Abstract

In the case of optimal excitation of a multimode graded-index fiber by a laser diode, the coupling efficiency κ0 between the Gaussian laser beam and the fundamental mode of the fiber describes the input mode power distribution uniquely. Using this result, fiber impulse responses are calculated for two realistic excitations, first, by a gain-guided laser diode and second, by an index-guided laser diode. Also, the commonly used uniform and stationary excitations are given for comparison. The calculations yielding these results are based on the power diffusion equations and include profile dispersion, material dispersion, mode-dependent attenuation, and mode coupling. The mode group delay times have been computed for a parabolic profile using the scalar wave equation. However, delay times for other profiles can be introduced in the calculations. As κ0 characterizes laser fiber coupling uniquely and because it can simply be measured, we propose the use of κ0 as a characteristic launching parameter which allows easy comparison of measured impulse responses.

© 1983 Optical Society of America

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References

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  1. R. Olshansky, D. B. Keck, Appl. Opt. 15, 483 (1976).
    [CrossRef] [PubMed]
  2. J. J. Ramskov Hansen, E. Nicolaisen, Appl. Opt. 17, 2831 (1978).
    [CrossRef]
  3. K. Tatekura et al., Trans. IECE Jpn. E61, 809 (1978).
  4. K. Kitayama et al., IEEE J. Quantum Electron QE-16, 356 (1980).
    [CrossRef]
  5. D. Marcuse, Bell Syst. Tech. J 51, 229 (1972).
  6. H. W. Kogelnik, in Microwave Research Institute Symposia Series, Vol 14, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 333.
  7. S. Nemoto et al., Appl. Opt. 14, 1543 (1975).
    [CrossRef] [PubMed]
  8. G. K. Grau et al., AEU 34, 259 (1980).
  9. J. Saijonmaa, S. J. Halme, Appl. Opt. 20, 4302 (1981).
    [CrossRef] [PubMed]
  10. M. Nishimura, S. Suzuki, in Technical Digest, Symposium on Optical Fiber Measurements, D. L. Franzen et al., Eds. (National Bureau of Standards, Boulder, Colo., 1982), p. 21.
  11. C. R. Hammond, Opt. Quantum Electron. 10, 163 (1978).
    [CrossRef]
  12. J. J. Ramskov Hansen, Ph.D. thesis, Technical University of Denmark, Lyngby, Denmark (1979).
  13. K. Nagano, S. Kawakami, Appl. Opt. 21, 542 (1982).
    [CrossRef] [PubMed]
  14. T. P. Lee et al., Electron. Lett. 18, 902 (1982).
    [CrossRef]
  15. A. Nicia, Appl. Opt. 21, 4280 (1982).
    [CrossRef] [PubMed]

1982 (3)

1981 (1)

1980 (1)

K. Kitayama et al., IEEE J. Quantum Electron QE-16, 356 (1980).
[CrossRef]

1978 (3)

J. J. Ramskov Hansen, E. Nicolaisen, Appl. Opt. 17, 2831 (1978).
[CrossRef]

K. Tatekura et al., Trans. IECE Jpn. E61, 809 (1978).

C. R. Hammond, Opt. Quantum Electron. 10, 163 (1978).
[CrossRef]

1976 (1)

1975 (1)

1972 (1)

D. Marcuse, Bell Syst. Tech. J 51, 229 (1972).

Grau, G. K.

G. K. Grau et al., AEU 34, 259 (1980).

Halme, S. J.

Hammond, C. R.

C. R. Hammond, Opt. Quantum Electron. 10, 163 (1978).
[CrossRef]

Kawakami, S.

Keck, D. B.

Kitayama, K.

K. Kitayama et al., IEEE J. Quantum Electron QE-16, 356 (1980).
[CrossRef]

Kogelnik, H. W.

H. W. Kogelnik, in Microwave Research Institute Symposia Series, Vol 14, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 333.

Lee, T. P.

T. P. Lee et al., Electron. Lett. 18, 902 (1982).
[CrossRef]

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J 51, 229 (1972).

Nagano, K.

Nemoto, S.

Nicia, A.

Nicolaisen, E.

Nishimura, M.

M. Nishimura, S. Suzuki, in Technical Digest, Symposium on Optical Fiber Measurements, D. L. Franzen et al., Eds. (National Bureau of Standards, Boulder, Colo., 1982), p. 21.

Olshansky, R.

Ramskov Hansen, J. J.

J. J. Ramskov Hansen, E. Nicolaisen, Appl. Opt. 17, 2831 (1978).
[CrossRef]

J. J. Ramskov Hansen, Ph.D. thesis, Technical University of Denmark, Lyngby, Denmark (1979).

Saijonmaa, J.

Suzuki, S.

M. Nishimura, S. Suzuki, in Technical Digest, Symposium on Optical Fiber Measurements, D. L. Franzen et al., Eds. (National Bureau of Standards, Boulder, Colo., 1982), p. 21.

Tatekura, K.

