Abstract

We present a detailed analysis of the modal properties, dispersive behavior, and nonlinear mode coupling in graded-index multimode fibers (GIMFs), and lay out a simplified form of a generalized nonlinear Schrödinger equation, which can be used to explore the rich nonlinear dynamics related to the propagation and interaction of light pulses in GIMFs in a tractable manner. We also briefly discuss an application of the presented formalism in the study of four-wave mixing in these fibers. While the reported formalism is fairly general, our presentation is mainly targeted at device applications in which short segments of GIMFs are used.

© 2012 IEEE

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  1. M. B. Shemirani, W. Mao, R. A. Panickar, J. M. Kahn, "Principal modes in graded-index multimode fiber in presence of spatial- and polarization-mode coupling," J. Lightw. Technol. 27, 1248-1261 (2009).
  2. E. Ding, S. Lefrancois, J. N. Kutz, F. W. Wise, "Scaling fiber lasers to large mode-area: An investigation of passive mode-locking using multi-mode fiber," IEEE J. Quantum Electron. 47, 597-606 (2011).
  3. A. Mafi, P. Hofmann, C. J. Salvin, A. Schülzgen, "Low-loss coupling between two single-mode optical fibers with different mode-field diameters using a graded-index multimode optical fiber," Opt. Lett. 36, 3596-3598 (2011).
  4. P. Hofmann, A. Mafi, C. J. Salvin, T. Tiess, N. Peyghambarian, A. Schülzgen, "Detailed investigation of mode-field adapters utilizing multimode-interference in graded index fibers," J. Lightw. Technol. 30, 2289-2298 (2012).
  5. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).
  6. G. P. Agrawal, "Nonlinear fiber optics: Its history and recent progress [invited]," J. Opt. Soc. Amer. B 28, A1-A10 (2011).
  7. R. H. Stolen, J. E. Bjorkholm, A. Ashkin, "Phase-matched three-wave mixing in silica fiber optical waveguides," Appl. Phys. Lett. 24, 308-310 (1974).
  8. C. Lin, M. A. Bösch, "Large-Stokes-shift stimulated fourphoton mixing in optical fibers," Appl. Phys. Lett. 38, 479-481 (1981).
  9. B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, J. M. Dudley, "The peregrine soliton in nonlinear fibre optics," Nat. Phys. 6, 790-795 (2010).
  10. F. Poletti, P. Horak, "Description of ultrashort pulse propagation in multimode optical fibers," J. Opt. Soc. Amer. B 25, 1645-1654 (2008).
  11. D. Gloge, E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell. Syst. Tech. J. 52, 1563-1578 (1973).
  12. A. Mafi, "Bandwidth improvement in multimode optical fibers via scattering from core inclusions," J. Lightw. Technol. 28, 1547-1555 (2010).
  13. K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2006).
  14. N. Shibata, T. Edahiro, "Refractive index dispersion properties of glasses for optical fibers," Japan (1980) pp. 114-118 Paper of Technical Group, IEICE, no. OQE80.
  15. T. Izawa, S. Sudo, Optical Fibers: Materials and Fabrication (KTK Scientific Publisher, 1987).
  16. R. Olshansky, D. B. Keck, "Pulse broadening in graded-index optical fibers," Appl. Opt. 15, 483-491 (1976).
  17. T. A. Lenahan, "Calculation of modes in an optical fiber using the finite element method and EISPACK," Bell Syst. Tech. J. 62, 2663-2694 (1983).
  18. M. Kolesik, J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell's to unidirectional equations," Phys. Rev. E 70, 036604 (2004).
  19. K. O. Hill, D. C. Johnson, B. S. Kawasaki, "Efficient conversion of light over a wide spectral range by four-photon mixing in a multimode graded-index fiber," Appl. Opt. 20, 1075-1079 (1981).
  20. S. D. Personick, "Time dispersion in dielectric waveguides," Bell Syst. Tech. J. 50, 843-859 (1971).
  21. P. Pepeljugoski, S. E. Golowich, A. J. Ritger, P. Kolesar, A. Risteski, "Modeling and simulation of next-generation multimode fiber links," J. Lightw. Technol. 21, 1242-1255 (2003).
  22. I. Gasulla, J. Capmany, "Transfer function of multimode fiber links using an electric field propagation model: Application to radio over fibre systems," Opt. Express 14, 9051-9070 (2006).
  23. D. Gloge, "Optical power flow in multimode fibers," Bell Syst. Tech. J. 51, 1767-1780 (1972).
  24. R. Olshansky, "Mode coupling effects in graded-index optical fibers," Appl. Opt. 14, 935-945 (1975).
  25. D. Marcuse, H. M. Presby, "Mode coupling in an optical fiber with core distortions," Bell Syst. Tech. J. 54, 3-15 (1975).

