Abstract

We present an analysis and describe the design of supercontinuum (SC) pulse generation in a single-mode optical fiber. SC generation with a dispersion-decreasing fiber with a convex dispersion profile is contrasted with other approaches to obtaining conditions for generating a flat, broadened spectrum. We present general criteria for SC generation by introducing normalized parameters that allow the shape of the SC spectrum to be invariant for several SC-generating fibers and optical pump pulses. Based on these results, we designed a SC fiber and experimentally generated SC pulses that were in good agreement with theory.

© 2001 Optical Society of America

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Corrections

Kunihiko Mori, Hidehiko Takara, and Satoki Kawanishi, "Analysis and design of supercontinuum pulse generation in a single-mode optical fiber: erratum," J. Opt. Soc. Am. B 32, 1174-1175 (2015)
https://www.osapublishing.org/josab/abstract.cfm?uri=josab-32-6-1174

References

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    [CrossRef]
  27. T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Transform-limited, femtosecond WDM pulse generation by spectral filtering of gigahertz supercontinuum,” Electron. Lett. 30, 1166–1167 (1994).
    [CrossRef]
  28. T. Morioka, S. Kawanishi, H. Takara, O. Kamatani, M. Yamada, T. Kanamori, K. Uchiyama, and M. Saruwatari, “100 Gbit/s×4ch, 100 km repeaterless TDM-WDM transmission using a single supercontinuum source,” Electron. Lett. 32, 468–469 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2000 (2)

1999 (1)

S. Kawanishi, H. Takara, K. Uchiyama, I. Shake, and K. Mori, “3 Tbit/s (160 Gbit/s × 19 channel) optical TDM and WDM transmission experiment,” Electron. Lett. 35, 826–827 (1999).
[CrossRef]

1998 (1)

T. Okuno, M. Onishi, and M. Nishimura, “Generation of ultra-broad-band supercontinuum by dispersion-flattened and decreasing fiber,” IEEE Photon. Technol. Lett. 10, 72–74 (1998).
[CrossRef]

1997 (1)

K. Mori, H. Takara, S. Kawanishi, M. Saruwatari, and T. Morioka, “Flatly broadened supercontinuum spectrum generated in a dispersion decreasing fibre with convex dispersion profile,” Electron. Lett. 33, 1806–1808 (1997).
[CrossRef]

1996 (2)

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

T. Morioka, S. Kawanishi, H. Takara, O. Kamatani, M. Yamada, T. Kanamori, K. Uchiyama, and M. Saruwatari, “100 Gbit/s×4ch, 100 km repeaterless TDM-WDM transmission using a single supercontinuum source,” Electron. Lett. 32, 468–469 (1996).
[CrossRef]

1995 (1)

K. Mori, T. Morioka, and M. Saruwatari, “Ultrawide spectral range group-velocity dispersion measurement utilizing supercontinuum in an optical fiber pumped by a 1.5 μm compact laser source,” IEEE Trans. Instrum. Meas. 44, 712–715 (1995).
[CrossRef]

1994 (2)

T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Nearly penalty-free, <4 ps supercontinuum Gbit/s pulse generation over 1535–1560 nm,” Electron. Lett. 30, 790–791 (1994).
[CrossRef]

T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Transform-limited, femtosecond WDM pulse generation by spectral filtering of gigahertz supercontinuum,” Electron. Lett. 30, 1166–1167 (1994).
[CrossRef]

1991 (2)

P. L. François, “Nonlinear propagation of ultrashort pulses in optical fibers: total field formulation in the frequency domain,” J. Opt. Soc. Am. B 8, 276–293 (1991).
[CrossRef]

B. Gross and J. T. Manassah, “The spectral distribution and the frequency shift of the supercontinuum,” Phys. Lett. A 160, 261–270 (1991).
[CrossRef]

1989 (2)

1986 (1)

C. Pask and A. Vatarescu, “Spectral approach to pulse propagation in a dispersive nonlinear medium,” J. Appl. Phys. 3, 5098–5106 (1986).

