International Journal of Computational Engineering Research||Vol, 03||Issue, 5|| www.ijceronline.com ||May ||2013|| Page 8 Design of Uniform Fiber Bragg grating using Transfer matrix method Deba Kumar Mahanta Department of Electrical Engineering, Assam Engineering College, Guwahat- 781013 I. INTRODUCTION: Fiber Bragg grating is attracting considerable interest for application as sensing element, because of their intrinsic nature and inherent wavelength encoded operation. Fiber optic photosensitivity has indeed opened a new era in the field of fiber optic based devices [1]. The photosensitivity of optical fiber was discovered at the Canadian Communications Research Center in 1978 by Ken Hill et al. [2] during experiments using germanium- doped silica fiber and visible argon ion laser radiation. It was noted that as a function of time, light launched into the fiber was being increasingly reflected. This was recognized to be due to a refractive index grating written into the core of the optical fiber. It has the ability to alter the core index of refraction in a single-mode optical fiber by optical absorption of UV light. The photosensitivity of optical fibers allows the fabrication of phase structures directly into the fiber core, called fiber Bragg gratings. Photosensitivity refers to a permanent change in the index of refraction of the fiber core when exposed to light with characteristic wavelength and intensity that depend on the core material. Fiber Bragg gratings, which operate at wavelengths other than near the writing wavelength , are fabricated by techniques that broadly fall into two categories: those that are holographic [3] and those that are noninterferometric, based on simple exposure to UV radiation periodically along a piece of fiber [4]. The former techniques use a beam splitter to divide a single input UV beam into two, interfering them at the fiber; the latter depend on periodic exposure of a fiber to pulsed sources or through a spatially periodic amplitude mask. There are several laser sources that can be used, depending on the type of fiber used for the grating, the type of grating, or the intended application. The holographic technique for grating fabrication has two principal advantages. Bragg gratings could be photoimprinted in the fiber core without removing the glass cladding. Furthermore, the period of the photoinduced grating depends on the angle between the two interfering coherent ultraviolet light beams. Thus even though ultraviolet light is used to fabricate the grating, Bragg gratings could be made to function at much longer wavelengths in a spectral region of interest for devices which have applications in fiber optic communications and optical sensors. The design of fiber Bragg grating depends on various parameters e.g length of the grating, period of gratings, refractive index of core and cladding, mode of excitation conditions and temperature. In this paper, the effect on the reflection spectra of fiber Bragg grating is analyzed at the varied grating length along with the variation of spectral shape with changing refractive index. ABSTRACT: The performance of a uniform fiber Bragg grating is depends on it reflectivity. The reflectivity is again depends on change of effective refractive index and length of the grating. This paper presents the design aspect of an optical fiber Bragg grating for maximum reflectivity. As fiber grating allows considerable amount of energy exchange between different modes of the fiber, couple mode theory which is solved by transfer matrix method is considered as good approximation to calculate the spectral response of fiber Bragg grating. Key words: Fiber Bragg grating, couple mode theory, transfer matrix method, reflectivity.