An index grating is a periodic perturbation of the refractive index in a waveguide's axial direction. Gratings have important roles in optical communication as spectral filters and dispersion compensators. The spectral response characteristics of gratings can be controlled by shaping the profile of the index modulation, a process called apodization.

Apodizing different layers of the grating using different apodizing functions is proposed for adding more degrees of freedom to the design. An approach to designing a two-layer separately apodized grating that yields virtually the same reflectivity and dispersion responses as an arbitrary zero-"dc", apodized, un-chirped grating is proposed. A design example is presented, and coupled-mode theory is employed to compute the reflectivity responses of the original zero-"dc" design and the nearly equivalent separately-apodized design proposed in this thesis.

An approach to designing a four-layer separately apodized grating that yields virtually the same reflectivity and dispersion responses as an arbitrary chirped grating is proposed. The largest bandwidth a four-layer separately-apodized grating designed using this approach can yield is as large as the largest bandwidth a variable-period conventional design can yield. Also, a similar, less-capable design approach is proposed for two-layer separately apodized gratings that are equivalent to conventional, chirped gratings. Design examples are presented.

For all of the separately apodized gratings designed, the layers have a varying "dc" index change that is proportional to the varying "ac" index change. Furthermore, the period, which is the same in every layer, is constant, i.e. independent of the position. Both considerations enhance the prospects of fabricating the separately-apodized designs using a simple, reproducible technique. One such technique is proposed that separately-apodizes halves of the waveguide, instead of layers, but the design approaches are easily adjusted to this case.