Vol. 34

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

Accurate and Fast Extraction of the Bloch Eigenmodes of Fiber Gratings

By Amir M. Jazayeri
Progress In Electromagnetics Research M, Vol. 34, 29-37, 2014


Based on Bloch-Floquet's theorem and ordinary matrix calculations, a rigorous method for extraction of the eigenmodes of fiber gratings is developed. This method is also applicable to fiber gratings which are either physically multilayer or mathematically divided into layers along the radial coordinate. Although the well-known coupled mode theory (CMT) is accounted a method for extraction of the coefficients of reflection and transmission of finite-length FBGs, its inadequacy for extraction of the Bloch eigenmodes of FBGs is illustrated, even if the modulation depth of refractive index is small and the Bragg condition is satisfied.


Amir M. Jazayeri, "Accurate and Fast Extraction of the Bloch Eigenmodes of Fiber Gratings," Progress In Electromagnetics Research M, Vol. 34, 29-37, 2014.


    1. Passaro, R. Diana, and M. N. Armenise, "Optical fiber Bragg gratings. Part I. Modeling of infinitely long gratings," JOSA A, Vol. 19, No. 9, 1844-1854, 2002.

    2. Lalanne, P. and E. Silberstein, "Fourier-modal methods applied to waveguide computational problems," Opt. Lett., Vol. 25, No. 15, 1092-1094, 2000.

    3. Silberstein, E., P. Lalanne, J. P. Hugonin, and Q. Cao, \, "Use of grating theories in integrated optics," JOSA A, Vol. 18, No. 11, 2865-2875, 2001.

    4. Lu, Y. C., L. Yang, W. P. Huang, and S. S. Jian, "Unified approach for coupling to cladding and radiation modes in fiber Bragg and long-period gratings," IEEE J. Lightw. Techn., Vol. 27, No. 11, 1461-1468, 2009.

    5. Song, N., J. Mu, and W. P. Huang, "Application of the complex coupled-mode theory to optical fiber grating structures," IEEE J. Lightw. Techn., Vol. 28, No. 5, 761-767, 2010.

    6. Li, L., "Note on the S-matrix propagation algorithm ," JOSA A, Vol. 20, No. 4, 655-660, 2003.

    7. Moharam, M. G. and T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," JOSA, Vol. 73, No. 9, 1105-1112, 1983.

    8. Szkopek, T., V. Pasupathy, J. E. Sipe, and P. W. E. Smith, "Novel multimode fiber for narrow-band Bragg gratings," IEEE J. Sel. Top. Quant. Electr., Vol. 7, No. 3, 425-433, 2001.

    9. Mohammed, W., X. Gu, and P. W. E. Smith, "Full vectorial modal analysis of specialty fibers and their Bragg grating characterization," Appl. Opt., Vol. 45, No. 14, 3307-3316, 2006.

    10. Erdogan, T. and J. E. Sipe, "Tilted fiber phase gratings," JOSA A, Vol. 13, No. 2, 296-313, 1996.

    11. Erdogan, T., "Fiber grating spectr," IEEE J. Lightw. Techn., Vol. 15, No. 8, 1277-1294, 1997.

    12. Erdogan, T., "Cladding-mode resonances in short- and long-period fiber grating filters," JOSA A, Vol. 14, No. 8, 1760-1773, 1997.

    13. Lu, C. and Y. Cui, "Fiber Bragg grating spectra in multimode optical fibers," IEEE J. Lightw. Techn., Vol. 24, No. 1, 598-604, 2006.

    14. Yariv, A. and P. Yeh, Photonics: Optical Electronics in Modern Communication, Oxford, New York.

    15. Li, L., "Use of Fourier series in the analysis of discontinuous periodic structures," JOSA A, Vol. 13, No. 9, 1870-1876, 1996.

    16. Nishihara, H., M. Haruna, and T. Suhara, Optical Integrated Circuits, McGraw-Hill, New York, 1989.