  This paper analyses theoretically and numerically the effect of varying
grating amplitude on the extremely asymmetrical scattering (EAS) of bulk and
guided optical modes in non-uniform strip-like periodic Bragg arrays with
stepwise and gradual variations in the grating amplitude across the array. A
recently developed new approach based on allowance for the diffractional
divergence of the scattered wave is used for this analysis. It is demonstrated
that gradual variations in magnitude of the grating amplitude may change the
pattern of EAS noticeably but not radically. On the other hand, phase
variations in the grating may result in a radically new type of Bragg
scattering - double-resonant EAS (DEAS). In this case, a combination of two
strong simultaneous resonances (one with respect to frequency, and another with
respect to the phase variation) is predicted to take place in non-uniform
arrays with a step-like phase and gradual magnitude variations of the grating
amplitude. The tolerances of EAS and DEAS to small gradual variations in the
grating amplitude are determined. The main features of these types of
scattering in non-uniform arrays are explained by the diffractional divergence
of the scattered wave inside and outside the array.