1983 (1)

P. L. François, “Zero dispersion in attenuation optimized doubly clad fibers,” J. Lightwave Technol. LT-1, 26–37 (1983).
[CrossRef]

1982 (2)

L. G. Cohen and W. L. Mammel, “Low-loss quadruple-clad single-mode lightguides with dispersion below 2 ps/km nm over the 1.28 μm–1.65 μm wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[CrossRef]

M. Monerie, “Propagation in doubly clad single-mode fibers,” IEEE J. Quantum Electron. QE-18, 535–542 (1982).
[CrossRef]

1978 (1)

1970 (1)

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970).
[CrossRef]

Alfano, R. R.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970).
[CrossRef]

Bar-Joseph, I.

Birks, T. A.

Chemla, D. S.

Cohen, L. G.

L. G. Cohen and W. L. Mammel, “Low-loss quadruple-clad single-mode lightguides with dispersion below 2 ps/km nm over the 1.28 μm–1.65 μm wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[CrossRef]

Dianov, E. M.

François, P. L.

Gordon, J. P.

Gross, B.

B. Gross and J. T. Manassah, “The spectral distribution and the frequency shift of the supercontinuum,” Phys. Lett. A 160, 261–270 (1991).
[CrossRef]

Hill, K. O.

Islam, M. N.

Johnson, D. C.

Kamatani, O.

T. Morioka, S. Kawanishi, H. Takara, O. Kamatani, M. Yamada, T. Kanamori, K. Uchiyama, and M. Saruwatari, “100 Gbit/s×4ch, 100 km repeaterless TDM-WDM transmission using a single supercontinuum source,” Electron. Lett. 32, 468–469 (1996).
[CrossRef]

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

Kanamori, T.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

T. Morioka, S. Kawanishi, H. Takara, O. Kamatani, M. Yamada, T. Kanamori, K. Uchiyama, and M. Saruwatari, “100 Gbit/s×4ch, 100 km repeaterless TDM-WDM transmission using a single supercontinuum source,” Electron. Lett. 32, 468–469 (1996).
[CrossRef]

Kawanishi, S.

S. Kawanishi, H. Takara, K. Uchiyama, I. Shake, and K. Mori, “3 Tbit/s (160 Gbit/s × 19 channel) optical TDM and WDM transmission experiment,” Electron. Lett. 35, 826–827 (1999).
[CrossRef]

K. Mori, H. Takara, S. Kawanishi, M. Saruwatari, and T. Morioka, “Flatly broadened supercontinuum spectrum generated in a dispersion decreasing fibre with convex dispersion profile,” Electron. Lett. 33, 1806–1808 (1997).
[CrossRef]

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

T. Morioka, S. Kawanishi, H. Takara, O. Kamatani, M. Yamada, T. Kanamori, K. Uchiyama, and M. Saruwatari, “100 Gbit/s×4ch, 100 km repeaterless TDM-WDM transmission using a single supercontinuum source,” Electron. Lett. 32, 468–469 (1996).
[CrossRef]

T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Nearly penalty-free, <4 ps supercontinuum Gbit/s pulse generation over 1535–1560 nm,” Electron. Lett. 30, 790–791 (1994).
[CrossRef]

T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Transform-limited, femtosecond WDM pulse generation by spectral filtering of gigahertz supercontinuum,” Electron. Lett. 30, 1166–1167 (1994).
[CrossRef]

Kawasaki, B. S.

MacDonald, R. I.

Mammel, W. L.

L. G. Cohen and W. L. Mammel, “Low-loss quadruple-clad single-mode lightguides with dispersion below 2 ps/km nm over the 1.28 μm–1.65 μm wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[CrossRef]

Mamyshev, P. V.

Manassah, J. T.

B. Gross and J. T. Manassah, “The spectral distribution and the frequency shift of the supercontinuum,” Phys. Lett. A 160, 261–270 (1991).
[CrossRef]

Miroshnichenko, S. I.