K. Tatekura et al., Trans. IECE Jpn. E61, 809 (1978).

Appl. Opt. (6)

Bell Syst. Tech. J (1)

D. Marcuse, Bell Syst. Tech. J 51, 229 (1972).

Electron. Lett. (1)

T. P. Lee et al., Electron. Lett. 18, 902 (1982).
[CrossRef]

IEEE J. Quantum Electron (1)

K. Kitayama et al., IEEE J. Quantum Electron QE-16, 356 (1980).
[CrossRef]

Opt. Quantum Electron. (1)

C. R. Hammond, Opt. Quantum Electron. 10, 163 (1978).
[CrossRef]

Trans. IECE Jpn. (1)

K. Tatekura et al., Trans. IECE Jpn. E61, 809 (1978).

Other (4)

H. W. Kogelnik, in Microwave Research Institute Symposia Series, Vol 14, J. Fox, Ed. (Polytechnic Press, Brooklyn, 1964), p. 333.

M. Nishimura, S. Suzuki, in Technical Digest, Symposium on Optical Fiber Measurements, D. L. Franzen et al., Eds. (National Bureau of Standards, Boulder, Colo., 1982), p. 21.

G. K. Grau et al., AEU 34, 259 (1980).

J. J. Ramskov Hansen, Ph.D. thesis, Technical University of Denmark, Lyngby, Denmark (1979).

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Figures (6)

Fig. 1
Fig. 1

Contours of a Gaussian beam of a laser diode, parallel and perpendicular to the active layer.

Fig. 2
Fig. 2

Relative distributions of the average mode power at three subsequent stages along the fiber: (□) fiber input, (○) 1-km long distance, and (△) infinitely long distance. Distributions are given for 830-nm wavelength and for four launching conditions: (a) excitation by a gain-guided laser; (b) excitation by an index-guided laser; (c) uniform excitation; and (d) stationary excitation.

Fig. 3
Fig. 3

Impulse responses of a 1-km long fiber for wavelengths of (□) 790, (○) 830, and (△) 870 nm for the same excitations as in Fig. 2: (a) excitation by a gain-guided laser; (b) excitation by an index-guided laser; (c) uniform excitation, and (d) stationary excitation.

Fig. 4
Fig. 4

3-dB bandwidth vs wavelength for the same excitations as in Fig. 2: excitation by a gain-guided laser (□), excitation by an index-guided laser (○), uniform excitation (△), and stationary excitation (◊).

Fig. 5
Fig. 5

Fiber attenuation due to mode attenuation and coupling as a function of fiber length for the same excitations as in Fig. 2: excitation by a gain-guided laser (□), excitation by an index-guided laser (○), uniform excitation (△), and stationary excitation (◊).

Fig. 6
Fig. 6

Impulse response of a 1-km long fiber (b) excited by the gain-guided laser (see Fig. 2) with a Gaussian-shaped spectrum around 830 nm (a).

Equations (18)

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n ( r , λ 0 ) = n 1 ( λ 0 ) [ 1 2 Δ ( λ 0 ) ( r / a ) 2 ] 1 / 2 , 0 r a , = n 1 ( λ 0 ) [ 1 2 Δ ( λ 0 ) ] 1 / 2 = n 2 ( λ 0 ) , r > a ,
β m = n 1 k 0 ( 1 2 Δ m / M ) 1 / 2 , m = 1 , 2 , , m max ,
M = 1 2 k 0 a n 1 ( 2 Δ ) 1 / 2 ,
n 2 k 0 β m n 1 k 0 ,
τ m = τ 0 [ 1 + 1 2 P Δ m / M + 1 2 ( 1 + P ) Δ 2 ( m / M ) 2 + 0 ( Δ 3 ) ] , m = 1 , 2 , , [ M ] ,
τ 0 = N 1 / c ,
N 1 = n 1 λ 0 d n 1 d λ 0 ,
P = n 1 N 1 λ 0 Δ d Δ d λ 0 ,
[ m + 1 2 ] d P ¯ m d z + j ω τ m P ¯ m = [ m + 1 2 ] a m P ¯ m + [ m + 1 2 ] d m ( P ¯ m + 1 P ¯ m ) + [ m 2 ] d m 1 ( P ¯ m 1 P ¯ m ) , m = 1 , 2 , , [ M ]
P m = [ m + 1 2 ] P ¯ m .
a m = 10 7 m 2 / m ,
d m = 0.01 / m .
P ¯ m ( ω , 0 ) = c m P ( ω , 0 ) ,
w , = λ 0 ( 2 ln 2 ) 1 / 2 2 π tan ( θ , / 2 ) .
κ 0 = 4 2 + ( α + α 1 ) ( 1 + b / ( α + α 1 ) ) 1 / 2
α = w / w ,
b = λ 0 δ w w .
c m = κ 0 m = 1 , = 1 [ ( m + 1 ) / 2 ] κ 0 ( 1 κ 0 ) ( m 1 ) / 2 , m = 3 , 5 , , = 0 , m = 2 , 4 , .

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