Abstract

We calculate the pulse compression in a tapered microstructure optical fiber with four layers of holes. We show that the primary limitation on pulse compression is the loss due to mode leakage. As a fiber’s diameter decreases due to the tapering, so does the air-hole diameter, and at a sufficiently small diameter the guided mode loss becomes unacceptably high. For the four-layer geometry we considered, a compression factor of 10 can be achieved by a pulse with an initial FWHM duration of 3 ps in a tapered fiber that is 28 m long. We find that there is little difference in the pulse compression between a linear taper profile and a Gaussian taper profile. More layers of air-holes allows the pitch to decrease considerably before losses become unacceptable, but only a moderate increase in the degree of pulse compression is obtained.

©2006 Optical Society of America

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References

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    [Crossref]
  29. A. Mostofi, H. Hatami-Hanza, and P. L. Chu, “Optimum dispersion profile for compression of fundamental solitons in dispersion decreasing fibers,” IEEE J. Quantum Electron. 33, 620–628 (1997).
    [Crossref]
  30. M. D. Pelusi, Y. Matsui, and A. Suzuki, “Design of short dispersion decreasing fibre for enhanced compression of higher-order soliton pulses around 1550 nm,” Electron. Lett. 35, 61–63 (1999).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]

2005 (4)

2004 (6)

2003 (3)

2002 (4)

2001 (3)

1999 (1)

M. D. Pelusi, Y. Matsui, and A. Suzuki, “Design of short dispersion decreasing fibre for enhanced compression of higher-order soliton pulses around 1550 nm,” Electron. Lett. 35, 61–63 (1999).
[Crossref]

1997 (2)

M. D. Pelusi and H.-F. Liu, “Higher order soliton pulse compression in dispersion-decreasing optical fibers,” IEEE J. Quantum Electron. 33, 1430–1439 (1997).
[Crossref]

A. Mostofi, H. Hatami-Hanza, and P. L. Chu, “Optimum dispersion profile for compression of fundamental solitons in dispersion decreasing fibers,” IEEE J. Quantum Electron. 33, 620–628 (1997).
[Crossref]

1993 (1)

1992 (2)

D. Marcuse, “Solution of the vector wave equation for general dielectric waveguides by the Galerkin method,” IEEE J. Quantum Electron. 28, 459–465 (1992).
[Crossref]

T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438, (1992).
[Crossref]

1991 (1)

1988 (2)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, (3rd ed., Academic Press, San Diego, CA, 2001).

Birks, T. A.

Bjarklev, A.

Blow, K. J.

Bolger, J. A.

Botten, L. C.

Cao, Q.

Chandalia, J. K.

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photonics Technol. Lett. 13, 52–54 (2001).
[Crossref]

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001).
[Crossref]

Chernikov, S. V.

Chu, P. L.

A. Mostofi, H. Hatami-Hanza, and P. L. Chu, “Optimum dispersion profile for compression of fundamental solitons in dispersion decreasing fibers,” IEEE J. Quantum Electron. 33, 620–628 (1997).
[Crossref]

Chung, Y.

J. Kim, U.-C. Paek, D. Y. Kim, and Y. Chung, “Analysis of the dispersion properties of holey optical fibers using normalized dispersion,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, Washington DC, 2001), WDD86-1.

de Sterke, C. M.

Dianov, E. M.

Doran, N. J.

Eggleton, B. J.

H. C. Nguyen, B. T. Kuhlmey, M. J. Steel, C. L. Smith, E. C. Mägi, R. C. McPhedran, and B. J. Eggleton, “Leakage of the fundamental mode in photonic crystal fiber tapers,” Opt. Lett. 30, 1123–1125 (2005).
[Crossref] [PubMed]

D. J. Moss, Y. Miao, V. Ta’eed, E. C. Mägi, and B. J. Eggleton, “Coupling to high-index waveguides via tapered microstructured optical fibre,” Electron. Lett. 41, 951–953 (2005).
[Crossref]

E. C. Mägi, P. Steinvurzel, and B. J. Eggleton, “Transverse characterization of tapered photonic crystal fibers,” J. Appl. Phys. 96, 3976–3982 (2004).
[Crossref]

Y. K. Lizé, E. C. Mägi, V. G. Ta’eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12, 3209–3217 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-14-3209.
[Crossref] [PubMed]

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photonics Technol. Lett. 13, 52–54 (2001).
[Crossref]

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001).
[Crossref]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, in Numerical Recipes in C++, (2nd ed., Cambridge University Press, Cambridge, UK, 2003), Chap. 10.2, pp. 406–410.

