Abstract

We present a new approach to the design of optical microstructured fibers that have group velocity dispersion (GVD) and effective nonlinear coefficient (y) tailored for supercontinuum (SC) generation. This hybrid approach combines a genetic algorithm (GA) with pulse propagation modeling, but without include it into the GA loop, to allow the efficient design of fibers that are capable of generating highly coherent and large bandwidth SC in the mid-infrared (Mid-IR) spectrum. To the best of our knowledge, this is the first use of a GA to design fiber for SC generation. We investigate the robustness of these fiber designs to variation in the fiber’s structural parameters. The optimized fiber structure based on a type of tellurite glass (70TeO 2-10Na 2 O-20ZnF 2) is predicted to have near-zero group velocity dispersion (<±2ps/nm/km) from 2 to 3 µm, and a effective nonlinear coefficient of y≈174W-1 km -1 at 2 µm. The SC output of this fiber shows a significant bandwidth and coherence increase compare to a fiber with a single zero group velocity dispersion wavelength at 2 µm.

© 2009 Optical Society of America

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2009

2008

D. Pestov, X. Wang, G. Ariunbold, R. Murawski, V. Sautenkov, A. Dogariu, A. Sokolov, and M. Scully, "Singleshot detection of bacterial endospores via coherent raman spectroscopy," P. Natl. Acad. Sci. USA 105, 422-427 (2008).
[CrossRef]

W. Zhang, S. V, H. Ebendorff-Heidepriem, and T. Monro, "Record nonlinearity in optical fibre," Electron. Lett. 44, 1453-1455 (2008).
[CrossRef]

P. Domachuk, N. A. Wolchover, M. Cronin-Golomb, A. Wang, A. K. George, C. M. B. Cordeiro, J. C. Knight, and F. G. Omenetto, "Over 4000 nm bandwidth of mid-IR supercontinuum generation in sub-centimeter segments of highly nonlinear tellurite PCFs," Opt. Express 16, 7161-7168 (2008).
[CrossRef] [PubMed]

2007

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, M. Feng, and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured optical fibers," IEEE J. Sel. Topics Quantum Electron. 13, 738-749 (2007).
[CrossRef]

S. Kaasalainen, T. Lindroos, and J. Hyyppa, "Toward hyperspectral lidar: Measurement of spectral backscatter intensity with a supercontinuum laser source," IEEE Geosci. Remote Sens. Lett. 4, 211-215 (2007).
[CrossRef]

C. Colley, J. Hebden, D. Delpy, A. Cambrey, R. Brown, E. Zibik, W. Ng, L. Wilson, and J. Cockburn, "Midinfrared optical coherence tomography," Rev. Sci. Instrum.78 (2007).
[CrossRef]

J. Hult, R. S. Watt, and C. F. Kaminski, "High bandwidth absorption spectroscopy with a dispersed supercontinuum source," Opt. Express 15, 11385-11395 (2007).
[CrossRef] [PubMed]

K. Shi, P. Li, and Z. Liu, "Broadband coherent anti-Stokes raman scattering spectroscopy in supercontinuum optical trap," Appl. Phys. Lett.90 (2007).
[CrossRef]

H. Kano and H. o Hamaguchi, "Coherent raman imaging of human living cells using a supercontinuum light source," Jpn. J. Appl. Phys. 146, 6875-6877 (2007).
[CrossRef]

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

D. Lorenc, D. Velic, A. N. Markevitch, and R. J. Levis, "Adaptive ferntosecond pulse shaping to control supercontinuum generation in a microstructure fiber," Opt. Commum. 276, 288-292 (2007).
[CrossRef]

C. Gross, T. Best, D. van Oosten, and I. Bloch, "Coherent and incoherent spectral broadening in a photonic crystal fiber," Opt. Lett. 32, 1767-1769 (2007).
[CrossRef] [PubMed]

N. Nishizawa and J. Takayanagi, "Octave spanning high-quality supercontinuum generation in all-fiber system," J. Opt. Soc. Am. B 24, 1786-1792 (2007).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves," Nature 450, 1054-1057 (2007).
[CrossRef] [PubMed]

2006

2005

2004

2003

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography - principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

2002

J. M. Dudley and S. Coen, "Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers," Opt. Lett. 27, 1180-1182 (2002).
[CrossRef]

J. Dudley and S. Coen, "Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers," IEEE J. Sel. Topics Quantum Electron. 8, 651-659 (2002).
[CrossRef]

2001

2000

R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000).
[CrossRef] [PubMed]

1994

1989

1970

R. R. Alfano and S. L. Shapiro, "Emission in the region 4000 to 7000 °A via Four-Photon coupling in glass," Phys. Rev. Lett. 24, 584 (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 (1970).
[CrossRef]

Alfano, R. R.