Monerie, M.

M. Monerie, “Propagation in doubly clad single-mode fibers,” IEEE J. Quantum Electron. QE-18, 535–542 (1982).
[CrossRef]

Mori, K.

S. Kawanishi, H. Takara, K. Uchiyama, I. Shake, and K. Mori, “3 Tbit/s (160 Gbit/s × 19 channel) optical TDM and WDM transmission experiment,” Electron. Lett. 35, 826–827 (1999).
[CrossRef]

K. Mori, H. Takara, S. Kawanishi, M. Saruwatari, and T. Morioka, “Flatly broadened supercontinuum spectrum generated in a dispersion decreasing fibre with convex dispersion profile,” Electron. Lett. 33, 1806–1808 (1997).
[CrossRef]

K. Mori, T. Morioka, and M. Saruwatari, “Ultrawide spectral range group-velocity dispersion measurement utilizing supercontinuum in an optical fiber pumped by a 1.5 μm compact laser source,” IEEE Trans. Instrum. Meas. 44, 712–715 (1995).
[CrossRef]

T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Transform-limited, femtosecond WDM pulse generation by spectral filtering of gigahertz supercontinuum,” Electron. Lett. 30, 1166–1167 (1994).
[CrossRef]

T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Nearly penalty-free, <4 ps supercontinuum Gbit/s pulse generation over 1535–1560 nm,” Electron. Lett. 30, 790–791 (1994).
[CrossRef]

Morioka, T.

K. Mori, H. Takara, S. Kawanishi, M. Saruwatari, and T. Morioka, “Flatly broadened supercontinuum spectrum generated in a dispersion decreasing fibre with convex dispersion profile,” Electron. Lett. 33, 1806–1808 (1997).
[CrossRef]

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

T. Morioka, S. Kawanishi, H. Takara, O. Kamatani, M. Yamada, T. Kanamori, K. Uchiyama, and M. Saruwatari, “100 Gbit/s×4ch, 100 km repeaterless TDM-WDM transmission using a single supercontinuum source,” Electron. Lett. 32, 468–469 (1996).
[CrossRef]

K. Mori, T. Morioka, and M. Saruwatari, “Ultrawide spectral range group-velocity dispersion measurement utilizing supercontinuum in an optical fiber pumped by a 1.5 μm compact laser source,” IEEE Trans. Instrum. Meas. 44, 712–715 (1995).
[CrossRef]

T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Transform-limited, femtosecond WDM pulse generation by spectral filtering of gigahertz supercontinuum,” Electron. Lett. 30, 1166–1167 (1994).
[CrossRef]

T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Nearly penalty-free, <4 ps supercontinuum Gbit/s pulse generation over 1535–1560 nm,” Electron. Lett. 30, 790–791 (1994).
[CrossRef]

Nishimura, M.

T. Okuno, M. Onishi, and M. Nishimura, “Generation of ultra-broad-band supercontinuum by dispersion-flattened and decreasing fiber,” IEEE Photon. Technol. Lett. 10, 72–74 (1998).
[CrossRef]

Okuno, T.

T. Okuno, M. Onishi, and M. Nishimura, “Generation of ultra-broad-band supercontinuum by dispersion-flattened and decreasing fiber,” IEEE Photon. Technol. Lett. 10, 72–74 (1998).
[CrossRef]

Onishi, M.

T. Okuno, M. Onishi, and M. Nishimura, “Generation of ultra-broad-band supercontinuum by dispersion-flattened and decreasing fiber,” IEEE Photon. Technol. Lett. 10, 72–74 (1998).
[CrossRef]

Ono, H.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

Pask, C.

C. Pask and A. Vatarescu, “Spectral approach to pulse propagation in a dispersive nonlinear medium,” J. Appl. Phys. 3, 5098–5106 (1986).

Ranka, J. K.

Russell, P. St. J.

Saruwatari, M.

