Abstract

I introduce the problem of transforming one optical pulse into another via nonlinear propagation in a length of dispersion varying optical fibre. Then using a genetic algorithm to design the dispersion profiles, I show that the problem can be solved leading to high quality pulse transforms that are significantly better than what has been published previously. Finally I suggestion further work and other applications for this method.

© 2010 Optical Society of America

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  1. H. Kuehl, "Solitons on an axially nonuniform optical fiber," J. Opt. Soc. Am. B 5, 709-713 (1988).
    [CrossRef]
  2. S. V. Chernikov, E. M. Dianov, D. J. Richardson, and D. N. Payne, "Soliton pulse-compression in dispersion-decreasing fiber," Opt. Lett. 18, 476-478 (1993).
    [CrossRef] [PubMed]
  3. T. Hirooka, and M. Nakazawa, "Parabolic pulse generation by use of a dispersion-decreasing fiber with normal group-velocity dispersion," Opt. Lett. 29, 498-500 (2004).
    [CrossRef] [PubMed]
  4. A. Hasegawa, and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. anomalous dispersion," Appl. Phys. Lett. 23, 142-144 (1973).
    [CrossRef]
  5. N. Broderick, D. Richardson, and L. Dong, "Distributed dispersion measurements and control within continuously varying dispersion tapered fibers," IEEE Photon. Technol. Lett. 9, 1511-1513 (1997).
    [CrossRef]
  6. S. Chernikov, and P. Mamyshev, "Femtosecond soliton propagation in fibers with slowly decreasing dispersion," J. Opt. Soc. Am. B 8, 1633-1641 (1991).
    [CrossRef]
  7. N. Vukovic, N. G. R. Broderick, M. Petrovich, and G. Brambilla, "Novel method for the fabrication of long optical tapers," IEEE Photon. Technol. Lett. 20, 1264-1266 (2008).
    [CrossRef]
  8. M. Sumetsky, Y. Dulashko, and S. Ghalmi, "Fabrication of miniature optical fiber and microfiber coils," Opt. Lasers Eng. 48, 272-275 (2010).
    [CrossRef]
  9. N. Vukovic, F. Parmigiani, A. Camerlingo, M. Petrovich, P. Petropoulos, and N. G. R. Broderick, "Experimental investigation of a parabolic pulse generation using tapered microstructured optical fibres," Proc. SPIE, Photonics Europe 2010 (2010).
  10. N. Vukovic, and N. Broderick, "Improved flatness of a supercontinuum at 1.55 microns in tapered microstructured optical fibres," Phys. Rev. A. submitted.
    [CrossRef]
  11. A. Peacock, N. Broderick, and T. Monro, "Numerical study of parabolic pulse generation in microstructured fibre Raman amplifiers," Opt. Commun. 218, 167-172 (2003).
    [CrossRef]
  12. C. Billet, P. Lacourt, R. Ferriere, L. Larger, and J. Dudley, "Parabolic pulse generation in comb-like profiled dispersion decreasing fibre," Electron. Lett. 42, 965-966 (2006).
    [CrossRef]
  13. C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, "Optical parabolic pulse generation and applications," IEEE J. Quantum Electron. 45, 1482-1489 (2009).
    [CrossRef]
  14. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84, 6010-6013 (2000).
    [CrossRef] [PubMed]
  15. N. T. Vukovic, and N. G. R. Broderick, "Parabolic pulse generation using tapered microstructured optical fibres," Adv. Non. Opt. (2008).
  16. C. Finot, L. Provost, P. Petropoulos, and D. Richardson, "Parabolic pulse generation through passive nonlinear pulse reshaping in a normally dispersive two segment fiber device," Opt. Express 15, 852-864 (2007).
    [CrossRef] [PubMed]
  17. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, "Holey Optical Fibres: An efficient Modal Model," J. Lightwave Technol. 17(6), 1093 (1999).
    [CrossRef]

2010 (1)

M. Sumetsky, Y. Dulashko, and S. Ghalmi, "Fabrication of miniature optical fiber and microfiber coils," Opt. Lasers Eng. 48, 272-275 (2010).
[CrossRef]

2009 (1)

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, "Optical parabolic pulse generation and applications," IEEE J. Quantum Electron. 45, 1482-1489 (2009).
[CrossRef]

