Abstract

A procedure based on the variational method is presented for the analysis of optical fibers with arbitrary gain or loss profiles. The procedure is validated by comparison with earlier reported results for a step gain profile. The use of the procedure for arbitrary profiles is illustrated on typical gain profiles of a fiber used in amplifiers.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. J. Mears, S. R. Baker, Opt. Quantum Electron. 24, 538 (1991).
  2. B. J. Ainslie, J. Lightwave Technol. 9, 220 (1991).
    [CrossRef]
  3. S. B. Poole, D. N. Payne, M. E. Fermann, Electron. Lett. 21, 737 (1985).
    [CrossRef]
  4. J. E. Sader, Opt. Lett. 15, 105 (1990).
    [CrossRef] [PubMed]
  5. A. Kumar, S. I. Hosain, A. K. Ghatak, Opt. Acta 28, 559 (1981).
    [CrossRef]
  6. K. Thyagarajan, S. Diggavi, A. Taneja, A. K. Ghatak, Appl. Opt. 30, 3877 (1991).
    [CrossRef] [PubMed]
  7. A. Sharma, S. Banerjee, J. Lightwave Technol. 7, 1919 (1989).
    [CrossRef]
  8. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 11, p. 214.

1991

R. J. Mears, S. R. Baker, Opt. Quantum Electron. 24, 538 (1991).

B. J. Ainslie, J. Lightwave Technol. 9, 220 (1991).
[CrossRef]

K. Thyagarajan, S. Diggavi, A. Taneja, A. K. Ghatak, Appl. Opt. 30, 3877 (1991).
[CrossRef] [PubMed]

1990

1989

A. Sharma, S. Banerjee, J. Lightwave Technol. 7, 1919 (1989).
[CrossRef]

1985

S. B. Poole, D. N. Payne, M. E. Fermann, Electron. Lett. 21, 737 (1985).
[CrossRef]

1981

A. Kumar, S. I. Hosain, A. K. Ghatak, Opt. Acta 28, 559 (1981).
[CrossRef]

Ainslie, B. J.

B. J. Ainslie, J. Lightwave Technol. 9, 220 (1991).
[CrossRef]

Baker, S. R.

R. J. Mears, S. R. Baker, Opt. Quantum Electron. 24, 538 (1991).

Banerjee, S.

A. Sharma, S. Banerjee, J. Lightwave Technol. 7, 1919 (1989).
[CrossRef]

Diggavi, S.

Fermann, M. E.

S. B. Poole, D. N. Payne, M. E. Fermann, Electron. Lett. 21, 737 (1985).
[CrossRef]

Ghatak, A. K.

Hosain, S. I.

A. Kumar, S. I. Hosain, A. K. Ghatak, Opt. Acta 28, 559 (1981).
[CrossRef]

Kumar, A.

A. Kumar, S. I. Hosain, A. K. Ghatak, Opt. Acta 28, 559 (1981).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 11, p. 214.

Mears, R. J.

R. J. Mears, S. R. Baker, Opt. Quantum Electron. 24, 538 (1991).

Payne, D. N.

S. B. Poole, D. N. Payne, M. E. Fermann, Electron. Lett. 21, 737 (1985).
[CrossRef]

Poole, S. B.

S. B. Poole, D. N. Payne, M. E. Fermann, Electron. Lett. 21, 737 (1985).
[CrossRef]

Sader, J. E.

Sharma, A.

A. Sharma, S. Banerjee, J. Lightwave Technol. 7, 1919 (1989).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 11, p. 214.

Taneja, A.

Thyagarajan, K.

Appl. Opt.

Electron. Lett.

S. B. Poole, D. N. Payne, M. E. Fermann, Electron. Lett. 21, 737 (1985).
[CrossRef]

J. Lightwave Technol.

B. J. Ainslie, J. Lightwave Technol. 9, 220 (1991).
[CrossRef]

A. Sharma, S. Banerjee, J. Lightwave Technol. 7, 1919 (1989).
[CrossRef]

Opt. Acta

A. Kumar, S. I. Hosain, A. K. Ghatak, Opt. Acta 28, 559 (1981).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

R. J. Mears, S. R. Baker, Opt. Quantum Electron. 24, 538 (1991).

Other

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Chap. 11, p. 214.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Gain as a function of the width parameter (W).

Fig. 2
Fig. 2

Amplitude and phase of the fundamental modal field of a fiber with complex refractive-index distribution with step-index real part (n0 = 1.475, n2 = 1.458) and a Gaussian imaginary part [Eqs. (17)]. The dashed and dashed–dotted curves show the variation of phase for W = 10 μm and W = 0.1 μm, respectively. The field profiles, shown by the solid curve, are indistinguishable for the two W values.

Tables (1)

Tables Icon

Table 1 Convergence of Results with Matrix Size for the Profile Given by Eqs. (15)a

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

n 2 ( R ) = n r 2 ( R ) + i n i 2 ( R ) , R 1 , = n r 2 , R < 1 ,
β 2 = 0 Ψ t { 1 ρ ( d 2 Ψ t d R 2 + 1 R d Ψ t d R ) + [ k 0 2 n 2 ( R ) ] Ψ t } R d R 0 Ψ t 2 R d R ,
Ψ t = m = 0 N 1 a m ϕ m ,
ϕ m ( R ) = exp ( ξ / 2 ) L m ( ξ ) ,
d 2 ϕ m d R 2 + 1 R d ϕ m d R = [ α 2 R 2 2 α ( 2 m + 1 ) ] ϕ m
0 ϕ m ( R ) ϕ n ( R ) R d R = 1 2 1 α δ m n .
ρ 2 β 2 m a m 2 δ m n / 2 α = α 2 m , n a m a n 0 ϕ m ϕ n R 3 d R m a m 2 ( 2 m + 1 ) + ρ 2 k 0 2 m , n a m a n 0 n 2 ( R ) ϕ m ϕ n R d R .
H A = β 2 A .
H n m = H n m r + i H n m i ,
H n m r = α / ρ 2 T n m + k 0 2 n 2 2 δ n m + k 0 2 2 α 0 1 [ n r 2 ( R ) n 2 2 ] ϕ n ϕ m R d R ,
H n m i = k 0 2 2 α 0 1 [ n i 2 ( R ) ϕ n ϕ m R d R ,
T n m = ( 2 m + 1 ) δ m n n δ m , n 1 m δ m 1 , n .
0 Ψ j Ψ k R d R = δ j k .
A j T A k = 0 for j k ,
H A 1 = β 1 2 A 1 , H A 2 = β 2 2 A 2 ,
A 2 T H A 1 = β 1 A 2 T A 1
A 1 T H T A 2 = β 1 2 A 1 T A 2 .
A 1 T H A 2 = β 2 2 A 1 T A 2 .
A 1 T A 2 ( β 1 2 β 2 2 ) = 0
A 1 T A 2 = 0
A ¯ 1 T H ¯ T A 2 = β 1 2 A ¯ 1 T A 2 .
n ( R ) = n 1 + i n c , R 1 , = n n , R > 1 ,
U = k 0 ρ ( n 1 2 n e 2 ) 1 / 2 ,
n 2 ( R ) = n 1 2 ( R ) + i n i 2 ( R ) , R 1 , = n 2 2 , R > 1 ,
n i ( R ) = n i ( 0 ) exp ( R 2 / W 2 ) .
0 1 n i ( R ) R d R = constant ( n i 0 )
n i ( 0 ) = 2 n i 0 / W 2 [ 1 exp ( 1 / W 2 ) ] ,

Metrics