Abstract

In this Letter, we propose a generic nonlinear coupling coefficient, ηNL2=η|γ/β2|fiber2/|γ/β2|fiber1, which gives a quantitative measure for the efficiency of nonlinear matching of optical fibers by describing how a fundamental soliton couples from one fiber into another. Specifically, we use ηNL to demonstrate a significant soliton self- frequency shift of a fundamental soliton, and we show that nonlinear matching can take precedence over linear mode matching. The nonlinear coupling coefficient depends on both the dispersion (β2) and nonlinearity (γ), as well as on the power coupling efficiency η. Being generic, ηNL enables engineering of general waveguide systems, e.g., for optimized Raman redshift or supercontinuum generation.

© 2011 Optical Society of America

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References

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    [CrossRef] [PubMed]
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2010 (2)

M. H. Frosz, Opt. Express 18, 14778 (2010).
[CrossRef] [PubMed]

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, Appl. Phys. Lett. 97, 061106(2010).
[CrossRef]

2009 (1)

C. Xia, Z. Xu, M. Islam, F. Terry, M. Freeman, A. Zakel, and J. Mauricio, IEEE J. Sel. Top. Quantum Electron. 15, 422 (2009).
[CrossRef]

2007 (1)

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

2006 (3)

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2006).

P. S. Russell, J. Lightwave Technol. 24, 4729 (2006).
[CrossRef]

K. Okamoto, Fundamentals of Optical Waveguides(Elsevier, 2006).

2005 (1)

2003 (1)

1995 (1)

F. Gan, J. Non-Cryst. Solids 184, 9 (1995).
[CrossRef]

1986 (1)

1977 (1)

D. Marcuse, Bell Syst. Tech. J. 56, 703 (1977).

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2006).

Bang, O.

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, Appl. Phys. Lett. 97, 061106(2010).
[CrossRef]

Buccoliero, D.

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, Appl. Phys. Lett. 97, 061106(2010).
[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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

Ebendorff-Heidepriem, H.

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, Appl. Phys. Lett. 97, 061106(2010).
[CrossRef]

Freeman, M.

C. Xia, Z. Xu, M. Islam, F. Terry, M. Freeman, A. Zakel, and J. Mauricio, IEEE J. Sel. Top. Quantum Electron. 15, 422 (2009).
[CrossRef]

Frosz, M. H.

Furniss, D.

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

Gan, F.

F. Gan, J. Non-Cryst. Solids 184, 9 (1995).
[CrossRef]

Holzlöhner, R.

Islam, M.

C. Xia, Z. Xu, M. Islam, F. Terry, M. Freeman, A. Zakel, and J. Mauricio, IEEE J. Sel. Top. Quantum Electron. 15, 422 (2009).
[CrossRef]

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 56, 703 (1977).

Mauricio, J.

C. Xia, Z. Xu, M. Islam, F. Terry, M. Freeman, A. Zakel, and J. Mauricio, IEEE J. Sel. Top. Quantum Electron. 15, 422 (2009).
[CrossRef]

Menyuk, C. R.

Mitschke, F. M.

Mollenauer, L. F.

Monro, T. M.

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, Appl. Phys. Lett. 97, 061106(2010).
[CrossRef]

O’Donnell, M. D.

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides(Elsevier, 2006).

Popov, S. V.

Ramme, 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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

Richardson, K.

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

Rivero, C.

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

Russell, P. S.

Seddon, A. B.

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

Sinkin, O. V.

Steffensen, H.

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, Appl. Phys. Lett. 97, 061106(2010).
[CrossRef]

Stegeman, G.

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

Stegeman, R.

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

Stolen, R.

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

Taylor, J. R.

Terry, F.

C. Xia, Z. Xu, M. Islam, F. Terry, M. Freeman, A. Zakel, and J. Mauricio, IEEE J. Sel. Top. Quantum Electron. 15, 422 (2009).
[CrossRef]

Tikhomirov, V. K.

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

Travers, J. C.

Xia, C.

C. Xia, Z. Xu, M. Islam, F. Terry, M. Freeman, A. Zakel, and J. Mauricio, IEEE J. Sel. Top. Quantum Electron. 15, 422 (2009).
[CrossRef]

Xu, Z.

C. Xia, Z. Xu, M. Islam, F. Terry, M. Freeman, A. Zakel, and J. Mauricio, IEEE J. Sel. Top. Quantum Electron. 15, 422 (2009).
[CrossRef]

Zakel, A.

C. Xia, Z. Xu, M. Islam, F. Terry, M. Freeman, A. Zakel, and J. Mauricio, IEEE J. Sel. Top. Quantum Electron. 15, 422 (2009).
[CrossRef]

Zweck, J.

Appl. Phys. Lett. (1)

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, Appl. Phys. Lett. 97, 061106(2010).
[CrossRef]

Bell Syst. Tech. J. (1)

D. Marcuse, Bell Syst. Tech. J. 56, 703 (1977).

IEEE J. Sel. Top. Quantum Electron. (1)

C. Xia, Z. Xu, M. Islam, F. Terry, M. Freeman, A. Zakel, and J. Mauricio, IEEE J. Sel. Top. Quantum Electron. 15, 422 (2009).
[CrossRef]

J. Am. Ceram. Soc. (1)

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, J. Am. Ceram. Soc. 90, 1448 (2007).
[CrossRef]

J. Lightwave Technol. (2)

J. Non-Cryst. Solids (1)

F. Gan, J. Non-Cryst. Solids 184, 9 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (2)

K. Okamoto, Fundamentals of Optical Waveguides(Elsevier, 2006).

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2006).

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Figures (4)

Fig. 1
Fig. 1

Energy spectral density evolution in a generic fiber system. Initially an N = 1 soliton redshifts in fiber 1, and the output is coupled into fiber 2.

Fig. 2
Fig. 2

(a) GVD parameter β 2 and (b) effective area A eff of the fibers. Vertical line marks λ c = 1816 nm . For fiber parameters, see Table 1.

Fig. 3
Fig. 3

Nonlinear coupling coefficient, η NL , for fiber 2a (dash dotted) and fiber 2b (dashed) with η = 1 . For fiber 2a is also shown η NL , with η = η MFD ( λ c ) . The black vertical line marks λ c = 1816 nm .

Fig. 4
Fig. 4

Evolution of the energy spectral density in (a) fiber 1 and fiber 2a and (b) fiber 1 and fiber 2b. In (a)  η NL = 9.73 3 / 2 , and a higher-order soliton undergoes soliton fission in fiber 2a. In (b)  η NL = 1.22 , and a fundamental soliton propagates throughout the system. In both simulations the power coupling efficiency is η = 1 . White vertical line marks λ ZD of fiber 2.

Tables (2)

Tables Icon

Table 1 Fiber Parameters Used in the Setup

Tables Icon

Table 2 Pulse and Derived Parameters Used in Calculations

Equations (3)

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N 1 2 = T 01 2 P 01 γ 1 / | β 21 | = 1 ,
η NL 2 N 2 2 / N 1 2 = η ( γ 2 / | β 22 | ) / ( γ 1 / | β 21 | ) ,
η MFD = 4 ( A eff , 1 A eff,2 ) 2 / ( A eff , 1 2 + A eff , 2 2 ) 2 .

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