2012

P. Hofmann, A. Mafi, C. J. Salvin, T. Tiess, N. Peyghambarian, A. Schülzgen, "Detailed investigation of mode-field adapters utilizing multimode-interference in graded index fibers," J. Lightw. Technol. 30, 2289-2298 (2012).

2011

G. P. Agrawal, "Nonlinear fiber optics: Its history and recent progress [invited]," J. Opt. Soc. Amer. B 28, A1-A10 (2011).

E. Ding, S. Lefrancois, J. N. Kutz, F. W. Wise, "Scaling fiber lasers to large mode-area: An investigation of passive mode-locking using multi-mode fiber," IEEE J. Quantum Electron. 47, 597-606 (2011).

A. Mafi, P. Hofmann, C. J. Salvin, A. Schülzgen, "Low-loss coupling between two single-mode optical fibers with different mode-field diameters using a graded-index multimode optical fiber," Opt. Lett. 36, 3596-3598 (2011).

2010

A. Mafi, "Bandwidth improvement in multimode optical fibers via scattering from core inclusions," J. Lightw. Technol. 28, 1547-1555 (2010).

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, J. M. Dudley, "The peregrine soliton in nonlinear fibre optics," Nat. Phys. 6, 790-795 (2010).

2009

M. B. Shemirani, W. Mao, R. A. Panickar, J. M. Kahn, "Principal modes in graded-index multimode fiber in presence of spatial- and polarization-mode coupling," J. Lightw. Technol. 27, 1248-1261 (2009).

2008

F. Poletti, P. Horak, "Description of ultrashort pulse propagation in multimode optical fibers," J. Opt. Soc. Amer. B 25, 1645-1654 (2008).

2006

2004

M. Kolesik, J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell's to unidirectional equations," Phys. Rev. E 70, 036604 (2004).

2003

P. Pepeljugoski, S. E. Golowich, A. J. Ritger, P. Kolesar, A. Risteski, "Modeling and simulation of next-generation multimode fiber links," J. Lightw. Technol. 21, 1242-1255 (2003).

1983

T. A. Lenahan, "Calculation of modes in an optical fiber using the finite element method and EISPACK," Bell Syst. Tech. J. 62, 2663-2694 (1983).

1981

C. Lin, M. A. Bösch, "Large-Stokes-shift stimulated fourphoton mixing in optical fibers," Appl. Phys. Lett. 38, 479-481 (1981).

K. O. Hill, D. C. Johnson, B. S. Kawasaki, "Efficient conversion of light over a wide spectral range by four-photon mixing in a multimode graded-index fiber," Appl. Opt. 20, 1075-1079 (1981).

1976

1975

D. Marcuse, H. M. Presby, "Mode coupling in an optical fiber with core distortions," Bell Syst. Tech. J. 54, 3-15 (1975).

R. Olshansky, "Mode coupling effects in graded-index optical fibers," Appl. Opt. 14, 935-945 (1975).

1974

R. H. Stolen, J. E. Bjorkholm, A. Ashkin, "Phase-matched three-wave mixing in silica fiber optical waveguides," Appl. Phys. Lett. 24, 308-310 (1974).

