Abstract

An effective hybrid genetic algorithm (GA) for optimizing air–silica nanowires, the incident pulse, and supercontinuum (SC) generation, is proposed in this paper. Based on the proposed algorithm, the dispersion and nonlinearity of air–silica nanowires, as well as the duration and chirp of incident pulses, are optimized to achieve SC generation with a broader, smoother, and more intense spectrum. It is found that the optimized spectrum becomes smoother from 740to1500nm and is broadened by 300nm. Meanwhile, the spectral intensity in the range of 450945nm is significantly increased by a factor of 10.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  32. L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004).
    [CrossRef] [PubMed]
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2008 (1)

2006 (3)

2005 (1)

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

2004 (7)

2003 (6)

2002 (3)

2001 (3)

2000 (4)

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
[CrossRef]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Optical properties of high-delta air–silica microstructure optical fibers,” Opt. Lett. 25, 796–798 (2000).
[CrossRef]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

R. Chelouah and P. Siarry, “A continuous genetic algorithm designed for the global optimization of multimodal functions,” J. Heuristics 6, 191–213 (2000).
[CrossRef]

1984 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

1970 (2)

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000to7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970).
[CrossRef]

R. R. Alfano and S. L. Shapiro, “Observation of self phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24, 592–594 (1970).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), 49.8.

Alfano, R. R.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000to7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970).
[CrossRef]

R. R. Alfano and S. L. Shapiro, “Observation of self phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24, 592–594 (1970).
[CrossRef]

Ashcom, J. B.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef] [PubMed]

Birks, T. A.

Brown, T.

Brown, T. G.

Campbell, S.

Cao, Q.

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Chandalia, J. K.

Chang, G. Q.

Chelouah, R.

R. Chelouah and P. Siarry, “A continuous genetic algorithm designed for the global optimization of multimodal functions,” J. Heuristics 6, 191–213 (2000).
[CrossRef]

Chudoba, C.

Coen, S.

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Dane, R. A.

de Sterke, C. M.

Diddams, S. A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Dudley, J.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1185 (2006).
[CrossRef]

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

J. M. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air–silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19, 765–771 (2002).
[CrossRef]

Eggleton, B. J.

Foster, M.

Foster, M. A.

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16, 1300–1320 (2008).
[CrossRef] [PubMed]

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Fujimoto, J. G.

Gaeta, A.

Gaeta, A. L.

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16, 1300–1320 (2008).
[CrossRef] [PubMed]

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Gattass, R. R.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef] [PubMed]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Genty, G.

Ghanta, R. K.

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

Griebner, U.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of high-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Grossard, N.

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Hartl, I.

Harvey, J. D.

He, S. L.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef] [PubMed]

Herrmann, J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of high-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

A. V. Husakou and J. Herrmann, “Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers,” J. Opt. Soc. Am. B 19, 2171–2182 (2002).
[CrossRef]

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

Hilligsøe, K. M.

Husakou, A.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of high-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Husakou, A. V.

A. V. Husakou and J. Herrmann, “Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers,” J. Opt. Soc. Am. B 19, 2171–2182 (2002).
[CrossRef]

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

Jain, R. K.

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Keiding, S. R.

Kibler, B.

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Knight, J.

Knight, J. C.

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28, 2225–2227 (2003).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of high-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Knox, W. H.

Ko, T. H.

Korn, G.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of high-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Kosinski, S. G.

Larsen, J. J.

Lee, B.

X. Liu and B. Lee, “A fast method for nonlinear Schrödinger equation,” IEEE Photonics Technol. Lett. 15, 1549–1551 (2003).
[CrossRef]

Lee, C.

Lee, D.

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Lehtonen, M.

Leonhardt, R.

Leon-Saval, S. G.

Li, X. D.

Lipson, M.

Liu, X.

Lou, J. Y.

Luan, F.

Ludvigsen, H.

Maillotte, H.

Mangan, B.

Maxwell, I.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef] [PubMed]

Mazur, E.

L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004).
[CrossRef] [PubMed]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef] [PubMed]

Moll, K.

Nickel, D.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of high-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Norris, T. B.

Paulsen, H. N.

Provino, L.

Ranka, J. K.

Reid, D.

Roberts, P.

Russell, P.

Russell, P. St. J.

Shapiro, S. L.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000to7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970).
[CrossRef]

R. R. Alfano and S. L. Shapiro, “Observation of self phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24, 592–594 (1970).
[CrossRef]

Shen, M. Y.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef] [PubMed]

Siarry, P.

