Abstract

We present N-fold symmetric gratings as gain-flattening filters, since they are polarization insensitive and capable of exhibiting low back reflection. These gratings consist of N superimposed identical tilted gratings which are evenly distributed azimuthally. The coupling interactions between the forward propagating core mode and the backward propagating cladding modes are analyzed, including the limit when N --> infinity which is a rotationally symmetric grating. The fiber grating parameters are optimized to equalize the gain profile of a typical erbium doped fiber amplifier to within 0.07 dB. Finally, we examine how the performance of the gain-flattening filter depends on the blaze angle and the effect of an uneven azimuthal distribution of the grating.

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  1. A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano and C. R. Davidson, "Long-period fiber-grating-based gain equalizers", Opt. Lett., vol. 21, no. 5, pp. 336-338, 1996.
  2. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan and J. E. Sipe, "Long-period fiber gratings as band-rejection filters", J. Lightw. Technol., vol. 14, no. 1, pp. 58-64, Jan. 1996.
  3. R. Kashyap, R. Wyatt and R. J. Campbell, "Wideband gain flattened erbium fiber amplifier using a photosensitive fiber blazed grating", Electron. Lett., vol. 29, no. 2, pp. 154-156, 1993.
  4. R. Kashyap, R. Wyatt and P. F. McKee, "Wavelength flattened saturated erbium amplifier using multiple side-tap bragg gratings", Electron. Lett., vol. 29, no. 11, pp. 1025-1026, 1993.
  5. K. S. Lee and T. Erdogan, "Fiber mode coupling in transmissive and reflective tilted fiber gratings", Appl. Opt., vol. 39, no. 9, pp. 1394 -1404, 2000.
  6. K. S. Lee, "Mode coupling in tilted planar waveguide gratings", Appl. Opt., vol. 39, no. 33, pp. 6144-6149, 2000.
  7. T. Erdogan and J. E. Sipe, "Tilted fiber phase gratings", J. Opt. Soc. Amer. A, vol. 13, pp. 296-313, 1996.
  8. K. S. Lee and T. Erdogan, "Fiber mode conversion with tilted gratings in an optical fiber", J. Opt. Soc. Amer. A, vol. 18, no. 5, pp. 1176-1185, 2001.
  9. L. Dong, B. Ortega and L. Reekie, "Coupling characteristics of cladding modes in tilted optical fiber Bragg gratings", Appl. Opt., vol. 37, no. 22, pp. 5099-5105, 1998.
  10. A. E. Lobo, J. A. Besley and C. M. de Sterke, "Gain-flattening filter design using rotationally symmetric crossed gratings", J. Lightw. Technol., vol. 21, no. 9, pp. 2084-2088, Sep. 2003.
  11. R. Parker and C. M. de Sterke, "Reduced cladding mode losses in tilted gratings that are rotationally symmetric", J. Lightw. Technol., vol. 18, no. 12, pp. 2133-2138, Dec. 2000.
  12. T. Erdogan, "Cladding-mode resonances in short-and long-period fiber grating filters", J. Opt. Soc. Amer. A, vol. 14, pp. 1760-1773, 1997.
  13. M. Abramowitz, and I. A. Stegun, Eds. Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables, New York: Dover, 1972, ch. 9.
  14. M. Ibsen, M. K. Durkin, M. N. Zervas, A. B. Grudinin and R. I. Laming, "Custom design of long chirped Bragg gratings: application to gain-flattening filter with incorporated dispersion compensation", IEEE Photon. Technol. Lett., vol. 12, no. 5, pp. 498-500, May 2000.
  15. W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, Numerical Recipes the Art of Scientific Computing [Fortran Version], Cambridge: U.K.: Cambridge Univ. Press, 1989, ch. 12.
  16. M. J. Holmes, R. Kashyap and R. Wyatt, "Physical properties of optical fiber sidetap grating filters: Free-space model", IEEE J. Sel. Topics Quantum Electron. , vol. 5, no. 5, pp. 1353-1365, Sep.-Oct. 1999.
  17. D. Marcuse, "Gaussian approximation of the fundamental modes of graded-index fibers", J. Opt. Soc. Amer., vol. 68, no. 1, pp. 103-109, 1978.
  18. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. New York: Academic, 1991.

Other (18)

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano and C. R. Davidson, "Long-period fiber-grating-based gain equalizers", Opt. Lett., vol. 21, no. 5, pp. 336-338, 1996.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan and J. E. Sipe, "Long-period fiber gratings as band-rejection filters", J. Lightw. Technol., vol. 14, no. 1, pp. 58-64, Jan. 1996.

R. Kashyap, R. Wyatt and R. J. Campbell, "Wideband gain flattened erbium fiber amplifier using a photosensitive fiber blazed grating", Electron. Lett., vol. 29, no. 2, pp. 154-156, 1993.

R. Kashyap, R. Wyatt and P. F. McKee, "Wavelength flattened saturated erbium amplifier using multiple side-tap bragg gratings", Electron. Lett., vol. 29, no. 11, pp. 1025-1026, 1993.

K. S. Lee and T. Erdogan, "Fiber mode coupling in transmissive and reflective tilted fiber gratings", Appl. Opt., vol. 39, no. 9, pp. 1394 -1404, 2000.

K. S. Lee, "Mode coupling in tilted planar waveguide gratings", Appl. Opt., vol. 39, no. 33, pp. 6144-6149, 2000.

T. Erdogan and J. E. Sipe, "Tilted fiber phase gratings", J. Opt. Soc. Amer. A, vol. 13, pp. 296-313, 1996.

K. S. Lee and T. Erdogan, "Fiber mode conversion with tilted gratings in an optical fiber", J. Opt. Soc. Amer. A, vol. 18, no. 5, pp. 1176-1185, 2001.

L. Dong, B. Ortega and L. Reekie, "Coupling characteristics of cladding modes in tilted optical fiber Bragg gratings", Appl. Opt., vol. 37, no. 22, pp. 5099-5105, 1998.

A. E. Lobo, J. A. Besley and C. M. de Sterke, "Gain-flattening filter design using rotationally symmetric crossed gratings", J. Lightw. Technol., vol. 21, no. 9, pp. 2084-2088, Sep. 2003.

R. Parker and C. M. de Sterke, "Reduced cladding mode losses in tilted gratings that are rotationally symmetric", J. Lightw. Technol., vol. 18, no. 12, pp. 2133-2138, Dec. 2000.

T. Erdogan, "Cladding-mode resonances in short-and long-period fiber grating filters", J. Opt. Soc. Amer. A, vol. 14, pp. 1760-1773, 1997.

M. Abramowitz, and I. A. Stegun, Eds. Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables, New York: Dover, 1972, ch. 9.

M. Ibsen, M. K. Durkin, M. N. Zervas, A. B. Grudinin and R. I. Laming, "Custom design of long chirped Bragg gratings: application to gain-flattening filter with incorporated dispersion compensation", IEEE Photon. Technol. Lett., vol. 12, no. 5, pp. 498-500, May 2000.

W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, Numerical Recipes the Art of Scientific Computing [Fortran Version], Cambridge: U.K.: Cambridge Univ. Press, 1989, ch. 12.

M. J. Holmes, R. Kashyap and R. Wyatt, "Physical properties of optical fiber sidetap grating filters: Free-space model", IEEE J. Sel. Topics Quantum Electron. , vol. 5, no. 5, pp. 1353-1365, Sep.-Oct. 1999.

D. Marcuse, "Gaussian approximation of the fundamental modes of graded-index fibers", J. Opt. Soc. Amer., vol. 68, no. 1, pp. 103-109, 1978.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. New York: Academic, 1991.

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