Page 222 - Fiber Bragg Gratings

5.2 Basic principles and methodology 199

a function of wavelength, of the apodization profiles shown in Fig 5.1 is
demonstrated in Fig. 5.2. The role of the ripple is considered in Chapter 7.

5.2 Basic principles and methodology

In the discussion that follows, the aim of the exercise is to ensure that the
effective index of the grating remains constant, even though the coupling
constant becomes a slowly varying function of grating length. The ap-
proaches taken to solve this problem are either optical or mechanical, i.e.,
to program the variation in the coupling constant of the grating at a point,
or a combination of both. Optical methods include the use of coherence
properties of the UV source and the stamping of short overlapping gratings
to build a composite. Mechanical techniques rely of physically blurring
out the fringes in a controlled manner, by physically stretching the fiber
or shaking it. Finally, a combination of the two may also be used to make
complex gratings. Also discussed in the following sections is a specific
example of the "top-hat" grating, one with the ideal filter characteristics:
a reflectivity that is constant in-band and zero out-of-band, being another
form of apodization. This type of a function is highly desirable for a
vast number of applications in telecommunications but is restricted to
unchirped gratings. Chirping apodizes a uniform refractive index modula-
tion grating as well and may be used for broadband reflectors. Chirped

Figure 5.2: The effect on the relative group delay of the apodization profiles
used for Fig. 5.1. Although the tanh profile has a flatter characteristic, it also
has more residual ripple.