Foster, M.

Foster, M. A.

Fujita, M.

H. Kubota, K. Suzuki, S. Kawanishi, M. Nakazawa, M. Tanaka, and M. Fujita, “Low-loss, 2 km-long photonics crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band,” Conference on Lasers and Electro-Optics, Baltimore, MD, 2001, paper CPD3-1.

Gaeta, A.

Gaeta, A. L.

Hatami-Hanza, H.

A. Mostofi, H. Hatami-Hanza, and P. L. Chu, “Optimum dispersion profile for compression of fundamental solitons in dispersion decreasing fibers,” IEEE J. Quantum Electron. 33, 620–628 (1997).
[Crossref]

Holzlöhner, R.

Kawanishi, S.

H. Kubota, K. Suzuki, S. Kawanishi, M. Nakazawa, M. Tanaka, and M. Fujita, “Low-loss, 2 km-long photonics crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band,” Conference on Lasers and Electro-Optics, Baltimore, MD, 2001, paper CPD3-1.

Khoo, E. H.

Kim, D. Y.

Y. Youk, D. Y. Kim, and K. W. Park, “Guiding properties of a tapered photonic crystal fiber compared with those of a tapered single-mode fiber,” Fiber Int. Opt. 23, 439–446 (2004).
[Crossref]

J. Kim, U.-C. Paek, D. Y. Kim, and Y. Chung, “Analysis of the dispersion properties of holey optical fibers using normalized dispersion,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, Washington DC, 2001), WDD86-1.

Kim, J.

J. Kim, U.-C. Paek, D. Y. Kim, and Y. Chung, “Analysis of the dispersion properties of holey optical fibers using normalized dispersion,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, Washington DC, 2001), WDD86-1.

Knox, W. H.

Kosinski, S. G.

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001).
[Crossref]

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photonics Technol. Lett. 13, 52–54 (2001).
[Crossref]

Kubota, H.

H. Kubota, K. Suzuki, S. Kawanishi, M. Nakazawa, M. Tanaka, and M. Fujita, “Low-loss, 2 km-long photonics crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band,” Conference on Lasers and Electro-Optics, Baltimore, MD, 2001, paper CPD3-1.

Kuehl, H. H.

Kuhlmey, B. T.

Lægsgaard, J.

Leon-Saval, S. G.

Li, Y. W.

T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438, (1992).
[Crossref]

Liu, A. Q.

Liu, H.-F.

M. D. Pelusi and H.-F. Liu, “Higher order soliton pulse compression in dispersion-decreasing optical fibers,” IEEE J. Quantum Electron. 33, 1430–1439 (1997).
[Crossref]

Liu, X.

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001).
[Crossref]

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photonics Technol. Lett. 13, 52–54 (2001).
[Crossref]

Lizé, Y. K.

Lizier, J. T.

Mägi, E. C.

Mamyshev, P. V.

Marcuse, D.

D. Marcuse, “Solution of the vector wave equation for general dielectric waveguides by the Galerkin method,” IEEE J. Quantum Electron. 28, 459–465 (1992).
[Crossref]

Mason, M. W.

Matsui, Y.

M. D. Pelusi, Y. Matsui, and A. Suzuki, “Design of short dispersion decreasing fibre for enhanced compression of higher-order soliton pulses around 1550 nm,” Electron. Lett. 35, 61–63 (1999).
[Crossref]

Maystre, D.

McPhedran, R. C.

Menyuk, C. R.

Miao, Y.

D. J. Moss, Y. Miao, V. Ta’eed, E. C. Mägi, and B. J. Eggleton, “Coupling to high-index waveguides via tapered microstructured optical fibre,” Electron. Lett. 41, 951–953 (2005).
[Crossref]

Moll, K.

Mortensen, N. A.

Moss, D. J.

D. J. Moss, Y. Miao, V. Ta’eed, E. C. Mägi, and B. J. Eggleton, “Coupling to high-index waveguides via tapered microstructured optical fibre,” Electron. Lett. 41, 951–953 (2005).
[Crossref]

Mostofi, A.

