148 Theory of Fiber Bragg Gratings 4.6 PROPERTIES OF UNIFORM BRAGG GRATINGS Quantities of interest are the bandwidth, Dl, reflectivity, transmissivity, the variation in the phase f, and the grating dispersion D as a function of detuning. For the purpose of illustration, Fig. 4.11 shows the reflection spectrum of two Bragg gratings with different coupling constants k ac L of 2 and 8 calculated from Eq. (4.3.16). Note that the central peak is bounded on either side by a number of subpeaks. This feature is characteristic of a uniform-period grating of finite length, with a constant fringe visibility. The abrupt start and end to the grating is responsible for the side structure. In the weak grating limit (R < 0.2), the Fourier transform of the variation in the index modulation results in the reflection spectrum [5]. Thus, a uniform period and index-modulation grating ("top hat") will produce side lobes. However, for stronger gratings, a Fourier transform for the fundamental component of the refractive index modulation alone is no longer appropriate and gives rise to increasing errors. For the uniform grating, df/dz ¼ 0, the peak reflectivity occurs at a wave- length at which d ¼ 0 (and therefore, a ¼ k ac ), and Eq. (4.3.16) leads to k dc þ Db ¼ 0: 2 ð4:6:1Þ