K. Mori, H. Takara, S. Kawanishi, M. Saruwatari, and T. Morioka, “Flatly broadened supercontinuum spectrum generated in a dispersion decreasing fibre with convex dispersion profile,” Electron. Lett. 33, 1806–1808 (1997).
[CrossRef]

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

T. Morioka, S. Kawanishi, H. Takara, O. Kamatani, M. Yamada, T. Kanamori, K. Uchiyama, and M. Saruwatari, “100 Gbit/s×4ch, 100 km repeaterless TDM-WDM transmission using a single supercontinuum source,” Electron. Lett. 32, 468–469 (1996).
[CrossRef]

K. Mori, T. Morioka, and M. Saruwatari, “Ultrawide spectral range group-velocity dispersion measurement utilizing supercontinuum in an optical fiber pumped by a 1.5 μm compact laser source,” IEEE Trans. Instrum. Meas. 44, 712–715 (1995).
[CrossRef]

T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Nearly penalty-free, <4 ps supercontinuum Gbit/s pulse generation over 1535–1560 nm,” Electron. Lett. 30, 790–791 (1994).
[CrossRef]

T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Transform-limited, femtosecond WDM pulse generation by spectral filtering of gigahertz supercontinuum,” Electron. Lett. 30, 1166–1167 (1994).
[CrossRef]

Semenov, V. A.

Shake, I.

S. Kawanishi, H. Takara, K. Uchiyama, I. Shake, and K. Mori, “3 Tbit/s (160 Gbit/s × 19 channel) optical TDM and WDM transmission experiment,” Electron. Lett. 35, 826–827 (1999).
[CrossRef]

Shapiro, S. L.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å four-photon coupling in glass,” Phys. Rev. Lett. 24, 584–587 (1970).
[CrossRef]

Stegeman, G. I.

Stentz, A. J.

Sucha, G.

Takahashi, H.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

Takara, H.

S. Kawanishi, H. Takara, K. Uchiyama, I. Shake, and K. Mori, “3 Tbit/s (160 Gbit/s × 19 channel) optical TDM and WDM transmission experiment,” Electron. Lett. 35, 826–827 (1999).
[CrossRef]

K. Mori, H. Takara, S. Kawanishi, M. Saruwatari, and T. Morioka, “Flatly broadened supercontinuum spectrum generated in a dispersion decreasing fibre with convex dispersion profile,” Electron. Lett. 33, 1806–1808 (1997).
[CrossRef]

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

T. Morioka, S. Kawanishi, H. Takara, O. Kamatani, M. Yamada, T. Kanamori, K. Uchiyama, and M. Saruwatari, “100 Gbit/s×4ch, 100 km repeaterless TDM-WDM transmission using a single supercontinuum source,” Electron. Lett. 32, 468–469 (1996).
[CrossRef]

Takiguchi, K.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

Uchiyama, K.

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[CrossRef]

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

T. Morioka, S. Kawanishi, H. Takara, O. Kamatani, M. Yamada, T. Kanamori, K. Uchiyama, and M. Saruwatari, “100 Gbit/s×4ch, 100 km repeaterless TDM-WDM transmission using a single supercontinuum source,” Electron. Lett. 32, 468–469 (1996).
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T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, “1 Tbit/s (100 Gbit/s × 10 channel) OTDM/WDM transmission using a single supercontinuum WDM source,” Electron. Lett. 32, 906–907 (1996).
[CrossRef]

T. Morioka, S. Kawanishi, H. Takara, O. Kamatani, M. Yamada, T. Kanamori, K. Uchiyama, and M. Saruwatari, “100 Gbit/s×4ch, 100 km repeaterless TDM-WDM transmission using a single supercontinuum source,” Electron. Lett. 32, 468–469 (1996).
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[CrossRef]

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[CrossRef]

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Other (14)

K. Mori, T. Morioka, H. Takara, and M. Saruwatari, “Continuously tunable optical pulse generation utilizing supercontinuum in an optical fiber pumped by amplified gain-switched LD pulses,” in Optical Amplifiers and Their Applications, Vol. 14 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), paper MD11.