2008 (1)

N. Vukovic, N. G. R. Broderick, M. Petrovich, and G. Brambilla, "Novel method for the fabrication of long optical tapers," IEEE Photon. Technol. Lett. 20, 1264-1266 (2008).
[CrossRef]

2007 (1)

2006 (1)

C. Billet, P. Lacourt, R. Ferriere, L. Larger, and J. Dudley, "Parabolic pulse generation in comb-like profiled dispersion decreasing fibre," Electron. Lett. 42, 965-966 (2006).
[CrossRef]

2004 (1)

2003 (1)

A. Peacock, N. Broderick, and T. Monro, "Numerical study of parabolic pulse generation in microstructured fibre Raman amplifiers," Opt. Commun. 218, 167-172 (2003).
[CrossRef]

2000 (1)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

1999 (1)

1997 (1)

N. Broderick, D. Richardson, and L. Dong, "Distributed dispersion measurements and control within continuously varying dispersion tapered fibers," IEEE Photon. Technol. Lett. 9, 1511-1513 (1997).
[CrossRef]

1993 (1)

1991 (1)

1988 (1)

1973 (1)

A. Hasegawa, and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. anomalous dispersion," Appl. Phys. Lett. 23, 142-144 (1973).
[CrossRef]

Bennett, P. J.

Billet, C.

C. Billet, P. Lacourt, R. Ferriere, L. Larger, and J. Dudley, "Parabolic pulse generation in comb-like profiled dispersion decreasing fibre," Electron. Lett. 42, 965-966 (2006).
[CrossRef]

Brambilla, G.

N. Vukovic, N. G. R. Broderick, M. Petrovich, and G. Brambilla, "Novel method for the fabrication of long optical tapers," IEEE Photon. Technol. Lett. 20, 1264-1266 (2008).
[CrossRef]

Broderick, N.

A. Peacock, N. Broderick, and T. Monro, "Numerical study of parabolic pulse generation in microstructured fibre Raman amplifiers," Opt. Commun. 218, 167-172 (2003).
[CrossRef]

N. Broderick, D. Richardson, and L. Dong, "Distributed dispersion measurements and control within continuously varying dispersion tapered fibers," IEEE Photon. Technol. Lett. 9, 1511-1513 (1997).
[CrossRef]

N. Vukovic, and N. Broderick, "Improved flatness of a supercontinuum at 1.55 microns in tapered microstructured optical fibres," Phys. Rev. A. submitted.
[CrossRef]

Broderick, N. G. R.

N. Vukovic, N. G. R. Broderick, M. Petrovich, and G. Brambilla, "Novel method for the fabrication of long optical tapers," IEEE Photon. Technol. Lett. 20, 1264-1266 (2008).
[CrossRef]

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, "Holey Optical Fibres: An efficient Modal Model," J. Lightwave Technol. 17(6), 1093 (1999).
[CrossRef]

Chernikov, S.

Chernikov, S. V.

Dianov, E. M.

Dong, L.

N. Broderick, D. Richardson, and L. Dong, "Distributed dispersion measurements and control within continuously varying dispersion tapered fibers," IEEE Photon. Technol. Lett. 9, 1511-1513 (1997).
[CrossRef]

Dudley, J.

C. Billet, P. Lacourt, R. Ferriere, L. Larger, and J. Dudley, "Parabolic pulse generation in comb-like profiled dispersion decreasing fibre," Electron. Lett. 42, 965-966 (2006).
[CrossRef]

Dudley, J. M.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, "Optical parabolic pulse generation and applications," IEEE J. Quantum Electron. 45, 1482-1489 (2009).
[CrossRef]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

Dulashko, Y.

M. Sumetsky, Y. Dulashko, and S. Ghalmi, "Fabrication of miniature optical fiber and microfiber coils," Opt. Lasers Eng. 48, 272-275 (2010).
[CrossRef]

Fermann, M. E.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

Ferriere, R.

