Guoliang, “A sub-mm and waveguide made of gold-coated glass tube,” Chin. J. Infrared Res. 5, 161–166 (1986).

Kneububl, F. K.

F. K. Kneububl and E. Affolter, in Infrared and Millimeter Waves, K. J. Button, ed. (Academic, New York, 1959), Vol. 1, p. 235.

Ohlmann, R. C.

Peisheng, Shi

Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “Optically pumped submillimeter-wave laser in formic acid vapor and in formic acid–methanol vapor,” Acta Opt. Sin. 3, 603–609 (1983).

Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “CwCH3OH far infrared lasers,” Acta Opt. Sin. 2, 9–17 (1982).

Richards, P. L.

Shouren, Xiong

Xiong Shouren, Su Jinwen, and Shi Guoliang, “A sub-mm and waveguide made of gold-coated glass tube,” Chin. J. Infrared Res. 5, 161–166 (1986).

Tinkham, M.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 8, p. 370.

Zhongzhi, Wang

Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “Optically pumped submillimeter-wave laser in formic acid vapor and in formic acid–methanol vapor,” Acta Opt. Sin. 3, 603–609 (1983).

Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “CwCH3OH far infrared lasers,” Acta Opt. Sin. 2, 9–17 (1982).

Acta Opt. Sin. (2)

Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “CwCH3OH far infrared lasers,” Acta Opt. Sin. 2, 9–17 (1982).

Fu Ensheng, Wang Zhongzhi, and Shi Peisheng, “Optically pumped submillimeter-wave laser in formic acid vapor and in formic acid–methanol vapor,” Acta Opt. Sin. 3, 603–609 (1983).

Appl. Opt. (1)

Chin. J. Infrared Res. (1)

Xiong Shouren, Su Jinwen, and Shi Guoliang, “A sub-mm and waveguide made of gold-coated glass tube,” Chin. J. Infrared Res. 5, 161–166 (1986).

J. Opt. Soc. Am. (1)

Other (3)

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 8, p. 370.

In Refs. 1, 2, and 7 this formula reads asT=12exp(−2q)+[1−exp(−q/2F2)]F2/q≃12[1+exp(−2q)]−q/3F2, but the correct formula should be relation (26).

F. K. Kneububl and E. Affolter, in Infrared and Millimeter Waves, K. J. Button, ed. (Academic, New York, 1959), Vol. 1, p. 235.

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Figures (3)

Fig. 1
Fig. 1

Electrical vector when the azimuth of the incident radiation is θ.

Fig. 2
Fig. 2

Parameters for radiation passing through the light pipe.

Fig. 3
Fig. 3

Transmissivities of light pipes made of different materials relative to the parameter L / ( d λ ).

Tables (1)

Tables Icon

Table 1 Experimental and Theoretical Values of Transmissivity of a Metal Pipe

Equations (27)

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R = ( cos α i n ˆ cos α t cos α i + n ˆ cos α t ) 2 ,
sin α t = 1 n ˆ sin α i ,
n ˆ = cos α t = p + i q ;
R = ( cos α i p ) 2 + q 2 ( cos α i + p ) 2 + q 2 .
p 2 = 1 2 ( { [ n 2 ( 1 k 2 ) sin 2 α i ] 2 + 4 n 4 k 2 } 1 / 2 + [ n 2 ( 1 k 2 ) sin 2 α i ] ) ,
q 2 = 1 2 ( { [ n 2 ( 1 k 2 ) sin 2 α i ] 2 + 4 n 4 k 2 } 1 / 2 [ n 2 ( 1 k 2 ) sin 2 α i ] ) .
n 2 ( 1 k 2 ) = μ ,
n 2 k = μ σ / ν ,
p 2 = 1 2 { [ ( μ 1 ) 2 + 4 ( μ σ ν ) 2 ] 1 / 2 + ( μ 1 ) } .
q 2 = 1 2 { [ ( μ 1 ) 2 + 4 ( μ σ ν ) 2 ] 1 / 2 ( μ 1 ) } .
p 2 q 2 σ / ν
p = σ / ν .
R = 2 p 2 2 p φ + φ 2 2 p 2 + 2 p φ + φ 2 exp ( 2 ν σ φ ) .
R = ( n ˆ cos α i cos α t n ˆ cos α i + cos α t ) 2 = [ n 2 ( 1 k 2 ) cos α i p ] 2 + ( 2 n 2 k cos α i q ) 2 [ n 2 ( 1 k 2 ) cos α i + p ] 2 + ( 2 n 2 k cos α i + q ) 2 2 p 2 φ 2 2 p φ + 1 2 p 2 φ 2 + 2 p φ + 1 exp ( 2 ν σ / φ ) .
r ( θ ) = [ exp ( 2 ν σ φ ) ] cos 2 θ ,
r ( θ ) = [ exp ( 2 ν σ φ ) ] sin 2 θ .
R ¯ = 0 π / 2 ( r + r ) π / 2 d θ , = 1 2 [ exp ( 2 ν σ φ ) + exp ( 2 ν σ / φ ) ] .
m L φ / d ,
R ¯ m = 1 2 m [ exp ( 2 ν σ φ ) + exp ( 2 ν σ / φ ) ] m .
T = Ω 0 Ω m R ¯ m d Ω Ω 0 Ω m d Ω + T 0 ,
T 1 φ m 2 ( φ 0 φ m exp ( 2 ν σ L φ 2 d ) 2 L φ / d × { 1 + L φ d exp [ 2 ν σ ( 1 φ φ ) L φ / d ] } d φ 2 ) + T 0 .
T exp ( ν σ L φ m 2 2 d ) 2 L φ m / 2 d × [ 1 + L φ m 2 d exp ( 4 ν σ 1 φ m ) ] L φ m 2 d + T 0 .
T [ 1 2 ν / σ φ m 1 + 4 ( ν / σ φ m 1 ) 2 ] exp ( ν / σ L / d ) . L φ m / 2 d
T = ( I b d b 2 ) / ( I a d a 2 ) ,
Δ T T = Δ I a I a + Δ I b I b + 2 ( Δ d a d a + Δ d b d b ) ,
T = 1 2 exp ( 2 q ) + [ 1 exp ( 1 2 q F 2 ) ] / q F 2 1 2 [ 1 + exp ( 2 q ) ] q F 2 / 8 ,
T=12exp(2q)+[1exp(q/2F2)]F2/q12[1+exp(2q)]q/3F2,

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