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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References

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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. of 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. Laser 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) (2010).
    [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 (2)

M. Sumetsky, Y. Dulashko, and S. Ghalmi, “Fabrication of miniature optical fiber and microfiber coils,” Opt. Laser Eng. 48, 272–275 (2010).
[Crossref]

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).

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)

S. Chernikov and P. Mamyshev, “Femtosecond soliton propagation in fibers with slowly decreasing dispersion,” J. Opt. Soc. of Am. B 8, 1633–1641 (1991).
[Crossref]

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) (2010).
[Crossref]

Broderick, N. G. R.

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).

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]

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

Camerlingo, A.

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).

Chernikov, S.

S. Chernikov and P. Mamyshev, “Femtosecond soliton propagation in fibers with slowly decreasing dispersion,” J. Opt. Soc. of Am. B 8, 1633–1641 (1991).
[Crossref]

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. Laser 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. Laser 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.

S. Chernikov and P. Mamyshev, “Femtosecond soliton propagation in fibers with slowly decreasing dispersion,” J. Opt. Soc. of Am. B 8, 1633–1641 (1991).
[Crossref]

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.

Parmigiani, F.

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).

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.

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).

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]

Petrovich, M.

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).

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. Laser 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, 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).

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) (2010).
[Crossref]

Vukovic, N. T.

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

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. 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. 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]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

J. Opt. Soc. of Am. B (1)

S. Chernikov and P. Mamyshev, “Femtosecond soliton propagation in fibers with slowly decreasing dispersion,” J. Opt. Soc. of Am. B 8, 1633–1641 (1991).
[Crossref]

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. Laser Eng. (1)

M. Sumetsky, Y. Dulashko, and S. Ghalmi, “Fabrication of miniature optical fiber and microfiber coils,” Opt. Laser Eng. 48, 272–275 (2010).
[Crossref]

Opt. Lett. (2)

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]

Proc. SPIE, Photonics Europe 2010 (1)

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).

Other (2)

N. Vukovic and N. Broderick, “Improved flatness of a supercontinuum at 1.55 microns in tapered microstructured optical fibres,” Phys. Rev. A. (submitted) (2010).
[Crossref]

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

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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.

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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.

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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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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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