Abstract

A new class of index profiles called vertically displaced Gaussian α profiles is introduced. These profiles make it possible to study the effect of tails on ordinary power-law profiles. The modal dispersion properties are calculated numerically using the WKB method, and the results are compared with single-α profiles.

© 1980 Optical Society of America

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References

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  1. R. Olshansky, Appl. Opt. 18, 683 (1979).
    [CrossRef] [PubMed]
  2. R. Olshansky, D. B. Keck, Appl. Opt. 15, 483 (1976).
    [CrossRef] [PubMed]
  3. E. A. J. Marcatili, Bell Syst. Tech. J. 56, 49 (1977).

1979 (1)

1977 (1)

E. A. J. Marcatili, Bell Syst. Tech. J. 56, 49 (1977).

1976 (1)

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

E. A. J. Marcatili, Bell Syst. Tech. J. 56, 49 (1977).

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Figures (2)

Fig. 1
Fig. 1

Example of vertically displaced Gaussian α profile, h = ∞ corresponds to an ordinary single-α profile.

Fig. 2
Fig. 2

The rms modal dispersion at 0.9 μm as a function of α for different values of parameter h. The numerical aperture is 0.15. The curves labeled α correspond to h = ∞, i.e., a single-α profile with radius A, the dashed curve is for a wavelength of 1.3 μm.

Tables (1)

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Table I Value of Rc for Some Combinations of a and h

Equations (15)

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n 2 ( r ) = n 1 2 [ 1 F ( r , λ ) ] ,
F ( r , λ ) = i = 1 N 2 Δ i ( λ ) ( r / A ) α i , i = 1 N Δ i = Δ ,
F G ( r , λ ) = 2 Δ ( λ ) ( 1 + h ) { 1 exp [ ( r / a ) α ] } ,
n G 2 ( r = A ) = n α 2 ( r = A ) .
a = A ( 1 + h ) 1 / α .
R c = A [ ( 1 + h ) ln ( 1 + 1 / h ) ] 1 / α .
R c A ,
τ μ ν = N 1 c L 1 B [ 1 B × r 1 r 2 ( 1 p 2 ) F κ dr r 1 r 2 ( 1 + r F 2 F r ) F κ dr ] ,
p = n 1 N 1 λ F F λ ,
N 1 = n 1 λ n 1 λ ,
B = 1 ( β / k 0 ) 2 n 1 2 ,
κ = [ k 0 2 n 2 ( r ) β 2 ν 2 r 2 ] 1 / 2 ,
p G = n 1 N 1 λ Δ Δ λ ,
r 2 F F r = α 2 ( r a ) α exp [ ( r / a ) α ] 1 exp [ ( r / a ) α ] .
1 + r 2 F F λ 1 p 2 = D ( λ ) ,

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