  Adiabatic following has been an widely-employed technique for achieving
near-complete population transfer in a two-level quantum mechanical system. The
theoretical basis, however, could be generalized to a broad class of systems
exhibiting SU(2) symmetry. In the present work, we present an analogy of
population transfer dynamics of two level system with that of light propagation
in a classical one-dimensional photonic crystal, commonly known as
distributed-Bragg-reflector (DBR).This formalism facilitates in adapting the
idea of adiabatic following, more precisely the rapid adiabatic passage (RAP)
which is usually encountered in a broad class of quantum-mechanical systems.We
present two different DBR configurations in which the adiabatic constraints are
obeyed along the DBR length by virtue of optimum design. The reflection
spectrum for both the configurations exhibit broadening of photonic bandgap
(PBG) in addition to a varying degree of suppression of sharp transmission
resonances. The inter modal coupling between counter-propagating modes as well
as their phase-mismatch, for both the DBR configuration, exhibits a
longitudinal variation which is usually observed in Allen-Eberly scheme of
adiabatic population transfer in two-level atomic systems.
