Abstract

In this paper we present the results of an in-depth analysis of the problem of Gaussian beam excitation of optical fibers at normal incidence. The method entails the application of the continuity conditions at the interface located at the fiber end using Gaussian beams with different spot sizes as our excitation source. Next, the simultaneous set of equations obtained is numerically solved for the reflected, guided, and radiated modal coefficients and their corresponding powers.

© 1975 Optical Society of America

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References

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  1. A. W. Snyder, J. Opt. Soc. Am. 56, 601 (1966).
    [Crossref]
  2. A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
    [Crossref]
  3. D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).
  4. A. W. Snyder, J. Opt. Soc. Am. 63, 59 (1973).
    [Crossref] [PubMed]
  5. R. Sammut, C. Pask, A. W. Snyder, Proc. IEEE (Lond.) 122, 25 (1975).
  6. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).
  7. A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
    [Crossref]
  8. E. Snitzer, J. Opt. Soc. Am. 51, 491, (1961).
    [Crossref]
  9. D. Marcuse, Bell Syst. Tech. J. 49, 1665 (1970).
  10. A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-19, 720 (1971).
    [Crossref]

1975 (1)

R. Sammut, C. Pask, A. W. Snyder, Proc. IEEE (Lond.) 122, 25 (1975).

1973 (1)

1971 (1)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-19, 720 (1971).
[Crossref]

1970 (2)

D. Marcuse, Bell Syst. Tech. J. 49, 1665 (1970).

D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).

1969 (2)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
[Crossref]

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
[Crossref]

1966 (1)

1961 (1)

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).

D. Marcuse, Bell Syst. Tech. J. 49, 1665 (1970).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

Pask, C.

R. Sammut, C. Pask, A. W. Snyder, Proc. IEEE (Lond.) 122, 25 (1975).

Sammut, R.

R. Sammut, C. Pask, A. W. Snyder, Proc. IEEE (Lond.) 122, 25 (1975).

Snitzer, E.

Snyder, A. W.

R. Sammut, C. Pask, A. W. Snyder, Proc. IEEE (Lond.) 122, 25 (1975).

A. W. Snyder, J. Opt. Soc. Am. 63, 59 (1973).
[Crossref] [PubMed]

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-19, 720 (1971).
[Crossref]

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
[Crossref]

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
[Crossref]

A. W. Snyder, J. Opt. Soc. Am. 56, 601 (1966).
[Crossref]

Bell Syst. Tech. J. (2)

D. Marcuse, Bell Syst. Tech. J. 49, 1695 (1970).

D. Marcuse, Bell Syst. Tech. J. 49, 1665 (1970).

IEEE Trans. Microwave Theory Tech. (3)

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-19, 720 (1971).
[Crossref]

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1130 (1969).
[Crossref]

A. W. Snyder, IEEE Trans. Microwave Theory Tech. MTT-17, 1138 (1969).
[Crossref]

J. Opt. Soc. Am. (3)

Proc. IEEE (Lond.) (1)

R. Sammut, C. Pask, A. W. Snyder, Proc. IEEE (Lond.) 122, 25 (1975).

Other (1)

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

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Figures (5)

Fig. 1
Fig. 1

Gaussian beam normally incident at the end of a semiinfinite optical fiber with 1 and 2 as dielectric constants of core and cladding, respectively. The cladding radius d/2 approaches ∞.

Fig. 2
Fig. 2

Excitation of a round fiber at normal incidence by a Gaussian beam with spot size α0 = 2a, a = 5 μm.

Fig. 3
Fig. 3

Excitation of a round fiber at normal incidence by a Gaussian beam with spot size α0 = a, a = 5 μm.

Fig. 4
Fig. 4

Excitation of a round fiber at normal incidence by a Gaussian beam with spot size α0 = a/2, a = 5 μm.

Fig. 5
Fig. 5

Normalized magnitude and phase of the radiation coefficient Ar (even and odd) vs the continuous eigenvalue λ, excited by a Gaussian beam with α0 = 2a at V = 2.

Tables (1)

Tables Icon

Table I Guided, Radiated, and Reflected Power Excited by Three Different Gaussian Beams at V = 4.5, 1 = 2.25 0, δ = 0.02

Equations (16)

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δ = 1 ( 2 / 1 )
E t inc ( r , z ) z = 0 = x ̂ Y ( r , z ) z = 0 ;
H ¯ t inc ( r , z ) z = 0 = ŷ 1 η Y ( r , z ) z = 0 .
Y ( r , z ) = C 0 α 0 α exp [ i ( k z Φ ) r 2 ( 1 α 2 + i k 2 ρ ) ] .
Ē t inc ( r , 0 ) + Ē t ref ( r , 0 ) = Ē t g ( r , 0 ) + Ē t r ( r , 0 ) ,
H ¯ t inc ( r , 0 ) + H ¯ t ref ( r , 0 ) = H ¯ t g ( r , 0 ) + H ¯ t r ( r , 0 ) ,
ρ = 1 0 1 + 0 .
| ρ ext | 2 < P ref / P inc < | ρ | 2 ,
ρ ext = 2 0 2 + 0 .
E t inc ( r , 0 ) + l = 0 B l Y ( r , 0 ) L l 0 ( 2 r 2 α 0 2 ) x ̂ = n = 0 p = 1 P A g ( u p , n ) ē ( u p , n ) + n = 0 [ A r ( e ) ( λ , n ) ē ( e ) ( λ , n ) + A r ( O ) ( λ , n ) ē ( O ) ( λ , n ) ] d λ ,
H ¯ t inc ( r , 0 ) l = 0 B l ( 0 μ 0 ) 1 / 2 Y ( r , 0 ) L l 0 ( 2 r 2 α 0 2 ) ŷ = n = 0 p = 1 P A g ( u p , n ) h ¯ ( u p , n ) + n = 0 [ A r ( e ) ( λ , n ) h ¯ ( e ) ( λ , n ) + A r ( O ) ( λ , n ) h ¯ ( O ) ( λ , n ) ] d λ ,
1 N ( u p ) 0 2 π 0 [ E t inc × h ¯ * ( u p , 1 ) : + l = 0 B l Y L l 0 ( 2 r 2 α 0 2 ) x ̂ × h ¯ * ( u p , 1 ) · ] rdrd ϕ = A g ( u p , 1 ) p = 1 , . . . P ;
1 N ( u p ) 0 2 π 0 { ē * ( u p , 1 ) × H ¯ t inc · l = 0 ( 0 μ 0 ) 1 / 2 B l [ ē * ( u p , 1 ) × Y L l 0 ( 2 r 2 α 0 2 ) ŷ ] · } r dr d ϕ = A g ( u p , 1 ) ,
N ( u p ) = 0 2 π 0 ē ( u p , 1 ) × h ¯ * ( u p , 1 ) · r dr d ϕ
P g ( u p , n ) = 1 2 | A g | 2 0 2 π 0 ē ( u p , n ) × h ¯ * ( u p , n ) · r dr d ϕ . n = 1
P r = 1 2 0 a k 2 { | A r ( e ) ( λ , n ) | 2 + | A r ( O ) ( λ , n ) | 2 } d λ . n = 1 or 1 .

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