H. Takara, S. Kawanishi, A. Yokoo, S. Tomaru, and M. Saruwatari, “Eye-diagram measurement of 100 Gbit/s optical signal using optical sampling,” in Proceedings of the European Conference on Optical Communication (Telenor R&D, Kjeller, Norway, 1996), pp. 4.7–4.10, paper ThB.1.2.

Y. Takushima, and K. Kikuchi, “Analysis of super-continuum generation in positive group-velocity dispersion fibers,” in Proceedings of the 1997 Electronics Society Conference of IEICE (Institute of Electronics, Information and Communication Engineers, Tokyo, 1997) p. 250, paper C-4–4 (in Japanese).

F. Futami, Y. Takushima, and K. Kikuchi, “Generation of supercontinuum with extremely wideband and flat spectra from a dispersion-flattened fiber in the positive dispersion profile,” in Proceedings of the Optoelectronics and Communications Conference (Institute of Electronics, Information and Communication Engineers, Tokyo, 1998), pp. 378–379, paper 15C3–2.

S. Kawanishi, H. Takara, K. Uchiyama, I. Shake, O. Kamatani, and H. Takahashi, “1.4 Tbit/s (200 Gbit/s×7 channel), 50 km OTDM-WDM transmission experiment,” in Proceedings of the Optoelectronics and Communications Conference (Institute of Electronics, Information and Communication Engineers, Tokyo, 1998), pp. 14–15, paper PDP2–2.

J. Kim, Ö. Boyras, and M. N. Islam, “150+ channel ultra-DWDM source with N×10 GHz spacing utilizing longitudinal mode slicing of supercontinuum,” in Optical Fiber Communications Conference (OFC), Vol. 37 of OSA trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThA2.

H. Takara, T. Ohara, K. Mori, K. Sato, E. Yamada, K. Jinguji, Y. Inoue, T. Shibata, T. Morioka, and K.-I. Sato, “Over 1000 channel optical frequency chain generation from a single supercontinuum source with 12.5 GHz channel spacing for DWDM and frequency standards,” in Proceedings of the European Conference on Optical Communication (VDE Verlag, Berlin, 2000), paper PD 3.1.

E. Yamada, H. Takara, T. Ohara, K. Sato, and T. Morioka, “A high SNR, 150 ch supercontinuum cw optical source with precise 25 GHz spacing for 10 Gbit/s DWDM systems,” in Optical Fiber Communications Conference (OFC), Vol. XX of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper ME2.

H. Takara, E. Yamada, T. Ohara, K. Sato, K. Jinguji, Y. Inoue, T. Shibata, and T. Morioka, “106×10 Gbit/s, 25 GHz-spaced, 640 km DWDM transmission employing a single supercontinuum multi-carrier source,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper PD11.

J. W. Lou, T. J. Xia, O. Boyraz, C.-X. Shi, G. A. Nowak, and M. N. Islam, “Broader and flatter supercontinuum spectra in dispersion tailored fibers,” in Optical Fiber Communication Conference, Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 32–34, paper TuH6.

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T. Okuno, M. Onishi, and M. Nishimura, “Dispersion-flattened and decreasing fiber for ultra-broadband supercontinuum generation,” in Proceedings of the European Conference on Optical Communication, postdeadline papers (Institution of Electrical Engineers, London, 1997), pp. 77–80.

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K. Mori, H. Takara, and S. Kawanishi, “The effect of pump fluctuation in supercontinuum pulse generation,” in Nonlinear Guided Waves and Their Applications, Vol. 5 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 276–278.

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Figures (18)

Fig. 1
Fig. 1

Idealized chromatic dispersion of the SC fiber in which the peak wavelength of dispersion λpeak is constant and is equal to pump wavelength λ0.

Fig. 2
Fig. 2

Evolution of the SC spectrum, where L0=600 m. Dashed lines, zero-dispersion wavelengths.

