Abstract

An expression for the transmission characteristics of a conical coupling is derived. This expression is shown to be useful for choosing an optimum coupling length.

© 1976 Optical Society of America

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References

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  1. R. C. Ohlmann, P. L. Richard, M. Tinkham, J. Opt. Soc. Am. 48, 531 (1958).
  2. S. H. Lin, E. M. Sparrow, Appl. Opt. 4, 277 (1965).
  3. D. E. Williamson, J. Opt. Soc. Am. 42, 712 (1952).
  4. W. R. Powell, Appl. Opt. 13, 952 (1974).
  5. M. D. Wagh, Appl. Opt. 15, 2816 (1976).

1976 (1)

M. D. Wagh, Appl. Opt. 15, 2816 (1976).

1974 (1)

1965 (1)

1958 (1)

1952 (1)

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Figures (2)

Fig. 1
Fig. 1

Conical coupling between two cylindrical light pipes.

Fig. 2
Fig. 2

Plot of efficiency of the coupling η against the semiangle of the coupling ψ for various values of wall reflectivity ρ.

Equations (13)

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η = 1 π a 2 0 a δ r 2 π r d r ,
z n + 1 ( a - b ) / tan ψ ,
z n + 1 = a tan ψ ( ( 1 - 1 T n ) + z 1 T n ,
T n = sin ( 2 n + 1 ψ ¯ ) / sin ψ ,
maximum value of n = [ π / 4 ψ ] ,
z 1 = ( a - r ) / tan ψ .
r b T n .
b T n - 1 < r b T n , δ r = ρ n .
η = ( b / a ) 2 + n = 1 [ π / 4 ψ ] A n · ρ n ,
A n = ( b / a ) 2 ( T n 2 - T n - 1 2 ) if b T n a = ( b / a ) 2 ( a 2 - T n - 1 2 ) if b T n > a b T n - 1 = 0 if b T n - 1 > a .
η = min { 1 , ( b / a ) 2 T 2 [ π / 4 ψ ] } .
b T [ π / 4 ψ ] a ,
b T [ π / 4 ψ ] = a

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