1973

D. Gloge, E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell. Syst. Tech. J. 52, 1563-1578 (1973).

1972

D. Gloge, "Optical power flow in multimode fibers," Bell Syst. Tech. J. 51, 1767-1780 (1972).

1971

S. D. Personick, "Time dispersion in dielectric waveguides," Bell Syst. Tech. J. 50, 843-859 (1971).

Appl. Phys. Lett.

C. Lin, M. A. Bösch, "Large-Stokes-shift stimulated fourphoton mixing in optical fibers," Appl. Phys. Lett. 38, 479-481 (1981).

Appl. Opt.

Appl. Phys. Lett.

R. H. Stolen, J. E. Bjorkholm, A. Ashkin, "Phase-matched three-wave mixing in silica fiber optical waveguides," Appl. Phys. Lett. 24, 308-310 (1974).

Bell Syst. Tech. J.

D. Marcuse, H. M. Presby, "Mode coupling in an optical fiber with core distortions," Bell Syst. Tech. J. 54, 3-15 (1975).

Bell Syst. Tech. J.

D. Gloge, "Optical power flow in multimode fibers," Bell Syst. Tech. J. 51, 1767-1780 (1972).

T. A. Lenahan, "Calculation of modes in an optical fiber using the finite element method and EISPACK," Bell Syst. Tech. J. 62, 2663-2694 (1983).

S. D. Personick, "Time dispersion in dielectric waveguides," Bell Syst. Tech. J. 50, 843-859 (1971).

Bell. Syst. Tech. J.

D. Gloge, E. A. J. Marcatili, "Multimode theory of graded-core fibers," Bell. Syst. Tech. J. 52, 1563-1578 (1973).

IEEE J. Quantum Electron.

E. Ding, S. Lefrancois, J. N. Kutz, F. W. Wise, "Scaling fiber lasers to large mode-area: An investigation of passive mode-locking using multi-mode fiber," IEEE J. Quantum Electron. 47, 597-606 (2011).

J. Lightw. Technol.

A. Mafi, "Bandwidth improvement in multimode optical fibers via scattering from core inclusions," J. Lightw. Technol. 28, 1547-1555 (2010).

P. Hofmann, A. Mafi, C. J. Salvin, T. Tiess, N. Peyghambarian, A. Schülzgen, "Detailed investigation of mode-field adapters utilizing multimode-interference in graded index fibers," J. Lightw. Technol. 30, 2289-2298 (2012).

J. Lightw. Technol.

P. Pepeljugoski, S. E. Golowich, A. J. Ritger, P. Kolesar, A. Risteski, "Modeling and simulation of next-generation multimode fiber links," J. Lightw. Technol. 21, 1242-1255 (2003).

J. Lightw. Technol.

M. B. Shemirani, W. Mao, R. A. Panickar, J. M. Kahn, "Principal modes in graded-index multimode fiber in presence of spatial- and polarization-mode coupling," J. Lightw. Technol. 27, 1248-1261 (2009).

J. Opt. Soc. Amer. B

G. P. Agrawal, "Nonlinear fiber optics: Its history and recent progress [invited]," J. Opt. Soc. Amer. B 28, A1-A10 (2011).

J. Opt. Soc. Amer. B

F. Poletti, P. Horak, "Description of ultrashort pulse propagation in multimode optical fibers," J. Opt. Soc. Amer. B 25, 1645-1654 (2008).

Nat. Phys.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, J. M. Dudley, "The peregrine soliton in nonlinear fibre optics," Nat. Phys. 6, 790-795 (2010).

Opt. Express

Opt. Lett.

Phys. Rev. E

M. Kolesik, J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell's to unidirectional equations," Phys. Rev. E 70, 036604 (2004).

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2006).

N. Shibata, T. Edahiro, "Refractive index dispersion properties of glasses for optical fibers," Japan (1980) pp. 114-118 Paper of Technical Group, IEICE, no. OQE80.

T. Izawa, S. Sudo, Optical Fibers: Materials and Fabrication (KTK Scientific Publisher, 1987).

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