Fig. 3
Fig. 3

Time-resolved spectra of a SC pulse under the same condition as those of Fig. 2; vertical and horizontal axes indicate wavelength and time delay, respectively. Dashed lines, zero-dispersion wavelengths. Shaded areas, anomalous dispersion regions.

Fig. 4
Fig. 4

Spectrum generated by a convex dispersion fiber that has no decrease in chromatic dispersion.

Fig. 5
Fig. 5

Spectrum generated by a dispersion-decreasing fiber that has only one zero-dispersion wavelength.

Fig. 6
Fig. 6

Spectrum generated by a nondecreasing dispersion fiber that has normal dispersion. Note that the parameters of the pump pulse are different from those of the other pulses.

Fig. 7
Fig. 7

Numerical SC spectra output from fibers specified by the normalized parameters Δ0=0.25, Δ2=-2.0×10-6, and ζ0=3.5. Dashed lines mark a level 27 dB down from the spectral peak. (a) γP0=2.9 km-1, TFWHM=4 ps, D0=3 ps/(nm/km), D2=-0.000075 ps/(nm3/km), and L0=1200 m. (b) γP0=5.8km-1, TFWHM=4 ps, D0=6 ps/(nm/km), D2=-0.00015ps/(nm3/km), and L0=600 m. (c) γP0=11.6 km-1, TFWHM=4 ps, D0=12 ps/(nm/km), D2=-0.00030 ps/(nm3/km), and L0=300 m. (d) γP0=5.8 km-1, TFWHM=2 ps, D0=1.5ps/(nm/km), D2=-0.0000093ps/(nm3/km), and L0=600 m. (e) γP0=5.8 km-1, TFWHM=6 ps, D0=13.5 ps/(nm/km), D2=-0.00076 ps/(nm3/km), and L0=600 m. Spectra (a)–(c) are offset 80 dB from one another. Note that (d) and (e) have different scales in their horizontal axes from that of the others.

Fig. 8
Fig. 8

Map of SC bandwidth in which the vertical and horizontal axes represent normalized chromatic dispersion Δ0 and normalized effective length ζ0, respectively. Dashed curve, condition for generating the flattest spectrum. Effective peak power γP0 and FWHM T0 of the pump pulses are constant at 5.84 km-1 and 4 ps, respectively. Δ2 is constant at -2.0×10-6.

Fig. 9
Fig. 9

Map of SC bandwidth in which the vertical and horizontal axes represent normalized pulse duration τ0 and normalized peak power ρ0, respectively. Dashed curve, the condition for generating the flattest spectrum. Input chromatic dispersion D0, quadratic dispersion D2, and effective length L0 of the SC fiber are constant at 6 ps/(nm/km), -0.0002 ps/(nm3/km), and 600 m, respectively.

Fig. 10
Fig. 10

Example of a chromatic-dispersion characteristic in a typical SC fiber. Solid curves, dispersion characteristics at the input and output of the SC fiber. Dashed curve, dispersion characteristic at z=L0, where the dispersion curve is tangent to the horizontal axis.

Fig. 11
Fig. 11

SC spectra simulated in a dispersion-decreasing–dispersion-convex fiber with a 20-nm shift in the dispersion peak and a 1-ps/(nm/km) decrease in the peak dispersion. (a) Pump wavelength is set equal to the peak wavelength of dispersion curve at z=L0. (b) Improvement of flatness in the SC spectrum by when the pump wavelength is shifted 10 nm toward longer wavelengths.

Fig. 12
Fig. 12

SC spectra including SRS effect. Dotted curves above the SC spectra, imaginary part of the Raman susceptibility. The same parameters for the pump pulse and the SC fiber as those in Fig. 7 are assigned to the corresponding parts of the figure, except for effective length L0 to satisfy ζ0=2.82.