C. Billet, P. Lacourt, R. Ferriere, L. Larger, and J. Dudley, "Parabolic pulse generation in comb-like profiled dispersion decreasing fibre," Electron. Lett. 42, 965-966 (2006).
[CrossRef]

Finot, C.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, "Optical parabolic pulse generation and applications," IEEE J. Quantum Electron. 45, 1482-1489 (2009).
[CrossRef]

C. Finot, L. Provost, P. Petropoulos, and D. Richardson, "Parabolic pulse generation through passive nonlinear pulse reshaping in a normally dispersive two segment fiber device," Opt. Express 15, 852-864 (2007).
[CrossRef] [PubMed]

Ghalmi, S.

M. Sumetsky, Y. Dulashko, and S. Ghalmi, "Fabrication of miniature optical fiber and microfiber coils," Opt. Lasers Eng. 48, 272-275 (2010).
[CrossRef]

Harvey, J. D.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

Hasegawa, A.

A. Hasegawa, and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. anomalous dispersion," Appl. Phys. Lett. 23, 142-144 (1973).
[CrossRef]

Hirooka, T.

Kibler, B.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, "Optical parabolic pulse generation and applications," IEEE J. Quantum Electron. 45, 1482-1489 (2009).
[CrossRef]

Kruglov, V. I.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

Kuehl, H.

Lacourt, P.

C. Billet, P. Lacourt, R. Ferriere, L. Larger, and J. Dudley, "Parabolic pulse generation in comb-like profiled dispersion decreasing fibre," Electron. Lett. 42, 965-966 (2006).
[CrossRef]

Larger, L.

C. Billet, P. Lacourt, R. Ferriere, L. Larger, and J. Dudley, "Parabolic pulse generation in comb-like profiled dispersion decreasing fibre," Electron. Lett. 42, 965-966 (2006).
[CrossRef]

Mamyshev, P.

Millot, G.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, "Optical parabolic pulse generation and applications," IEEE J. Quantum Electron. 45, 1482-1489 (2009).
[CrossRef]

Monro, T.

A. Peacock, N. Broderick, and T. Monro, "Numerical study of parabolic pulse generation in microstructured fibre Raman amplifiers," Opt. Commun. 218, 167-172 (2003).
[CrossRef]

Monro, T. M.

Nakazawa, M.

Payne, D. N.

Peacock, A.

A. Peacock, N. Broderick, and T. Monro, "Numerical study of parabolic pulse generation in microstructured fibre Raman amplifiers," Opt. Commun. 218, 167-172 (2003).
[CrossRef]

Petropoulos, P.

Petrovich, M.

N. Vukovic, N. G. R. Broderick, M. Petrovich, and G. Brambilla, "Novel method for the fabrication of long optical tapers," IEEE Photon. Technol. Lett. 20, 1264-1266 (2008).
[CrossRef]

Provost, L.

Richardson, D.

C. Finot, L. Provost, P. Petropoulos, and D. Richardson, "Parabolic pulse generation through passive nonlinear pulse reshaping in a normally dispersive two segment fiber device," Opt. Express 15, 852-864 (2007).
[CrossRef] [PubMed]

N. Broderick, D. Richardson, and L. Dong, "Distributed dispersion measurements and control within continuously varying dispersion tapered fibers," IEEE Photon. Technol. Lett. 9, 1511-1513 (1997).
[CrossRef]

Richardson, D. J.

Sumetsky, M.

M. Sumetsky, Y. Dulashko, and S. Ghalmi, "Fabrication of miniature optical fiber and microfiber coils," Opt. Lasers Eng. 48, 272-275 (2010).
[CrossRef]

Tappert, F.

A. Hasegawa, and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. anomalous dispersion," Appl. Phys. Lett. 23, 142-144 (1973).
[CrossRef]

Thomsen, B. C.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

Vukovic, N.

