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]
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  28. 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]
  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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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)

Birks, T. A.

Bjarklev, A.

Blow, K. J.

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 selffrequency 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]

de Sterke, C. M.

Dianov, E. M.

Doran, N. J.

Eggleton, B. J.

E. C. M¨agi, P. Steinvurzel, and B. J.  Eggleton, "Transverse characterization of tapered photonic crystal fibers," J. Appl. Phys. 96, 3976-3982 (2004).
[CrossRef]

Eggleton, B. J.

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler "Soliton selffrequency 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]

Foster, M.

Foster, M. A.

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]

Khoo, E. H.

Kim, D. Y.

Y. Youk, D. Y. Kim, 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]

Knox, W. H.

Kosinski, S. G.

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 selffrequency shift in a short tapered air-silica microstructure fiber," Opt. Lett. 26, 358-360 (2001).
[CrossRef]

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 selffrequency 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]

Liz´e, Y. K.

Lizier, J. T.

M¨agi, E. C.

E. C. M¨agi, P. Steinvurzel, and B. J.  Eggleton, "Transverse characterization of tapered photonic crystal fibers," J. Appl. Phys. 96, 3976-3982 (2004).
[CrossRef]

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.

Miao, Y.

D. J. Moss, Y. Miao, V. Ta’eed, E. C. M¨agi, 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. M¨agi, 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]

Nguyen, H. C.

Park, K. W.

Y. Youk, D. Y. Kim, 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]

Renversez, G.

Richardson, D. J.

Robinson, P. A.

Russell, P. St. J.

Sinkin, O. V.

Smith, C. L.

Steel, M. J.

Steinvurzel, P.

E. C. M¨agi, P. Steinvurzel, and B. J.  Eggleton, "Transverse characterization of tapered photonic crystal fibers," J. Appl. Phys. 96, 3976-3982 (2004).
[CrossRef]

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]

Ta’eed, V.

D. J. Moss, Y. Miao, V. Ta’eed, E. C. M¨agi, and B. J. Eggleton, "Coupling to high-index waveguides via tapered microstructured optical fibre," Electron. Lett. 41, 951-953 (2005).
[CrossRef]

Town, G. E.

Trebino, R.

Wadsworth, W. J.

White, T. P.

Windeler, R. S.

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 selffrequency shift in a short tapered air-silica microstructure fiber," Opt. Lett. 26, 358-360 (2001).
[CrossRef]

Wood, D.

Wu, J. H.

Xu, C.

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 selffrequency shift in a short tapered air-silica microstructure fiber," Opt. Lett. 26, 358-360 (2001).
[CrossRef]

Youk, Y.

Y. Youk, D. Y. Kim, 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]

Electron. Lett. (2)

D. J. Moss, Y. Miao, V. Ta’eed, E. C. M¨agi, 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, 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. M¨agi, 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)

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)

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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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