R. R. Alfano and S. L. Shapiro, "Emission in the region 4000 to 7000 °A via Four-Photon coupling in glass," Phys. Rev. Lett. 24, 584 (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 (1970).
[CrossRef]

Andr’es, P.

Andres, M.

Andres, P.

Ariunbold, G.

D. Pestov, X. Wang, G. Ariunbold, R. Murawski, V. Sautenkov, A. Dogariu, A. Sokolov, and M. Scully, "Singleshot detection of bacterial endospores via coherent raman spectroscopy," P. Natl. Acad. Sci. USA 105, 422-427 (2008).
[CrossRef]

Asimakis, S.

Bergquist, J. C.

Best, T.

Bigot, L.

Bloch, I.

Brambilla, G.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, M. Feng, and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured optical fibers," IEEE J. Sel. Topics Quantum Electron. 13, 738-749 (2007).
[CrossRef]

Brown, R.

C. Colley, J. Hebden, D. Delpy, A. Cambrey, R. Brown, E. Zibik, W. Ng, L. Wilson, and J. Cockburn, "Midinfrared optical coherence tomography," Rev. Sci. Instrum.78 (2007).
[CrossRef]

Brown, T.

Cambrey, A.

C. Colley, J. Hebden, D. Delpy, A. Cambrey, R. Brown, E. Zibik, W. Ng, L. Wilson, and J. Cockburn, "Midinfrared optical coherence tomography," Rev. Sci. Instrum.78 (2007).
[CrossRef]

Cardinal, T.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Cockburn, J.

C. Colley, J. Hebden, D. Delpy, A. Cambrey, R. Brown, E. Zibik, W. Ng, L. Wilson, and J. Cockburn, "Midinfrared optical coherence tomography," Rev. Sci. Instrum.78 (2007).
[CrossRef]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

J. M. Dudley and S. Coen, "Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers," Opt. Lett. 27, 1180-1182 (2002).
[CrossRef]

J. Dudley and S. Coen, "Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers," IEEE J. Sel. Topics Quantum Electron. 8, 651-659 (2002).
[CrossRef]

Colley, C.

C. Colley, J. Hebden, D. Delpy, A. Cambrey, R. Brown, E. Zibik, W. Ng, L. Wilson, and J. Cockburn, "Midinfrared optical coherence tomography," Rev. Sci. Instrum.78 (2007).
[CrossRef]

Cordeiro, C. M. B.

Couzi, M.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Cronin-Golomb, M.

Curtis, E. A.

Delpy, D.

C. Colley, J. Hebden, D. Delpy, A. Cambrey, R. Brown, E. Zibik, W. Ng, L. Wilson, and J. Cockburn, "Midinfrared optical coherence tomography," Rev. Sci. Instrum.78 (2007).
[CrossRef]

Diddams, S. A.

Dogariu, A.

D. Pestov, X. Wang, G. Ariunbold, R. Murawski, V. Sautenkov, A. Dogariu, A. Sokolov, and M. Scully, "Singleshot detection of bacterial endospores via coherent raman spectroscopy," P. Natl. Acad. Sci. USA 105, 422-427 (2008).
[CrossRef]

Domachuk, P.

Douay, M.

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography - principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Dudley, J.

J. Dudley and S. Coen, "Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers," IEEE J. Sel. Topics Quantum Electron. 8, 651-659 (2002).
[CrossRef]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

J. M. Dudley and S. Coen, "Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers," Opt. Lett. 27, 1180-1182 (2002).
[CrossRef]

Ebendorff-Heidepriem, H.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, M. Feng, and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured optical fibers," IEEE J. Sel. Topics Quantum Electron. 13, 738-749 (2007).
[CrossRef]

T. M. Monro and H. Ebendorff-Heidepriem, "Progress in microstructured optical fibers," Annu. Rev. Mater. Res. 36, 467-495 (2006).
[CrossRef]

J. Y. Y. Leong, P. Petropoulos, J. H. V. Price, H. Ebendorff-Heidepriem, S. Asimakis, R. C. Moore, K. E. Frampton, V. Finazzi, X. Feng, T. M. Monro, and D. J. Richardson, "High-nonlinearity dispersion-shifted lead-silicate holey fibers for efficient 1-mu m pumped supercontinuum generation," J. Lightwave Technol. 24, 183-190 (2006).
[CrossRef]

Feder, K.

Feng, M.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, M. Feng, and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured optical fibers," IEEE J. Sel. Topics Quantum Electron. 13, 738-749 (2007).
[CrossRef]

Feng, X.

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography - principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Ferrando, A.

