volume | PIER Journals

Abstract

This paper deals with a group velocity dispersion issue and a peak reflectivity issue in a non-uniform fiber Bragg gratings (FBG) due to an arbitrary refractive index profile along the length of grating. The paper shows that by using more complicated refractive index profile one can significantly reduce the group velocity dispersion and side lobes intensity and that in main lobe the bandwidth of reflectivity would also increase substantially due to a complicated refractive index profile. To the authors' knowledge, there has not been any work reported in this direction. Generally, coupled mode theory is used to analyze the uniform fiber Bragg grating (UFBG). The analysis results in two coupled first order ordinary differential equations with constant coefficients for which closed form solutions can be found for appropriate boundary conditions. Most fiber gratings designed for practical applications, however, are non uniform. The main reason for using non uniform grating is that it reduces the side lobes in the reflectivity spectrum. Due to the complexity of analysis, no particular method for an analysis of the non-uniform fiber Bragg grating would be found. The two standard approaches for calculating the reflection and transmission spectra of a non uniform FBG are direct numerical integration of coupled mode equations and piecewise uniform approximation approach. The former is more accurate but computationally intensive. In this paper, piecewise uniform approximation approach is used to study a dispersion characteristic due to an arbitrary refractive index profile. The usefulness in FBG based sensors has been demonstrated.

1. Chen, , L. R., S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, , "Ultra short pulse reflection from fiber gratings: A numerical investigation," J. Lightwave Technol., Vol. 15, 1503-1512, 1997.
doi:10.1109/50.618383

2. Narayankhedkar, , S. K., , "Performance study of some WDM components for fiber optic networks," Ph.D. Thesis, Department of Electrical Engineering, Indian Institute of Technology Bombay,, 2001.

3. Erdogan, , T., , "Fiber grating spectra," J. Lightwave Technol.,, Vol. 15, 1277-1294, 1997.
doi:10.1109/50.618322

4. Raghuwanshi, , S. K., S. Talabattula, and , "Analytical method to estimate the bandwidth of an uniform FBG based instrument," J. Instrum. Soc. India, Vol. 37, No. 4, 297-308, 2007.

5. Raghuwanshi, , S. K. and S. Talabattula, "Asymmetric dispersion and pulse distortion in an uniform fiber Bragg gratings," Indian J. Phys., Vol. 82, No. 12, 1-7, 2008.

6. Raghuwanshi, , S. K., "Analytical and numerical study of propagation in optical waveguides and devices in linear and nonlinear domains," Ph.D. Thesis, Department of Electrical Communication Engineering, Indian Institute of Science Bangalore, , 2008.

7. Hill, , K. O., "Fiber Bragg grating technology fundamentals and overview," J. Lightwave Technol., Vol. 18, 1263-1276, 1997.
doi:10.1109/50.618320

8. Pal, , B. P., Fundamentals of Fiber Optics in Telecommunication and Sensor Systems, , New Age International (P) Limited, Publishers, , 1997.

9. Agarwal, , G. P., , Nonlinear Fiber Optics, , Academic Press, 2001.

10. Othonos, , A., K. Kalli, and , Fiber Bragg Gratings Fundamentals and Applications in Telecommunications and Sensing,, Artech House, 1999.

11. Giles, C. R., , "Light wave applications of ¯ber Bragg gratings," J. Lightwave Technol.,, Vol. 15, 1391-1404, 1997.
doi:10.1109/50.618357

12. Ouellette, , F., , "Dispersion cancellation using linearly chirped Bragg grating ¯lters in optical waveguides," Optics Letters,, Vol. 16, 847-849, 1987.
doi:10.1364/OL.12.000847

13. Marti, , J., D. Pastor, M. Tortola, and J. Capmany, "Optical equlization of dispersion-induced distortion in subcarrier systems using tapered linearly chirped grating," Electronics Lett., Vol. 32, 236-237, 1996.
doi:10.1049/el:19960131

14. Morey, "Recent advances in fiber grating sensors for utility industry application," Proc. SPIE, , Vol. 2594, 90-98, 1995.

15. Mcghan, , D., C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O. Sullivan, "5120km RZ-DPSK transmission over G652 fiber at 10 G-bit/s with no optical dispersion compensation," Proc. OFC, Anaheim, CA, post-deadline paper PDP27, , 2005.

16. Gerstoft, , P., L. Rogers, J. Krolik, and W. Hodgkiss, "Inversion for refractivity parameters from radar sea clutter," Radio Science, Vol. 38, No. 3, , 122, , 2003.
doi:10.1029/2002RS002640

17. Barclay, , L., , Propagation of Radiowaves, , Inst. of Engineering & Technology, , 2003.

18. Hitney, , H., J. Richter, R. Pappert, K. Anderson, and G. Baum-gartner, Jr., , "Tropospheric radio propagation assessment," Pro-ceedings of the IEEE,, Vol. 73, No. 2, , 265-283, , 1985.
doi:10.1109/PROC.1985.13138

19. Antoine, , X., A. Arnold, C. Besse, M. Ehrhardt, and A. Schdle, "Review of transparent and artificial boundary conditions techniques for linear and nonlinear SchrÄodinger equations," Communications in Computational Physics, Vol. 4, No. 4, 729-796, 2008.

20. Daubechies, I., , "Orthonormal bases of compactly supported wavelets," Communications on Pure and Applied Mathematics, Vol. 41, No. 7, 909-996, 1988..
doi:10.1002/cpa.3160410705

21. Chui, , C. K., , "An Introduction to Wavelets," Academic Press, , 1992.

22. Restrepo, J., G. Leaf, and , "Inner product computations using periodized daubechies wavelets," International Journal forNumerical Methods in Engineering, Vol. 40, No. 19, , 3557-3578, 1997.
doi:10.1002/(SICI)1097-0207(19971015)40:19<3557::AID-NME227>3.0.CO;2-A

23. Latto, , A., H. Resnikoff, and E. Tenenbaum, "The evaluation of connection coeffcients of compactly supported wavelets," Proceedings of the Princeton Conference on Wavelets and Turbulence, , 1991.

24. Beylkin, G., , "On the representation of operators in bases of compactly supported wavelets," SIAM Journal on Numerical Analysis,, Vol. 29, No. 6, 1716-1740, 1992..
doi:10.1137/0729097

25. Rino, C. L., V. R. Kruger, and , "A comparison of forward-boundary-integral and parabolic-wave-equation propagation models," IEEE Transactions on Antennas and Propagation,, Vol. 49, No. 4, 574-582, 200.
doi:10.1109/8.923317

26. Hitney, H. V., , "Hybrid ray optics and parabolic equation methods for radar propagation modeling," International Conference Radar, 58-61, 1992.

Dr. Sanjeev Kumar Raghuwanshi

Prof. Virendra Kumar

Dr. Srinivas Talabattula