N. Vukovic, N. G. R. Broderick, M. Petrovich, and G. Brambilla, "Novel method for the fabrication of long optical tapers," IEEE Photon. Technol. Lett. 20, 1264-1266 (2008).
[CrossRef]

N. Vukovic, and N. Broderick, "Improved flatness of a supercontinuum at 1.55 microns in tapered microstructured optical fibres," Phys. Rev. A. submitted.
[CrossRef]

Appl. Phys. Lett. (1)

A. Hasegawa, and F. Tappert, "Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. 1. anomalous dispersion," Appl. Phys. Lett. 23, 142-144 (1973).
[CrossRef]

Electron. Lett. (1)

C. Billet, P. Lacourt, R. Ferriere, L. Larger, and J. Dudley, "Parabolic pulse generation in comb-like profiled dispersion decreasing fibre," Electron. Lett. 42, 965-966 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, "Optical parabolic pulse generation and applications," IEEE J. Quantum Electron. 45, 1482-1489 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

N. Broderick, D. Richardson, and L. Dong, "Distributed dispersion measurements and control within continuously varying dispersion tapered fibers," IEEE Photon. Technol. Lett. 9, 1511-1513 (1997).
[CrossRef]

N. Vukovic, N. G. R. Broderick, M. Petrovich, and G. Brambilla, "Novel method for the fabrication of long optical tapers," IEEE Photon. Technol. Lett. 20, 1264-1266 (2008).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

A. Peacock, N. Broderick, and T. Monro, "Numerical study of parabolic pulse generation in microstructured fibre Raman amplifiers," Opt. Commun. 218, 167-172 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

M. Sumetsky, Y. Dulashko, and S. Ghalmi, "Fabrication of miniature optical fiber and microfiber coils," Opt. Lasers Eng. 48, 272-275 (2010).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

N. Vukovic, and N. Broderick, "Improved flatness of a supercontinuum at 1.55 microns in tapered microstructured optical fibres," Phys. Rev. A. submitted.
[CrossRef]

Phys. Rev. Lett. (1)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, "Self-similar propagation and amplification of parabolic pulses in optical fibers," Phys. Rev. Lett. 84, 6010-6013 (2000).
[CrossRef] [PubMed]

Other (2)

N. T. Vukovic, and N. G. R. Broderick, "Parabolic pulse generation using tapered microstructured optical fibres," Adv. Non. Opt. (2008).

N. Vukovic, F. Parmigiani, A. Camerlingo, M. Petrovich, P. Petropoulos, and N. G. R. Broderick, "Experimental investigation of a parabolic pulse generation using tapered microstructured optical fibres," Proc. SPIE, Photonics Europe 2010 (2010).

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Figures (5)

Fig. 1
Fig. 1

(a) Intensity profile of the output pulse (black line) alone with the best parabolic fit (green line). (b) Dispersion profile (green line) and evolution of the misfit parameter (red dotted line) for the optimum fibre taper.

Fig. 2
Fig. 2

(a) Differing dispersion profiles for different runs of the genetic algorithm. The green and red line are the results when there are 21 different polynomials but with different random seeds. The black line is the case for 31 polynomials. (b) The black line shows the optimised profile for converting a sech shaped pulse into a parabolic pulse while the green line shows the profile for a high intensity Gaussian pulse.

Fig. 3
Fig. 3

(a) Intensity profile of the output pulse (black line) alone with the best sech shaped fit (green line). (b) Dispersion profile (green line) and evolution of the misfit parameter (red dotted line) for the optimum fibre taper.

Fig. 4
Fig. 4

(a) Intensity profile of the output pulse (black line) alone with the best square shaped fit (green line). (b) Dispersion profile (green line) and evolution of the misfit parameter (red dotted line) for the optimum fibre taper.

Fig. 5
Fig. 5

(a) Intensity profile of the output pulse (black line) alone with the best super-Gaussian shaped fit (green line). (b) Dispersion profile (green line) and evolution of the misfit parameter (red dotted line) for the optimum fibre taper.

Equations (9)

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

i ψ z β 2 2 2 ψ t 2 + i α 2 ψ + γ | ψ | 2 ψ = 0 ,
t t T 0 , and β 2 ( z ) β 2 ( z ) T 0 2 .
γ γ P 0 2 , and ψ P 0 ψ .
M = ( | ψ ( L , t ) | 2 | ϕ 2 ( t ) | 2 ) 2 dt | ψ ( L , t ) | 4 dt .
β 2 ( z ) = Σ n = 0 n = N a n z n n !
ϕ 1 ( t ) = 5 e t 2 .
ϕ 2 ( t ) = { a ( 1 ( t / b ) 2 ) | t | < b 0 otherwise .
ϕ 2 ( t ) = a sech ( t / b ) .
ϕ 2 ( t ) = { a | t | < b 0 otherwise .

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