A. Mostofi, H. Hatami-Hanza, and P. L. Chu, “Optimum dispersion profile for compression of fundamental solitons in dispersion decreasing fibers,” IEEE J. Quantum Electron. 33, 620–628 (1997).
[Crossref]

Nakazawa, M.

H. Kubota, K. Suzuki, S. Kawanishi, M. Nakazawa, M. Tanaka, and M. Fujita, “Low-loss, 2 km-long photonics crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band,” Conference on Lasers and Electro-Optics, Baltimore, MD, 2001, paper CPD3-1.

Nguyen, H. C.

Paek, U.-C.

J. Kim, U.-C. Paek, D. Y. Kim, and Y. Chung, “Analysis of the dispersion properties of holey optical fibers using normalized dispersion,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, Washington DC, 2001), WDD86-1.

Park, K. W.

Y. Youk, D. Y. Kim, and K. W. Park, “Guiding properties of a tapered photonic crystal fiber compared with those of a tapered single-mode fiber,” Fiber Int. Opt. 23, 439–446 (2004).
[Crossref]

Payne, D. N.

Pelusi, M. D.

M. D. Pelusi, Y. Matsui, and A. Suzuki, “Design of short dispersion decreasing fibre for enhanced compression of higher-order soliton pulses around 1550 nm,” Electron. Lett. 35, 61–63 (1999).
[Crossref]

M. D. Pelusi and H.-F. Liu, “Higher order soliton pulse compression in dispersion-decreasing optical fibers,” IEEE J. Quantum Electron. 33, 1430–1439 (1997).
[Crossref]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, in Numerical Recipes in C++, (2nd ed., Cambridge University Press, Cambridge, UK, 2003), Chap. 10.2, pp. 406–410.

Renversez, G.

Richardson, D. J.

Robinson, P. A.

Russell, P. St. J.

Sinkin, O. V.

Smith, C. L.

Steel, M. J.

Steinvurzel, P.

Suzuki, A.

M. D. Pelusi, Y. Matsui, and A. Suzuki, “Design of short dispersion decreasing fibre for enhanced compression of higher-order soliton pulses around 1550 nm,” Electron. Lett. 35, 61–63 (1999).
[Crossref]

Suzuki, K.

H. Kubota, K. Suzuki, S. Kawanishi, M. Nakazawa, M. Tanaka, and M. Fujita, “Low-loss, 2 km-long photonics crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band,” Conference on Lasers and Electro-Optics, Baltimore, MD, 2001, paper CPD3-1.

Ta’eed, V.

D. J. Moss, Y. Miao, V. Ta’eed, E. C. Mägi, and B. J. Eggleton, “Coupling to high-index waveguides via tapered microstructured optical fibre,” Electron. Lett. 41, 951–953 (2005).
[Crossref]

Ta’eed, V. G.

Tanaka, M.

H. Kubota, K. Suzuki, S. Kawanishi, M. Nakazawa, M. Tanaka, and M. Fujita, “Low-loss, 2 km-long photonics crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band,” Conference on Lasers and Electro-Optics, Baltimore, MD, 2001, paper CPD3-1.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, in Numerical Recipes in C++, (2nd ed., Cambridge University Press, Cambridge, UK, 2003), Chap. 10.2, pp. 406–410.

Town, G. E.

Trebino, R.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, in Numerical Recipes in C++, (2nd ed., Cambridge University Press, Cambridge, UK, 2003), Chap. 10.2, pp. 406–410.

Wadsworth, W. J.

White, T. P.

Windeler, R. S.

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001).
[Crossref]

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photonics Technol. Lett. 13, 52–54 (2001).
[Crossref]

Wood, D.

Wu, J. H.

Xu, C.

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001).
[Crossref]

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photonics Technol. Lett. 13, 52–54 (2001).
[Crossref]

Youk, Y.

Y. Youk, D. Y. Kim, and K. W. Park, “Guiding properties of a tapered photonic crystal fiber compared with those of a tapered single-mode fiber,” Fiber Int. Opt. 23, 439–446 (2004).
[Crossref]

Zheltikov, A. M.