R. Chelouah and P. Siarry, “A continuous genetic algorithm designed for the global optimization of multimodal functions,” J. Heuristics 6, 191–213 (2000).
[CrossRef]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[CrossRef] [PubMed]

Stentz, A. J.

Stolen, R. H.

Thøgersen, J.

Tong, L. M.

Trebino, R.

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Turner, A. C.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Wadsworth, W. J.

Williams, D.

Windeler, R. S.

Winful, H. G.

Wong, G. K. L.

Xiao, D.

Xu, C.

Ye, Z. Z.

Zhavoronkov, N.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of high-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Zhu, Z. M.

Appl. Phys. B (1)

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

X. Liu and B. Lee, “A fast method for nonlinear Schrödinger equation,” IEEE Photonics Technol. Lett. 15, 1549–1551 (2003).
[CrossRef]

J. Heuristics (1)

R. Chelouah and P. Siarry, “A continuous genetic algorithm designed for the global optimization of multimodal functions,” J. Heuristics 6, 191–213 (2000).
[CrossRef]

J. Opt. Soc. Am. B (4)

Nature (1)

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef] [PubMed]

Opt. Express (10)

Z. M. Zhu and T. Brown, “Experimental studies of polarization properties of supercontinua generated in a birefringent photonic crystal fiber,” Opt. Express 12, 791–796 (2004).
[CrossRef] [PubMed]

F. Luan, J. Knight, P. Russell, S. Campbell, D. Xiao, D. Reid, B. Mangan, D. Williams, and P. Roberts, “Femtosecond soliton pulse delivery at 800 nm wavelength in hollow-core photonic bandgap fibers,” Opt. Express 12, 835–840 (2004).
[CrossRef] [PubMed]

L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004).
[CrossRef] [PubMed]

J. Dudley and S. Coen, “Fundamental limits to few-cycle pulse generation from compression of supercontinuum spectra generated in photonic crystal fiber,” Opt. Express 12, 2423–2428 (2004).
[CrossRef] [PubMed]

S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12, 2864–2870 (2004).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

GVD in air–silica nanowires with 700 900 nm core diameter. When the pulse wavelength is chosen at 800 nm , the nanowires locate in the anomalous dispersion region.

Fig. 2
Fig. 2

Diameter-dependent nonlinearity of air–silica nanowires for 800 nm wavelength.

Fig. 3
Fig. 3

The spectral profiles of SC in an 800 nm core-diameter nanowire after propagating 0 and 6.87 mm , respectively.

Fig. 4
Fig. 4

Searching the maxima of Eq. (8) and Eq. (9) through the proposed hybrid GA. (a) x values: 0.0184, 0.1575, and 0.3444. (b) x values: 1.5736, 2.9135, and 4.2045.

Fig. 5
Fig. 5

The spectra after optimization. The corresponding parameters used are (a) D core = 717.71 nm , z = 6.68 mm , C = 0.30 , T 0 = 79.72 fs , (b) D core = 847.09 nm , z = 5.80 mm , C = 1.30 , T 0 = 76.95 fs , and (c) D core = 838.00 nm , z = 5.47 mm , C = 0.200 , T 0 = 78.98 fs .

Fig. 6
Fig. 6

The SC spectra before (dashed curve) and after (solid curve) optimization.

Tables (1)

Tables Icon

Table 1 Values and Nonlinear Coefficients at the Boundary and Optimal Core Diameters with Wavelength 800 nm

Equations (9)

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( t 2 + n 2 k 0 2 β 2 ) e = 0.
{ J 1 ( U ) U J 1 ( U ) + K 1 ( W ) W K 1 ( W ) } { J 1 ( U ) U J 1 ( U ) + n 2 2 K 1 ( W ) n 1 2 W K 1 ( W ) } = ( β k 0 n 1 ) ( V U W ) 4 .
v g = d w d β = 2 π c λ 2 d λ d β ,
D = d ( v g 1 ) d λ .
γ = 2 π λ n 2 S z 2 d 2 r ( S z d 2 r ) 2 2 π λ 0 a n 2 S z 1 2 r d r 0 2 π d ϕ ( 0 a S z 1 r d r 0 2 π d ϕ + a S z 2 r d r 0 2 π d ϕ ) 2 .
A z + α 2 A i k 2 i k β k k ! k A T k = i γ ( | A | 2 A + i w 0 T ( | A | 2 A ) T R A | A | 2 T ) ,
F = w 1 w 2 I ( w ) d w ,
y = cos 4 ( 5 π ( x 0.75 0.05 ) ) 0 x 0.45 ,
y = x + 10 sin ( 5 x ) + 7 cos ( 4 x ) 1.0 x 4.5 .

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