Fig. 13
Fig. 13

Map of SC bandwidth including the SRS effect in which the vertical and horizontal axes represent normalized chromatic dispersion Δ0 and normalized effective length ζ0, respectively. Effective peak power γP0 and FWHM T0 of the pump pulses are constant at 5.84 km-1 and 4 ps, respectively. Δ2 is constant at -2.0×10-6.

Fig. 14
Fig. 14

Map of SC bandwidth with the effect of SRS in which the vertical and horizontal axes represent normalized pulse duration τ0 and normalized peak power ρ0, respectively. Dashed curve, condition for generating the flattest spectrum. Input chromatic dispersion D0, quadratic dispersion D2, and effective length L0 of the SC fiber are constant at 6 ps/(nm/km), -0.0002 ps/(nm3/km), and 600 m, respectively.

Fig. 15
Fig. 15

Dependence of a 27-dB-bandwidth spectrum on normalized effective length ζ0 for five values of normalized loss Λ. Dashed curve, trace of the condition for generating a flat broadened spectrum.

Fig. 16
Fig. 16

Spectrum of the experimentally observed SC pulse. The spectrum of the input pump pulse is superimposed.

Fig. 17
Fig. 17

Time-resolved spectrum of the SC pulse experimentally observed by a monochromator and a streak camera. Inset, image of the pump pulse input into the SC fiber.

Fig. 18
Fig. 18

27-dB bandwidth of the SC spectrum, depending on the peak power of the pump pulses. Open circles, experimental result. Solid curve, simulated result that includes frequency chirping in the pump pulse, as illustrated in Fig. 17. Dashed curve, no frequency chirping in the pump pulse.

Equations (20)

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E(t, r, z)=12π -dω[exp(iwt)A˜(ω, z)E(ω, r)+c.c.]/2
S˜(Ω, z)=ε0nc2P01/2A˜(ω, z)×expi 0z dx[β(ω0, x)+Ωβ1(ω0, x)],
zS˜(Ω, z)=-i[β(ω0+Ω, z)-β(ω0, z)-Ωβ1(ω0, z)-iα(ω0+Ω, z)]S˜(Ω, z)-iγP01+Ωω0 12π - dTexp(-iΩT)S(T, z)|S(T, z)|2+12π - dΩexp(iΩT)R(Ω) 12π -dT[exp(-iΩT)|S(T, z)|2],
D(λ, z)=D01-zL0+D22(λ-λpeak)2,
ζU˜(ϕ, ζ)
=-iB(ϕ, ζ)U˜(ϕ, ζ)-i1+Ω0ω0ϕ×12π - dτexp(-iϕτ)U(τ, ζ)|U(τ, ζ)|2+12π - dϕexp(iϕτ)R(Ω0ϕ) 12π ×- dτ[exp(-iϕτ)|U(τ, ζ)|2],
B(ϕ, ζ)=1γP0 βω0+Ω0ϕ, ζγP0-βω0, ζγP0-Ω0ϕβ1ω0, ζγP0-iαω0+Ω0ϕ, ζγP0.
B(ϕ, ζ)=1γP0n=2 (Ω0ϕ)nn!βnω0, ζγP0,
β2ω0, ζγP0=-λ022πcD01-ζγP0L0,
β3ω0, ζγP0=2λ03(2πc)2D01-ζγP0L0,
β4ω0, ζγP0=-λ04(2πc)3 6D01-ζγP0L0+λ02D2,
β5ω0, ζγP0=12λ05(2πc)4 2D01-ζγP0L0+λ02D2.
-12 λ022πc D0γP0T02ϕ2.
-124 λ022πc3 D2γP0T04ϕ4.
Δ0=λ022πc D0γP0T02,
Δ2=λ022πc3 D2γP0T04,
ζ0=γP0L0.
τ0=-Δ0Δ21/2=2πcλ02 -D0D2 1/2T0.
R(Ω)=GRn2 1ΩR2-Ω2+iΓRΩmaxΩ Im1ΩR2-Ω2+iΓRΩ,
Λ=α[ω0+Ω0ϕ,(ζ/γP0)]γP0.

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