A. M. Zheltikov, “The physical limit for the waveguide enhancement of nonlinear-optical processes,” Optics and Spectroscopy 95, 410–415 (2003).
[Crossref]

Zweck, J.

Electron. Lett. (2)

D. J. Moss, Y. Miao, V. Ta’eed, E. C. Mägi, and B. J. Eggleton, “Coupling to high-index waveguides via tapered microstructured optical fibre,” Electron. Lett. 41, 951–953 (2005).
[Crossref]

M. D. Pelusi, Y. Matsui, and A. Suzuki, “Design of short dispersion decreasing fibre for enhanced compression of higher-order soliton pulses around 1550 nm,” Electron. Lett. 35, 61–63 (1999).
[Crossref]

Fiber Int. Opt. (1)

Y. Youk, D. Y. Kim, and K. W. Park, “Guiding properties of a tapered photonic crystal fiber compared with those of a tapered single-mode fiber,” Fiber Int. Opt. 23, 439–446 (2004).
[Crossref]

IEEE J. Quantum Electron. (3)

D. Marcuse, “Solution of the vector wave equation for general dielectric waveguides by the Galerkin method,” IEEE J. Quantum Electron. 28, 459–465 (1992).
[Crossref]

M. D. Pelusi and H.-F. Liu, “Higher order soliton pulse compression in dispersion-decreasing optical fibers,” IEEE J. Quantum Electron. 33, 1430–1439 (1997).
[Crossref]

A. Mostofi, H. Hatami-Hanza, and P. L. Chu, “Optimum dispersion profile for compression of fundamental solitons in dispersion decreasing fibers,” IEEE J. Quantum Electron. 33, 620–628 (1997).
[Crossref]

IEEE Photonics Technol. Lett. (1)

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Liu, and C. Xu “Adiabatic coupling in tapered air-silica microstructured optical fiber,” IEEE Photonics Technol. Lett. 13, 52–54 (2001).
[Crossref]

J. Appl. Phys. (1)

E. C. Mägi, P. Steinvurzel, and B. J. Eggleton, “Transverse characterization of tapered photonic crystal fibers,” J. Appl. Phys. 96, 3976–3982 (2004).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (6)

Opt. Express (8)

B. T. Kuhlmey, R. C. McPhedran, C. M. de Sterke, P. A. Robinson, G. Renversez, and D. Maystre, “Microstructured optical fibers: where’s the edge?,” Opt. Express 10, 1285–1290 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
[PubMed]

N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Express 10, 341–348 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-7-341.
[PubMed]

M. Foster, K. Moll, and A. Gaeta, ”Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12, 2880–2887 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-13-2880.
[Crossref] [PubMed]

M. A. Foster and A. L. Gaeta, “Ultra-low threshold supercontinuum generation in sub-wavelength waveguides,” Opt. Express 12, 3137–3143 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-14-3137.
[Crossref] [PubMed]

M. Foster, A. Gaeta, Q. Cao, and R. Trebino, “Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires,” Opt. Express 13, 6848–6855 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-18-6848.
[Crossref] [PubMed]

Y. K. Lizé, E. C. Mägi, V. G. Ta’eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12, 3209–3217 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-14-3209.
[Crossref] [PubMed]

S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12, 2864–2869 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-2864.
[Crossref] [PubMed]

E. H. Khoo, A. Q. Liu, and J. H. Wu, “Nonuniform photonic crystal taper for high-efficiency mode coupling,” Opt. Express 13, 7748–7759 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-20-7748.
[Crossref] [PubMed]

Opt. Lett. (4)

Optics and Spectroscopy (1)

A. M. Zheltikov, “The physical limit for the waveguide enhancement of nonlinear-optical processes,” Optics and Spectroscopy 95, 410–415 (2003).
[Crossref]

Other (4)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, in Numerical Recipes in C++, (2nd ed., Cambridge University Press, Cambridge, UK, 2003), Chap. 10.2, pp. 406–410.

G. P. Agrawal, Nonlinear Fiber Optics, (3rd ed., Academic Press, San Diego, CA, 2001).

J. Kim, U.-C. Paek, D. Y. Kim, and Y. Chung, “Analysis of the dispersion properties of holey optical fibers using normalized dispersion,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, Washington DC, 2001), WDD86-1.