Finazzi, V.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, M. Feng, and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured optical fibers," IEEE J. Sel. Topics Quantum Electron. 13, 738-749 (2007).
[CrossRef]

J. Y. Y. Leong, P. Petropoulos, J. H. V. Price, H. Ebendorff-Heidepriem, S. Asimakis, R. C. Moore, K. E. Frampton, V. Finazzi, X. Feng, T. M. Monro, and D. J. Richardson, "High-nonlinearity dispersion-shifted lead-silicate holey fibers for efficient 1-mu m pumped supercontinuum generation," J. Lightwave Technol. 24, 183-190 (2006).
[CrossRef]

Flanagan, J. C.

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Figures (14)

Fig. 1.
Fig. 1.

Schematics of full and hybrid GA approach. Dashed blue arrows form the full GA loop, solid red lines form the hybrid GA loop.

Fig. 2.
Fig. 2.

Raman gain spectrum of 70TeO-10Na 2 O-20ZnF 2 glass, pumped at 1060nm [37] (left) and calculated Raman response function using the maximum Raman gain at 1155nm (right)

Fig. 3.
Fig. 3.

20dB Bandwidth, in µ m, of generated SC output with different constant dispersion D and nonlinearity γ at different propagation length.

Fig. 4.
Fig. 4.

Coherence <|g (1) 12|> of the outputs of SC generation with different constant dispersion and nonlinearity at different propagation length. <|g (1) 12|>=1 is maximum value associated with perfect coherence

Fig. 5.
Fig. 5.

Initial design of the fiber structure.

Fig. 6.
Fig. 6.

Optimized structure (a) and its corresponding dispersion and nonlinearity (b).

Fig. 7.
Fig. 7.

Dispersion(left) and nonlinearity(right) of a range of samples.

Fig. 8.
Fig. 8.

Bandwidth (left) and coherence (right) of SC outputs with different pump wavelengths in the optimized fiber. Between the vertical dashed lines is the region of optimization.

Fig. 9.
Fig. 9.

Normalized intensity (left) and coherence (right) spectrums of pulses propagating along the optimized fiber pump at 2, 2.2, 2.5 µm from top to bottom respectively.

Fig. 10.
Fig. 10.

Normalized intensity (left) and coherence (right) spectrums of pulses propagating along the optimized fiber pump at 2.9, 3, 3.2 µm from top to bottom respectively.

Fig. 11.
Fig. 11.

Dispersion and nonlinearity of a 10µm diameter Tellurite rod surrounded by air.

Fig. 12.
Fig. 12.

Intensity (left) and coherence (right) spectra of a pulse propagating along the fiber with different dispersions and nonlinearities. a) For dispersion and nonlinearity profiles of optimized structure, shown in Fig. 6, b) for dispersion and nonlinearity profiles of 10 µm diameter rod, shown in Fig. 11, c) for dispersion profile of 10 µm diameter rod with nonlinearity profile of the optimized structure.

Fig. 13.
Fig. 13.

20dB bandwidth (left) and coherence (right) of SCG with dispersion and nonlinearity profiles of optimized structure (Fig. 6), 10 µm diameter rod (Fig. 11) and 10 µm diameter rod with nonlinearity profile of optimized structure.

Fig. 14.
Fig. 14.

Dispersion curves and corresponding coherence of the SC outputs. Curve ORG is the original dispersion curve calculated from GA modeling, MOD1 to MOD3 are the artificial dispersion curves

Tables (1)

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Table 1. Statistics of the structure parameters

Equations (16)

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A(z,t)z + α2 A (z,t)k2ik+1k!βkkA(z,t)Tk=
(1+shockT)(A(z,t)R(T)×A(z,TT)2dT)
g12(1)(λ,t1t2)=E1*(λ,t1)E2(λ,t2)<E1(λ,t1)2><E2(λ,t2)2>,
F = γpump×(iDi)1
Psetnew(1) = α×Psetold(1)+(1α)×Psetold(2)
Psetnew(2) = (1α)×Psetold(1)+α×Psetold(2)
γ = 2πλ0 n2,effAeff
n2,eff = (n2(x,y)F2dxdy)2F4dxdy ,
Aeff = (F2dxdy)2F4dxdy .
τshock = 1ω0 1neff(ω0) neff(ω)ω ω0 1Aeff(ω0) Aeff(ω)ω ω0
R (t)=(1fR)δ(t)+fRhR(t)
N2 (Ω)=fRN2(0)h˜R(Ω)
I m (N2(Ω))=λ0g(Ω)4π
N2 (Ω) = (λ04π1π𝒫dΩg(Ω)ΩΩ+i(g(Ω)λ04π))
hR (t)=𝓕1(N2(Ω))0𝓕1(N2(Ω))dt
fR = 0𝓕1(N2(Ω))dtN2(0)

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