volume | PIER Journals

Abstract

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.

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.
doi:10.1364/JOSAA.19.001844

2. Lalanne, P. and E. Silberstein, "Fourier-modal methods applied to waveguide computational problems," Opt. Lett., Vol. 25, No. 15, 1092-1094, 2000.
doi:10.1364/OL.25.001092

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.
doi:10.1364/JOSAA.18.002865

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.
doi:10.1109/JLT.2009.2012725

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.
doi:10.1109/JLT.2010.2041428

6. Li, L., "Note on the S-matrix propagation algorithm ," JOSA A, Vol. 20, No. 4, 655-660, 2003.
doi:10.1364/JOSAA.20.000655

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.
doi:10.1364/JOSA.73.001105

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.
doi:10.1109/2944.962266

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.
doi:10.1364/AO.45.003307

10. Erdogan, T. and J. E. Sipe, "Tilted fiber phase gratings," JOSA A, Vol. 13, No. 2, 296-313, 1996.
doi:10.1364/JOSAA.13.000296

11. Erdogan, T., "Fiber grating spectr," IEEE J. Lightw. Techn., Vol. 15, No. 8, 1277-1294, 1997.
doi:10.1109/50.618322

12. Erdogan, T., "Cladding-mode resonances in short- and long-period fiber grating filters," JOSA A, Vol. 14, No. 8, 1760-1773, 1997.
doi:10.1364/JOSAA.14.001760

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.
doi:10.1109/JLT.2005.859841

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.
doi:10.1364/JOSAA.13.001870

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

Dr. Amir M. Jazayeri