H. Kubota, K. Suzuki, S. Kawanishi, M. Nakazawa, M. Tanaka, and M. Fujita, “Low-loss, 2 km-long photonics crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band,” Conference on Lasers and Electro-Optics, Baltimore, MD, 2001, paper CPD3-1.

Supplementary Material (1)

» Media 1: GIF (912 KB)     

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Figures (10)

Fig. 1.
Fig. 1. The MOF mode dispersion as a function of pitch. The red solid, green dashed-dot, and blue dashed curves correspond, respectively, to air-filling factors of 0.5, 0.55, and 0.6 and are calculated using the multipole method. The crosses indicate results from the Galerkin method with an air-filling factor of 0.6.

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Fig. 2.
Fig. 2. The MOF mode loss as a function of pitch, calculated using the multipole method. The red solid, green dashed-dot, and blue dashed curves correspond, respectively, to air-filling factors of 0.5, 0.55, and 0.6.

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Fig. 3.
Fig. 3. The MOF effective area as a function of pitch. The red solid, green dashed-dot, and blue dashed curves correspond, respectively, to air-filling factors of 0.5, 0.55, and 0.6 and are calculated using the multipole method. The crosses indicate results from the Galerkin method with an air-filling factor of 0.6.

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Fig. 4.
Fig. 4. (912 KB) Animation of the four-layer MOF geometry and mode profile. The black circles show the holes. The color contour plot represents the magnitude of the Poynting vector |Sz |. The air-filling factor is 0.6.

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Fig. 5.
Fig. 5. The contour plot for the optimized compression factor for a hyperbolic-secant-shaped pulse when the fiber length is varied using (a) a linear and (b) a Gaussian taper profile. In this contour plot, the x-axis represents input pulse FWHM, which varies from 1 ps to 4 ps. The y-axis presents the average input power, which varies from 300 mW to 700 mW. We use a 10 Gb/s repetition rate in our simulation.

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Fig. 6.
Fig. 6. The contour plot for the output pulse FWHM factor for a hyperbolic-secant-shaped pulse when the fiber length is varied using (a) a linear and (b) a Gaussian taper profile. In this contour plot, the x-axis represents input pulse FWHM, which varies from 1 ps to 4 ps. The y-axis presents an input average power that varies from 300 mW to 700 mW. We use a 10 Gb/s repetition rate in our simulation.

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Fig. 7.
Fig. 7. Compression factor as a function of fiber length for an input pulse FWHM of (a) 1 ps, (b) 2 ps, (c) 3 ps, and (d) 4 ps with 500 mW average input power, (e) 3 ps with 400 mW average input power, and (f) 3 ps with 300 mW average input power. The corresponding peak powers are 44W, 22W, 14.7W, 11W, 11.8W, and 8.8 Wfor (a), (b), (c), (d), (e), and (f), respectively. The red solid and blue dashed curves represent the linear and Gaussian taper profile, respectively.

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Fig. 8.
Fig. 8. Compression factor as a function of fiber length for an input pulse FWHM of (a) 1 ps, (b) 2 ps, (c) 3 ps, and (d) 4 ps with a peak input power of 10 W. The red solid and blue dashed curves represent the linear and Gaussian taper profile, respectively.

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Fig. 9.
Fig. 9. Pitch as a function of distance. The red solid and blue dashed curves represent a linear and Gaussian taper profile, respectively.

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Fig. 10.
Fig. 10. Input and output pulse shapes for the tapered MOF. The green dash-dot curve represents the 3-ps input pulse. The red solid and blue dashed curves represent, respectively, the output pulses after transmission through the MOF with the linear and Gaussian taper profiles shown in Fig. 9.

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Equations (2)

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n ̅ 2 = ∫ ∫ − ∞ ∞ n 2 ( x , y ) ∣ S z ( x , y ) ∣ 2 d x d y ∫ ∫ − ∞ ∞ ∣ S z ( x , y ) ∣ 2 d x d y , A eff = ( ∫ ∫ − ∞ ∞ ∣ S z ( x , y ) ∣ d x d y ) 2 ∫ ∫ − ∞ ∞ ∣ S z ( x , y ) ∣ 2 d x d y ,
i ∂ u ∂ z − 1 2 β 2 ( z ) ∂ 2 u ∂ t 2 + γ ( z ) ∣ u ∣ 2 u + i α 2 u = 0 ,

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